Can one infallibly detect self-evident truths?

There’s been an interesting conversation at UD over self-evident truths lately. I think I’ve run up against the Uncommon Descent policy on dissent (don’t dissent), and the whole thing has devolved into “we are right” and “they are liars and also dumb.” But the underlying conversation was interesting, and I’d like to get some outside opinions on it. Especially KN, or anyone else with actual training in philosophy. I’m going to number positions for the sake of convenience, so that people with an opinion can react to any that interest them without feeling the need to engage them all. I’d love to hear where I’m wrong.

So as to my position:

  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.
  3. 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 counter-example because it’s perfectly true, or because I have an imperfect and limited mind? I can’t know without a perfect, limitless mind, so I have to say even here, it’s not logically absolutely certain. (But obviously practically certain, and I don’t doubt it in practice.)

Does that make sense?

 

Now as to StephenB and Barry Arrington’s position.

  1. I think one major motivator of the “you’re a liar!” style of debate they’ve adopted is community identification. I’ve been thinking of this as building a wall. The point of the conversation is largely, not entirely, to show that “we think like this:” and “they think like that:”, or more pointedly, “look how stupid and ugly they are.” It makes it very easy to avoid questioning beliefs, because we cling particularly to those notions that separate us from them. It identifies and strengthens the community of us by redefining it in opposition to the ugliness and stupidity of them. And once that wall is built, it’s extremely hard to dismantle. Why on earth would you stop and seriously consider something a stupid and dishonest person says? And what would it say about you if you agreed with them? The wall exists to separate.
    1. This is not to say their positions are dishonest—I think they’re very upfront with their beliefs, and mean what they say.
    2. I think this is demonstrated particularly by BA’s habit of bailing out of a conversation and posting a new thread that very explicitly says look at how stupid and ugly those people are!
    3. I think I’m doing the same thing right now. I think that wall-building is wrong, but I don’t know how not to do it—especially as observing that someone else is building a wall is as good as laying a brick in your own.
    4. I can try to fight back against that by observing that walls exist to keep people in as well as out; the point is largely to have a bulwark against having to reconsider one’s beliefs and identity. So it’s important to ask, “Am I wrong?” Which I’m doing here, and attempting with some success to do in my own head.

And now the conversation itself. This is tricky because they’re cagey about answering questions. I suspect they know they’re on uncertain ground, and don’t want to commit to a position whose implications they can’t perfectly predict. I think they’re leery of inadvertently contradicting each other, too, because they’re aware that it would be awkward for two people professing infallibility to disagree. So gathering dribs and drabs of what they’ve said, I think this is a reasonably fair representation of their position. I’m not confident that it is, but I’m doing my best.

  1. Self-evident truths (SETs) exist.
  2. People can perceive SETs. I refer to the faculty for doing so as “SET-sense,” because it’s alliterative.
  3. People do not use reason to perceive SETs. If one needs reason to arrive at a truth, it is not a SET.
  4. People can be uncertain about whether a SET exists.
  5. People cannot be wrong when they identify something as a SET. No false positives are possible.
    1. This is some guesswork on my part; SB started calling me a liar rather than answer, and I didn’t bother to ask BA. I think he’s said in the past that no such error is possible, but I can’t recall where.
    2. I think their position entails “no false positives.” If you can falsely believe that something is a SET, then the very existence of undoubtable SETs is out of reach.
  6. I’m not certain whether false negatives are possible.
    1. BA and SB have both suggested in the past that anyone who disagrees with them that it is self-evident that certain moral truths are objectively wrong must be lying, which suggests that the answer is “no.”
    2. On the other hand, uncertainty is possible for them, which suggests that false negatives might be too.
  7. Mathematical operations can be SETs.
  8. 2+2=4 is a SET.
  9. 17*45=765 is not a SET.
    1. I don’t think the operation itself, + or *, makes a difference.
    2. Things that have to be reasoned out aren’t SETs. I think that must include calculation, and I think BA at least agreed with that.
  10. There is no grey area, in which it’s impossible to tell whether a truth is self-evident or just a possibly flawed intuition.
    1. This is BA’s position, at least.
  11. For n+n=2n, we know that:
    1. If n=2, we have a SET.
    2. If n+n has to be calculated to get the answer, we don’t have a SET.
  12. So for those values where n>2 and n+n can be known without reasoning through the addition, we may or may not have a SET.
  13. Pursuant to F, there are no false positives.
  14. Pursuant to J, there are no grey areas. It’s a SET or it isn’t.

Whoo! This is improbably great fun. So with all that as background, let’s do a thought experiment. Let’s increment n and see what happens!

If we tested one million people by asking them to solve the iterations (what’s 2+2, 3+3, 4+4, etc.) we could chart out the percentage that got it right. For n=2 and probably 3 and 4 and 5, we’d get pretty much 100%. But that number would start to decline pretty quickly!

Some people, especially uneducated people, would start being unable to answer without doing a calculation. And remember, if you have to calculate it, you aren’t using SET-sense. Others will be uncertain, so also not using their SET-sense. They’re out of the sample—we only care about people who are arriving at an answer without having to guess or calculate it. That means we’re at 100% getting the problem right… or are we?

Some number of people are going to get the problem wrong. As n increases, more and more will do so. At some point, say n=17, we’ll have two groups of people left in the study: those who were confident they were right and answered 34, and those who were confident they were right and answered something else.

Uh oh. Now we have people believing they’ve arrived at a self-evident truth, but being wrong about it. False positives.

It’s possible to be in error about at least some apparent SETs. SteRusJon escaped this by identifying all math problems as SETs, but that’s not BA’s or SB’s position, and I don’t think they’ll back down. That’s one consequence of building a wall: you can’t leave the walled-in area very easily. Having belittled and insulted those who doubted them, it’ll be very difficult for them to consider whether their confidently-asserted positions had inconvenient entailments.

Another escape, and the one I think they’d prefer to use, is to mind-read. Those people who got n=17 wrong didn’t really believe that 17*2=38. They just thought they believed it. I’m dubious of any solution that requires redefining someone else’s belief, and this again introduces the possibility of error. If you can think you’re using your SET-sense, then how do you ever know for a fact that you are?

I think probably BA regrets trying to use math to show how obviously right he is, and will rely in the near future on simpler, more aggressive tactics to build the wall.

But! Maybe I’m wrong. Maybe my logic is off, in one way or many. What do you guys think?

125 thoughts on “Can one infallibly detect self-evident truths?

  1. Okay, Mung, let’s hear your explanation of how

    …I the Lord have deceived that prophet.

    …doesn’t mean:

    …I the Lord have deceived that prophet.

  2. keiths believes he might be deceived, but just not by God. hilarious. actually. What’s left, other than self-deception? Being deceived by Satan? Another being keiths doesn’t believe exists?

    self-deception it is. so much for any argument keiths might think he has. he’s deceived. god. satan. himself. what are the odds.

  3. Mung,

    keiths believes he might be deceived, but just not by God. hilarious.

    Of course I think I could be deceived by God. It’s right there in the thread you were too lazy to read:

    In the hopes of making some progress in this thread, let me lay out my argument systematically, with numbered statements, so that it will be easier for people to specify exactly what they disagree with and why.

    1. It’s possible that God exists. (or Satan, or demons, etc.)

    2. If God (or Satan, etc.) exists, then it is possible that he has the power to deceive us.

    3. If he has the power to deceive us, then he might be exercising that power at any particular time.

    4. Being human, we cannot reliably determine when he is deceiving us and when he isn’t.

    5. Any particular thought we have might coincide with a time when God/Satan/the demon is deceiving us.

    6. Thus, any particular thought might be mistaken.

    7. If we claim to be absolutely certain of something that isn’t true, we have erred.

    8. Therefore we should never claim absolute certainty for a thought that might be mistaken.

    9. Since any particular thought might be mistaken (by #6), we should never claim absolute certainty for any thought.

    Note that this argument can also be made simply by appealing to the imperfection of human cognition, but it’s more fun this way.

    Also note that the argument applies to atheists and theists equally. Atheists don’t think there is a God, of course, but it is still possible that there is a God, and possibility is all that is necessary for the argument to work.

    [Emphasis added]

    Mung, I’m afraid this one is above your pay grade. Could you send for vjtorley or another of the smarter Christians?

  4. keiths: Of course I think I could be deceived by God.

    Well if you believe that, you must believe you could be deceived by Satan too then. And you must also then believe that you could be self deceived. You could be deceived by an innumerable number of possible sources of deception, as long as they were logically possible. In fact, given what you believe, it is much more likely that you are deceived than that you are not deceived.

    Admit it.

  5. As I said:

    Mung, I’m afraid this one is above your pay grade. Could you send for vjtorley or another of the smarter Christians?

  6. fifthmonarchyman: more teenage apostate bible study— goodie

    And in the first paragraph of your first link it says

    But God does ordain that lying happen as part of his judgment on the guilty.

    I did not have sexual relations with that woman!

  7. Mung: keiths, do you believe that you can infallibly detect what the Bible says?

    You lot should do a special bible, where each part is colored according to if it’s supposed to be taken literally or not.

    That should keep you all busy for the next 100 years as you argue endlessly over what is and what is not metaphorical.

    This has been a vastly amusing thread.

    Take an old book full of contradictions (unsurprising for it had many authors!) and for each contradiction invent a back story that resolves those contradictions.

    The bible says that god lies, but a good god could not lie. Therefore god never lied, it “caused lies to be believed as truth”.

    The bible says that women should be subservient. That’s not so politically correct these days so it’s become that man and woman should be subservient to the word of god.

    And on and on endlessly. And now we have Mung arguing that people can be thrown into metaphorical lakes of fire. Do tell how the “lake of fire” is really saying that our sins will be burnt away until we are left with nothing but purity……

  8. Advocacy of “self evident” truth is nonsense, but even supposing such things exist, it is moot.

    Even supposing there exists self-evident truths, it is moot and irrelevant to the great questions that cannot be accessed through formal proof but can only be accessed through grace and faith.

    For non-trivial questions, “self-evident’ truths (if they exist) could not apply even in principle as illustrated by Gödel’s incompleteness theorem and the Heisenberg Uncertainty prinicple. I tried to explain it to StephenB, but he’s stuck in Thomas Aquinas “reasoning unto God” antiquated thinking and gobledygook.

    God can allow a person to be deceived, God can send delusion into someone’s mind. How do we know that? We’re mistaken so many times. We’ve been created with software and hardware that computes wrong inferences, we misperceive reality. What guarantee then is there that if someone accepts the existence of self-evident truths that they will arrive at the right answers to questions when it really counts 100% of the time? None.

    The discussion is pointless and just an delusionary device to make someone think they know more and have deeper insight about reality than they really do than actually dealing with facts and measurements and counterintuitive truths that are more the norm in the real world and in the questions of ID. That’s why StephenB doesn’t post on the more technical side of ID as it pertains to biology, physics, chemistry, mathematics, cybernetics, population genetics. He just wallows in the philosophy of “self-evident” truths as if it gives him special leverage and insight to the ID discussion and that he can somehow prove ID through self-evident truths.

    I tried to point out, the question of ID is more about it’s reasonableness as a hypothesis, not some absolute proof, and the proper viewpoint is whether one will wager it is right or wrong.

    From Heisenberg we know there is uncertainty, from Gödel we know there is incompleteness in understanding. And finally, for someone who keeps arguing theology, StephenB has a curious lack of relating his ideas to the Bible. Had he bothered to acknowledge that the Bible teaches that God lets minds be deceived, he wouldn’t be thinking so highly of his own ability to reason about the great questions of reality through “self-evident” truths but rather say, “it’s only by grace we know anything, and because we don’t know everything and are not omniscient, the ultimate truth can only be accessed through faith like a little child and God’s grace that the little child’s faith is well-placed rather than faith-based delusion” I realized these things now more in light of 21st century understanding of math and physics rather than the antiquated philosophical traditions the presume we can reason unto God.

  9. stcordova: the questions of ID

    There’s a simple solution Sal. Do some actual work. You know, research something and publish a paper. Simples!

    Except it’s hard work and you don’t seem willing to put yourself to the effort. And that’s why ID is going nowhere fast. Criticising StephenB is not going to advance ID.

  10. OMagain,

    Before I forget, thank you for posting those Bible verses about God putting delusions in people’s minds.

    Those verses show that “self-evident truths as a means of answering the great questions” isn’t exactly what the Bible teaches. “Self-evident truths” is antiquated philosophy pretending to be a foundation of Christian doctrine.

  11. Salvador, do you think if you add 2 + 2 and then keep adding 2 to the previous sum that you will eventually get an odd number, if you just keep doing it long enough?

  12. I don’t see why it should puzzle or bother anyone that we can and should assert such humdrum sentences as

    “2+2=4” is true by meaning alone

    or

    “2+2=4” is an analytic truth.

    — assuming that one accepts the analytic/synthetic distinction, as indeed I am.

    The more interesting question, perhaps, is whether analytic truths are self-evident.

    And the short answer is, “yes — an analytic truth will be self-evident to anyone who has acquired the relevant concepts.” 2+2=4 is self-evidently true to anyone who has acquired the concepts “2” and “4”, plus the concepts of addition and identity.

    Likewise, “torturing people is wrong” is a self-evident moral truth — for those of us who have been raised within a roughly post-Enlightenment moral sensibility.

    (Some might urge I should have said, “torturing innocent people is wrong,” with the suggestion that it is morally permissible to torture those who have committed some wrongdoing. I regard this suggestion as indicative of the barbarism into which the United States has sunk in reaction to 9/11.)

    The problem is that every self-evident truth — whether mathematical, physical, or moral — is self-evident only from within the overall conceptual framework in terms of which the self-evident truth makes any sense in the first place.

    Therefore, no appeal to self-evident truths can help us determine which conceptual framework, out of the plurality with which we can confronted, is the right one — if any of them is, or if “correctness” even makes sense here at all.

  13. Kantian Naturalist:

    — assuming that one accepts the analytic/synthetic distinction, as indeed I am.

    The more interesting question, perhaps, is whether analytic truths are self-evident.

    And the short answer is, “yes — an analytic truth will be self-evident to anyone who has acquired the relevant concepts.

    Do you agree mathematics is a priori? And that some complex mathematical statements are not self-evident even though one has the relevant concepts and the statement is provable (and so true, at least mathematically-speaking). Hence if analytic implies self evident, then not self-evident means not analytic.

    If you are in agreement with above, does that mean you agree there are synthetic, a priori truths?

    By the way, in the “Things are Not so simple thread”, Walt noted you’d uploaded a new conference presentation. I posted a brief comment there in case you are interested in discussing that paper further.

  14. Kantian Naturalist: Therefore, no appeal to self-evident truths can help us determine which conceptual framework, out of the plurality with which we can confronted, is the right one — if any of them is, or if “correctness” even makes sense here at all.

    This is why I take the view that scientific theories are neither true nor false.

  15. BruceS: Do you agree mathematics is a priori? And that some complex mathematical statements are not self-evident even though one has the relevant concepts and the statement is provable (and so true, at least mathematically-speaking). Hence if analytic implies self evident, then not self-evident means not analytic.

    I am reminded of a story told about Hermann Weyl, though it has probably been told of other mathematicians.

    According to the story, Weyl was teaching a class at Princeton. As part of his lecture he said “It is obvious that …” (the details of “…” don’t matter here).

    A student interrupted him, and asked “Is it really obvious?”

    Weyl stopped, and appeared to be thinking. He scribbled some notes on the board (for his own use). This went on for 15 minutes.

    Then Weyl said “Yes, it is obvious”, and resumed the lecture where he had left off.

  16. Neil Rickert: This is why I take the view that scientific theories are neither true nor false.

    A lot of discussion would be short circuited by realizing that science is useful rather than true.

    The use could be in advancing technology, or it could be in making better models possible. “Better” could be thought of a s circular were it not for the tendency for models eventually to become technology.

    I think of it as the argument from digital watches, after Douglas Adams.
    He was being ironic, perhaps doubly so.

  17. Is the notion of “self-evident” itself self-evident? If not, then claims that something is self-evident are debatable. Gödel showed problems with self-reference. Self-evident is likely a faulty notion given that it cannot reliably assert that anything self-evident exists. Why? The notion of “self-evident” itself is not self-evident. The whole “self-evident” crusade is a pointless sideshow.

    This was insightful:
    http://www.phy.duke.edu/~rgb/Philosophy/axioms/axioms/node27.html

    ….
    The last two elements – completeness and consistency – are fairly recent additions to logical and mathematical theory. In fact, there is a conflict of sorts between consistency and completeness, where a consistent system of more than a certain degree of complexity must be incomplete and contain statements that (for example) are true but cannot be proven, statements that are neither true nor false. Note that such a system can always be made to be complete by adding more axioms to specifically assign truth or falsity to these “ambiguous” or “self-contradictory” propositions but this, of course, generally can be done only at the expense of no longer being consistent.

    This leads us in the most natural of ways to Gödel, who was the primary logician responsible for proving that logic is a tragically flawed tool even for the purpose of guiding abstract reasoning, let alone for fulfilling the rationalists’ dream of deducing the True Nature of Being from Reason Alone.

  18. Kantian Naturalist:
    The problem is that every self-evident truth — whether mathematical, physical, or moral — is self-evident only from within the overall conceptual framework in terms of which the self-evident truth makes any sense in the first place.

    This is not a problem at all. This is how it should be. E.g. “2+2=4” should be self-evident to you, and not to your dog – that’s the difference between you and your dog. It’s a rather important defining difference. There are good reasons why “self-evidence” should not be blown out of proportions.

    Kantian Naturalist:
    Therefore, no appeal to self-evident truths can help us determine which conceptual framework, out of the plurality with which we can confronted, is the right one — if any of them is, or if “correctness” even makes sense here at all.

    And from this you apparently draw the conclusion that “correctness” cannot be had at all, ever. This only makes sense if you assume that the standard of truth should be your dog, not yourself.

  19. Neil Rickert: I am reminded of a story told about Hermann Weyl, though it has probably been told of other mathematicians.

    I think you’ve referenced that story before. But I still appreciate it.

    It reminds me of the story of von Neumann and a problem (of a bird flying between converging trains or similar) which could be solved quickly by seeing a “trick” or more slowly by summing an infinite series.

    When the problem was posed to von Neumann, he answered quickly.

    The person posing the problem said that he was surprised, since mathematicians tended to automatically choose the slow approach by summing an infinite series.

    von Neumann’s reply: “There is another way?”

  20. My take is that “self-evident” is a rhetorical device intended to shut out questioning on the truth of what is asserted.

    My sentiments exactly. Here is an alternate definition of “self-evident truth”.

    An assertion that if not professed by someone will invite labeling and demonizing of them as stupid, insane, liars, etc.

  21. Neil Rickert: No, it isn’t.

    My take is that “self-evident” is a rhetorical device intended to shut out questioning on the truth of what is asserted.

    You mean like calling something one disagrees with “sophistimacated bullshit”?

  22. Colin I see that you have got embroiled with Barry again on this subject. I didn’t expect him to move beyond “You are nuts/stupid/lying if you disagree with me”.

    One thing that interests me is the assumption that you somehow have to subscribe to the laws of logic to be rational. This suggests that particular deductions are true because they are examples of general rules.  If I state that Barry is either crazy or not crazy, then is it true because of the law of the excluded middle or do I just accept the specific statement as rather obviously true? To put it another way – do I have to accept that it is always true that either A or ~A before I can have a rational discussion about a specific case where I happen to assert either A or ~A.

    I don’t think it makes sense to say that specific deductions are true because of the laws of logic because it leads to a kind of circularity/infinite regress.

    Statement A: Barry is either crazy or not crazy.

    Why?

    Because A is an example of the law of the excluded middle and the law of the excluded middle is always true?

    But this is itself a specific deduction (of the form all X’s are Ys, A is an X, therefore A is a Y). So what general law makes this true?

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