Uncommon Descent Serving The Intelligent Design Community

“Self-Evident” Does Not Mean “Apparent”

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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.

Comments
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)?Learned Hand
September 2, 2015
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I am interested in Barry and StephenB's response to LH's question. At what point does n+n=2n stop being a SET?zeroseven
September 2, 2015
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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.StephenB
September 2, 2015
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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.Aleta
September 2, 2015
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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.Learned Hand
September 2, 2015
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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. Barry Arrington
September 2, 2015
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Aleta @ 159. Unless you are counting actual pink unicorns, then yes they were immaterial mental representations of pink unicorns.Barry Arrington
September 2, 2015
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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?Learned Hand
September 2, 2015
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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.Learned Hand
September 2, 2015
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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.Aleta
September 2, 2015
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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.StephenB
September 2, 2015
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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?StephenB
September 2, 2015
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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.Barry Arrington
September 2, 2015
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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.Barry Arrington
September 2, 2015
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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.)Learned Hand
September 2, 2015
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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?Learned Hand
September 2, 2015
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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?Learned Hand
September 2, 2015
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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. Aleta
September 2, 2015
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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?StephenB
September 2, 2015
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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.”Barry Arrington
September 2, 2015
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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.Barry Arrington
September 2, 2015
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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.Learned Hand
September 2, 2015
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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?Learned Hand
September 2, 2015
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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.StephenB
September 2, 2015
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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.GCS
September 2, 2015
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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.Aleta
September 2, 2015
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BTW if it helps think of two pink unicorns. Now think of two more. How many pink unicorns Aleta?Barry Arrington
September 2, 2015
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Alexa How many material things did you count? Dodging the question a second time will be very telling.Barry Arrington
September 2, 2015
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To Barry: apples are material things. 2 + 2 = 4 because those are names for things and operations about how the material world works.Aleta
September 2, 2015
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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.Aleta
September 2, 2015
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