Intelligent Design

“Self-Evident” Does Not Mean “Apparent”

Spread the love

Many of our materialist friends do not seem to know the difference between the epistemological categories of “self-evident” and “apparent.” I am providing this primer on the difference to help them understand.

Here is a typical exchange where a materialist makes this category error.

Barry: It is self-evident that torturing an infant for pleasure is evil.

Materialist: Yeah, lots of things that have seemed self-evident have turned out to be false. For example, people used to believe it is self-evident that the earth is flat, and they were dead wrong.

Where has M gone wrong? First, M has gone wrong on the basic factual premise of his comparison. The ancients knew the earth was round and even measured its circumference. Great discussion here.

But the fact that materialists continue to spew this factually incorrect chestnut over and over after repeated correction is secondary for our purposes today. More importantly, M has failed to understand the epistemological difference between “apparent” and “self-evident.” “Apparent” means “according to appearances.” M has asserted that it is apparent to many people that the earth is flat. That appearance is false. And by equivocating between “apparent” and “self-evident” he attempts to prove that some self-evident propositions are false.

Nonsense. In the sense we are using it, “self-evident” is not a synonym for “apparent.” Instead, a self-evident proposition is defined as a proposition that is known to be true merely by understanding its meaning without proof. In that sense, is the proposition “the earth is flat” a self-evident proposition? Let’s see.

P1: The earth is flat.

P2: How do you know?

P1: Just go outside and look at it.

What has P1 just done? He has appealed to evidence in order to prove his statement. That very appeal means that his statement cannot be considered self-evident. Go back to our definition. A self-evident claim is one that we know to be true without proof.

An example of a self-evident claim is that 2+2=4. I cannot “prove” that 2+2=4. But does the fact that I cannot prove the proposition mean that I must conclude it is false? Of course not. I know the proposition to be true without proof merely because I understand what it means. Another way of looking at it is that I know for an absolute certain fact that the proposition “2+2 is not 4” is absurd in the sense that it cannot possibly be true, and in order to accept it as true I would have to reject rationality itself.

Unlike the statement “the earth is flat,” the statement 2+2=4 is not merely apparently true, it is necessarily true in any rational universe.

We have a clue that we are not talking about a self-evident truth when a proposition is appended to the word “believe.” Yes, people believe self-evident truths in the sense that they must necessarily accede to the fact that they are true. But people do not “believe” self-evident truths in the sense that they have evaluated the evidence and reached a conclusion they think is justified. Self-evident propositions are not subject to proof or disproof by empirical evidence. They are necessarily true. A person’s belief about a self-evident truth is irrelevant and is therefore rarely expressed. Thus, when one talks about a proposition that is either “believed” or “disbelieved” it is a clue that the proposition is not a proposition of self-evident truth.

This brings me back to my original statement. Numerous materialists with whom I have argued have denied that the statement “torturing an infant for pleasure is evil” is self-evidently true. They always agree that it is true. They never agree that it is self-evidently, necessarily true.

And I always ask them this question: Please describe the circumstances under which the proposition “torturing an infant for pleasure is not evil” is true. I say we can know for an absolute certain fact that the proposition “2+2 is not 4” is absurd because it cannot possibly be true, and in order to accept it as true we would have to reject rationality itself. The same is true of all self-evident propositions. The negation of any self-evident truth is absurd and rationality itself must be rejected in order to accept such a negation. I say the proposition “torturing an infant for pleasure is not evil” is just such an absurd negation of a self-evident truth. You, materialist, say it is not. Please support your assertion.

Dear readers, note that my challenge is extremely risky, epistemologically speaking, because even a single instance where it is met will shatter my project into a million pieces.

Happily, no one has ever come remotely close to answering this challenge. And it is easy to see why.

228 Replies to ““Self-Evident” Does Not Mean “Apparent”

  1. 1
    kairosfocus says:

    BA,

    A good post.

    However, there is one other key feature to self-evident truths, when one attempts to deny them, the result is immediately and patently absurd.

    Once, you have sufficient background experience of reality to understand what is meant when the truth is asserted. (That can be a problem; as Aquinas pointed out, i.e. there is such a thing as a pons asinorum.)

    True per understanding what is being said, necessarily true and this on pain of immediate patent absurdity on attempted dismissal or denial.

    The problem we are seeing is one of lack of understanding, as is manifest in the confusion between the obvious or apparent and the properly self-evident.

    This is backed up by clinging to absurdity due to ideological programming, dominance of agendas and the like.

    In the case of moral SETs, too often there is endarkenment due to the hardness of heart and/or the need to benumb oneself to fend off guilt and linked cognitive dissonance.

    I think it is critical to underscore, too, that when one believes error to be truth, the real truth will usually contradict it and therefore will seem false to you. But error will soon enough manifest its true status, on close examination.

    But that can be hard, and may require for one’s life to go crash for it to be believed. Pain and grief do a lot to open closed minds and hardened hearts, if we are willing to listen to that still small voice saying, y’know, you were wrong way back there and that’s why this is happening, why things have fallen apart.

    KF

  2. 2
    REC says:

    An example of a self-evident claim is that 2+2+4. I cannot “prove” that 2+2=4.

    Proof of theorem 1 Two plus two equals four:
    http://www.cs.yale.edu/homes/as2446/224.pdf

  3. 3
    Virgil Cain says:

    You can demonstrate, 100% of the time, that 2+2=4. Self-evident

  4. 4
    Barry Arrington says:

    REC believes “logorrhea” = “proof.” That is kind of pathetic.

    REC, are you really expecting us to believe that you did not immediately apprehend that 2+2=4 prior to reading that?

    That was a rhetorical question.

    To respond further, “prove” does not mean “talk a lot.” For example, I could pull the same stunt REC did linguistically. I could say a number is a mathematical object used to count, measure and label. An “integer” means a number that can be written without a fractional component. Two is the English word for the integer between one and three. And if I have one set with two members and another set with two members and I combine them the resulting set will have four members. Therefore, two plus two equals four.

    None of that “proves” that two plus two equals four. It is merely a wordier way of saying the same thing.

  5. 5
    Barry Arrington says:

    To those who believe I am too hard on REC when I call his attempt at sophistry “pathetic,” I say all sophistry is dishonest. Every attempt at sophistry is essentially a lie. The sophist knows the truth; yet he employs sophistry in an effort to point people away from the truth. “Pathetic” is the kindest thing I can say of such.

  6. 6
    Silver Asiatic says:

    We use self-evident axioms to define what “2” “+” and “=” means.

    The ‘proof’ given by REC to apparently argue against the self-evident truth uses self-evident axioms (e.g. 2 is an integer).

  7. 7
    daveS says:

    Virgil Cain,

    You can demonstrate, 100% of the time, that 2+2=4.

    In other words, you can prove that 2 + 2 = 4, correct?

    See this, for example.

  8. 8
    mjoels says:

    The point is that it does not require proof. Certain statements, like the car is red, or 2+2=4, no matter how they are written, are always true. I am assuming that was a joke there… otherwise you are saying that 2+2=4 is a subjective idea…
    That would truly be insanity.
    Proofing of that kind is simply a way to formalize an idea. That is an exceptionally long winded 2+2=4…
    And that really just proves the point, now, doesn’t it.

  9. 9
    Barry Arrington says:

    daveS @ 7.

    Sigh. Today is materialist whack-a-mole. See REC @ 3 and the replies. That stunt has already been pulled.

    It really is pathetic. They are saying, “It never was proved that 2+2=4 until such and such “proof” was published.”

    Liars.

  10. 10
    daveS says:

    Barry,

    How am I lying? Of course you can prove that 2 + 2 = 4.

    Edit: Here are some other approaches.

  11. 11
    mjoels says:

    Well BA, there is only a difference in presentation of the idea there. Not a new or novel idea. It really doesn’t prove 2+2=4 any more than the statement 2+2=4, it is just a long winded abstracted version of it. Not really worth bringing in imo except to rile you up. Stay calm brother.

  12. 12
    Dr JDD says:

    Ha! Classic materialistic response here!

    The whole point of BA’s post is absolutely nothing to do with 2+2=4. That was merely an example to illustrate a point and use of terminology.

    Yet this is precisely what the materialist attacks – because they cannot attack the actual argument itself.

    And that is the key to understanding materialist responses to many of the arguments against them: they attack subtleties in your argument because they cannot sufficiently demonstrate your argument is incorrect. It is a clever game because it detracts from the actual argument and to some shortsighted (including themselves) it appears as though they have successfully mounted a challenge to the argument.

    It really is classic!

  13. 13
    mjoels says:

    Exactly.

  14. 14
    daveS says:

    Dr JDD,

    Ha! Classic materialistic response here!

    The whole point of BA’s post is absolutely nothing to do with 2+2=4.

    ??

    It says right in the OP that you cannot prove 2 + 2 = 4. This is not true.

  15. 15
    mjoels says:

    And that is a distraction from the point because the content is uncomfortable DaveS.

  16. 16
    mjoels says:

    And for the record he said that “I can’t prove” not that it cannot be proven.

  17. 17
    Barry Arrington says:

    mjoels

    Stay calm brother.

    I hear you, but you need not worry. I am perfectly calm. Indeed, I fully expected the materialists to pull the exact stunt they pulled. They are so full of lies, deceit and confusion, that they must pounce on even the most basic truth in their feverish, frenzied, frenetic efforts to undermine all truth.

    So, I calmly demonstrate they are liars and then label them as such. Somewhere someone came up with the idea that it is impolite or something to call a liar out on his lies. I no longer believe that.

  18. 18
    Barry Arrington says:

    mjoels @ 16

    And for the record he said that “I can’t prove” not that it cannot be proven.

    No, you’ve misunderstood me. I mean exactly what daveS understood me to mean. No one can prove 2+2=4. It is either accepted as self-evidently true or it is not.

    None of daveS’ examples prove that 2+2=4. They simply say the same thing in a wordier format and then append the word “proof” to it.

    It is all so pathetic.

  19. 19
    bornagain77 says:

    First incompleteness theorem
    Excerpt: Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.
    http://plato.stanford.edu/entr.....pleteness/

    Gödel’s Incompleteness: The #1 Mathematical Breakthrough of the 20th Century
    Excerpt: Gödel’s Incompleteness Theorem says:
    “Anything you can draw a circle around cannot explain itself without referring to something outside the circle – something you have to assume to be true but cannot prove “mathematically” to be true.”
    http://www.cosmicfingerprints......pleteness/

  20. 20
    Starbuck says:

    That is like saying it is self evident that 98divided by 14 equals 7. You wouldnt say that because you would need to work it out, 2+2 = 4 and there are formal proofs, and if you know the definition of each term you can see it with your own eyes using apples , it is a proven assertion unlike most of what theists say

  21. 21
    Barry Arrington says:

    Dr JDD’s point at 12 is good. The materialist playbook: When confronted with an indisputable truth, then confuse the issue, misdirect, employ sophistry, dissemble.

    I have never met a materialist who was not an inveterate liar.

  22. 22
    Barry Arrington says:

    I am not sure what Starbuck is trying to say at 20. But if he is saying that 98/14=7 is not self-evident in the same way that 2+2=4 is, then I agree with him for the reasons he states.

    His swipe at theists is particularly ironic given that prior to his comment only theists have spoken truth in this thread, and two of his fellow materialists have posted statements that he agrees to be false.

  23. 23
    Barry Arrington says:

    daveS and REC want to talk about axiomatic statements. Well, here is an axiom that is invariably true in my experience:

    There is no truth so simple, clear, beautiful and pristine that some materialist will not try to shit on it.

  24. 24
    Learned Hand says:

    I assume there’s a grey area between “self evidence” and “needs to be reasoned out.” For example, I doubt anyone thinks there’s a bright line between 2+2 type of questions and the 98/14 type of questions. It’s going to vary depending on a person’s education and experience. (For example, 256*2 is intuitively obvious to people who have experience with computers; I’m pretty sure my parents’ generation would need to calculate it.)

    So, I assume that such a grey area exists. Please yell at me and call me a liar if my assumption is wrong.

    If it does, then how does one tell whether their perception of a self-evident truth is accurate or in error? Staying in the realm of mathematics for now, 2+2 is an easy example; what about 5*15? Some people will think it’s intuitively as easy as 2+2… but if you tested them, some of those people would intuitively get the wrong answer. Granting arguendo that there’s a core of beliefs like 2+2 about which no error is reasonably possible, how do you know when you’ve left that area and you could be in error? Self-certainty seems like the answer on display… but humans are fallible, even when (especially when?) we’re certain about our own perceptions.

  25. 25
    Barry Arrington says:

    I announce my axiom in comment 23 and LH jumps in and provides a lovely example of the axiom in action in comment 24. Thanks LH!

    Yes, a proposition that is self-evident to one person may not be to another who is less intelligent or educated.

    Thanks for admitting that 2+2=4 is an example of a self-evident truth and that therefore self-evident truths exist.

  26. 26
    asauber says:

    “the earth is flat”

    I would submit that such a statement cannot be made if the whole earth can’t be perceived. 😉

    Andrew

  27. 27
    mjoels says:

    Sorry to have put words in your mouth there BA. You are of course right. A self evident truth = that which is true regardless of opinion, perception or ability to grasp…

  28. 28
    Barry Arrington says:

    No prob mj.

  29. 29
    Daniel King says:

    Barry: It is self-evident that torturing an infant for pleasure is evil.

    One less thing for THE OBJECTIVE MORAL CODE to address.

  30. 30
    Barry Arrington says:

    DK @ 29.

    Thank you for being succinct, but you have have overdone it a tad. Because I have no idea what you are talking about.

  31. 31
    Starbuck says:

    “I am not sure what Starbuck is trying to say”

    That is truly self-evident. I knew one day the right would become so irrational we would have to go back to sesame street to re-educate them, that there are real reasons why 2+2=4

  32. 32
    Starbuck says:

    dupe

  33. 33
    Barry Arrington says:

    Starbuck,

    Forgive me for hoping in my comment 22 that you had had a momentary lapse of your normal incoherence.

  34. 34
    Aleta says:

    2 + 2 = 4 is “self-evident” because it’s a statement about definitions. It is based on material evidence: if I define “2” to represent a certain number of stones and “4” to represent a certain number of stones, then 2 + 2 = 4 is a true fact about happens when I put two piles of two stones each together. Among other things, 2 + 2 = 4 is only true of of things that have a definite, distinct identity. Two drops of mercury + two drops of mercury does not equal four drops of mercury.

  35. 35
    StephenB says:

    Starbuck, Daniel King, Learned Hand, Aleta, and all dedicated materialists, I would like to ask you a couple of questions based on an assertion:

    The amount of pepperoni in a whole pizza is equal to or greater than the amount found in one of the slices.

    [a] Is this statement self-evidently true?

    Yes or no.

    [b] If it is self-evidently true, can I reliably draw conclusions about other truths without appealing to empirical evidence of any kind?

    Yes or no.

  36. 36
    Barry Arrington says:

    Aleta, if your point is that there are self-evident truths, this being one of them, then it is well taken. Thanks.

  37. 37
    Aleta says:

    to StephenB: I am not a ‘dedicated materialist”.

    to Barry: My point is that it is self evident because it is based on definitions about simple material facts.

  38. 38
    Barry Arrington says:

    Aleta @ 37 informs us that the mathematical proposition 2+2=4 is “material.”

    Fascinating. Aleta, kindly tell us what the physical properties of this material thing are. Does it have mass? Or a specific gravity? Perhaps a wavelength?

  39. 39
    StephenB says:

    Aleta

    2 + 2 = 4 is “self-evident” because it’s a statement about definitions. It is based on material evidence:

    What kind of “material evidence” did Barry appeal to?

  40. 40
    Barry Arrington says:

    Aleta,

    Did you notice, like I have, that none of your fellow materialists was willing to acknowledge this challenge in the OP, far less try to meet it:

    And I always ask them this question: Please describe the circumstances under which the proposition “torturing an infant for pleasure is not evil” is true. I say we can know for an absolute certain fact that the proposition “2+2 is not 4” is absurd because it cannot possibly be true, and in order to accept it as true we would have to reject rationality itself. The same is true of all self-evident propositions. The negation of any self-evident truth is absurd and rationality itself must be rejected in order to accept such a negation. I say the proposition “torturing an infant for pleasure is not evil” is just such an absurd negation of a self-evident truth. You, materialist, say it is not. Please support your assertion.

    Perhaps you will take a crack at it.

  41. 41
    StephenB says:

    Aleta

    to StephenB: I am not a ‘dedicated materialist”.

    Is that you way of saying that you will not address my question @35?

  42. 42
    Aleta says:

    Barry writes, “Aleta @ 37 informs us that the mathematical proposition 2+2=4 is “material.”

    Fascinating. Aleta, kindly tell us what the physical properties of this material thing are. Does it have mass? Or a specific gravity? Perhaps a wavelength?”

    That is not what I said. Please re-read #34. It is hard to to respond to a statement that doesn’t accurately reflect what I said.

    StephenB writes, “What statement about “material evidence” did Barry appeal to?”

    He didn’t. I did.

    StephenB writes at #41, “Is that you way of saying that you will not address my question @35?”

    In the interest of both focus and time, I’m going to stick with discussing the 2 + 2 = 4 example for the time being. My statement about not being a “dedicated materialist” was because I don’t want to be mis-labeled. It’s not really the topic of this discussion, though.

  43. 43
    StephenB says:

    SB: “What statement about “material evidence” did Barry appeal to?”

    He didn’t. I did.

    If, as you acknowledge, Barry did not appeal to material evidence to establish a self-evident truth, then material evidence has nothing to do with the fact that it is true.

    The statement stands on its own and needs no empirical evidence to make it legitimate, just as my statement @35 needs no empirical evidence to make it legitimate, just as the principle in the OP needs no empirical evidence to make it legitimate.

    Here is the point that you do not understand: Evidence does not inform self-evident truths; self-evident truths inform evidence. Material evidence is for making inductive arguments, not for establishing self evident truths, without which no arguments at all can be made.

  44. 44
    kairosfocus says:

    Aleta:

    Your “definitions” have to do with understanding twoness, fourness, the operation of addition and the relationship, is the same as.

    Once one understands the concepts, one can see why 2 + 2 = 4 is true and cannot but be true on pain of patent absurdity.

    Last I checked crows cannot speak languages in which such definitions are laid out in painful detail, but I recall a story of a crow that realised that when two men and two men went into a tower but only three came out, one was still inside so there was danger.

    (I think that sense ran out at 5 or 6.)

    KF

  45. 45
    Aleta says:

    StephenB writes.

    If, as you acknowledge, Barry did not appeal to material evidence to establish his self-evident truth, then material evidence has nothing to do with it.

    No, the fact that Barry did not appeal to material evidence could be because Barry might be wrong that material evidence has nothing to do with it.

    StephenB writes,

    Here is the point that you do not understand: Evidence does not inform self-evident truths; self-evident truths inform evidence.

    This is not a matter of me not understanding – this is a matter of me disagreeing with you and Barry about the fundamental relationship between the material world and our knowledge of it.

  46. 46
    Barry Arrington says:

    Aleta,

    No, the fact that Barry did not appeal to material evidence could be because Barry might be wrong that material evidence has nothing to do with it.

    Are you suggesting that the mathematical statement 2+2=4 is subject to empirical invalidation?

    Are you suggesting that we need material evidence to know that it is true?

  47. 47
    Aleta says:

    KF’s example of the crow is instructive. Evidence shows that some animals have an understanding of small quantities that is obviously not dependent on a verbal or notational symbolic representation – it is a non-verbal understanding (as all of a crow’s understandings are, as far as we know) of the property of the material world that some things (those that have a definite, distinct existence that doesn’t blur into other objects) retain that distinctness as they move around.

  48. 48
    Barry Arrington says:

    Nominalism has driven many people insane.

  49. 49
    StephenB says:

    Aleta

    No, the fact that Barry did not appeal to material evidence could be because Barry might be wrong that material evidence has nothing to do with it.

    No, it could not be the case that Barry is wrong about that. It is not possible for material evidence to inform a self-evident truth because the latter is prior both logically and chronologically.

    This is not a matter of me not understanding – this is a matter of me disagreeing with you and Barry about the fundamental relationship between the material world and our knowledge of it.

    No, it is not a matter of your disagreement with Barry. The problem is your lack of understanding. A slice of pizza cannot contain more pepperoni than the whole pie. It is self-evidently true. Material evidence has nothing to do with it. Even if I had never observed, sliced, or tasted a pizza, I would know that it is true.

  50. 50
    StephenB says:

    Barry

    nominalism has driven many people insane

    .

    Yes, Barry, and we could also include that theme with your recent series of posts: Nominalism makes people stupid.

  51. 51
    Aleta says:

    Given that you guys dismiss one entire philosophical perspective on the nature of knowledge as stupid, insane and irrational, and are entirely 100% certain that the perspective you hold is true, discussion about these issues is a bit difficult and unproductive.

    There are problems/mysteries about both the idea that abstract quantities have a non-material, pre-existing reality separate from the material world that somehow we are able to apprehend (your position) and the idea that abstract understandings are built up as representations from experience with the material world as it appears to us (the position I am trying to describe). This distinction, and related issues, is a universal, perennial philosophical dilemma that many great thinkers have pondered for centuries. I don’t believe that we can know the truth of the matter, but I do think it’s reasonable to have a balanced view of the strengths and weaknesses of each view, and to have some humility about the nature of our understanding.

  52. 52
    StephenB says:

    Aleta

    My statement about not being a “dedicated materialist” was because I don’t want to be mis-labeled.

    What do you call someone who always takes the materialist side of an argument and never takes the opposite side? What label should we apply to you? Could we say that you are a Materialist sympathizer and enabler who does not want a label attached to the behavior?

    Or, if not that, what word or phrase would best describe your metaphysical world view. (Notice, that I said word or phrase, which does not mean three or four paragraphs).if you cannot summarize your world view in a word or two–or maybe three, then you don’t really know what you are.

  53. 53
    Barry Arrington says:

    For those who do not speak materialist-ese, I will translate Aleta’s comment at 51 into English:

    I can come into the UD combox and make literally insane statements and imply that 2+2=4 is subject to empirical invalidation. I will refuse to respond to counter-arguments. Instead, I will accuse my opponents of not being reasonable and having insufficient humility for clinging to rationality.

    Aleta has slipped into insane denial mode. There is no point in continuing the discussion with him.

  54. 54
    Aleta says:

    Barry, I did not say that 2 + 2 = 4 was subject to empirical invalidation.

    I also did not accuse you of not being reasonable, other than in your excessive certainty about being right.

    I did say, or at least imply, that you lack humility because you are so certain that you are right, and because you believe that any differing opinion is “insane denial.”

  55. 55
    Aleta says:

    To StephenB: I am a militant agnostic existentialist neo-Taoist sympathizer. 🙂

    Out of curiosity, how would you describe yourself in a few words?

  56. 56
    StephenB says:

    Aleta

    Given that you guys dismiss one entire philosophical perspective on the nature of knowledge as stupid, insane and irrational, and are entirely 100% certain that the perspective you hold is true, discussion about these issues is a bit difficult and unproductive.

    There are problems/mysteries about both the idea that abstract quantities have a non-material, pre-existing reality separate from the material world that somehow we are able to apprehend (your position) and the idea that abstract understandings are built up as representations from experience with the material world as it appears to us (the position I am trying to describe). This distinction, and related issues, is a universal, perennial philosophical dilemma that many great thinkers have pondered for centuries. I don’t believe that we can know the truth of the matter, but I do think it’s reasonable to have a balanced view of the strengths and weaknesses of each view, and to have some humility about the nature of our understanding.

    Can I take all this rambling to mean that you cannot answer my refutation @49. Or, would you like to argue that a slice of pizza can contain more pepperoni than the whole pie.

    Also, just so that you will know,

    Humility = bringing your desires into conformity with the truth.

    Pride = twisting the truth so that it conforms to your desires.

  57. 57
    Silver Asiatic says:

    Aleta

    Your example of 2+2=4 as a representation of material events seemed good to me. But the use of the term “evidence” is the problem. The two rocks added to two rocks is not “evidence” of the formula. The formula is symbolic for what is observed.

    Adding two rocks to two rocks gives more than two rocks. The number that results is four. This is self-evident.

    The reason it’s not evidence based is that 2+2+4 is the law of identification. As you said, we define the symbols and they represent something self-evident. It’s by the nature of reality.

    Positive finite quantities added increase by a positive finite amount.

    That’s the self-evident truth. We don’t look for “evidence” to support that. Otherwise, we would have to check all the positive finite quantities of things with the belief that at some point, the addition of the same would not be an increase.

    The law of identification is easier. 2 = 2. That is self-evident. It can’t be proven. It’s not evidence-based. 2+2=4 is merely an extrapolation of 2=2.

    There are problems/mysteries about both the idea that abstract quantities have a non-material, pre-existing reality separate from the material world that somehow we are able to apprehend (your position) and the idea that abstract understandings are built up as representations from experience with the material world as it appears to us (the position I am trying to describe).

    Yes, you could say that an abstraction like 2+2=4 is built from material representations. However, the problem is with something like the square root of 2.

  58. 58
    REC says:

    So self-evident is what you learned at a young age, or believe firmly?

    Barry: “a self-evident proposition is defined as a proposition that is known to be true merely by understanding its meaning without proof.”

    I’m not sure this is true of 2+2=4. A child (or according to some anthropologists, someone from a culture that counts 1,2, many) might take 2 sets of 2 objects, and see that together that are now 4. Always. As we grow past this empirical demonstration, it becomes apparent to us that these mathematical truths exist.

    But what does arguing this truth is “self evident” vs. apparent or empirical get us? I guess it is a convenient tool to squash discussion.

  59. 59
    StephenB says:

    Aleta

    To StephenB: I am a militant agnostic existentialist neo-Taoist sympathizer. 🙂

    I thank you for disclosing that portion, (and I appreciate the humor inherent in the “sympathizer” attachment [that was cute]) but it tells me nothing about your orientation to matter. Do you accept a realm of being (spirit) that transcend matter or not? If not, then you are, among other things, a materialist.

    Out of curiosity, how would you describe yourself in a few words?

    I am a Catholic moderate dualist (not a Cartesian substance dualist).

  60. 60
    Barry Arrington says:

    Aleta

    I did say, or at least imply, that you lack humility because you are so certain that you are right, and because you believe that any differing opinion is “insane denial.”

    Yes, I am absolutely certain that it is self-evident that 2+2=4. And for that I lack humility says Aleta.

    Let me tell you something else about which I am certain, Aleta. You are a fool.

  61. 61
    Barry Arrington says:

    REC:

    So self-evident is what you learned at a young age, or believe firmly?

    Sigh. I have already addressed both of these issues. Do you think repeating them after their refutation gives them additional force? REC, let me give you a clue: The ability to keep typing is not the same as making a rational argument, especially after what you’ve just typed has been addressed.

    Barry: “a self-evident proposition is defined as a proposition that is known to be true merely by understanding its meaning without proof.”

    REC: I’m not sure this is true of 2+2=4. A child (or according to some anthropologists, someone from a culture that counts 1,2, many) might take 2 sets of 2 objects, and see that together that are now 4. Always.

    Are you suggesting that the truth of the proposition 2+2=4 hangs in suspension until some child grows up to understand it? Are you suggesting that before any human walked this planet to understand mathematics that 2+2=4 was not yet true?

    As we grow past this empirical demonstration, it becomes apparent to us that these mathematical truths exist.

    There is that word “apparent.” Are you suggesting that it merely appears on the surface of things that 2+2=4? If not, then why did you use the word “apparent”?

    But what does arguing this truth is “self evident” vs. apparent or empirical get us? I guess it is a convenient tool to squash discussion.

    What does self-evident truth get us? Why rationality itself REC. If you don’t understand why that is true let me know and I will explain it to you, but 30 seconds of thought will get you there. I will understand if you don’t put in the effort though, since materialists are not big on the whole rationality thing anyway, and thinking is hard work, and 30 seconds is a long time.

  62. 62
    Bob O'H says:

    Nice to see that REC and Barry agree on something. 🙂

  63. 63
    Barry Arrington says:

    To those who think I am too rough on REC and Aleta, let me say this. I despise their efforts to undermine rationality itself. If we were merely engaged in an academic discussion with no real world consequences, I wouldn’t bother dignifying their lunacy with a response. But we are not.

    Dear readers, have you ever wondered why there is a nearly one-to-one correlation between those who would attempt to argue with the proposition that 2+2=4 is a self-evident truth and those who would say that it is OK to kill little boys and girls, chop their bodies into pieces and sell the pieces like so much meat?

    The same spirit animates both assertions.

  64. 64
    Aleta says:

    When I described myself as a “militant agnostic existentialist neo-Taoist sympathizer”, StephenB writes,

    I thank you for disclosing that portion, (and I appreciate the humor inherent in the “sympathizer” attachment [that was cute]) but it tells me nothing about your orientation to matter. Do you accept a realm of being (spirit) that transcend matter or not? If not, then you are, among other things, a materialist.

    Actually, my description does tell you something about my orientation towards matter, if I unpack some of the understandings that I attach to it.

    First, the “militant agnostic” parts means that, in respect to the ultimate nature of the world, including whatever might exist beyond/behind/embedded in the world we experience, “I don’t know, and you don’t know either.” Human beings can’t know. We are limited creatures, and no matter how much we might learn through empirical investigation, there will always be mysteries. Those perspectives which attempt to address those mysteries as if we do know, including all religious explanations, are things we have made up – rationalizations, to try to answer the unanswerable.

    Second, the neo-Taoist “sympathizer” part: I wasn’t trying to be cute with “sympathizer”. Given my miltant agnosticism, I certainly can’t say that I believe that a neo-Taoist perspective is “true”. It is the perspective, however, that makes the most sense to me – that appeals the most to the whole complex of my philosophical, religious, and scientific understandings.

    The neo-Taoist part refers to my “belief” (qualified by my agnosticism) that there is likely to be a set of principles (metaphysical forces, if you will) that provide the dynamics that inform the structure and motion of the world, that the activity of those principles is beyond what we can actually empirically experience (we just experience the effects), and that the overriding principle is that of “complementary duality” – the push and pull of forces which help each other bring about their effects.

    So to be specific, this view would certain hold that there is something more than matter and energy – something underlying matter and energy, but that it would not be reasonable to call this “spirit” or “being” if that implies a conscious, willful entity of some sort.

    The existentialist part means that, again, given my militant agnosticism, that as human beings we are “doomed to make choices” (as some existentialist philosopher said), but I believe strongly that there are principles embedded in our human nature to which we can refer as we make those choices. Also, the Taoist part implies that moderation and balance in all things is necessary, and that all black-and-white dichotomies which don’t acknowledge complementary duality are wrong.

    So, short answer: I am not a “dedicated materialist”, but to whatever extent I think some non-material aspect of the world might exist, I think it is likely to be in the form of metaphysical principles, not anything resembling a spiritual “being”.

  65. 65
    Barry Arrington says:

    Aleta,

    Those perspectives which attempt to address those mysteries as if we do know, including all religious explanations, are things we have made up.

    But wait a minute. You just got through telling me, and I quote, “in respect to the ultimate nature of the world, including whatever might exist beyond/behind/embedded in the world we experience, ‘I don’t know . . .”

    But now you are telling me that you do know something about that with apparently absolute certainty, to wit, whatever happened God didn’t do it.

    Contradict yourself much?

  66. 66
    Barry Arrington says:

    Aleta,

    The neo-Taoist part refers to my “belief” (qualified by my agnosticism) that there is likely to be a set of principles (metaphysical forces, if you will) that provide the dynamics that inform the structure and motion of the world . . .

    But you are absolutely certain the Christian God is not behind those metaphysical forces.

    You seem to have a strange combination of agnosticism and dogmatic certainty.

  67. 67
    Barry Arrington says:

    Aleta,

    I believe strongly that there are principles embedded in our human nature to which we can refer as we make those choices.

    Finally, something we can agree on. The only difference is that I am more open-minded than you regarding the possible source of those principles and how they were embedded.

    You appoint yourself arbiter of the existence of God and close your mind to any possibility that you may be wrong. And you accuse me of lacking humility. Staggering.

  68. 68
    Aleta says:

    Barry, it’s hard to want to reply to someone who calls me a fool, which I am not. Why should I bother, I wonder?

  69. 69
    Barry Arrington says:

    Aleta,

    Why should I bother, I wonder?

    Oh, I dunno, to prove me wrong? BTW, here’s a hint. Trying to argue that 2+2+4 is not self-evidently true won’t help in that project.

  70. 70
    Barry Arrington says:

    Aleta raises a fair point in 68. Why am I not content to prove them wrong? Why do I go on to point out that they are foolish or (as is often the case) evil?

    I answered that question at 63.

  71. 71
    Aleta says:

    I don’t rule out theism as a possibility. I am not 100% certain about anything metaphysical, but there is no way to constantly qualify everything I say about what I believe with a disclaimer to that effect. But given how much I know about religion in general, and how unlikely Christian dogma appears to me to be, I see little reason to entertain it as a possibility. Being an agnostic doesn’t mean that I don’t have strong beliefs about things based on all my education and experience – taking together everything I know about the world, theistic religious explanations seem very unlikely.

  72. 72
    Barry Arrington says:

    Aleta @ 64:

    Those perspectives which attempt to address those mysteries as if we do know, including all religious explanations, are things we have made up

    Aleta @ 71:

    I don’t rule out theism as a possibility.

    Yes, you do. You just did. Until you got caught being irrational. Then you backtracked with the whole “I don’t always include disclaimers” nonsense. Sigh.

  73. 73
    bornagain77 says:

    as to:

    “I am not 100% certain about anything metaphysical”

    if you are 100% certain about you not being 100% certain then there is at least one metaphysical assumption that you are 100% certain about. 🙂

    Myself, I consider your position to be the same ole hyper-selective skepticism that Charles Darwin himself employed whenever he was faced with the reasonableness of God:

    i.e. Charles Darwin’s infamous ‘horrid doubt’, contrary to popular opinion, was used in a hyper-selective fashion.
    Nancy Pearcey goes over the fallacious nature in which Charles Darwin employed his ‘horrid doubt’ here:

    podcast – Is Human Reason Reliable? Interview with Nancy Pearcey (Darwin’s ‘horrid doubt’)
    http://www.discovery.org/multi.....y-pearcey/

    Why Evolutionary Theory Cannot Survive Itself – Nancy Pearcey – March 8, 2015
    Excerpt: Darwin’s Selective Skepticism
    People are sometimes under the impression that Darwin himself recognized the problem. They typically cite Darwin’s famous “horrid doubt” passage where he questions whether the human mind can be trustworthy if it is a product of evolution: “With me, the horrid doubt always arises whether the convictions of man’s mind, which has been developed from the mind of the lower animals, are of any value or at all trustworthy.”
    But, of course, Darwin’s theory itself was a “conviction of man’s mind.” So why should it be “at all trustworthy”?
    Surprisingly, however, Darwin never confronted this internal contradiction in his theory. Why not? Because he expressed his “horrid doubt” selectively — only when considering the case for a Creator.
    From time to time, Darwin admitted that he still found the idea of God persuasive. He once confessed his “inward conviction … that the Universe is not the result of chance.” It was in the next sentence that he expressed his “horrid doubt.” So the “conviction” he mistrusted was his lingering conviction that the universe is not the result of chance.
    In another passage Darwin admitted, “I feel compelled to look to a First Cause having an intelligent mind in some degree analogous to that of man.” Again, however, he immediately veered off into skepticism: “But then arises the doubt — can the mind of man, which has, as I fully believe, been developed from a mind as low as that possessed by the lowest animal, be trusted when it draws such grand conclusions?”
    That is, can it be trusted when it draws “grand conclusions” about a First Cause? Perhaps the concept of God is merely an instinct programmed into us by natural selection, Darwin added, like a monkey’s “instinctive fear and hatred of a snake.”
    In short, it was on occasions when Darwin’s mind led him to a theistic conclusion that he dismissed the mind as untrustworthy. He failed to recognize that, to be logically consistent, he needed to apply the same skepticism to his own theory.
    http://www.evolutionnews.org/2.....94171.html

    Moreover, when the ‘internal contradiction’ in Darwin’s theory is examined, it is found that the contradiction does indeed lead to epistemological failure:

    Why No One (Can) Believe Atheism/Naturalism to be True (Plantinga’s Evolutionary Argument Against Naturalism) – video
    Excerpt: “Since we are creatures of natural selection, we cannot totally trust our senses. Evolution only passes on traits that help a species survive, and not concerned with preserving traits that tell a species what is actually true about life.”
    Richard Dawkins – quoted from “The God Delusion”
    http://www.youtube.com/watch?v=N4QFsKevTXs

    Quote: “In evolutionary games we put truth (true perception) on the stage and it dies. And in genetic algorithms it (true perception) never gets on the stage”
    Donald Hoffman PhD. – Consciousness and The Interface Theory of Perception – 7:19 to 9:20 minute mark – video
    https://www.youtube.com/watch?feature=player_detailpage&v=dqDP34a-epI#t=439

    Why Evolutionary Theory Cannot Survive Itself – Nancy Pearcey – March 8, 2015
    Excerpt: Steven Pinker writes, “Our brains were shaped for fitness, not for truth. Sometimes the truth is adaptive, but sometimes it is not.” The upshot is that survival is no guarantee of truth. If survival is the only standard, we can never know which ideas are true and which are adaptive but false.
    To make the dilemma even more puzzling, evolutionists tell us that natural selection has produced all sorts of false concepts in the human mind. Many evolutionary materialists maintain that free will is an illusion, consciousness is an illusion, even our sense of self is an illusion — and that all these false ideas were selected for their survival value.
    So how can we know whether the theory of evolution itself is one of those false ideas? The theory undercuts itself.,,,
    Of course, the atheist pursuing his research has no choice but to rely on rationality, just as everyone else does. The point is that he has no philosophical basis for doing so. Only those who affirm a rational Creator have a basis for trusting human rationality.
    The reason so few atheists and materialists seem to recognize the problem is that, like Darwin, they apply their skepticism selectively. They apply it to undercut only ideas they reject, especially ideas about God. They make a tacit exception for their own worldview commitments.
    http://www.evolutionnews.org/2.....94171.html

    In fact, the epistemological failure inherent in evolutionary naturalism goes much deeper than illustrated by Plantinga’s argument in that both free will and consciousness themselves become illusions (i.e. under naturalism it is not just perceptions that are illusions):

    The Confidence of Jerry Coyne – Ross Douthat – January 6, 2014
    Excerpt: then halfway through this peroration, we have as an aside the confession that yes, okay, it’s quite possible given materialist premises that “our sense of self is a neuronal illusion.” At which point the entire edifice suddenly looks terribly wobbly — because who, exactly, is doing all of this forging and shaping and purpose-creating if Jerry Coyne, as I understand him (and I assume he understands himself) quite possibly does not actually exist at all? The theme of his argument is the crucial importance of human agency under eliminative materialism, but if under materialist premises the actual agent is quite possibly a fiction, then who exactly is this I who “reads” and “learns” and “teaches,” and why in the universe’s name should my illusory self believe Coyne’s bold proclamation that his illusory self’s purposes are somehow “real” and worthy of devotion and pursuit? (Let alone that they’re morally significant:,,) Read more here:
    http://douthat.blogs.nytimes.c.....oyne/?_r=0

    Sam Harris’s Free Will: The Medial Pre-Frontal Cortex Did It – Martin Cothran – November 9, 2012
    Excerpt: There is something ironic about the position of thinkers like Harris on issues like this: they claim that their position is the result of the irresistible necessity of logic (in fact, they pride themselves on their logic). Their belief is the consequent, in a ground/consequent relation between their evidence and their conclusion. But their very stated position is that any mental state — including their position on this issue — is the effect of a physical, not logical cause.
    By their own logic, it isn’t logic that demands their assent to the claim that free will is an illusion, but the prior chemical state of their brains. The only condition under which we could possibly find their argument convincing is if they are not true. The claim that free will is an illusion requires the possibility that minds have the freedom to assent to a logical argument, a freedom denied by the claim itself. It is an assent that must, in order to remain logical and not physiological, presume a perspective outside the physical order.
    http://www.evolutionnews.org/2.....66221.html

    (1) rationality implies a thinker in control of thoughts.
    (2) under materialism a thinker is an effect caused by processes in the brain.
    (3) in order for materialism to ground rationality a thinker (an effect) must control processes in the brain (a cause). (1)&(2)
    (4) no effect can control its cause.
    Therefore materialism cannot ground rationality.
    per Box UD

  74. 74
    kairosfocus says:

    REC:

    self-evident is what you learned at a young age, or believe firmly?

    Predictable, predictably wrong.

    I suggest, cf 1 above:

    http://www.uncommondescent.com.....ent-578142

    The pons asinorum effect applies, i.e. there is a threshold of experience of the world to understand enough to see what a claim means and why on what it means it is and must be true on pain of patent absurdity.

    SETs are foundational, some of them are learned early indeed but many lie beyond issues that will not be crossed for any number of reasons, ideological indoctrination and commitment to the contrary being important cases.

    KF

  75. 75
    REC says:

    Ok KF to the original Pons asinorum: is the statement that the angles opposite the equal sides of an isosceles triangle are themselves equal self-evidently true? Is it provable? Does it require proof?

    If I merely say that it that statement is true (and eliminate self-evidently), what is lost in the field of geometry?

  76. 76
    Aleta says:

    to Barry: As I said, I think Christian theology is extremely unlikely to be true, based on all I know about religion in general and Christianity in particular. For all practical purposes, I rule it out as a possibility worth my consideration.

    As Dylan said in “High Water”, “You can’t open up your mind, boys, to every conceivable point of view.” As an agnostic, I am willing to live with uncertainty and understand the limitations of my knowledge, but as an existentialist, I have to make choices to live by, based as best I can on what I know, and as a Taoist sympathizer I need to balance the provisional uncertainty of belief with the certainty inherent in action.

  77. 77
    daveS says:

    KF,

    Do you agree with Learned Hand at #24, that there is no clear line between self-evident and non-self-evident statements concerning integer arithmetic?

  78. 78
    bornagain77 says:

    ” I think Christian theology is extremely unlikely to be true”

    Funny considering the fact that I know, via personal experience and evidence, for 100% certainty that Christianity is true.

  79. 79
    Barry Arrington says:

    daveS,

    Do you agree with me that just as soon as you posit the existence of a line between self-evident truths and non-self-evident truths, you have given away the store?

    The point of the OP is that self-evident truths exist. It is no response to that post to say, “yeah, but so do non-self-evident truths.”

  80. 80
    kairosfocus says:

    REC, gotta go, but Pons Asinorum proper is necessarily but not self-evidently true as those who have had to learn how to prove it know. But the effect of being a litmus test of whether one will be able to do Geometry brings out the threshold of background effect. Aquinas spoke to this long ago. KF

  81. 81
    Silver Asiatic says:

    Law of identity. 2 = 2

    The first principles of geometry (or logic in this case) are self-evidently true.

    You can’t prove the first principles since they’re axiomatic. They have to be accepted, otherwise logic is impossible.

  82. 82
    kairosfocus says:

    DS, Basic arithmetic does have a fuzziness involved, especially on the patent absurdity side. Fuzzy thresholds are a familiar pattern, but that full head to bald head is fuzzy does not eliminate the clear difference. A good test for public discussion is whether an intelligent 12 yo could be led to understand the matter through a reasonable discussion at his level, and then whether the absurd consequences of attempted denial would be immediately, readily apparent. But that would not change the fact of necessary truth, e.g. that the side and diagonal of a square are incommensurate is necessary but it is by no means self-evident. That demonstrable fact can be learned and then used, but such will depend on authority or else fairly serious study. 2 + 3 = 5, or || + ||| –> ||||| is very different. KF

  83. 83
    daveS says:

    Barry @79,

    No, I never denied that self-evident truths exist. I merely pointed out that proofs that 2 + 2 = 4 do exist.

    *Edit: As did REC before me.

  84. 84
    Barry Arrington says:

    REC:

    But what does arguing this truth is “self evident” vs. apparent or empirical get us?

    Barry responds:

    What does self-evident truth get us? Why rationality itself REC. If you don’t understand why that is true let me know and I will explain it to you, but 30 seconds of thought will get you there. I will understand if you don’t put in the effort though, since materialists are not big on the whole rationality thing anyway, and thinking is hard work, and 30 seconds is a long time.

    REC:

    [crickets]

    Silver Asiatic:

    Law of identity. 2 = 2

    The first principles of geometry (or logic in this case) are self-evidently true.

    You can’t prove the first principles since they’re axiomatic. They have to be accepted, otherwise logic is impossible.

    SA, on behalf of REC, who was apparently not able to work this out for himself, thank you.

  85. 85
    daveS says:

    KF @82,

    Thanks, I think we’re on the same page then.

  86. 86
    Barry Arrington says:

    daveS,

    Are you suggesting that a “proof” based on propositions more fundamental than:

    || + || –> ||||

    exists?

  87. 87
    kairosfocus says:

    BA, what goes beyond this is axiomatisation and construction of algebraic structures and definitions more carefully worked out than terms of a difficult contract. For instance, just to get to numbers via sets, one has to cover the holes posed by naive theories then set up the set that collects no members — you should hear my son’e objections to that concept — and assign that cardinality 0, then the set that collects this is cardinality 1, then the set that collects these has cardinality 2 and so forth. Then you have to specify what it means to join sets, and so forth. Such help you to address just what is implicit in 2 + 2 = 4 or the like, but it does not really establish this to be so, that was shown once two-ness, joining and cardinality more broadly as well as equivalence were understood as opposed to defined to fit somebody’s schematisation. best of all, the process through sets does not depend on any material artifacts whatsoever, as sets are essentially abstract . . . my bars earlier were in reality ways of setting up sets in familiar ways. And, lo and behold, cardinality has physical effects when manifested in material entities. In short the self evidence stands apart from the various possible axiomatisations and deduced theorems. And a crow can understand enough through number sense, we extend that through counting etc. KF

  88. 88
    Andre says:

    And there it is the materialist Mantra and at least half the reason the world is broken…..

    “I know that I cannot know”

    Simple question then dear materialist… How do you know that you cannot know?

  89. 89
    Barry Arrington says:

    Andre @ 88:

    Yes, Aleta, had a little “whoopsie” on that above where in one sentence he said “I don’t know” and in two sentences later asserted dogmatic knowledge. And then the backpedaling began.

  90. 90
    daveS says:

    Barry,

    I’d have to first ask what the meaning of the “->” is. Once we got the notation and your background assumptions squared away, we would probably be looking at something comparable to the Peano-type proofs I linked to on the MathExchange website yesterday.

  91. 91
    StephenB says:

    Aleta

    But given how much I know about religion in general, and how unlikely Christian dogma appears to me to be, I see little reason to entertain it as a possibility. Being an agnostic doesn’t mean that I don’t have strong beliefs about things based on all my education and experience – taking together everything I know about the world, theistic religious explanations seem very unlikely.

    If you are uncertain about self-evident truths, then you are confessing, unwittingly, that you are not capable of rational thought. This is not just some idle accusation. All thought and all logic is based on the recognition that self-evident truths serve as the foundation for logical thinking.

    It isn’t just the case that a rational person “assumes” the law of non-contradiction–he knows that it is true– without a doubt. So it is with the proposition that 2 +2 is 4. So it is with the proposition that a slice of pizza weighs less than the whole pie.

    I know these things with absolute certainty and certitude. Further, I hold that anyone who does not know it with absolute certitude, or claims not to, is either an idiot or a liar. For those who bristle at the prospect of being called by those names, I would say this: Stop being idiots and liars.

  92. 92
    Barry Arrington says:

    daveS,

    I am confused. You say you don’t deny that self-evident truth exists. Are you saying that 2+2=4 just isn’t one of them?

  93. 93
    Andre says:

    Why has the world abandoned Aristotle’s laws of thought? It puzzles me greatly.

  94. 94
    Barry Arrington says:

    SB @ 91:

    or those who bristle at the prospect of being called [idiots and liars] . . .

    SB, you are as gentle as a kitten compared to Avicenna:

    Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.

  95. 95
    Barry Arrington says:

    Andre @ 93:

    Why has the world abandoned Aristotle’s laws of thought? It puzzles me greatly.

    Oh, the answer to that one is easy enough. Because they stand as barriers to the unfettered autonomous will. See my comment at 63.

  96. 96
    daveS says:

    Barry @ 92,

    AFAIK, 2 + 2 = 4 could very well be a self-evident truth.

  97. 97
    Barry Arrington says:

    daveS @ 96,

    AFAIK, 2 + 2 = 4 could very well be a self-evident truth.

    I assume “AFAIK” means “as far as I know.”

    If that is the case, you should know that it is in the nature of self-evident truth that putting the qualifiers “AFAIK” and “could very well be” in front of the self-evident truth MYLLAI.

    “MYLLAI” for those who don’t know, means “makes you look like an idiot.”

  98. 98
    daveS says:

    What can I say? I’m no philosopher, and not all philosophers agree that self-evident propositions exist. If there are such things, 2 + 2 = 4 would be a likely candidate, I suppose.

    Edit: As you mentioned above, what is self-evident to some may not be so to others, depending on education and background.

  99. 99
    asauber says:

    Some things are self-evident or we would not exist in a noise-less, imageless, tasteless, non-odorus, textureless, non-informational void.

    Andrew

  100. 100
    Barry Arrington says:

    daveS

    As you mentioned above, what is self-evident to some may not be so to others, depending on education and background.

    That is true, but it does not get you off the hook. I’m asking you daveS, with your education and background. Is 2+2=4 self-evidently true?

  101. 101
    Learned Hand says:

    SB,

    Sorry for the delay in answering your question—busy couple of days.

    The amount of pepperoni in a whole pizza is equal to or greater than the amount found in one of the slices.
    [a] Is this statement self-evidently true?
    Yes or no.
    [b] If it is self-evidently true, can I reliably draw conclusions about other truths without appealing to empirical evidence of any kind?
    Yes or no.

    I assume the pizza example is getting at asking whether A=A, or some other essential proposition. I’ll use it as a shorthand.

    Does being self-evidently true mean that something is logically proven, or merely that we have no good reason to doubt it? That’s a serious question, not a rhetorical one. If the latter, then yes. I don’t doubt it, and can’t think of any case or reason that would cause me to.

    If the former, though, then no. It would assume that fundamental assumptions can be proven. I don’t think that’s the case, as a matter of logic. They’re assumptions, not amenable to proof. (They can be objectively demonstrated, though, which is an interesting difference between basic logical notions and the moral beliefs you describe as self-evident.) So while I don’t doubt that A=A, I don’t think it’s proven–or that it proves itself. I’m not a philosopher, and would be interested in any reading you’d recommend (although I can’t promise I could get to it soon).

    Let’s take this to the mathematical example. I tried to ask some questions earlier to better understand the proposition. Barry took it with his usual grace, so I don’t really have any answers. I have to infer, therefore, that it is your position (or at least his) that something is not self-evident if it has to be calculated, but is self-evident if the answer is obvious without calculating it.

    I’m not convinced that 2+2 is fundamentally different from 952+952. I think they’re essentially the thing, different only in scale. The bigger number takes a rational calculation, while the smaller is easy enough for us to calculate based on our long lifetimes of experience seeing 2 and 2 equal 4. But underlying that knowledge is the calculation. If 2+2 couldn’t be calculated, I don’t think it would be proven–and if it’s necessary to be able to calculate it to prove it, then it isn’t self-evident.

    There is additionally an obvious grey area, at least, in which error is possible. Moreover, error is possible in determining what’s in and what’s outside of the grey area. I often get tripped up by the captcha on this site, when I think the answer to an arithmetic problem is very obvious and then have it rubbed in my face that 6*7 is not, in fact, 35. (I don’t know why that one always gets me.) My confidence is sometimes misplaced. Is yours?

  102. 102
    Cross says:

    Here we are at post 101 and the materialists that hang out here are still arguing maths and ignoring the point about self-evident thruth.

    Just to remind you:

    Barry: It is self-evident that torturing an infant for pleasure is evil.

    Anyone going to address this self-evident truth or are you stuck on the math?

    You are making Barry’s point as usual, please try harder.

  103. 103
    Learned Hand says:

    Everyone agrees that that’s evil. As Barry acknowledges in the OP. I think a conversation about how to define, determine self-evident truths is interesting.

    (ETA: if for no other reason, than because I still don’t understand how to exclude error from that determination. And if our conclusions about a self-evident truth can be in error, we’re one giant step closer to living in a subjectivist world anyway.)

  104. 104
    Barry Arrington says:

    LH @ 103:

    Consider the following proposition: 2+2=4.

    If you were asked whether the proposition is true, is there any possibility that you would get the answer wrong?

  105. 105
    Cross says:

    LH @ 103

    “Everyone agrees that that’s evil.”

    I actually haven’t seen them saying that.

    So are you saying that morally speaking, some things are evil and are self-evidently so? There is self-evident good and evil, true and false, a moral standard that is built in?

  106. 106
    kairosfocus says:

    DS, Take a two set and a five set, then join them forming a composite set — and that is the meaning of that little arrow. What is its cardinality? Can it be other than it is, why or why not? KF

  107. 107
    kairosfocus says:

    Andre, you cannot actually in praxis abandon the LOI, LNC and LEM, just, you can refuse to acknowledge them when they are inconvenient. Or, you can be confused, but they are laws of reality before ever being formulated in words. To communicate there must be distinct symbols forming a definite code, for just one instance. As we see in the very posts trying to deny such laws. The squiggles, the observations and so on of Quantum physics pivot on those same laws every time someone tries to use that to suggest otherwise. And much more. But ideology can make us cling to absurdity. KF

  108. 108
    daveS says:

    Barry @ 100,

    I don’t know. If there’s disagreement among the experts on this question, then I don’t think I can make a convincing case either way.

  109. 109
    daveS says:

    KF @ 106,

    The union? Assuming all seven elements are distinct, then the cardinality would be seven. As long as I’m not making an error, it cannot be any other number.

  110. 110
    Barry Arrington says:

    daveS

    I don’t know. If there’s disagreement among the experts on this question, then I don’t think I can make a convincing case either way.

    So if some experts in say, eugenics, said that Jews should be tossed into ovens and other experts said no they should not be tossed into ovens, you would be stymied?

    God help us.

  111. 111
    kairosfocus says:

    DS, The joining — addition — of a three set and a two set gives a seven-set? I think some wires got crossed there. KF

  112. 112
    Daniel King says:

    Barry wrote:

    Barry: It is self-evident that torturing an infant for pleasure is evil.

    I replied:

    One less thing for THE OBJECTIVE MORAL CODE to address.

    Barry then replied:

    Thank you for being succinct, but you have have overdone it a tad. Because I have no idea what you are talking about.

    This is what I meant:

    If a moral judgment is self-evident, that moral judgment doesn’t need to be ascribed to the OBJECTIVE MORAL CODE.

    In UDLand, there seem to be two kinds of moral principles, (1) those that are self-evident and (2) those that are included in the OBJECTIVE MORAL CODE.

    I ask, because if all moral principles are self-evident, an OBJECTIVE MORAL CODE is superfluous. But if no moral principles are self-evident, then maybe we need that OBJECTIVE MORAL CODE.

    We need guidance as to which moral judgments fit into each category.

    Hope that helps.

  113. 113
    Barry Arrington says:

    In UDLand, there seem to be two kinds of moral principles, (1) those that are self-evident and (2) those that are included in the OBJECTIVE MORAL CODE.

    I can’t imagine why you would suggest that (1) and (2) are mutually exclusive. It should be obvious that (1)is a subset of (2).

    I ask, because if all moral principles are self-evident, an OBJECTIVE MORAL CODE is superfluous. But if no moral principles are self-evident, then maybe we need that OBJECTIVE MORAL CODE.

    Not everything having to do with morality is self-evident. Some things are. Again, (1) is a subset of (2).

    We need guidance as to which moral judgments fit into each category.

    We do not need guidance about the matters that fit within the “self-evident” category. That is what it means for them to be SELF-evident. For example, do you, DK, need to consult with anyone – anyone at all – about whether the Holocaust was evil? Of course not. You know that. You needed no guidance from anyone to understand that the wanton murder of 18 million innocent men, women and children was evil.

    DK, you are deeply confused about these matters. I am glad I could help you sort them out.

  114. 114
    daveS says:

    KF,

    I think it was two and five in the question. I forgot to explain my reasoning, but the inclusion-exclusion rule tells us the cardinality would be seven, assuming no intersection of the original sets.

  115. 115
    kairosfocus says:

    DS, in 86, BA used || + || –> ||||, where is your case? KF

  116. 116
    daveS says:

    KF,

    In your post #106.

  117. 117
    SteRusJon says:

    It seems to me, there is some confusion above as to what the “self” in self-evident is referencing. It is not a reference to the person contemplating the truth value of a proposition. It is referencing the proposition itself. The proposition contains all the information necessary to determine the truth or falsity of the proposition. There is no need to consider Lemma, Fermats and Fibanocci, Oh my. (See link in #2) That is as true of 98/14=7 as it is of 2+2=4. If you wish to engage the proposition or not, whether you care to ruminate about it or not, whether you understand any math lingo or not, both of those propositions contain all the information needed to determine and know their truthfulness. They are self-evidently true. Their truthfulness does not depend on such extraneous things as the day of the week or the color of the morning sky or your education level. All the relevant information is invoked by the symbols for 2-ness, 4-ness, addition and equality. If you do not understand the symbols you can not know if the proposition 2+2=4 is true or false. Because you, yourself, do not know the truthfulness does not change the truthfulness of the proposition. It still contains all the information needed to determine its truthfulness. More than that. It is still true. If you do understand the symbols, the proposition’s symbols convey all the information needed for you to know with certainty that the proposition is true and not false. The proposition is self-evidently true.

    For some propositions, some just can’t (think) or won’t (consider) to go where the self-evidence leads.

    Where does it lead? In the larger context of these OPs, it leads to- The killing of the unborn for the convenience of the mother and the financial gain of the doctors and staff is evil, evil, evil.

    Stephen

  118. 118
    Learned Hand says:

    Barry,

    Consider the following proposition: 2+2=4.
    If you were asked whether the proposition is true, is there any possibility that you would get the answer wrong?

    I hope not!

    No, in all seriousness. But what does that have to do with my comment? I acknowledge that no adult of normal faculties will get 2+2=4 wrong. That doesn’t make it self-evident if the calculation is intuitive; the identity still rests ultimately on the calculation. I think. I can’t prove it.

    If I drop a ball from my hand, I know instantly it will fall, and I will never be wrong about that. Is the fact that object move in gravity self-evident, or merely intuitive? In other words, what’s the difference between a self-evident fact and an intuitive fact?

    (ETA: my answer assumes that you agree that something which must be calculated is not self-evident. Your responses above seemed to indicate that, but I don’t think you’ve said one way or the other. SteRusJohn above seems to take the position that all math problems are self-evident.)

  119. 119
    Learned Hand says:

    Cross,

    I’d rather not derail the thread; I’ve written my position elsewhere. I realize there’s a lot to dig through to find it, and sorry about that, but I’ve got to plead limited time.

  120. 120
    Learned Hand says:

    In UDLand, there seem to be two kinds of moral principles, (1) those that are self-evident and (2) those that are included in the OBJECTIVE MORAL CODE.

    I can’t imagine why you would suggest that (1) and (2) are mutually exclusive. It should be obvious that (1)is a subset of (2).

    Is 1 a subset of 2, or is 2 a subset of 1? If all self-evident truths are a subset of the OMC, then 2+2=4 is an objective moral belief, right?

  121. 121
    RDM says:

    Perhaps the greatest irony of this whole discussion, given that it is primarily dealing with materialists and their objections to self-evident moral truths, is two-fold.

    First, consider that in many respects, philosophical arguments are simply plausibility comparisons. One argument/view is simply more plausible than another. Now, in terms of a plausibility comparison between “it is always and everywhere wrong and evil to torture a child for fun” and “materialism is true and thus it is not always wrong to torture a child for fun”, the former is light-years more plausible and certain than the latter. Any worldview that rejects that moral truth is infinitely less plausible than the moral truth itself. In fact, that moral truth is more plausible than the claim that “matter itself exists”. And so, the irony here is the following: the moment that I doubt the truth of that moral statement is the moment that I gain infinitely more reason to doubt the truth of materialism (or naturalism, to use a different name for it).

    Now the second great irony in hearing the materialist argue, in part, against self-evident truths, is that materialism, at its core, depends, in a certain way, on the idea of self-evidence. And not in the ways already mentioned—although in those as well—but rather in that the existence of matter itself is arguably supported by nothing but self-evidence. After all, what is the materialist’s proof or empirical evidence that matter actually exists? As Berkeley and others showed, not only is there nothing that can “prove” that matter exists, but there are actual good arguments against the existence of matter. And so, for the existence of matter, the materialist can offer, as inferential evidence or proof, nothing more than the person who says that “it is always wrong to torture a child for fun” can offer for his view. And remember, the burden of proof is on the materialist, for he asserts the existence of matter. And so, if you think yourself justified to rejecting the aforementioned moral claim, than you are doubly justified in rejecting the very existence of matter, and, in turn, in rejecting materialism. So, in rejecting the very moral claim that it must reject in order to be coherent, materialism simultaneously provides us with the very grounds to deny the existence of matter, and thus to deny materialism itself. Materialism, in essence, loses no matter which way it turns.

  122. 122
    Barry Arrington says:

    Barry: Consider the following proposition: 2+2=4. If you were asked whether the proposition is true, is there any possibility that you would get the answer wrong?

    LH: No . . . I acknowledge that no adult of normal faculties will get 2+2=4 wrong.

    Progress.

    Now the next step. Please answer these questions: (1) If someone were to say to you that the proposition 2+2=4 is false, would you would think their statement is absurd? (2) Can you even imagine a universe in which 2+2=4 is false?

    LH: Is the fact that object move in gravity self-evident, or merely intuitive?

    Actually, this is a very good example. I can imagine a universe in which I dropped something and it did not fall to the ground. The operation of gravity is a matter of empirical observation. Propositions about gravity are not “necessary” truths in the same way that no circle can ever be square or 2+2=4. As Chesterton said:

    [Natural law] is not a necessity, for though we can count on it happening practically, we have no right to say that it must always happen. It is no argument for unalterable law (as Huxley fancied) that we count on the ordinary course of things. We do not count on it; we bet on it.

    Therefore, propositions about gravity are not self-evident. Any particular proposition may or may not be true. It is certainly not self-evident.

    In other words, what’s the difference between a self-evident fact and an intuitive fact?

    Chesterton described the difference very nicely. One is necessary. The other is not.

  123. 123
    Barry Arrington says:

    LH

    Is 1 a subset of 2, or is 2 a subset of 1? If all self-evident truths are a subset of the OMC, then 2+2=4 is an objective moral belief, right?

    LH, read what set (1) is again carefully. It is a set of “those” [i.e., those moral principles] that are self-evident. 2+2=4 is is indeed self-evident. It is not a moral statement.

  124. 124
    StephenB says:

    Learned Hand

    I assume the pizza example is getting at asking whether A=A, or some other essential proposition. I’ll use it as a shorthand.

    No, it is based on the self-evident principle that a part cannot be greater that the whole of which it is a part. Do you agree that this principle is self-evidently true?

    Does being self-evidently true mean that something is logically proven, or merely that we have no good reason to doubt it?

    A self-evident truth is one that is immediately understood to be infallibly true. It cannot be logically proven. If proof was necessary or even possible, then it would not be a self-evident proposition. A self-evident truth comes before proof, not after. It isn’t just that there is “no good reason” to doubt it. More to the point, it would be irrational, absurd, and unthinkable to doubt it. You cannot possibly be wrong about it.

    Do you agree, for example, that it is absurd to suggest that a slice of pizza could contain more pepperoni than the whole pie? Do you, in other words, agree with the following proposition: It is self-evidently true that the whole pepperoni pizza (any pepperoni pizza) must contain at least as much or more pepperoni than any one of the slices?

    Do you also agree that you cannot possibly be wrong in making this judgment? Put another way, do you agree that you can have infallible certitude that you are right? The question can be answered with a simple yes or no. If the answer is no, please explain why you have any doubts.

    Let’s take this to the mathematical example.

    Perhaps we can take that up later.

  125. 125
    Learned Hand says:

    Please answer these questions: (1) If someone were to say to you that the proposition 2+2=4 is false, would you would think their statement is absurd? (2) Can you even imagine a universe in which 2+2=4 is false?

    Yes, and no.

    Your reference to Chesterton answers a lot of other questions I had, thank you.

    It seems that you agree that people can be mistaken about apparently self-evident facts (such as someone who makes a mistake solving a simple math problem). Can you distinguish between facts about which no error is possible, and ones where error is possible? And is it possible for that distinction to be in error?

  126. 126
    Learned Hand says:

    No, it is based on the self-evident principle that a part cannot be greater that the whole of which it is a part. Do you agree that this principle is self-evidently true?

    No, which is one reason I was trying to simplify the question. My immediate objection is that in the statement “2+(-2)+(-2)=-2”, the whole is less than one of its constituent parts. I don’t know much about mathematics, so I’m not sure if that’s a legitimate counter-example or not. It doesn’t apply to pizza, and I don’t think it’s a serious problem for your overall point. But it means when you back the pizza question out to a general principle, I have a question that keeps me from agreeing.

    Do you agree, for example, that it is absurd to suggest that a slice of pizza could contain more pepperoni than the whole pie? Do you, in other words, agree with the following proposition: It is self-evidently true that the whole pepperoni pizza (any pepperoni pizza) must contain at least as much or more pepperoni than any one of the slices?

    Yes, and yes, with the caveat that we’re talking about pepperoni, not abstractions. I could be persuaded it’s logically possible to prove or disprove that a whole must be greater than the sum of its parts, such as with negative numbers.

    This is one reason I suggested “A=A.” I think I’d say without reservation that’s a truth that can’t be proven.

    Do you also agree that you cannot possibly be wrong in making this judgment? Put another way, do you agree that you can have infallible certitude that you are right? The question can be answered with a simple yes or no. If the answer is no, please explain why you have any doubts.

    Yes, as for pizza. If we’re talking general concepts, well, see my thoughts above.

    So, my questions for you are:

    Can a self-evident truth be one that takes an adult of normal faculties some reasoning or experience to perceive? (Such as experience that ingrains an understanding of what 256×2 is.)

    Does “you cannot possibly be wrong about it” mean that you can’t make a type I error, a type II error, or both?

    Can you distinguish between facts about which no error is possible, and ones where error is possible?

    And is it possible for that distinction to be in error?

    I don’t need a “yes or no” answer. I’d rather hear whatever you have to say.

  127. 127
    Andre says:

    Learned Hand

    It seems that you agree that people can be mistaken about apparently self-evident facts (such as someone who makes a mistake solving a simple math problem). Can you distinguish between facts about which no error is possible, and ones where error is possible? And is it possible for that distinction to be in error?

    Consider, “I think therefor I am”

    Over to you.

  128. 128
    Barry Arrington says:

    Barry: Please answer these questions: (1) If someone were to say to you that the proposition 2+2=4 is false, would you would think their statement is absurd? (2) Can you even imagine a universe in which 2+2=4 is false?

    LH: Yes, and no.

    I appreciate your candor and your succinct responses. We agree that any person of reasonable intelligence immediately understands that 2+2=4 is infallibly true. As SB says, it isn’t just that there is no good reason to doubt it. It would be irrational, absurd, and unthinkable to doubt that 2+2=4. You cannot possibly be wrong about it.

    In summary, you believe that 2+2=4 is a self-evident truth.

    Your reference to Chesterton answers a lot of other questions I had, thank you.

    You’re welcome. He has answered many of my questions over the years. Whenever I think I’m smart, I think about someone who is really smart like Chesterton (or Lewis) and I realize that in comparison to those greats, I am a babbling simpleton.

    It seems that you agree that people can be mistaken about apparently self-evident facts (such as someone who makes a mistake solving a simple math problem). Can you distinguish between facts about which no error is possible, and ones where error is possible? And is it possible for that distinction to be in error?

    No, by definition, a self-evident truth is immediately apprehended to be infallibly true merely by virtue of the fact that the observer understands it. Therefore, if a person understands a self-evidently true proposition at all, it is not possible for him to be in error about it.

  129. 129
    Barry Arrington says:

    Learned Hand:

    Now that we agree that some truths are self-evident, let’s apply the concept to a moral proposition. I am going to set out your answers to the math questions and then I am going to set out what I presume your answers to the moral questions would be.

    Consider the following proposition: 2+2=4.

    If you were asked whether the proposition is true, is there any possibility that you would get the answer wrong?

    LH’s Answer: No.

    Consider the following proposition: Torturing an infant for pleasure is evil.

    If you were asked whether the proposition is true, is there any possibility that you would get the answer wrong?

    LH’s Presumed Answer: No.

    Please answer these questions: (1) If someone were to say to you that the proposition 2+2=4 is false, would you would think their statement is absurd? (2) Can you even imagine a universe in which 2+2=4 is false?

    LH’s Answer: Yes and no.

    Please answer these questions: (1) If someone were to say to you that the proposition “torturing an infant for pleasure is evil” is false, would you would think their statement is absurd? (2) Can you even imagine a universe in which “torturing an infant for pleasure is evil” is false?

    LH’s Presumed Answer: Yes and no.

    Have I gotten any of your presumed answers wrong? If not, then you agree that the proposition “torturing an infant for pleasure is evil” is self-evidently true in exactly the same way you believe that the proposition 2+2=4 is self-evidently true.

    If I have gotten your presumed answers wrong, then please explain why you disagree.

  130. 130
    mugwump3 says:

    SteRusJon had the best response here.

    Self-evident truths are defined by their needing no outside data to be true. Messing about with man’s subjective failure to understand is irrelevant. All math is identity, at least if you understand what the “=” means. Man’s use of math to dis-cover deeper self-evident truths is just pragmatic use of symbols with which to dis-cover the truths. Need we explain the etymological sources of the words “under-stand” and “dis-cover?”

    Truths precede man’s ability to dis-cover them, both logically and chronologically, and, as another commenter added, these truths are more self-evident than the existence of matter.

    I believe God exists more than I believe I do….logically. One is necessary; the other is gratefully contingent.

  131. 131
    Barry Arrington says:

    mugwump3 @ 130.

    I agree that all true mathematical equations are necessarily true. I do not agree that they are all self-evidently true.

    All self-evident truths are necessary truths. Not all necessary truths are self-evident truths.

    Consider the most necessary truth of all — God. Hebrews 11:6 says that He requires us to approach him in faith. It is a reasoned and reasonable faith to be sure. But it is still faith. And what is faith? Believing in the face of possible doubt. If doubt were not possible, faith would not be possible either. They are opposite sides of the same coin. The proposition “God exists” is true. I agree with you that it is even necessarily true. But it is not self-evident.

  132. 132
    mugwump3 says:

    Don’t think I disagree with you, Barry. I might have omitted the message there.

    All mathematical truths are derived by and under-stood by self-evident truths. Not that being necessary is equal to self-evident. I intended to communicate that both necessary truths and self-evident truths, both as a subset and basis of necessary truths, do not require man’s assent to be true. I was just disarming the main defense launched by the subjectivists.

    General revelation written on the hearts of man are pronouncedly different than special revelation. Prophecy and miracle (intentionally within the restrictions of time and spacial law), of course, as gracious evidences…thus not self-evident, as you say.

  133. 133
    mugwump3 says:

    Thinking on it a little more, rather than sleeping as I should, the next obvious question to answer would be: why are the Declaration of Independence’s truths held self-evident in this sense? Wondering if someone might explain them in light of necessary truths understood and held by Jefferson and the signers? And why, since modern materialists reject the assumptions, they should themselves hold to any of the self-evident truths therein?

  134. 134
    Bob O'H says:

    Silver Asiatic @ 81 –

    The first principles of geometry (or logic in this case) are self-evidently true.

    You can’t prove the first principles since they’re axiomatic. They have to be accepted, otherwise logic is impossible.

    You have to be careful here. Axioms are assumptions, so yes they have to be accepted, but that doesn’t mean they are self-evidently true. Leaving aside sets of axioms that are contradictory, there’s no reason for the axions to be true outside of the system of axioms. Geometry is a great example of this: although the parallel line postulate seems obvious, there are geometries where is it not true.

  135. 135
    kairosfocus says:

    DS, oh, I see — I typed five not three. Pardon. KF

  136. 136
    kairosfocus says:

    Folks,

    There may be some progress here, some degree of general understanding on what SETs are, and a glimmer of hope that their foundational significance will be grasped.

    That is very important.

    Going back to comment no 1:

    . . . there is one other key feature to self-evident truths, when one attempts to deny them, the result is immediately and patently absurd.

    Once, you have sufficient background experience of reality to understand what is meant when the truth is asserted. (That can be a problem; as Aquinas pointed out, i.e. there is such a thing as a pons asinorum.)

    True per understanding what is being said, necessarily true and this on pain of immediate patent absurdity on attempted dismissal or denial.

    The problem we are seeing is one of lack of understanding, as is manifest in the confusion between the obvious or apparent and the properly self-evident.

    This is backed up by clinging to absurdity due to ideological programming, dominance of agendas and the like.

    In the case of moral SETs, too often there is endarkenment due to the hardness of heart and/or the need to benumb oneself to fend off guilt and linked cognitive dissonance.

    I think it is critical to underscore, too, that when one believes error to be truth, the real truth will usually contradict it and therefore will seem false to you. But error will soon enough manifest its true status, on close examination.

    But that can be hard, and may require for one’s life to go crash for it to be believed. Pain and grief do a lot to open closed minds and hardened hearts, if we are willing to listen to that still small voice saying, y’know, you were wrong way back there and that’s why this is happening, why things have fallen apart.

    In short, SETs are a peculiar subset of necessary truths, those that simply by understanding what is being claimed, will be seen as so, as necessarily so, and as this on pain of patent absurdity. As SB put it in 124 above “it would be irrational, absurd, and unthinkable to doubt it.”

    Now, as BA cited from Chesterton in 122:

    [Natural law] is not a necessity, for though we can count on it happening practically, we have no right to say that it must always happen. It is no argument for unalterable law (as Huxley fancied) that we count on the ordinary course of things. We do not count on it; we bet on it.

    This brings out an important point.

    Laws of nature are from our perspective so-far successful summaries of empirically reliable circumstances, forces and factors that we see generally obtaining. They need not always obtain, nor are the statements of them necessarily ultimately true, they are provisional. We may be confident, but indeed, we are betting.

    Similarly, matters of fact in the world of experience are generally contingently so, what did turn out, and are attested to by witnesses, traces, record and circumstances, etc. We may hold moral certainty, but there is an irreducible possibility of error. Moral certainty, meaning, that we would be irresponsible to act on a serious matter, as though the relevant facts in question were false.

    Matters of fact are not matters of self-evident truth.

    But what about experience, understanding etc.?

    These, are required for us to make proper sense of circumstances, it is not just a matter for SETs.

    You really do need to know some things to make sense of 2 + 3 = 5.

    Failing which, you are at the pons asinorum.

    And, if you are lacking in experience or are beclouded by clinging to error, you will unjustifiably doubt or may even dismiss SETs that cut across your agenda. However, at the price of being forced to cling to absurdity.

    For instance, it is a commonplace that we have rights, reasonable expectations that we be respected in certain ways. It is also a commonplace that we are intelligent and rational, capable of thinking and understanding for ourselves. This last is locked into our immediate, personal, direct awareness that we are self-aware beings. Which, BTW is “fact no 1” or indeed truth no 1.

    Even if we are deluded about circumstances, once we understand what being self aware means, the very act of being aware makes it plain that it would be absurd to doubt our consciousness. (One may doubt that of perceived others [per all sorts of possibilities or speculations], but not one’s own consciousness.)

    This is thus a SET: we are self-aware, and rational.

    If you doubt that we have a faculty of reason, consider that the act of doubt is . . . an act of reason i/l/o the possibility of error. (And that error exists is undeniably, self evidently true, showing warranted, credibly true belief, here to undeniable certainty; decisively undermining vast swathes of systems that reduce truth and knowledge to opinion etc.)

    Therefore, what runs contrary to that, we have a right to doubt or even dismiss.

    Such become particularly important in assessing moral truths.

    First, we do have a faculty, conscience, that informs us that we are under moral government, as a part and parcel of our self-aware inner, rational life.

    To reject such as delusional, because of that integral status, then would spread grand delusion across that inner life.

    We cannot but live based on the premise of rationality and so any scheme of grand delusion (as opposed to mere commonplace or widespread specific error) can be held absurd. Bye bye Plato’s cave worlds, etc. But, we expect to find points of error, we are fallible.

    In that light, we have every good reason to see that it is immoral, evil, even demonically wicked and “sick” for someone to kidnap, bind, gag, sexually assault and murder a young child going home from school for reasons of twisted pleasure. Not least, as such violation of person and robbing of life destroys the potential to exercise any other rights. Similarly, the violation of an infant for similarly sick pleasure is undeniably wrong. Were such to spread across society unchecked, chaos and disintegration would be the obvious consequences.

    It is certainly more plausible that such are true than that their denial is true, and what is more, the attempted denial is absurd. (That is why skeptics routinely skirt such denial.)

    Now, too, RDM at 121 writes:

    in many respects, philosophical arguments are simply plausibility comparisons. One argument/view is simply more plausible than another. Now, in terms of a plausibility comparison between “it is always and everywhere wrong and evil to torture a child for fun” and “materialism is true and thus it is not always wrong to torture a child for fun”, the former is light-years more plausible and certain than the latter. Any worldview that rejects that moral truth is infinitely less plausible than the moral truth itself. In fact, that moral truth is more plausible than the claim that “matter itself exists”. And so, the irony here is the following: the moment that I doubt the truth of that moral statement is the moment that I gain infinitely more reason to doubt the truth of materialism (or naturalism, to use a different name for it).

    Now the second great irony in hearing the materialist argue, in part, against self-evident truths, is that materialism, at its core, depends, in a certain way, on the idea of self-evidence. And not in the ways already mentioned—although in those as well—but rather in that the existence of matter itself is arguably supported by nothing but self-evidence. After all, what is the materialist’s proof or empirical evidence that matter actually exists?

    Yes, if we include within plausibility, that there is a context of worldviews level comparative difficulties and that some forms of implausibility spring from being found incoherent or otherwise absurd. Which, in certain cases, can be patent and undeniable, on pain of clinging to error.

    The connexion to “matter exists” of course, is that our first fact and SET is our self aware conscious rationality.

    To deny or reject that is absurd.

    But, we access the external world of facts including matter, energy and space-time, through that self-aware rational consciousness. So, if a belief about the external world undermines our inner life, spreading grand delusion through it, it saws off the branch on which it must sit.

    As Haldane put it:

    “It seems to me immensely unlikely that mind is a mere by-product of matter. For if my mental processes are determined wholly by the motions of atoms in my brain I have no reason to suppose that my beliefs are true. They may be sound chemically, but that does not make them sound logically. And hence I have no reason for supposing my brain to be composed of atoms. In order to escape from this necessity of sawing away the branch on which I am sitting, so to speak, I am compelled to believe that mind is not wholly conditioned by matter.” [[“When I am dead,” in Possible Worlds: And Other Essays [1927], Chatto and Windus: London, 1932, reprint, p.209.]

    So, RDM has hit the nail on the head.

    And from this point, we are in a position to see many other things.

    If we are willing to follow where this leads.

    Especially, if we are willing to ask, how can OUGHT be grounded in a world where matter, energy, space, time and arithmetical facts etc cannot do so?

    Are we stuck at Hume’s objection, arguing is, is then jumping across to ought, ought with no bridge possible between the two?

    Or, is it possible to look to the world root and find there an IS that can adequately ground OUGHT?

    In the words of the US Founders, in the 2nd para of the US DoI:

    We hold these truths to be self-evident, [cf Rom 1:18 – 21, 2:14 – 15, 13:8 – 10 — and given Locke and Blackstone etc all teh way back tot he opening passages of King Alfred’s Book of Dooms, those and other texts of like order patently lurk there . . . ], that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. –That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, –That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security . . .

    Okay, what results from trying to deny that such claimed moral truths are so?

    Where is such pointing?

    What, then, should we do?

    KF

  137. 137
    Aleta says:

    2 + 2 = 4 is true (and so simple that it is immediately seen as true). However, for someone to recognize it as true, one would have to understand what “2”, “+”, “=”, and “4”. I would like to challenge those who declare that that 2 + 2 = 4 is “self-evidently” true to define and explain those concepts in a way that doesn’t rely on referring to material properties of the world. My belief is that those beginning concepts are reflections or representations of basic facts about how, in our experience, objects exist as unique entities – they have distinct boundaries which separate them from other objects, and that they retain their “objectness” when they are moved around and combined with other objects. In a different material world, or in a purely mental world with no material world to reference, these properties might not be true.

    After establishing the beginning concepts, I think what one would find is that the reason 2 + 2 = 4 is self-evidently true is that it is true by definition. The reason we feel that is has some special self-evidencey is because our understanding of the basic concepts is so embedded in our understanding of how our world – our material world – works, and because, as KF’s crow example illustrates, the quantities are so small that we have a biological, pre-verbal ability to understand them

    So, in summary, 2 + 2 = 4 is self-evident because

    a) the underlying concepts are based on basic properties of the material world,
    b) we have created symbolic definitions that mirror those properties, and
    c) the quantities are so small so all normal humans can grasp them without any calculation involved.

  138. 138
    Barry Arrington says:

    Aleta @ 137

    Think of two apples in your mind. Then think of two more apples along with the first two. You are now thinking of four apples.

    How many material things did you count?

  139. 139
    Aleta says:

    A more general point. Our material world, at the level we experience it, has underlying properties which we have modeled through symbolic representations – through mathematics and logic. The most basic of those are understood by other animals, without any verbal or symbolic representation, such as the conservation of quantity. Because this is the only world we know of, we can’t imagine a world where one of those basic properties might not exist – for instance, we can’t imagine a world that is not three-dimensional. Because our material world is as it is, those basic properties seem self-evident.

    As we have built up more and more complex mathematics, we have discovered that it is not necessarily true that mathematics will continue to accurately model the world in all its aspects. The question of whether math accurately represents the world at some point has to be tested empirically. For instance, both relativity and quantum mechanics bring up situations where our mathematical models of the world based on our macroscopic experience don’t work any more.

    Not only that, but we have invented mathematical systems that don’t model the self-evident world we experience, although sometimes those models are later found to be useful. We have three different geometries based on different versions of the parallel postulate, we have non-commutative algebras, we have geometries we more than three dimensions, we have systems which fundamentally include probabilities, not certainties, etc.

    So, the basic idea is that mathematical systems can model the material world, but whether they are accurate in respect to any particular aspect of the world, in theory must be tested. Those aspects which are self-evident are self-evident because they successfully model very basic properties of the material world we live in. If we lived at a different scale, or in a different type of world (if you would like to imagine that possibility), different self-evident beginnings of math might exist.

  140. 140
    Aleta says:

    To Barry: apples are material things. 2 + 2 = 4 because those are names for things and operations about how the material world works.

  141. 141
    Barry Arrington says:

    Alexa
    How many material things did you count? Dodging the question a second time will be very telling.

  142. 142
    Barry Arrington says:

    BTW if it helps think of two pink unicorns. Now think of two more. How many pink unicorns Aleta?

  143. 143
    Aleta says:

    I’m not quite sure what question I am dodging: 2 apples + 2 apples = 4 apples, of course, because that is how apples work. 2 + 2 = 4 is true about things that behave like apples.

    However it might be instructive to consider this: suppose we were adding velocities instead. The theory of relativity tells us that , if v = a certain velocity, that 1v + 1v does not equal 2v. In fact, if v = the speed of light c, 1c + 1c = 1c

    So whether 1 + 1 = 2 depends on what you are adding.

    2 + 2 = 4 is self-evident because it expresses a fundamental fact about certain type of things in the material world – it is based on empirical experience.

  144. 144
    GCS says:

    Good Morning,

    Interesting thread (or should I say rope or cable!).

    It seems to me that the whole thread just proves the Christian case.

    Where did we get intellects that are powerful enough to argue any side of the issue?

    Answer: our intellect is given directly from God. I suspect that no other world view can truly explain why we have such intellectual power.

    Why do our intellects not come to similar conclusions?

    Answer: because our intellects are clouded by original sin.

    May the peace of God be with you.

  145. 145
    StephenB says:

    Learned Hand

    No, which is one reason I was trying to simplify the question. My immediate objection is that in the statement “2+(-2)+(-2)=-2”, the whole is less than one of its constituent parts.

    That is not really a part/whole relationship.

    SB: Do you agree, for example, that it is absurd to suggest that a slice of pizza could contain more pepperoni than the whole pie? Do you, in other words, agree with the following proposition: It is self-evidently true that the whole pepperoni pizza (any pepperoni pizza) must contain at least as much or more pepperoni than any one of the slices?

    Yes, and yes, with the caveat that we’re talking about pepperoni, not abstractions. I could be persuaded it’s logically possible to prove or disprove that a whole must be greater than the sum of its parts, such as with negative numbers.

    The reason that the application works is because the principle on which it is based is sound. If a part could be greater than the whole, then a slice of pizza could contain more pepperoni than the whole pie.

    This is one reason I suggested “A=A.” I think I’d say without reservation that’s a truth that can’t be proven.

    Yes, the law of Identity certainly qualifies as a self-evident truth.

    SB: Do you also agree that you cannot possibly be wrong in making this judgment? Put another way, do you agree that you can have infallible certitude that you are right? The question can be answered with a simple yes or no. If the answer is no, please explain why you have any doubts.

    Yes, as for pizza. If we’re talking general concepts, well, see my thoughts above.

    Recall that the general principle about parts and wholes informs the specific example of pizza slices and pizza pies. If the example that depends on the principle is true, then the principle upon which it depends must also be true.

    So, my questions for you are:
    Can a self-evident truth be one that takes an adult of normal faculties some reasoning or experience to perceive? (Such as experience that ingrains an understanding of what 256×2 is.)

    The standard would be this: Does the person understand the meaning of the terms being used? If so, then the principle will be self-evident to him. If not, then it will be self evident in itself, but not to him.

    It would not be related to a reasoning “process” such as If A, then B. If you must reason your way from A to B, then B is not self evident.

    Does “you cannot possibly be wrong about it” mean that you can’t make a type I error, a type II error, or both?

    Yes. I would mean that. These types of errors pertain to the statistical analysis of evidence. Self evident principles do not require empirical evidence to be understood or confirmed. Indeed, the process of induction as applied to scientific reasoning guarantees that some measure of error will be present in every analysis. Hence, the term, “margin of error.”

    Can you distinguish between facts about which no error is possible, and ones where error is possible?

    Yes. Let’s take the pizza. We have established the self-evident truth that the whole pizza contains more pepperoni than a slice. No error is possible on that point or on any conclusion derived from it using deductive reasoning. Example: The weight of a slice of pepperoni pizza will always be less than the weight of the whole pie. On just about any other point, however, an error would be possible and, in many cases, likely. Does this pizza contain pepperoni? How much does the pepperoni weight? How much space does it take up? – and on and on. We can be wrong about these and millions of other things.

    And is it possible for that distinction to be in error?

    Perhaps you mean this: Is it possible for a person to get confused about the distinction? Absolutely. That is what this thread is all about—marking the difference between real self evident truths and those infamous claims about things once thought to be obviously true that were found to not be true at all.

  146. 146
    Learned Hand says:

    Now that we agree that some truths are self-evident,

    We agree that there are truths I can’t imagine questioning, or being reasonably questioned. That does not establish that a truth is proven or even evidenced; it establishes only that I can’t imagine a case in which it would or could be untrue. Again, fallibility is an important concern for me. I am not infallible, nor do I accept that you are.

    To put a point on it, you apparently take the position that complex math problems aren’t really self-evident. The standards you set out for self-evident beliefs—can’t imagine it being false, think disagreement is absurd—apply to harder calculations too, though. I may need a calculator to figure out 204/17, but once I’ve done it, I’d put it in the same category as 2+2: can’t imagine questioning it, wouldn’t take questioning it seriously. (As an aside, I realize there are ways to redefine how the math is done to throw a wrench in the works. I think we’re all talking about bog-standard arithmetic here, not different bases or whatnot.)

    So now the realm of self-evidence has grown substantially, and gotten much fuzzier around the edges. We’re having to apply reason to get to the SE truths, so are they really SE? Or does having to apply reason exclude them from SE?

    And it’s even harder than that. Having done the calculation above, I know that 204/17=12. That memory will substitute for the calculation, and if that memory persists, will quickly become intuitive. So now is it a SE truth? And if not, what if 2+2 or the moral truths you espouse also came to occupy your heart through a period of education and acculturation?

    Consider the following proposition: Torturing an infant for pleasure is evil.
    If you were asked whether the proposition is true, is there any possibility that you would get the answer wrong?

    I’m a subjectivist. How can I be “wrong” about subjective, non-material beliefs? I don’t think there’s an external standard to which to compare them. I believe them or I don’t. I suppose I could be confused or conflicted about my own beliefs, but I don’t think that would ever be the case about such a stark example as TAIFP.

    In other words, no. But that “no” may not be the “no” you were looking for, as your question may presuppose objectivism.

    Please answer these questions: (1) If someone were to say to you that the proposition “torturing an infant for pleasure is evil” is false, would you would think their statement is absurd? (2) Can you even imagine a universe in which “torturing an infant for pleasure is evil” is false?

    Yes, and no. But again, I’m a subjectivist. I’m answering whether I can imagine a universe in which I would say TAIFP is good, and I can’t. (I suppose I could have been made into such a person had I been tortured as a child or brain-damaged or something, but then I wouldn’t be me, so no.)

    I can imagine other people believing that TAIFP is good. People have certainly believed things as bad or worse before. I think they’re wrong, but I have no external standard to resolve the dispute—only my own perceptions and beliefs.

    I hope that answers your questions. So, here’s a question for you: it seems we agree that there is a grey area, in which it’s impossible to tell whether a truth is self-evident or just a possibly flawed intuition. So how do you try to distinguish between self-evident truths and your own fallible intuition?

    Are there any SE truths that weren’t taught to you, or demonstrated to you through your culture or environment, before you consciously accepted them?

    If you’re familiar with Daniel Kahneman’s work, or the research generally, do you think a truth that has to be accessed through System II thinking can ever be a SE truth?

  147. 147
    Learned Hand says:

    SB,

    Does “you cannot possibly be wrong about it” mean that you can’t make a type I error, a type II error, or both?

    Yes. I would mean that. These types of errors pertain to the statistical analysis of evidence. Self evident principles do not require empirical evidence to be understood or confirmed. Indeed, the process of induction as applied to scientific reasoning guarantees that some measure of error will be present in every analysis. Hence, the term, “margin of error.”

    I don’t think you answered the question I intended to ask. Sorry if my terminology was misleading. I’m curious whether “you cannot possibly be wrong about it” means:

    (a) You cannot think that a SET is not a SET; or
    (b) You cannot think that a non-SET is a SET; or
    (c) Both.

    Can you distinguish between facts about which no error is possible, and ones where error is possible?

    Yes. Let’s take the pizza.

    Let’s take math if you don’t mind, to advance the conversation. If 2+2=4 is a SET, and 983/247=X isn’t, can you draw a firm line at the point where SETs stop? Is it the point at which you have to reason out the answer? I think that’s your position, but I’m not certain.

  148. 148
    Barry Arrington says:

    Aleta,

    I’m not quite sure what question I am dodging.

    Liar.

    You’ve dodged the question twice now. It is plain to me you don’t want an honest discussion. Goodbye.

  149. 149
    Barry Arrington says:

    Barry: Consider the following proposition: Torturing an infant for pleasure is evil.

    If you were asked whether the proposition is true, is there any possibility that you would get the answer wrong?

    LH’s answer: “No”

    Barry: Please answer these questions: (1) If someone were to say to you that the proposition “torturing an infant for pleasure is evil” is false, would you would think their statement is absurd? (2) Can you even imagine a universe in which “torturing an infant for pleasure is evil” is false?

    LH’s answers: “Yes, and no.”

    In summary, according to the definition of SET, you believe that torturing an infant for pleasure is evil is self-evidently true. Good for you.

    Your attempts to qualify your answers so that you can cling to subjectivism in the teeth of your own reason are sad.

    I can imagine other people believing that TAIFP is good.

    But you can’t imagine their belief being correct. You just told me so.

    So, here’s a question for you: it seems we agree that there is a grey area, in which it’s impossible to tell whether a truth is self-evident or just a possibly flawed intuition.

    No, we don’t agree on that. SETs admit of no grey areas.

    So how do you try to distinguish between self-evident truths and your own fallible intuition?

    Because my recognition of an SET is not based in even the slightest degree on my intuition.

    Are there any SE truths that weren’t taught to you, or demonstrated to you through your culture or environment, before you consciously accepted them?

    The question seems to be based on the flawed premise that I go around evaluating every proposition with respect to whether it is a SET. I do not.

    If you’re familiar with Daniel Kahneman’s work, or the research generally, do you think a truth that has to be accessed through System II thinking can ever be a SE truth?

    I am not. I read the Wiki entry on his book. “System II thinking is Slow, effortful, infrequent, logical, calculating, conscious.” Without committing myself (because I really don’t know what he says about the subject other than those adjectives), the answer would be “no.”

  150. 150
    StephenB says:

    Learned Hand to Barry

    We agree that there are truths I can’t imagine questioning, or being reasonably questioned. That does not establish that a truth is proven or even evidenced; it establishes only that I can’t imagine a case in which it would or could be untrue. Again, fallibility is an important concern for me. I am not infallible, nor do I accept that you are.

    I don’t understand this comment. You and I just agreed that there are some self evident truths about which you can be infallibly certain–with no possibility of error. You also agreed that they are true even though they cannot be proven.

    Now you are claiming that such truths “cannot be proven,” even after acknowledging that they don’t need to be proven, and you are also saying that neither you (or anyone else) can be infallibly certain about them due to our fallible nature.

    What gives? Are you now, all of a sudden, not sure that a slice of pizza cannot contain more pepperoni than the whole pie? Are you now not sure about the Law of Identity? Are you now not sure about the Law of Non-Contradiction?

  151. 151
    Aleta says:

    In 148, in reply to my saying “I’m not quite sure what question I am dodging”, Barry wrote

    Liar. You’ve dodged the question twice now. It is plain to me you don’t want an honest discussion. Goodbye.

    I went back to look at Barry’s question, and it was “Think of two apples in your mind. Then think of two more apples along with the first two. You are now thinking of four apples. How many material things did you count?”

    I had answered, “To Barry: apples are material things. 2 + 2 = 4 because those are names for things and operations about how the material world works.” and later “I’m not quite sure what question I am dodging: 2 apples + 2 apples = 4 apples, of course, because that is how apples work. 2 + 2 = 4 is true about things that behave like apples.”

    These are the answers I made that led Barry to call me a liar.

    I think I see the point Barry is wanting to make, although he could be a bit more civil about making it: that when I count by thinking of apples rather than having actual apples in front of me I’m using mental representations of apples, and, I gather Barry’s considers the “immateriality” of thoughts (which is probably another place where our philosophical views differ) to mean that 2 + 2 = 4 is an immaterial fact, not one embedded in or arising from the material world.

    Am I right, more or less, Barry – that that is the issue you think I’m dodging?

    And what do you think about the fact that when we add velocities, as opposed to apples, 1 + 1 can equal 1?

    UDEditors: You saw it all along. You are able to articulate it. You lied when you said you did not understand. You ask why I was not more civil to you? Because liars deserve to be called liars. Sometimes it shames them into recanting their lie, like you just did.

  152. 152
    Learned Hand says:

    No, we don’t agree on that. SETs admit of no grey areas.

    So if 2+2=4 is a SET, but more complex problems aren’t, where’s the dividing line? If you can’t be mistaken about what is and isn’t a SET, wouldn’t that mean you could draw a sharp line and say, “Here, this mathematical operation is an SET and that one isn’t.”? I don’t think that’s possible in practice, which seems to be in conflict with your position. If you can do it, I would be very interested to hear where the line is. (Presumably, given the distribution of math skills, it would be different from person to person.)

    Because my recognition of an SET is not based in even the slightest degree on my intuition.

    But if someone else erroneously says that something is an SET, such as “Allah is God,” presumably they’re speaking merely from their intuition (or cultural background, which would be largely the same thing). Or do you say it’s impossible to make a type 1 error, that no one can erroneously identify something as an SET? (I think you’ve taken that position before, but I’m not certain.)

    Are there any SE truths that weren’t taught to you, or demonstrated to you through your culture or environment, before you consciously accepted them?
    The question seems to be based on the flawed premise that I go around evaluating every proposition with respect to whether it is a SET. I do not.

    You do, however, have a set of SETs that you identify as such—particularly moral beliefs you credit to an objective source. Such as “abortion is wrong” and “slavery is wrong.” Are there any of those that weren’t first demonstrated to you by the humans around you? I ask because it appears that most people arrive at moral beliefs that are shared by their culture. I don’t think there was an epidemic of abolitionists cropping up in the South before the war, or Christians in pre-Columbian Mexico. (Although I’m not sure whether reverence for Jesus as the son of God is an SET in your opinion.)

    If you’re familiar with Daniel Kahneman’s work, or the research generally, do you think a truth that has to be accessed through System II thinking can ever be a SE truth?
    I read the Wiki entry on his book. System II thinking is Slow, effortful, infrequent, logical, calculating, conscious. Without committing myself (because I really don’t know what he says about the subject other than those adjectives), the answer would be “no.”

    I think the easiest summary would be that system 1 is intuitive, and system 2 is intentional thought. So it sounds like if you have to think about it, or reason it through, it’s not an SET. If that’s the case, then how do you distinguish your intuition from your infallible SET-sense? If you’re feeling the difference, aren’t human feelings fallible?

    That actually brings us back around to my first question. If you have an infallible SET-sense that is not intuition or culturally determined or reasoned or taken from anything but a perfect sense of what is and isn’t an SET, and there is no gray area… then where is the dividing line between 2+2=4 and the set of math problems that is not intuitive?

    Let’s say n+n=2n. We’re in agreement that no one can or would question n=1 or n=2 or n=3… How big does N have to get before the question is not an SET?

  153. 153
    Learned Hand says:

    I would love to run the following experiment: take two people, say conservative Christians, who each think of the other person as extremely honest. Hand each one a list of moral propositions drafted by tricksy lawyers: abortion is always wrong, abortion is wrong unless necessary to save the mother’s life, abortion is wrong unless the child has a terminal condition and the mother’s life is in danger, etc. The kind of difficult, finicky moral questions that people love to chew over.

    I would ask the participants to do two things: for each proposition, tell us whether it is true or false. And then tell us whether the answer is a self-evident moral truth.

    I think both sets of answers would diverge on the hardest questions. This presumes that at least one, if not both, of the participants is a liar, if we take BA’s position (as I tentatively understand it). Right? There’s one set of right answers to each of those tasks. And everyone should know what it is. What significance, if any, do you attach to the (presumed) difference in how people would identify SETs?

  154. 154
    Learned Hand says:

    We agree that there are truths I can’t imagine questioning, or being reasonably questioned. That does not establish that a truth is proven or even evidenced; it establishes only that I can’t imagine a case in which it would or could be untrue. Again, fallibility is an important concern for me. I am not infallible, nor do I accept that you are.

    I don’t understand this comment. You and I just agreed that there are some self evident truths about which you can be infallibly certain–with no possibility of error. You also agreed that they are true even though they cannot be proven.

    If I said there are any truths about which I can be absolutely infallibly certain, I overstepped my own position. I think I’ve been very clear that I think I’m fallible. How can I ever identify anything with infallible certainty, when the mind I would use to make that determination is fallible?

    I think that in practice I’m perfectly safe making some assumptions, and that I can’t really do much of anything without making assumptions like “A=A.” But I don’t know how I can be infallibly certain in the abstract. Fundamental premises are premises—assumptions. I don’t think they can be, or even need to be, proven in the abstract. Evident reliability is enough for me.

    In other words, I’m never really going to question “A=A.” But I don’t think it’s provable. And I don’t think it needs to be. It’s well-enough established to be perfectly reliable in life, and needn’t be logically provable in the abstract.

    What gives? Are you now, all of a sudden, not sure that a slice of pizza cannot contain more pepperoni than the whole pie? Are you now not sure about the Law of Identity? Are you now not sure about the Law of Non-Contradiction?

    I don’t think I’ve contradicted myself. This is one reason why I asked you about math rather than pizza. Pizza is easy. If we focus just on the easy questions, we make it almost impossible to tell whether an SET exists. Do we know that 2+2=4 because of an infallible SET sense, or because we can do the calculation intuitively? You seem to believe the former, but there’s no way to tell until we get out of pizza world and start looking at the edge cases.

    That takes us the questions I asked earlier: is it impossible for you to make a type I error, type II error, or both? And if both, then why can’t you define exactly how big N has to get before we’re out of SETworld if n+n=2n? “2” is an SET, “284” probably isn’t, right?

    I realize you’ve never claimed to be able to answer that question, but I don’t understand why you couldn’t if it’s impossible to be in error about what an SET is. Or how to resolve the apparent tension between your position and Barry’s. I think he said in an earlier comment, but I can’t find it now, that two people with different backgrounds could vary in terms of what math problems they’d identify as SETs. That presumes, though, that one of them is misidentifying a SET, which you seem say can’t happen. (Or else that they have different SETs, which oh boy, would be a whole other can of worms.)

  155. 155
    Barry Arrington says:

    LH,

    Give it a rest. You admit that a moral proposition is self-evidently true. Then you run away from the implications of that admission. And then you hide behind a barrage of logorrhea to hide the fact that you can’t face up to the truths revealed by your own reasoning. And you start repeating errors that have been corrected numerous times.

    LH, just because you can keep typing does not mean you should. Stop it.

  156. 156
    Barry Arrington says:

    SB,

    Learned Hand has gone into insane denial mode. He seems to be saying he cannot be infallibly certain that a slice of a pizza cannot be larger than the whole pizza. Idiot. I don’t see any sense engaging with him further. We’ve led him by the hand enough for one day.

  157. 157
    StephenB says:

    Learned Hand

    If I said there are any truths about which I can be absolutely infallibly certain, I overstepped my own position. I think I’ve been very clear that I think I’m fallible.

    I have one last question about our earlier exchange:

    SB: Do you agree, for example, that it is absurd to suggest that a slice of pizza could contain more pepperoni than the whole pie? Do you, in other words, agree with the following proposition: It is self-evidently true that the whole pepperoni pizza (any pepperoni pizza) must contain at least as much or more pepperoni than any one of the slices?

    Yes, and yes, with the caveat that we’re talking about pepperoni, not abstractions.

    SB: Do you also agree that you cannot possibly be wrong in making this judgment? Put another way, do you agree that you can have infallible certitude that you are right? The question can be answered with a simple yes or no.

    Yes, as for pizza.

    Are you not that same person?

  158. 158
    StephenB says:

    Barry,

    Learned Hand has gone into insane denial mode. He seems to be saying he cannot be infallibly certain that a slice of a pizza cannot be larger than the whole pizza. Idiot. I don’t see any sense engaging with him further. We’ve led him by the hand enough for one day.

    Barry, I agree. There is no further need for dialogue. To survive in the moment, he agreed that it cannot be so, but he has now reverted to the insane denial mode.

  159. 159
    Aleta says:

    In 151, The UDeditors, which I presume is Barry, added a comment to my post, and wrote,

    UDEditors: You saw it all along. You are able to articulate it. You lied when you said you did not understand. You ask why I was not more civil to you? Because liars deserve to be called liars. Sometimes it shames them into recanting their lie, like you just did.

    No Barry, I did not “see it all along.” I spent some time thinking about why you thought I was dodging a question that I thought I was answering, and only in re-reading did I realize your point, which I was then able to articulate.

    You are wrong to call me a liar – both wrong in that I did not lie, and wrong to generalize from one statement that you thought was a lie to a characterization of me as a liar.

    So, to return to the topic at hand, I repeat:

    I think I see the point Barry is wanting to make … – that when I count by thinking of apples rather than having actual apples in front of me I’m using mental representations of apples, and, I gather Barry’s considers the “immateriality” of thoughts (which is probably another place where our philosophical views differ) to mean that 2 + 2 = 4 is an immaterial fact, not one embedded in or arising from the material world.

    Am I right, more or less, Barry – is that the [point you want to make]?

    I would be interested in discussing this.

  160. 160
    Learned Hand says:

    SB,

    Fair enough, that’s a confusing position on my part. I guess I moved off of pepperoni too early. I agree that, to the utter limit of my ability to be certain about anything, I can be certain that the number of pepperonis on a slice won’t exceed the number on the pizza. I don’t believe I will ever have grounds to question that certainty, not on such a trivial example, so I’m comfortable with my answers to your previous questions.

    But once the conversation expands to the fundamental concept of self-evident truths, the answer gets more complicated. I know what I know about pepperonis with a mind that is fallible, and often in fact wrong. I have no way to step outside of my own mind and know in advance whether I’m wrong. And I have no way to check whether a slice can be greater than the whole other than by testing it, which can never prove absolutely as a logical matter that the proposition is true. So how can I know that the proposition is true? Your answer seems to be that you have a supernatural truth sense that will validate the proposition without doubt. But I don’t think any such sense exists, or can reasonably said to be infallible. I merely take necessary presuppositions as presuppositions, presumed to be true.

    Focusing on easy questions is a way of avoiding the hard ones. So is shouting “LIAR!!!!!!!” when someone doubts you.

    If your sense for self-evident truths is infallible, what is the largest value of n for which “n+n=2n” is a self-evident truth?

    I don’t think you or Barry can answer the question. I don’t think you want to examine the consequences of being unable to answer the question, or the others I’ve asked. I think “liar” and “insane denial” are ways to protect your beliefs and egos without putting them at risk in a civil, serious conversation in which your ideas might not bear up under critical scrutiny.

    But hey, reasonable people can disagree about that.

  161. 161
    Learned Hand says:

    Barry, you say it’s wrong to run away from the implications of one’s positions. I agree, and I’ve explained my position in way that you haven’t responded to in any real way but to scream, per usual, “liar! shut up! stop typing!”

    What about the implications of your own position? If you have an infallible SET-sense that is not intuition or culturally determined or reasoned or taken from anything but a perfect sense of what is and isn’t an SET, and there is no gray area… then where is the dividing line between 2+2=4 and the set of math problems that is not intuitive?

  162. 162
    Barry Arrington says:

    Aleta @ 159.

    Unless you are counting actual pink unicorns, then yes they were immaterial mental representations of pink unicorns.

  163. 163
    Barry Arrington says:

    LH,

    And I have no way to check whether a slice can be greater than the whole other than by testing it

    Only an idiot or a liar would type that sentence. It is profitable to dialogue with idiots and/or liars all the way up to the time one has exposed them as such, after which it is not.

    So, yes, stop it.

    And as for your attempt at turnabout, I am comfortable that the readers know the truth of the matter. I feel sorry for you LH. I really do.

  164. 164
    Learned Hand says:

    I’m comfortable leaving the conversation there, with my good-faith efforts to answer your questions and your hasty, angry retreat from mine. Good night! Please try to calm down.

    UDEditors: LH, we are perfectly calm. We don’t call you a liar and an idiot because we are not calm. We are merely making observations about the lies and idiotic statements you frequently drop into our combox.

    And you can label “I can’t really infallibly know that a part cannot be larger than the whole” as a good faith statement if you want. But for the life of me I don’t know why you bother. We both know that absolutely no one believes you.

  165. 165
    Aleta says:

    Barry writes, “… they were immaterial mental representations of pink unicorns.”

    So we have reached the much more general issue: what is the nature of our mathematical representations? Obviously written notations and verbal words are objects in the material world, but to a dualist such as Barry, there is some aspect of our mind, and the thoughts in our mind, that is immaterial. In such a case, 2 + 2 = 4 has a reality independent from the material world. It is an immaterial truth that our mind perceives, not by reference to the material world, but by looking, somehow, at an immaterial world of logically self-evident truths of various sorts.

    I don’t agree with Barry on these points, assuming I have summarized them somewhat accurately.

    First, I don’t believe thoughts are immaterial. I believe they are a product of our biological being. I don’t know – no one does – what consciousness is, but I believe there is a great deal more evidence that it is phenomenon that is directly tied to our biology – our brain and nervous system, than there is that it is some immaterial thing which exists independently from matter but somehow interfaces with matter. (The question I have for the dualist is just that: how does an immaterial mind act on the material world? I think that question is at least as unanswerable as how material activity in the brains gives rise to consciousness.)

    So when I count pink unicorns, I imagine creatures which have the same properties as other countable objects such as apples, and thus apply the fact about apples that I know is true: that 2 + 2 = 4.

    As I have been saying, in various ways, facts like 2 + 2 = 4 are self-evident because they represent basic facts about how certain kinds of objects in the material world work – they are generalizations from our experience as well as being embedded in our biological nature. (Other animals have some simple understandings of quantity.) Both out nature and our nurture, so to speak, make 2 + 2 = 4 self evident, and that fact is then formalized in the mathematical systems we have created. There need be no reference to any immaterial thing, either in our mind or in the world at large, for this fact to be self evident.

    I have also pointed out, and I note that no one has responded, that not everything has this additive property. In respective to velocities, 1v + 1v does not equal 2v. It was considered self evident that 1v + 1v = 2v until experiment and theoretical work by Einstein showed that it not true, and then we had to adjust our understandings of the world. Other “self evident” truths have found to be inapplicable as we have plumbed the depths of nature beyond our macroscopic experience.

  166. 166
    StephenB says:

    Learned Hand @160,

    You continue to contradict yourself at every turn. One minute you claim to know that wholes are greater than parts, and the next minute you reverse yourself, pleading fallible knowledge. One minute you accept the legitimacy of a concrete example, and the next minute you reject the principle that informs it.

    Your questions about Type I and II errors, or about mathematical sets, are irrelevant. There is no reason to discuss them in the context of the part/whole relationship. That you would try to inject them into the discussion is further evidence that you do not understand the subject matter.

  167. 167
    zeroseven says:

    I am interested in Barry and StephenB’s response to LH’s question. At what point does n+n=2n stop being a SET?

  168. 168
    Learned Hand says:

    You continue to contradict yourself at every turn. One minute you claim to know that wholes are greater than parts, and the next minute you reverse yourself, pleading fallible knowledge. One minute you accept the legitimacy of a concrete example, and the next minute you reject the principle that informs it.

    Why is that a contradiction? I know that the sun will rise tomorrow. I have as great a faith in that as anything I’ve ever believed. I would stake my life on it. But I don’t think that belief is infallible. The distinction to me is whether the confidence is practically total or absolutely, perfectly, logically total.

    I wrote up my beliefs this way at TSZ:

    1. I make mistakes. I know this as certainly as I know anything—certainly enough not to doubt it in practice. This shows that I do not have the ability to perfectly perceive error in my own thinking.

    2. I cannot therefore be logically, absolutely certain of anything—not even that A=A. Because the faculties I would use to be perfectly, logically certain of that are the same ones that are not perfect.

    I think the trickiest question here is whether I can be certain that “I think, therefore I am.” But even there, is the fact that I cannot imagine any reason to doubt it because it’s perfectly true, or because I have an imperfect and limited mind?

    Without a perfect, limitless mind, I can’t ever know whether I am able to perceive any/all possible holes in the proposition. So the fact that I don’t see any, and can’t imagine any, doesn’t ever mean that I can be perfectly, logically certain there aren’t any.

    And yet in practice, I never need to worry about that. I’ve lived my whole life with a limited mind. I can very often be certain enough for any human purpose.

    In other words, since all my knowledge is perceived with a flawed mind, including my ability to perceive the flaws in my reasoning, how can I ever confidently say “this conclusion is not flawed”? Proving it with external, objective evidence is maybe one way (your pepperoni example), but we don’t have that tool available for SETs, by definition. And of course my perception of evidence is, again, flawed.

    (ETA: this possibility of error is in the far, far background of my mind. I’m not sure I ever really thought about it explicitly before this week, which is why I love these conversations so much–even conversations with hostile and verbally abusive people. I reiterate that in practice I’d never doubt the basic mathematical principles at issue. The possibility of error is a logical formality: I have to admit it, because I have no flawless perceptual frame with which to assess any question, even the ones relating to whether error is possible.)

    I don’t understand why you’re comfortable taking a set of questions and saying, “There’s no error here,” when the mind reaching that conclusion is capable of error. I understand why you’re comfortable doing it in practice, in the real world–we all do that. But you’re going beyond that to logical absolutes, perceived by flawed non-absolute minds. (I think that concept of a flawed mind is consistent with your faith, but I’m not certain.)

    The reason I’m asking about type I/II is that I want to know where you think error is possible in determining whether a SET exists (as opposed to whether a proposed SET is true). Uncertainty is possible, if I understand you right, which suggests that a false negative is possible. Someone can honestly fail to grasp that a particular SET is a SET on one day, and accurately grasp it the next. (I think you don’t accept the possibility of false positives, because that would admit that people can be wrong when they think they’ve got a SET, but I don’t think you’ve said one way or the other.)

    That’s on detecting SETs. You also say it’s impossible to be in error about the substance of a SET. (The distinction is a bit fuzzy, but I think it’s one reason why you don’t see the relevance of my question.) One who understands the terms can’t be wrong about the truth of the SET. That seems very easy to test. Give people math problems! Some of them will confidently give wrong answers. 17+17=46, for example.

    Is someone who confidently says that 17+17=46 misidentifying a SET? They believed, for the sake of argument, that it was true, without any doubt whatsover. In their mind it was the same as 2+2=4: a self-evident truth. But they didn’t calculate it (because a truth you have to reason out isn’t a SET, you’ve said) and they got the answer wrong.

    So having a firm, fixed belief in one hand, and a wrong answer in the other, where did the error creep in? Was their identification of the SET a false positive (that is, can 17+17=x even be a SET), or did they misapprehend the truth of the SET (by believing in the wrong x)?

  169. 169
    zeroseven says:

    It seems clear, that in maths at least, identification of a SET depends on the person. 2+2=4 is obvious to me, but not to a 3 year old. On the other hand, 26539876 plus 28917644 is not obvious to me, but might be to a (I am sure there is bettr term) “idiot savant”, who can actually “see” the solution as clearly as I can see 2+2=4.

  170. 170
    Andre says:

    Learned Hand

    In the clearest most concise way I can possibly say this…..

    You don’t need a single human around. 2+2=4 self evident truth is independent and objective to any formal human verification.

    Put another way, does a tree that fall in the forest make a sound even if there is nobody there to hear it?

  171. 171
    Andre says:

    Learned Hand

    Why is that a contradiction? I know that the sun will rise tomorrow. I have as great a faith in that as anything I’ve ever believed. I would stake my life on it. But I don’t think that belief is infallible. The distinction to me is whether the confidence is practically total or absolutely, perfectly, logically total.

    But but……. Materialists have argued ad infinitum that the Bible is false because the sun does not rise as the Bible claims, why would you use a biblical term to state your case?

  172. 172
    StephenB says:

    SB: You continue to contradict yourself at every turn. One minute you claim to know that wholes are greater than parts, and the next minute you reverse yourself, pleading fallible knowledge. One minute you accept the legitimacy of a concrete example, and the next minute you reject the principle that informs it.

    Why is that a contradiction? I know that the sun will rise tomorrow. I have as great a faith in that as anything I’ve ever believed. I would stake my life on it. But I don’t think that belief is infallible.

    Good grief, do I really need to explain it again. A part cannot be greater than a whole. It is metaphysically, logically, and psychologically impossible. If you claim not to know that with infallible certainty, then you are either an irrational person, a dishonest person, or both. It is impossible not to know it. Your philosophy is the product of a bad education, grounded in the postmodernist idea that all truths are empirical and that no knowledge is certain. You have been lied to. It is time to rise above it and learn the ways of rational thinking.

    I know that the sun will rise tomorrow.

    No, you don’t. You only know that it will probably rise tomorrow. You still do not understand the difference between a self evident truth and a conviction based empirical evidence.

    I have as great a faith in that as anything I’ve ever believed. I would stake my life on it. But I don’t think that belief is infallible.

    That belief is, indeed, not infallible. Notice that you have contradicted yourself again. First, you say that you “know” the sun will rise tomorrow, then you confess that you only “believe” that it will. The problem here is that you don’t know the difference between absolute knowledge and reasonable faith.

    The distinction to me is whether the confidence is practically total or absolutely, perfectly, logically total.

    For you, everything is in the “practically total” category and nothing is in the “absolutely, perfectly, logically total category.” That is an intellectual error, and a serious one. The biggest problem is not that you don’t understand the subject matter. That part could be remedied. What really limits you is the fact that your ideology, which was drilled into you by the academy, has rendered you impervious to reason. You have allowed the elitists to convert you into a dutiful little worker bee in support of their cause.

    “I don’t want a nation of thinkers. I want a nation of workers.”
    –John D. Rockefeller.

  173. 173
    StephenB says:

    Learned Hand

    In other words, since all my knowledge is perceived with a flawed mind, including my ability to perceive the flaws in my reasoning, how can I ever confidently say “this conclusion is not flawed”?…(followed by a thousand plus words and irrelevant questions about mathematics……).

    [a] Because self evident truths are not conclusiosn. Self evident truths make conclusions possible.

    [b] Because the ability to perceive the flaws is based on the laws of logic, which are infallible, both metaphysically and psychologically.

  174. 174
    Aleta says:

    I am sympathetic to the point Learned Hand is making, and wrote something similar myself yesterday. What I have to balance in my life is, on the one hand, a commitment to living with uncertainty of various degrees rather than believing things that might not be true, and on the other hand, needing to make choices, from a practical point of view, to commit myself to believing things because one has to act – one can’t be frozen by skepticism.

    To be more specific about some issues being discussed here.

    In respect to metaphysics, I think there might be some immaterial aspect to the world – there are some arguments for such that resonate with me. On the other hand, I know enough about the whole propensity of humans to invent religions, and stories in general, that I don’t believe any of the world’s religions, great or small, are correct. It’s a matter of weighing all the evidence, as best I can, and making some practical choices as to what to believe in the context of the world of other humans that I have to live in.

    In respect to math: within any logical system, the truths of the system are absolute. In the whole edifice of math that starts with 1 + 1 = 2 and leads to such facts as e ^ (i?) = -1, the facts are true. Some are self-evidently true because they are so simple and so in accord with our experience of the material world that virtually all people old enough see them as so intuitive that they couldn’t possibly doubt them: hence self-evident. But 1 + 1 = 2 and e ^ (i?) = -1 are fundamentally no different.

    However, the question of how math relates to the material world is a different story. Models between a mathematical system and the world must be tested. Again, 1 + 1 = 2 models such a fundamentally basic fact about the macroscopic world we experience that that correspondence seems self-evidently true. But as I have pointed out, there are aspects of the world where that is not true (adding velocities).

    StephenB makes a revealing summarizing comment to Learned Hand:

    For you, everything is in the “practically total” category and nothing is in the “absolutely, perfectly, logically total category.” That is an intellectual error, and a serious one.

    It is StephenB, and others who think the actual world contains “absolutely, perfectly, logically total” truths, who are in error. Those truths which are totally true within the formal system which has been erected to contain them are not automatically applicable to the real world – perfect logical truths must be tested to see if they are empirically true, and if they meet the test of evidence they become provisional empirical truths – they are not, in regards to the world, absolute truths.

    Einstein summed this up excellently when he said,

    As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

    Absolute self-evident truths only exist in formal logical systems which make them self-evidently true as a consequence of the definitions and other axioms which underlie the system. Whether they accurately model reality is an empirical question that must be tested. Such examples as the parallel postulate, non-commutative algebras, the non-additive aspect of velocities, the probabilities inherent in quantum mechanics, etc., show us that what is obvious and self-evident about the macroscopic world which we experience is not necessarily true about aspects of the world at different scales.

    So, all of life is a balance between committing to beliefs that one feels are well-supported and likely to be successful guides to action, on the one hand, and having various levels of provisional skepticism so that one can change those beliefs if good reason to do so arises.

  175. 175
    daveS says:

    Aleta,

    You make some very good points. I, for one, think that if one wants to discuss self-evident moral truths, or self-evident truths about the “real world” in general, these mathematical examples end up creating more confusion than anything.

    I am not in the habit of using the concept of self-evidence (as defined here) in mathematics—there, a proposition is either true or not, period. 2 + 2 = 4, 98/14 = 7, Fermat’s Last Theorem are all equally true, and you don’t have to look at empirical evidence to see that.

  176. 176
    Barry Arrington says:

    Aleta,

    I am sympathetic to the point Learned Hand is making

    Over at The Skeptical Zone LH says he cannot be infallibly certain that A=A.

    Are you sympathetic to that point too Aleta?

  177. 177
    Barry Arrington says:

    LH:

    I know that the sun will rise tomorrow.

    Above, LH said that Chesterton’s take down of that chestnut was helpful.

    Apparently it was not.

  178. 178
    Aleta says:

    Hi Dave. First, I’m here to discuss mathematical truths, not moral ones. The topic of mathematical truths may be confusing (and far-reaching), but it is the one of interest to me.

    As to your second paragraph, I agree that within the logical system of math itself, mathematical facts are all equally true, and their truth has nothing to do with empirical evidence. But, what I add is if you want to apply math to the material world, you have to create a model whereby the elements of math are mapped to elements of the world, and then you can’t just assume that the mathematical facts will hold, because your model might be wrong. In that case, you do have to test, not the math itself, but the modeling relationship, with empirical evidence to see if the model is accurate.

  179. 179
    Barry Arrington says:

    Aleta:

    It is StephenB, and others who think the actual world contains “absolutely, perfectly, logically total” truths, who are in error.

    “Error exists.”

    Aleta, do you deny that that statement is an absolutely, perfectly, logically totally true statement?

  180. 180
    Barry Arrington says:

    BTW, your “adding velocities” example is false because it is a (rather simple and obvious) category error. I am weary of leading you people by the hand. Go back and think about it, and when you can explain why I would say that, we can discuss it. Kind of like when you claimed to not to know that I was distinguishing actual apples from mental images of apples, when any child would have known the distinction was critical.

  181. 181
    daveS says:

    Aleta,

    Hi Dave. First, I’m here to discuss mathematical truths, not moral ones. The topic of mathematical truths may be confusing (and far-reaching), but it is the one of interest to me.

    Same for me. I think our positions are quite close.

  182. 182
    Barry Arrington says:

    Aleta,

    perfect logical truths must be tested to see if they are empirically true

    This statement is literally insane. As SB says over and over, experience does not inform logic. Logic informs experience. And it cannot be otherwise.

    Do you agree with LH that it is impossible to know for certain that a slice of a pizza cannot be larger than the whole pizza?

  183. 183
    Aleta says:

    to Barry re 176: Hi Barry. A = A is about as fundamental a logical premise as there is, and one that I think we (humankind in general) would always apply to any situation in the material world. If we found something that seemed to cast doubt upon that I imagine we would instead decide that the two objects were not actually both A. A = A is a fundamental tool for reasoning.

    I’ve made many other points lately – do you have any comments? In particular, I wonder what you think about the fact that 1 + 1 = 2, while totally true within the system of basic arithmetic, as a logical system, was found to in fact not be true when adding velocities. That is, what do you think about my distinction between math, as a logical system in which the truths are absolute, and mathematical models applied to the world in which the conclusions must be tested to see if the model is correct? 1 + 1 = 2 does not apply to all situations in the real world.

  184. 184
    Aleta says:

    to Barry, re 180: Barry writes, “BTW, your “adding velocities” example is false because it is a (rather simple and obvious) category error.” Well, it’s a category error because velocities aren’t the kind of thing for which 1 + 1 = 2, but that’s pretty circular reasoning. There are some kinds of things for which 1 + 1 = 2 and some for which that is not true. That makes my point that while 1 + 1 = 2 is perfectly true within the system of arithmetic we can’t be absolutely sure that is true about everything in the world without at times doing some testing. People assumed that of course 1v + 1v = 2v until it was shown otherwise, and then we had to revise our categories to distinguish things for which quantity is conserved under addition and those for which it is not.

  185. 185
    Barry Arrington says:

    Aleta @ 183:

    You dodged my question at 176. Let me ask it again:

    Over at The Skeptical Zone LH says he cannot be infallibly certain that A=A.

    Are you sympathetic to that point too Aleta?

    You are either sympathetic to the point or you are not sympathetic to the point. The law of the excluded middle precludes any other position on your part.

    So a simple “yes” or “no” will answer the question.

  186. 186
    Aleta says:

    to Barry re 182. You quote me as saying “perfect logical truths must be tested to see if they are empirically true.”

    You took that phrase out of context, and then responded to something I did not say. I wrote,

    Those truths which are totally true within the formal system which has been erected to contain them are not automatically applicable to the real world – perfect logical truths must be tested to see if they are empirically true, and if they meet the test of evidence they become provisional empirical truths – they are not, in regards to the world, absolute truths.

    Perfect logical truths themselves, within the logical structure which contains them, need no empirical validation. When applied to the real world, the model which maps the logical truth to the world does need, in theory and in practice at times, empirical validation.

    What you quoted distorted the meaning of what I actually wrote.

  187. 187
    Aleta says:

    to Barry re 185. I answered that at 183, probably while you were writing 185.

  188. 188
    Barry Arrington says:

    Aleta,

    There are some kinds of things for which 1 + 1 = 2 and some for which that is not true.

    Wrong again Aleta. Your error is based on an equivocation. That you, Aleta, can come up with equivocations does not demonstrate anything other than that your understanding is faulty (or if you know what you are doing, that you are a liar).

  189. 189
    Barry Arrington says:

    Aleta,

    I answered that at 183, probably while you were writing 185.

    No, your answer at 183 is the dodge to which I was referring in 185.

  190. 190
    Aleta says:

    Barry, velocities do not follow the mathematical rule 1v + 1v = 2v. Why is it an error, therefore, to say there are some things for which 1 + 1 does not equal 2 when I have in fact provided an example? I assume you accept the fact about velocities, so what is my error? Be specific, please.

  191. 191
    Learned Hand says:

    Zeroseven:

    It seems clear, that in maths at least, identification of a SET depends on the person. 2+2=4 is obvious to me, but not to a 3 year old. On the other hand, 26539876 plus 28917644 is not obvious to me, but might be to a (I am sure there is bettr term) “idiot savant”, who can actually “see” the solution as clearly as I can see 2+2=4.

    We don’t really have a clear definition of SETs from BA or SB, something the conversation at TSZ made clear. But given what they’ve said, I think this is the cleanest way out of the dilemma of their position.
    It raises some difficulties when they try to extend the concept of SETs to moral truths. Once you’ve acknowledged that people of equivalent faculties and experience have different degrees of perception of SETs, you’re pretty much back in subjectivism land, because the person you’re talking might honestly not see the SET you do. Also, it doesn’t resolve the false positives/misapprehension dilemma above, as far as I can tell.

    Andre:

    You don’t need a single human around. 2+2=4 self evident truth is independent and objective to any formal human verification.

    That’s quite clear, thanks. SteRusJon made the same suggestion above. I can’t quite agree, given the lack of a real definition of SETs, but I like the idea that if any math problem is a SET then they all are. I don’t know if an actual mathematician would agree, since I think proofs are possible, but I don’t know for sure. On first blush it seems like the better approach to me. It seems more objective, clearer, and easier to defend than “it’s only a SET if you don’t have to reason it out.” But whatever its merits, it’s not the position that BA and SB take. Odd how objectivists disagree about what’s a self-evident truth and what isn’t, isn’t it?

    SB,

    Because the ability to perceive the flaws is based on the laws of logic, which are infallible, both metaphysically and psychologically.

    It doesn’t matter whether the laws of logic are perfect. Your mind is not, and your mind is what perceives the laws of logic. Whether this perfect abstraction exists, you cannot have a perfect conception of it unless you have a perfect ability to perceive. And how can you know whether your ability to perceive it is perfect? It’s an infinite regression. We know that humans are fallible, and we don’t have an infallible way to draw lines inside the human mind and say, “This part can make mistakes but that part can’t.” Because we can’t get outside of our own minds to infallibly draw that line.

    Look at it this way: how do you know your perception is perfect? Is your perception of that perception perfect? Ad infinitum? What other parts of your mind are infallible, and how do you know?

    I know you think I’m an insane idiot liar. That’s OK. What about your beliefs? Can you draw a line where the value of n is too large for n+n=2n to be a SET? And if someone confidently answers wrongly, why isn’t that a false positive for the value of the SET?

    Barry,

    What about you? Can you distinguish a line where a SET becomes a SET, and where it transitions to something else because the question is too complex? Above you firmly rejected the idea that a grey area exists, “in which it’s impossible to tell whether a truth is self-evident or just a possibly flawed intuition.” So when n gets too large for some people to calculate, but not others, is n+n=2n still a SET? Is the line drawn at the point where no human could know n+n=2n without calculating it?

  192. 192
    Learned Hand says:

    SB: You continue to contradict yourself at every turn. One minute you claim to know that wholes are greater than parts, and the next minute you reverse yourself, pleading fallible knowledge.

    That’s not a contradiction. I know it with fallible knowledge. Just like I know that 26+26=52, but I had to think about it for a second after I intuited the answer, because my intuition is fallible. I don’t think “know” means “to know without any logically possible uncertainty.” If you want to define knowledge that way, be my guest, but that doesn’t change the meaning of my answer—which I’ve explained several times, at pretty considerable length.

    One minute you accept the legitimacy of a concrete example, and the next minute you reject the principle that informs it.

    This, again, is not a contradiction. I’m perfectly comfortable agreeing that pep/slice cannot exceed pep/whole. I will never doubt it in practice. The same infallibility that keeps me from agreeing that the principle is perfectly accurate afflicts the concrete example; how can I know perfectly, when my ability to know and my ability to assess my knowledge are flawed?

    As I’ve said, this fallibility problem is so far in the back of my mind that it never really crops up. I can’t imagine any circumstances in which I would actually doubt the truth of your examples. But, again, my ability to imagine things is flawed and limited, and I don’t have any flawless faculty with which to say, “those flaws haven’t affected your perception of this logical rule.”

    Good grief, do I really need to explain it again. A part cannot be greater than a whole. It is metaphysically, logically, and psychologically impossible.

    Ancient philosophers might have said that a thing cannot move from point A to point C without passing through point B, defined as the point in between A and C. It is metaphysically, logically, and psychologically impossible. Then hey presto, quantum mechanics. Their ability to imagine possible exceptions to the rule was limited by the fact that they were humans, and their minds, like ours, could not perceive things that were beyond their faculties.
    That doesn’t mean that I think there’s some undiscovered rule of physics or logic that would break the identity of x+x=2x. It does mean that I need to be humble and acknowledge that I am not the perfect rule. I perceive what appears to be a perfect rule through a flawed lens, and I have no other lens to use. I can try to explore and limit the flaws in my perceptions, but without an external viewpoint and a flawless lens, I can’t ever be sure I’ve accurately perceived something—even a pure rule of logic.

    What really limits you is the fact that your ideology, which was drilled into you by the academy, has rendered you impervious to reason. You have allowed the elitists to convert you into a dutiful little worker bee in support of their cause.

    I may be impervious to reason. But have you tried? So far you’ve just insulted me and said that my beliefs cannot be true. Why not? How do I exclude the flaws in my perception from the thing being perceived, perfectly?

  193. 193
    Learned Hand says:

    Over at TSZ, Sal Cordova raises the Banach-Tarski paradox, which (a) blows my mind and (b) reinforces my belief that the world is stranger than I know. A good reason not to assume that any knowledge is completely, absolutely perfect, even when it’s seemingly as simple as “a pea is smaller than the sun.” I would never bet on anyone reassembling the pea into a sphere the size of the sun. But ten minutes ago, I wouldn’t have even conceived that such a thing might be logically possible.

  194. 194
    Aleta says:

    I googled the Banach-Tarski paradox. I assume the same reasoning applies to pepperoni pizza! 🙂

  195. 195
    daveS says:

    Learned Hand,

    I think the Banach Tarski paradox is a good illustration of a point similar to one you made earlier, “Yes, and yes, with the caveat that we’re talking about pepperoni, not abstractions”. Specifying the domain of discourse is critical.

    OTOH, I think it also shows how these mathematical examples can just add more confusion to a discussion of (potential) self-evident or necessary truths in the “real world”.

  196. 196
    Barry Arrington says:

    Aleta,

    Why is it an error,

    I am not going to lead you by the hand on this. I did that for LH yesterday, and when we got to a place he did not like he turned around and bit the hand that was leading him.

    I will, however, give you some clues: Think about the meaning of the term “2” in the proposition 2+2=4. What is a cardinal number? What is a set? And when you think about those things enough, ask yourself, how have I equivocated between a proposition regarding sets and one that does not?

    After all that, come back and give us a report.

  197. 197
    Aleta says:

    Dave writes, “Specifying the domain of discourse is critical.”

    Yes, the Banach Tarski paradox cannot be applied to a real pizza.

    More seriously, Dave says such examples add “confusion” to the discussion. However, I think they add important distinctions, and deepen the topic. That may be confusing at first, but if you avoid them for that reason you are stuck with incorrectly thinking that the simple (and possibly self-evident) is all there is.

  198. 198
    Aleta says:

    Yes, Barry, some things can have an cardinal number applied, and some can’t – some things are “things” in the sense that quantity is preserved under addition (I’ve already said that), and therefore 2 + 2 = 4 applies, and some things are not that kind of thing. But this is circular reasoning: it is saying that 2 + 2 = 4 applies if the things being referred to are the kind of things which 2 + 2 = 4 applies to. That doesn’t get around the fact that there is a difference between the purely logical fact and its applicability to the real world.

    This reinforces my point that we have to model or map our math to the world, and test it, before our model can be considered empirically true (as opposed to merely logically true).

  199. 199
    Barry Arrington says:

    Aleta,

    It is not circular. But as you demonstrated nicely, that truth, like almost all truths, can be obscured by a determined equivocator.

  200. 200
    Aleta says:

    I gather that discussion on the issues is not something you want to do, Barry. I’ve made many points on some major issues, and you dismiss them all as lies.

    It is an interesting experience for me to try to discuss something with someone whose world is black-and-white, and who considers himself infallibly correct.

    But that’s OK, because I’m not writing for you anyway. I have benefitted from articulating some of my thoughts, and there may be others who have gotten something out of this.

  201. 201
    Aleta says:

    Question for Barry, to try to find out if he understands and/or will acknowledge the difference between a logical system and its application to the real word.

    There are three different 2-D geometries, depending on which of the three versions of the parallel postulate you adopt. Each of these system is perfectly, absolutely, logically true within itself, even though though they reach conclusions that contradict similar conclusions reached in the other systems.

    Suppose we have a 2-D surface in the real world. Which of the three geometries apples? There is no logically correct answer to that question. Only by empirical testing could we decide which geometry fits the facts.

    How do you explain this, Barry?

  202. 202
    Barry Arrington says:

    Aleta,

    How do you explain this, Barry?

    I have nothing but your word for the proposition that there is a conflict. And you have no credibility. After all, you are fuzzy on the whole 2+2=4 thing. Maybe there’s a paradox, but no one in their right might would trust your word on it.

  203. 203
    Aleta says:

    Barry, I assumed you were familiar with the whole concept of the three possible versions of the parallel postulate and the three resulting 2-d geometries. You are, aren’t you? This is not a matter of trusting my word on anything – this a very well known story in the history and philosophy of math. See: https://en.wikipedia.org/wiki/Non-Euclidean_geometry#History

    Added in edit: the most famous conflict in the three systems concerns the sum of the three angles in a triangle, which can equal 180, or be more or less than 180. Did you know that, Barry?

  204. 204
    StephenB says:

    SB: One minute you accept the legitimacy of a concrete example, and the next minute you reject the principle that informs it.

    Learned Hand

    This, again, is not a contradiction.

    It is most definitely a contradiction. The principle can be no less certain than the example. It is the former that informs the latter.

    I’m perfectly comfortable agreeing that pep/slice cannot exceed pep/whole. I will never doubt it in practice.

    If you accept it in practice and doubt it in principle, then you have contradicted yourself. The irony is that you don’t even accept it in practice, as indicated in your following statement:

    I can’t imagine any circumstances in which I would actually doubt the truth of your examples.

    That’s not enough. You are supposed to know that there are no circumstances in which a slice of pizza cannot be greater than the whole pizza. You are supposed to know that that a slice of pizza cannot be greater than the whole pie because the principle says that no part can be greater than any whole. I provided the example so that you could understand the principle. You still don’t. You are trying to place one against the other, which is insane. Why you choose to remain uneducable is a mystery.

    (Your comments on ancient philosophy are totally incoherent).

  205. 205
    Barry Arrington says:

    Aleta,

    Barry, I assumed you were familiar with the whole concept

    Then your assumption was faulty.

  206. 206
    Aleta says:

    I see. Then I suggest you study the situation as it is instructive.

    I am also somewhat amazed that I have been trying to discuss the nature of the relationship between math and the real world – someone who seems so absolutely sure about the nature of self-evident mathematical truths – with someone who perhaps doesn’t have much of a background in the subject. The parallel postulate story is as basic of a story in the history of math as there is.

  207. 207
    zeroseven says:

    LH, there has been a deafening silence from Barry and SB on your repeated question about about whether n+n=2n is a SET for every value of n. Although Barry never admits to uncertainty, his failure to respond to this point clearly demonstrates that he is uncertain about this. He confidently pronounces 2+2=4 to be a SET. But then refuses to explore why it is and how this relates to other mathematical formulas. Sadly revealing, as another contributor to this board might say.

  208. 208
    Barry Arrington says:

    Aleta,

    I am also somewhat amazed . . .

    You have shown to be a fool, and I understand that makes you angry. You can retaliate by insulting my educational background as much as you like if that makes you feel better.

    And if you consider yourself an intellectual in math and are nevertheless fuzzy on the whole 2+2=4 thing, you are living proof that George Orwell was right when he said:

    Some ideas are so stupid that only intellectuals believe them

  209. 209
    Barry Arrington says:

    zeroseven,

    Although Barry never admits to uncertainty, his failure to respond to this point clearly demonstrates . . .

    that I have time to whack only so many moles.

  210. 210
    zeroseven says:

    Barry, great, once you have finished whacking moles, I look forward to finding out if 117+117=234 is a SET, and if not, why not.

  211. 211
    Learned Hand says:

    The principle can be no less certain than the example. It is the former that informs the latter.

    I don’t think I disagreed with that. As I’ve explained several times, I wouldn’t doubt either principle or example in practice. As a matter of absolute logic, I can’t be perfectly certain of them. As I said in the very beginning, “I don’t doubt it.” Not doubting is not the same thing as being absolutely certain. You yourself said the sun won’t absolutely certainly rise tomorrow; do you doubt that it will?

    I’ve certainly refined my thinking about my own thinking throughout this conversation, for which I thank you. I don’t think my underlying position has changed, and I don’t think I’ve contradicted any of my positions. If there’s a specific statement you can’t resolve, please let me know and I’ll take a closer look at it.

    I’m perfectly comfortable agreeing that pep/slice cannot exceed pep/whole. I will never doubt it in practice.

    If you accept it in practice and doubt it in principle, then you have contradicted yourself.

    I was sloppy when I wrote “I’m perfectly comfortable agreeing…”, because that can be read as a statement that I agree that I can be absolutely certain that p/slice can’t exceed p/whole. I didn’t mean that, though, only that if someone asks, “Can the part exceed the whole?”, I would be very comfortable saying “no” and not ever worry about being wrong. I think that’s very clear when you read the whole paragraph.

    I can’t imagine any circumstances in which I would actually doubt the truth of your examples.

    That’s not enough. You are supposed to know that there are no circumstances in which a slice of pizza cannot be greater than the whole pizza. You are supposed to know that that a slice of pizza cannot be greater than the whole pie because the principle says that no part can be greater than any whole.

    Oh, I’m supposed to? Yes, I know I’m supposed to agree with you. But I don’t, and I’ve explained at length why not. And your response, rather than to address those reasons, is literally to complain that I am “supposed to” agree with you. According to who? And how can I agree with you when you won’t actually address the points I’ve made about fallibility? You can repeat “insane,” “liar,” “idiot,” all you like; they don’t add up to an actual argument. I know you feel infallible. How do you know that you actually are? What are the conditions under which it is impossible for you to misunderstand or incompletely understand something?

    This seems a lot like my questions about n+n=2n and false positives; when your response is, “You are an insane uneducable elitist worker bee, etc. etc. etc.,” it rather begins to look like you don’t have an answer.

    (Your comments on ancient philosophy are totally incoherent).

    For example, if our positions were reversed, this is where you would say, “That’s a lie. You understand. You just don’t want to deal with the ramifications of your position.” I don’t think that you’re a liar, but I do think you’re reluctant to consider these questions—which is why you aren’t doing it.

    Ancient philosophers would have felt completely entitled saying, “A particle moving from point A to distant point C must first move through some separate point B.” Or in other words, you can’t get there from here without passing through some kind of middle. But then, physicists upset the apple cart; it turns out that actually there’s reason to doubt that principle under certain conditions.

    Similarly, ancient philosophers would have felt completely entitled saying, “A particle cannot be a wave; it is a particle. It cannot be both.” But then hey presto—those physicists again. It turns out that truth wasn’t so true after all.

    A philosopher predating modern physics would have no reason whatsoever to doubt those principles. He’d have felt self-sure, confident, and reasonably so. But he would have been wrong. Being human, with a limited and imperfect knowledge of reality, he was unable to predict that there were conditions under which his self-evident truths might not be true. An imperfect, limited being cannot know in advance whether there is something they don’t know.

    That doesn’t mean that I expect future physicists to upset the “A=A” cart. But what’s the objective, infallible principle dividing “A=A” from “particle=particle”? An imperfect, limited being cannot know in advance whether there is something they don’t know. We can be so sure of ourselves that we never actually doubt, and we can comfortably live our whole lives assuming the proposition is true, but as a matter of pure logic, we cannot be certain because we are imperfect, limited beings. We cannot know whether there is something we don’t know or are too limited to understand. Even if the principle is perfect and absolute, we aren’t, and we only perceive them with our own minds.

    So I know you have lots of mean things to say about me. Vent! Get it off your chest. But if you don’t mind, and if you’re able, can you also respond to the argument? Assuming you agree that you are fallible, how do you know that your perception of logical truths is infallible? What faculty do you use to conclude that, and how do you know it’s infallible?

  212. 212
    Barry Arrington says:

    zeroseven,

    I have time to whack only so many moles, and I am certainly not at your beck. And I certainly feel no compunction to whack again a particular mole that I have already whacked two or three times in the thread above just because you are too lazy to read those previous whacks.

  213. 213
    Barry Arrington says:

    LH,

    As I said in the very beginning, “I don’t doubt it.” Not doubting is not the same thing as being absolutely certain.

    Yes, actually, it is. Having no doubt means the same thing as being certain. Another contradiction. You act as if we don’t understand simple English words. Stop it LH. You are embarrassing yourself.

  214. 214
    Aleta says:

    Hi Barry. I’m not angry – amazement is not anger.

    Also, I’m not an “intellectual”, I don’t think. I am well-educated layperson who, as a long-time math teacher, has a special interest in the history and philosophy of math.

    But it seems to me that if you don’t understand the issues illuminated by the parallel postulate situation, because you weren’t aware of them, then you are not likely to have understood the points I was making in reference to 2 + 2 = 4.

  215. 215
    Barry Arrington says:

    Aleta,

    I am well-educated layperson who, as a long-time math teacher, has a special interest in the history and philosophy of math.

    God help your students. I hope they are smart enough not to fall for your “the whole 2+2=4 is fuzzy” routine.

    You seem to crave having the last word. OK, the floor is yours.

  216. 216
    Learned Hand says:

    LH, there has been a deafening silence from Barry and SB on your repeated question about about whether n+n=2n is a SET for every value of n.

    I think they would say “no,” based on various comments above. I go into more detail at TSZ; it’s long so I won’t paste it all here. So at some value of n, n+n=2n transitions from a SET to something else. BA says there are no grey areas, and I think they take the position that it also can’t vary from person to person. (Because while two people may vary in their ability to perceive a SET, that doesn’t change whether the SET is a SET.) So n must be some single, discrete number, no matter who’s answering the question.

    That doesn’t mean that we can actually know what it is, though. They’ve said it’s possible to be uncertain about whether a SET is a SET (I think), so maybe their answer would just be that we can’t know where the line is? It’s some discrete, single number, we just can’t identify it in practice?

    That would be a clean resolution in part, I think. Except I don’t know how to resolve the false positives problem under their assumptions. What do you do when two people confidently answer 17+17 confidently, without calculating it, but only one gets the right answer? Did one perceive a SET, and the other misperceived it? And the one who got it wrong, was he just acting on intuition or recollection of his training, rather than his SET-sense? That would imply that intuition and acculturation can be subjectively indistinguishable from the perception of a SET. I think that’s true, but I don’t think they agree. I can’t see how either would address the problem.

    To be fair, it is time-consuming to have these conversations. Maybe we’ll get a more thoughtful engagement from BA later, after COB. SB seems to have time to write, but no inclination to return to these questions, but that might change too.

  217. 217
    Learned Hand says:

    Yes, actually, it is. Having no doubt means the same thing as being certain. Another contradiction. You act as if we don’t understand simple English words. Stop it LH. You are embarrassing yourself.

    Do you doubt that the sun will rise tomorrow? Presumably no. Are you absolutely certain about it, in the same sense in which you’re certain that A=A? Presumably no. Then you can not doubt, but not be certain. Your response only makes sense under one particular definition of “certain,” which in the context of our discussion of absolute logical certainty is pretty obviously not the one I was using.

    (ETA: In context, I originally said, “Does being self-evidently true mean that something is logically proven, or merely that we have no good reason to doubt it? That’s a serious question, not a rhetorical one. If the latter, then yes. I don’t doubt it, and can’t think of any case or reason that would cause me to.”

    It can be the case both that (a) we’re formally uncertain about a proposition, but that (b) we don’t have a good reason to doubt it. Pretty standard use of the English language.)

    As I said to SB, if the situation was reversed, this is the point at which you’d be calling me a liar for pretending to misunderstand. I assume you legitimately didn’t understand.

  218. 218
    Aleta says:

    As the last word, then, I’ll point out that I was not “fuzzy” on 2 + 2 = 4. What I said, multiple times, about an idea Barry doesn’t seem to understand, is that when we apply math to the real world, we have to test our models. I used adding velocities as an example. I was quite specific, not fuzzy.

  219. 219
    Barry Arrington says:

    Aleta,

    I used adding velocities as an example. I was quite specific, not fuzzy.

    I can’t let that go. You say you are a math teacher. So I now know you are very familiar with cardinality and set theory. That means that when you equivocated regarding a proposition applicable to sets to an application that you knew does not involve sets, you were not doing so out of ignorance. You knew exactly what you were doing. And what you were doing was dishonest at its very core.

    You are so proud of your velocity example. I don’t know why, because it reflects very badly on you. Now you can have the last word.

  220. 220
    Barry Arrington says:

    LH:

    if the situation was reversed, this is the point at which you’d be calling me a liar for pretending to misunderstand.

    No, I say you are an idiot or a liar only if you make idiotic statements or tell lies, like:

    you are not infallibly sure that a part of a pizza cannot be larger than the whole pizza,

    or

    you are not infallibly sure that A=A,

    or

    you are logically perfectly certain only that you can’t be logically certain about anything else.

    Anyone who says any of those things, far less all three as you do, is an idiot or a liar. BTW, I am pretty sure you are not an idiot.

    LH, every time you whine about being called a liar, I will just put up your statements and let the readers judge. I’m happy to do that as many times as you like.

    The best way to get me to stop pointing out your lies, is to stop telling lies.

  221. 221
    Barry Arrington says:

    LH,

    Then you can not doubt, but not be certain.

    Only if you equivocate on the word “doubt” or the word “certain,” which you delight in doing.

  222. 222
    Learned Hand says:

    I’ve written paragraphs upon paragraphs explaining my beliefs. That’s not equivocating.

    I’ve also answered every question that’s been asked of me. Why are you so shy about answering these last questions?

    My guess is that it’s hard, and it’s risky. It’s hard because you jumped in with a bullish, confident, seemingly easy assertion: 2+2=4 is a SET, and SETs are easy to know! Shut up, doubters, you dummies! But having made assertions like “there is no grey area” and “2+2=4 is a SET,” suddenly implications and entailments you didn’t predict arose. And those are less fun to deal with. So rather than doing so, it’s back to personal insults to keep the conversation easy.

    I also think that actually discussing the ideas on the table would be risky for you. You’ve made bold, aggressive assertions of your own infallibility; that’s a hell of a thing to support in the face of questions that require careful answers, especially when those answers might themselves have unpredictable implications. Having a serious conversation about ideas means running the risk of being wrong, and that’s especially hard when you started out by assuming your own infallibility. But if a conversation is risky, insults aren’t–it feels good, and it’s easy, and it yanks your beliefs out of the spotlight.

    But BA, if there’s no grey area, what is the greatest value of n for which n+n=2n is a SET? And if someone gets it wrong but believes the answer is right, then isn’t it possible to misapprehend a SET? And if you have infallible beliefs, how do you know they’re infallible–wouldn’t you have to have an infallible faculty for answering that question?

    Those are hard questions, but it’s not like they don’t have answers, even from your perspective. But finding them and supporting them would be hard, and risky. “Liar!” is neither. Even if you can’t quite find an actual lie, as is evident from your comment at 220.

  223. 223
    Aleta says:

    Nice post, LH.

    When you write,

    And if you have infallible beliefs, how do you know they’re infallible–wouldn’t you have to have an infallible faculty for answering that question?

    I think I know what Barry believes.

    I’ll make my case, and Barry can correct or confirm. Barry is a theist (possibly a Catholic like StephenB). He believes, by faith, that a part of him is an immaterial spirit or soul that can access, through his God-given rationality, certain infallible beliefs that exist in the “mind of God”, so to speak, and are not dependent on experience or on validation from the material world.

    My best guess.

    [Added in edit] I’m sure Barry (and we’re really speaking about a particular religious worldview here that many hold) recognizes his human fallibility and limitations in many ways, but there is this element of infallibility that arises from the special relationship he has with God through his ability to reason.

    A quick search on “faith and reason” found this: http://www.catholiceducation.o.....eason.html

  224. 224
    Barry Arrington says:

    LH,

    Even if you can’t quite find an actual lie

    I say you are an idiot or a liar only if you make idiotic statements or tell lies, like:

    you are not infallibly sure that a part of a pizza cannot be larger than the whole pizza,

    or

    you are not infallibly sure that A=A,

    or

    you are logically perfectly certain only that you can’t be logically certain about anything else.

    Anyone who says any of those things, far less all three as you do, is an idiot or a liar.

    You insist over and over that you are not a liar. OK.

  225. 225
    StephenB says:

    Learned Hand

    As a matter of absolute logic, I can’t be perfectly certain of them. As I said in the very beginning, “I don’t doubt it.” Not doubting is not the same thing as being absolutely certain

    It is exactly that same thing. If you are not absolutely certain, then you have doubts. If you have no doubts, then you are absolutely certain. You are trying to make them different in an attempt to have it both ways.

    You yourself said the sun won’t absolutely certainly rise tomorrow; do you doubt that it will?

    Cut it out. I said that I can only know that sun will “probably” rise tomorrow to correct your erroneous claim that you “know” the sun will rise tomorrow. The broader point is that a lack of certainty about future sunrises is not at all comparable to a lack of certainty about first principles, such as the law of whole and parts or the law of non-contradiction.

    I was sloppy when I wrote “I’m perfectly comfortable agreeing…”, because that can be read as a statement that I agree that I can be absolutely certain that p/slice can’t exceed p/whole. I didn’t mean that, though, only that if someone asks, “Can the part exceed the whole?”, I would be very comfortable saying “no” and not ever worry about being wrong. I think that’s very clear when you read the whole paragraph.

    So, you are not certain that the part cannot exceed the whole, but if someone asks, you are comfortable saying so. You are reasonably certain that a slice of pizza may be less than a whole pizza, but you are a long way from being absolutely certain about it, nevertheless, when pressed, you will say it can’t happen—but when the heat is off, you will reverse your field say that you might be wrong about it after all because your mind is “fallible” and you “cannot know anything perfectly,” In summary, you always try to have it both ways. Is that about it?

    Oh, I’m supposed to? Yes, I know I’m supposed to agree with you. But I don’t, and I’ve explained at length why not. And your response, rather than to address those reasons, is literally to complain that I am “supposed to” agree with you. According to who? And how can I agree with you when you won’t actually address the points I’ve made about fallibility? You can repeat “insane,” “liar,” “idiot,” all you like; they don’t add up to an actual argument. I know you feel infallible. How do you know that you actually are? What are the conditions under which it is impossible for you to misunderstand or incompletely understand something?

    You are supposed to know that a slice of pizza cannot exceed a whole pizza. You are supposed to know that the laws of non-contradiction and identity are infallibly true and that you can be absolutely certain about it. You are supposed to know that nothing can change or come into existence unless an outside agent causes it to happen. You are supposed to know that it is wrong to slice up babies like pieces of meat while they are still alive and sell them. If you don’t know these things, then you are not a rational person. There are millions of things that we can misunderstand and be wrong about, but self-evident truths are not among them

    Ancient philosophers would have felt completely entitled saying, “A particle moving from point A to distant point C must first move through some separate point B.” Or in other words, you can’t get there from here without passing through some kind of middle. But then, physicists upset the apple cart; it turns out that actually there’s reason to doubt that principle under certain conditions.

    So what? You want me to respond to these and other points, but you don’t really make a point. Are you trying to say that since philosophers and scientists have changed their mind about many things, it follows that reasonable people will also change their minds about the laws of thought? Is that your point? If so, it doesn’t follow. So please don’t waste another thousand words to imply that point without making it.

    An imperfect, limited being cannot know in advance whether there is something they don’t know. We can be so sure of ourselves that we never actually doubt, and we can comfortably live our whole lives assuming the proposition is true, but as a matter of pure logic, we cannot be certain because we are imperfect, limited beings. We cannot know whether there is something we don’t know or are too limited to understand. Even if the principle is perfect and absolute, we aren’t, and we only perceive them with our own minds.

    You know this with absolute certainty, right?. You didn’t say you believe it or suspect it. You characterized it as a fact. You are infallibly sure that there is nothing we can be sure of. Whatever happened to your claim that your mind is “fallible” and that you cannot be perfectly certain about anything?.

    So I know you have lots of mean things to say about me. Vent! Get it off your chest. But if you don’t mind, and if you’re able, can you also respond to the argument? Assuming you agree that you are fallible, how do you know that your perception of logical truths is infallible? What faculty do you use to conclude that, and how do you know it’s infallible?

    My perception of logical truths is infallible for many reasons. I will list only three:

    First, I recognize the immediate absurdity of denying them. If the law of identity was not certain, Jupiter could be Saturn. You could be me. I am infallibly certain that Jupiter is not, or cannot be, Saturn. I am infallibly certain that you cannot be me. If the law of non-contradiction was not true, kindness could be cruelty, cowardice could be courage, and, life could be death. I am infallibly certain that these conditions and qualities are incompatible.

    Second, I can identify and recognize errors and flawed thinking only because there is an unchanging infallible logical standard that exposes them as errors.. I know the difference between a patently true statement and a patently false statement. If someone tells me that I am seven feet tall, I know infallibly that they have made an error because I know the difference between the truth and what was claimed. I am certain that truth is not error..

    Third, I know that my internal logic is perfectly consistent with the logic of the real world. The psychological portion of the law of logic tells me this: If it rains, the streets will get wet.. This fact is perfectly consistent with the laws of nature: when it rains, the streets get wet. I am infallibly certain that my internal logic corresponds perfectly to the logic of the real world. That is why I am also certain that a piece of pizza is less than a whole pie–every time. No pizza needs to be measured to confirm the point. The law covers them all.

  226. 226
    mugwump3 says:

    Briefly, in response to the claim made that theists believe by religious faith in the immaterial or otherness of mind, my path was quite the opposite.

    A former dogmatic Agnostic, doubting, as our commenting materialists display here, man’s ability to truly know anything, I was caught in a loop of agonizing hyperskepticism and religious insistence that my view was the intelligent view…that theists drew their truths written down by earlier theists…all hobbling around on crutches, furious at we brave nihilists for running about with no apparent rational impediment.

    I came to a point of mathematical and logical rigor…originally a form of escape from the Sartre-like futile machinations of man. I began to understand the presuppositions behind the most basic of thoughts, the first principles of logic….the necessity of the unmoved mover, a first cause, a place outside of godel’s circle.

    Douglas hofstader, author of “godel, escher, bach”, delighted in explaining the mind from the perspective of fractals, of digital and propostional recursions, of sudden unexpected flourishes from mere algorithms. And, while I’ll always love him, he only reinforced the necessity of immaterial mind, of irreducible complexity, of an original programmer, a creator.

    Presupposing mind… creating information, prefiguring causes realized into form. That 2 + 2 = 4 is outside of matter, or better, n + n = 2n.

    Once again, stressed over and over again in this thread: the self-evident nature of a proposition does not require human understanding. To be sure, many if not most of what is self-evident in a logical system requires a progression of first principles, of necessary truths. I’m not sure BA or SB are denying this fact….especially in light of the irrelevant counter-point thrusts upon this thread.

    In the above denials of self-evident truths, you mount a defense having borrowed nearly all of your presuppositions from a theistic system of logic only to then deny God’s existence…cutting away fervently at the branch upon which you stand. Like a former version of myself, and as some have pointed out, a denial of the ability to be certain about anything is to assert a dogmatic certainty….that one can know for certain that mind is fallible, so it must be comprehensively so…just a chemical collection of maybes…all the while forgetting that sufficient knowledge of the world, not complete omniscience, is possible and practical in making claims of certainty….especially in regards to those first principles…that First Cause.

    We don’t require a catechism to believe in the immaterial mind. One does, however, require an enormous degree of faith to deny the soul and to worship at the feet of Darwin, Huxley, Dawkins, and the like…just mere fallible wads of matter such as they are…

  227. 227
    Popperian says:

    In the sense we are using it, “self-evident” is not a synonym for “apparent.” Instead, a self-evident proposition is defined as a proposition that is known to be true merely by understanding its meaning without proof.

    First, I’m not sure what you’re referring to when you say “understanding its meaning” and “known to be true”. Can you elaborate this? For example, how do you known when you “understand somethings meaning”?

    This seems equivalent to “know its true nature or purpose” which itself would be a question of truth. For example, one might say once they understand that the ultimate purpose of marriage is to join a man and a woman, then it is self-evident marriage is between a man and a woman. Is that what you’re suggesting? But how do you know the ultimate nature of something? Furthermore, this suggests it is marriages “man-ness and woman-ness” that makes it a marriage. That’s essentialism.

    Second, as you pointed out, sometimes things are simple. What you call self-evident truths are just ideas that are very hard to vary, and which we lack good criticism of. For example what would evidence that 2 + 2 = 4 look like?

    Imagine someone with a box containing two cupcakes adds two more cupcakes but does not end up with four. This scenario indicates that one of our assumptions are incorrect. The question is, which one and why? You will decide it is the the box of cupcakes system does not model two, four and addition. And you will have done so after comparing the two assumptions against each other.

    What would a good explanation that 2 + 2 does not equal 4 look like? I can’t think of one. Why can’t I? Because the theory that 2 + 2 equals 4, in reality, is extremely hard to vary without significantly reducing its ability to explain what it purports to explain. Go ahead, try to think of one. This property of being “hard to vary” is why mathematicians mistake it for being self-evident or directly intuited. It is indeed my opinion that 2+2 really does equal 4, so I’m not expecting to find a contrary theory that is nearly as good as an explanation. But this isn’t to say that such an explanation could not exit. For example, the hard science fiction book “Dark Integers” explores this very possibility, but for only very large integers.

    So, I would say there are no special cases of “self-evident” truth. Rather, there are explantations that are harder to vary than others. Comparing them is what we do in practice.

    Another way of looking at it is that I know for an absolute certain fact that the proposition “2+2 is not 4” is absurd in the sense that it cannot possibly be true, and in order to accept it as true I would have to reject rationality itself.

    If 2 + 2 = 4 really is false, this would imply the operation of laws of physics that would directly interfere with the creation of knowledge in ways we would consider malevolent. Specifically, you’d end up with very bad explanations something along the lines of “there really is no such entity as the number 4 because the proofs of mathematics are profoundly inconsistent and we do not notice because there are laws of physics that act on the neurons in our brains that cause us to unconsciously fill in the gaps in a way that allow us to ignore the physical absence of such entity.”

    So, it’s not that we can be absolutely certain that 2 + 2 = 4, but any explanation for why it would be false would itself be a bad explanation. We simply lack a good explanation as to why it would be false.

    Again, sometimes it’s simple. You’re making it complicated.

  228. 228
    Learned Hand says:

    SB,

    If you are not absolutely certain, then you have doubts.

    I don’t think so. I think that if you aren’t absolutely certain then you can have doubts, but may not. I’m not absolutely, logically certain that the sun will rise tomorrow—but I don’t currently doubt it. This seems like a flexible area of language, so I won’t say that your thinking is wrong. It seems very unlikely that you will agree that disagreement is possible here.

    So, you are not certain that the part cannot exceed the whole, but if someone asks, you are comfortable saying so.

    Yes! I’m not absolutely certain that the sun will rise tomorrow, but if someone asks, “LH, will the sun rise tomorrow?” I will say yes. Not “probably” or “it’s always risen in the past, so I surmise…” or anything like that, unless it’s a specialized conversation about probability or certainty. I’ll just say “yes.” I’m comfortable saying the sun will rise tomorrow, even though I can’t be logically perfectly certain of it.

    There are millions of things that we can misunderstand and be wrong about, but self-evident truths are not among them

    Your ability to discriminate between “things I can be wrong about” and “things I cannot be wrong about” is suspect. It requires an infallible faculty for discriminating between fallibility and infallibility, for example. And didn’t we establish that it’s possible to be wrong about whether a truth is self-evident? (Else you’d be able to tell me at what value of n n+n=2n ceases being a self-evident truth.) If you can’t tell with certainty whether a given truth is self-evident or not, how do you discriminate with absolute perfection between SETs and suspicions? (At this level, bear in mind we’re talking about the identification of SETs, not the truth of any given SET. After all, how do you know you’re infallible on a question if you can’t tell a SET from a non-SET?)

    Are you trying to say that since philosophers and scientists have changed their mind about many things, it follows that reasonable people will also change their minds about the laws of thought? Is that your point? If so, it doesn’t follow. So please don’t waste another thousand words to imply that point without making it.

    First, please relax. Second, not quite. My point is that your self-certainty feels quite reasonable to you—just as a pre-QM thinker would have felt entirely justified feeling that it was indisputable that objects can’t move from point A to distant point C without passing through some intermediary point B. Not just undisputed, but indisputable—it would be irrational to believe that things can move without moving! But that belief was, in fact, wrong. Not because the believers weren’t justified based on their knowledge, but because that knowledge was limited—just as we are all limited. Their belief was equal to your belief in strength and surety. But it was wrong. Why are you infallible when they weren’t?

    I do also make the point that you’re supposing that you can perfectly perceive the limits of a proposition. A must equal A because there is no counter example, and nothing works without it. This is also equivalent to beliefs that, for example, a particle must be a particle and can’t also be a wave. Those prior beliefs were limited because the believers and their knowledge were limited; they could not predict counterexamples outside their experience and education. Why are you infallible when they weren’t?

    You know this with absolute certainty, right?. You didn’t say you believe it or suspect it. You characterized it as a fact. You are infallibly sure that there is nothing we can be sure of. Whatever happened to your claim that your mind is “fallible” and that you cannot be perfectly certain about anything?.

    It’s still there. Do I need to repeat, after every assertion, “but I take the formal position that one cannot be logically certain of anything without an infallible perspective from which to assess it”? As I’ve said elsewhere, I’m comfortable with something like, “I’m certain that I can be certain of nothing but my own uncertainty.” Probably someone else could word that more artfully. But no, I don’t think that any part of my assertions here are infallible. That would be incredibly arrogant.

    My perception of logical truths is infallible for many reasons. I will list only three:

    Each one of these arguments presupposes infallibility in order to demonstrate infallibility. It’s a little shocking—how did you not think that we’d see through these?

    First, I recognize the immediate absurdity of denying them. If the law of identity was not certain, Jupiter could be Saturn. You could be me. I am infallibly certain that Jupiter is not, or cannot be, Saturn. I am infallibly certain that you cannot be me. If the law of non-contradiction was not true, kindness could be cruelty, cowardice could be courage, and, life could be death. I am infallibly certain that these conditions and qualities are incompatible.

    And what if you’re mistaken about what would happen if the LOI were violated? Your perception of what would happen if the law of identity were “broken” is imperfect. This presupposes, for example, that the law of identity would be broken on a human scale if it weren’t absolute. It could be violated in ways that aren’t apparent to you, and thus not absurd. If a methane molecule on Saturn was also a helium molecule, would you notice? Would it mean you were me and I was you? I don’t think so. As a fallible being, you can never know for certain what would happen if the LOI were different than what you believe it is. Since you can’t be infallibly certain of what the result would be, that result can’t support a conclusion of infallibility, can it? The possibility of error has already crept in.

    The much greater flaw with this argument is that no part of it explains why the LOI can’t be broken. This is an argument for why you don’t want it to be broken. And I agree, the LOI underpins basically all rational thought. We need it to be true. We assume it to be true. It’s an axiom, not a conclusion—we assume that it’s true because the assumption works, and is important, not because it’s proven. It’s OK to make such assumptions.

    Second, I can identify and recognize errors and flawed thinking only because there is an unchanging infallible logical standard that exposes them as errors.. I know the difference between a patently true statement and a patently false statement. If someone tells me that I am seven feet tall, I know infallibly that they have made an error because I know the difference between the truth and what was claimed. I am certain that truth is not error..

    And what if your perception of the infallible external logical standard is in error? That’s what happened to people who thought a particle couldn’t also be a wave, for example. Granting the existence of an infallible logical standard, that standard’s name isn’t “StephenB.” Whether the standard is fallible isn’t the question—it’s whether you can infallible perceive it. Your example is amusing, but did you think it through? You know your own height because you can use a measuring stick. When we’re talking about axioms, what’s the measuring stick? You can’t measure all cases, to see whether A is literally always A. You assume that it is because you haven’t found a counter-example, and can’t imagine one. But your knowledge and ability to imagine are limited, fallible. You have only those limited faculties to observe and test the axiom. In other words, you can put the measuring stick of yourself up to any axiom, but how do you tell that the measuring stick is accurate? You have none other to use, and it can’t measure itself—if it’s in error, it will measure itself erroneously.

    Third, I know that my internal logic is perfectly consistent with the logic of the real world. The psychological portion of the law of logic tells me this: If it rains, the streets will get wet.. This fact is perfectly consistent with the laws of nature: when it rains, the streets get wet. I am infallibly certain that my internal logic corresponds perfectly to the logic of the real world. That is why I am also certain that a piece of pizza is less than a whole pie. (I also know that you are infallibly certain of same, which is why I am harsh with you).

    Oh? What if random Brownian motion evaporates each rain drop before it hits the ground? I agree that we would never expect to see such a thing in the real world; I don’t think, though, that it’s logically impossible. Your example of a logical impossibility is actually logically possible; if you failed to anticipate this condition, perhaps it’s an indication that you aren’t infallible? (I can’t believe I’m trying to persuade someone that he isn’t infallible. I think we’re both equally shocked with each other. I’m proud to remain civil though!)

    Or maybe you think it’s actually impossible for the rain to not make the street wet. How do you reach that conclusion? By experience of how rain works and reasoning out cause and effect; reason and experience both being limited faculties. As with the other examples, you’re assuming the infallibility of the faculties you’re using in these three approaches, then claiming you’ve used them to show that you have infallible faculties. You’re assuming your conclusion. Do you feel like that’s good logic?

    Let me ask it this way: how can you show us that you are infallible without assuming that you are infallible? Oh, and by the way, at what value of n does n+n=2n ceases being a self-evident truth? If you don’t know, why not?

Leave a Reply