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“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
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).Aleta
September 3, 2015
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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.Aleta
September 3, 2015
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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.Barry Arrington
September 3, 2015
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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".daveS
September 3, 2015
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I googled the Banach-Tarski paradox. I assume the same reasoning applies to pepperoni pizza! :-)Aleta
September 3, 2015
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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.Learned Hand
September 3, 2015
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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?Learned Hand
September 3, 2015
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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?Learned Hand
September 3, 2015
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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.Aleta
September 3, 2015
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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.Barry Arrington
September 3, 2015
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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). Barry Arrington
September 3, 2015
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to Barry re 185. I answered that at 183, probably while you were writing 185.Aleta
September 3, 2015
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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.Aleta
September 3, 2015
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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.Barry Arrington
September 3, 2015
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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.Aleta
September 3, 2015
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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.Aleta
September 3, 2015
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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?Barry Arrington
September 3, 2015
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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.daveS
September 3, 2015
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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.Barry Arrington
September 3, 2015
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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?Barry Arrington
September 3, 2015
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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.Aleta
September 3, 2015
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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.Barry Arrington
September 3, 2015
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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?Barry Arrington
September 3, 2015
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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.daveS
September 3, 2015
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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.Aleta
September 3, 2015
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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.StephenB
September 3, 2015
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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.StephenB
September 3, 2015
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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?Andre
September 2, 2015
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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?Andre
September 2, 2015
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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.zeroseven
September 2, 2015
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