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. I don’t mean to toot my own horn, but in the time I was writing this, BA was putting up a new post calling me a fool and inviting other to scorn me. Another brick in the wall.

  2. Oh, and I could have shortened this immensely by just saying, “But what about people who get a math problem wrong without calculating it?” I thought working through the steps would be useful, and it was, at least for me–one of the problems I thought I saw in their position, having to do with false negatives, went away as I did so.

  3. Hi Colin! Welcome.

    Barry has marked your post up in important looking black bold font. Top Christian.

  4. 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.

    It’s a self-evident truth.

    ETA: You can’t even be certain of your doubt. Read the thread by keiths on the Myth of Certainty.

  5. 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.

    Another self-evident truth then.

  6. 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.)

    Why is that a tricky question? Do you deny that you are thinking when you think that? Another self-evident truth.

  7. Richardthughes:
    Hi Colin! Welcome.

    Barry has marked your post up in important looking black bold font. Top Christian.

    Remarkable restraint by his own standards. I was pretty sure that he’d blocked me and the comment wouldn’t even go through.

  8. >Can one infallibly detect self-evident truths?

    No because one would have to be infallible, and if so, one would be God!

    Assertions about self-evident truths, especially by ID proponents, doesn’t reflect well on ID.

    UD has become a repository of such philosophical “defenses” of ID. They’ve wandered way off basic biology and chemistry. Other than Cornelius Hunter, I seemed to be the one of the few at UD that even had any desire to read and discuss scientific papers and even basic college science textbook material. They’ve gone the rout of verbose long winded philosophical opining that has marginal relevance to ID, imho.

    I wouldn’t teach ID to anyone using claims of “self-evident truths”.

    There is one self-evident truth, imho, but it’s not that relevant to ID, maybe to the notion of Hell, but not directly to ID.

    The only certainty is pain:
    http://theskepticalzone.com/wp/the-only-certainty-is-pain/

    FWIW, I mentioned the Nobel Laureate John Nash in that essay. He was brilliant, but his mind was fallible. Two of the greatest mathematical logicians in Cantor and Gödel lost their minds. If such first rate mathematicians and logicians can lose their minds, one should be a little careful about saying one can infallibly detect self-evident truths. Much of what Cantor discovered was not self-evident, in fact down right counter intuitive.

    Self evident truths, like in math? Not so straight forward. See Grandi Series:
    https://en.wikipedia.org/wiki/Grandi%27s_series

    or conditionally convergent

    http://mathworld.wolfram.com/ConditionalConvergence.html

    a conditionally convergent series may be made to converge to any desired value

    That is take conditionally convergent series that is equal to 1, then another equal to 1, but then sum the two series, do legit mathematical operations and get something other than 1+1 = 2.

    🙂

  9. Mung,

    You can’t even be certain of your doubt.

    I can by practical standards. It might be a paradox to say “I am logically perfectly certain that I can’t be logically certain about anything,” but I don’t. I just don’t say that I’m logically perfectly certain about anything. If I had to take a formal position, it would be, I suppose, “I am logically perfectly certain only that I can’t be logically certain about anything else.”

    Do you deny that you are thinking when you think that? Another self-evident truth.

    I don’t deny it! And I cannot think of any case in which I ever would. But to say it’s logically proven is to say there certainly is no case. And to do that, I’d need to be able to know that my perception of the logic is flawless. And I can’t know that, because I can never be perfectly sure I’m not in error.

    Are these self-evident truths? It depends on how you define a SET. BA and SB seem to take absolute self-certainty as part of the definition: if you can doubt it, it’s not a SET. So not by that definition, even though as I just said at UD, my doubt is a logical formality.

    (They also get really excercised about the stupidity of other people. They focus on how it would be insane to doubt a SET. I think that’s a really poor diagnostic criteria. And I don’t think they have a very good operational definition, partly because they define their operational SETs—the ones they think about most of the time, mostly in the moral sphere—primarily based on their culture and peer groups, rather than strict and formal definitions.)

    I don’t think that the basic premises of logic make a good case for the existence of SETs, because they’re premises. Why would you get worked up over proving a premise? It’s a premise. Like the use of math problems, they’re trying to build up to a more day-to-day use of SETs, like “abortion is self-evidently wrong.” But the ad-hoc nature of the beliefs they want to shoehorn into the set of SETs makes it hard for them to really rigorously define criteria for a SET without tripping over their own feet. I think they know that, and it’s one reason they’re so reluctant to just sit down and say, “Here’s the criteria for being a SET…”

    I think SB could do it, consistently with his core beliefs, but I think it would take a lot of work on his part.

  10. And Sal, also thanks to you. I’ll read that more carefully tomorrow; I don’t buy your argument because pain can also be subjective (one can mistakenly believe a perceived pain comes from an outside source), but it’s very interesting.

  11. Colin,

    But to say it’s logically proven is to say there certainly is no case. And to do that, I’d need to be able to know that my perception of the logic is flawless.

    Exactly. I’ve lost track of how many times Mung and others, in response to my claim that absolute certainty is unattainable, have asked “Are you absolutely certain of that?” as if it were a rebuttal.

    My answer is “No, of course not.”

    If you aren’t absolutely certain that your cognitive faculties are infallible, you can’t be absolutely certain of any conclusion they generate — including the conclusion that absolute certainty is impossible!

  12. Colin:
    Mung: You can’t even be certain of your doubt.
    Colin: I can by practical standards.

    Not if those “practical standards” are not self-evident truths.

  13. The claim by keiths that was refuted was the claim that even God could not have absolute certainty.

    And if God can have have absolute certainty then it follows that absolute certainty is in fact possible. Refuting the claim by keiths.

    The utterly pathetic non-response by keiths can be found … nowhere.

  14. Mung,

    Rich is asking for a link to the refutation you mentioned:

    This claim by keiths has been refuted and subsequently ignored.

    There is a refutation, right? You wouldn’t lie about that, would you?

  15. Much food for thought in your OP, Colin.

    I think this at ATBC is pretty perceptive, too.

    UD is pretty diverse. BA and SB fit into something I’ve been thinking about a lot lately: building walls. I think a lot of their efforts go into making sure their beliefs are protected from criticism or scrutiny. I used to think it was mostly self-gratification to call someone a liar, or a garbage spewer, or whatnot. And for BA I still think it is; he gets off on it as far as I can tell. SB doesn’t seem to relish it as much. He insults with a kind of monotonic intentness, without the rhetorical flourishes, but takes it deadly seriously.

    I think one reason people get stuck in that hostile, antagonistic mindset is that they’re building a wall. The more SB and BA define people who question them as liars or idiots, the less cause they have to ever think about those questions. If they feel some uncertainty in not being able to rigorously support their beliefs, building that wall would be an answer. Not to the uncertainty itself, but to the feeling of it. It gives them an incentive to attack, rather than think.

    That’s not to say that it’s something “they” do. For two reasons. One is that “us vs. them” is the primary tool in building walls. Why would I listen to what THEY have to say? They’re THEM. The other is that we do it do. Hell, I do it. When I make fun of KF by mocking his writing style, I’m making it harder for myself to pay attention to the substance of what he’s saying. (But I’m not making it as hard as he’s making it by writing that way. Zing!) So it’s not the worst thing in the world, and it’s probably inevitable to a certain extent.

    But I think self-awareness is important, and I don’t think SB or BA are, or want to be, aware of why they inject so much nastiness into every conversation.

    I like the analogy of building walls; it’s a bit more vivid than “erecting barriers to communication”. Seems to fit with the ethos of this site as expressed by Lizzie:

    …I started this site to be a place where people could discuss controversial positions about life, the universe and everything with minimal tribal rancour (pay no attention to the penguins….)

    My motivation for starting the site has been the experience of trying to discuss religion, politics, evolution, the Mind/Brain problem, creationism, ethics, exit polls, probability, intelligent design, and many other topics in venues where positions are strongly held and feelings run high. In most venues, one view dominates, and there is a kind of “resident prior” about the integrity, intelligence and motivation of those who differ from the majority view.

  16. This particular debate caught my eye as well.  I am glad you raised it here. Barry’s limited intelligence and unlimited aggression means it is tempting but actually unproductive to participate on UD.  (The subject gets raised about once a every three months, the same people make the same points, and everyone gets very cross and frustrated).

    I think the whole subject suffers from lack of attention to detail.

    1) Different types of statement have very different types of truth conditions. Moral, mathematical, psychology and empirical statements are true for  quote different reasons (compare “Abortion is evil”, “9/3 = 3”, “That hurts”, “The Sun is hot”). So even if one type of statement is self-evident that throws no light on the possibility of other types of statement being self-evident.

    2) There are several definitions of “self-evident” kicking around which need are not the same. I think everyone agrees that self-evident is not the same as “obvious” or “accepted by everyone”. Other candidates include:

    A) X is self-evident if anyone who understands it must also see that it is true

    B) X is self-evident if it is true and it is not possible to provide any evidence for it

    C) X is self-evident if it is true and it is not necessary to provide any evidence for it

    D) X is self-evident if denying its truth leads to utter absurdity

    I struggle to find statements which are self-evident in sense A. Historically there have been people who fully understood “torturing children for pleasure is always wrong” and have not thought it to be true. Children of a certain age (and mathematicians of sufficient sophistication) understand 2+2 = 4 but are not sure it is always true.

    Similarly with B. Most of us accept that 3 + 3 = 6 without any calculation or proof – but proofs and evidence are available.

    Many, many statements are candidates for C. But all it means is that it is possible to see that it is true without evidence. The problems being

    – some people can see that “log 9 to the base 3 is 2” without any evidence – others can understand it but need to prove it to themselves. So it seems to a function of the skills and experience of the person not the nature of the statement.

    – history is full of examples of statements that many, many people thought were self-evident in sense C and then turned out to be false (the sum of two velocities is a good example)

    The only candidates I have seen for D are some fundamental logical laws such as the excluded middle. I confess I am somewhat in two minds about the status of such laws. Certainly I have not seen a moral statement that is self-evidence in sense D – which is what was driving the UD debate to begin with.

  17. Excellent choice of topic! Two preliminary thoughts:

    (1) Are we talking about meaning or truth? When I “see” that 2+2=4 or see a red ball AS a red ball, is it that I grasp the meaning of the concepts? Or that I grasp that the world has the same structure as my thoughts about the world?

    (2) Are we talking about “non-inferential” knowledge or “presuppositionless” knowledge? The former just means that no inference is required to arrive at the assertion; the latter means that no other background knowledge is involved in making the assertion.

    Will weigh in later on the Myth of the Given and Agrippa’s Dilemma!

  18. Mark Frank:
    This particular debate caught my eye as well. I am glad you raised it here. Barry’s limited intelligence and unlimited aggression means it is tempting but actually unproductive to participate on UD. (The subject gets raised about once a every three months, the same people make the same points, and everyone gets very cross and frustrated).

    I think the whole subject suffers from lack of attention to detail.

    1) Different types of statement have very different types of truth conditions. Moral, mathematical, psychology and empirical statements are true for quote different reasons (compare “Abortion is evil”, “9/3 = 3”, “That hurts”, “The Sun is hot”). So even if one type of statement is self-evident that throws no light on the possibility of other types of statement being self-evident.

    2) There are several definitions of “self-evident” kicking around which need are not the same. I think everyone agrees that self-evident is not the same as “obvious” or “accepted by everyone”. Other candidates include:

    A) X is self-evident if anyone who understands it must also see that it is true

    B) X is self-evident if it is true and it is not possible to provide any evidence for it

    C) X is self-evident if it is true and it is not necessary to provide any evidence for it

    D) X is self-evident if denying its truth leads to utter absurdity

    I struggle to find statements which are self-evident in sense A. Historically there have been people who fully understood “torturing children for pleasure is always wrong” and have not thought it to be true. Children of a certain age (and mathematicians of sufficient sophistication) understand 2+2 = 4 but are not sure it is always true.

    Similarly with B. Most of us accept that 3 + 3 = 6 without any calculation or proof – but proofs and evidence are available.

    Many, many statements are candidates for C. But all it means is that it is possible to see that it is true without evidence. The problems being

    – some people can see that “log 9 to the base 3 is 2” without any evidence – others can understand it but need to prove it to themselves. So it seems to a function of the skills and experience of the person not the nature of the statement.

    – history is full of examples of statements that many, many people thought were self-evident in sense C and then turned out to be false (the sum of two velocities is a good example)

    The only candidates I have seen for D are some fundamental logical laws such as the excluded middle. I confess I am somewhat in two minds about the status of such laws. Certainly I have not seen a moral statement that is self-evidence in sense D – which is what was driving the UD debate to begin with.

    Nice post. I agree with you that the questions can be muddled a bit by imprecision. What I think tends to get messed up in these discussions are the psychological issues (“can’t not be believed”; “if understood, must be assented to”; etc.) and the modal status of the propositions in question (“true in every possible world”; “metaphysically necessary”; etc.). E.g., in the OP the business about “logically absolutely certain” already had me scratching my head.

    In another recent thread, I thought it was useful to define “certain belief” as something like a belief that could not be false–in virtue of the belief. In other words,

    P is certain for S =df. Necessarily, if S believes P, then P.

    isn’t quite right, because if P is necessarily true, the consequent will be true in every possible world, whether anybody believes P or not, making the whole if-then statement necessarily true.

    So it’s hard to get that immune to counterexamples, without making it long and ugly. But i+n any case, I think it’s clear that we want certainty to be something that we might call a transcendental property: it’s an psychological property of a person, but something non-psychological follows from it. If you have it with respect to any proposition, that proposition has simply got to be true.

    I agree with the OP that if there is any such property, it’s extremely rare. Maybe it takes place with respect to stuff like “I think” but even there, it seems to me that there are problems–partly with the self-referential aspects.

    The necessity of arithmetical truths can confuse people into thinking that our relations with them must involve something like the certainty I tried (but failed) to define above. But the logical (or metaphysical) status of a proposition is independent of that psychological stuff. (It’s all in Kripke.)

    Finally, I want to add that I agree with keiths that certainty (as so defined) is not required for knowledge, or for the refutation of assertions about knowledge or anything else. That’s a confusion that he’s outed nicely on any number of threads. One need not be certain of anything to deny the existence of certainty.

  19. walto,

    I agree with the thrust of what you are saying. If “self-evident” is interesting then it should be a property of a proposition not a property of the relationship between that proposition and one or more people. Different types of proposition have different types of appropriate evidence. I am willing to be convinced there are some true propositions for which there is either no appropriate evidence or no appropriate evidence is necessary – but they don’t include maths or ethics.

    Certainty is a psychological state and probably best kept out of the discussion.

  20. walto: I didn’t read all the comments, but, FWIW, I don’t think the OP is very helpful.

    Surely it isn’t, but where did I go wrong? What would have been a more helpful approach for me to have taken?

    I suspect that the main reason why anyone really cares about “self-evident truths” is that it seems to be a solution to Agrippa’s Trilemma.

    For those aren’t familiar with the term, the basic idea is clear enough.

    Suppose you want to justify some assertion p. You point to the method M whereby you arrived at p. But how do you know that M is reliable? Agrippa’s trilemma states that have three options:

    (1) The reliability of M is justified by other assertions, which terminate on p;
    (2) The reliability of M is justified by asserting q, which is justified because it relies on method N, which we know to be reliable because of assertion r, which is justified by method S . . .
    (3) The reliability of M is justified by asserting t just as dogmatically as one has asserted p.

    What we know of the Trilemma is recorded by Sextus Empiricus in his Outline of Pyrrhoism. The Pyrrhonian Skeptics taught that all anxiety arises from the search for knowledge; once we understand that knowledge is impossible, the anxiety goes away. The Trilemma is designed to show that knowledge is impossible, because we cannot avoid either (1) circularity, (2) infinite regress, or (3) unjustified dogmatism. No matter what, there’s no justification and so no knowledge.

    However, here’s one way out of the Trilemma: what if there are “self-evident truths”, or assertions that one can immediately see to be necessarily true? If there such claims, and if they can justify the method whereby one arrives at any other claims, then the Trilemma can be avoided. That’s the approach taken by Descartes in his Discourse on the Method and Meditations on First Philosophy, in contrast to the Pyrrhonian Skepticism advocated by his older countryman Montaigne.

    Unfortunately, as many philosophers have pointed out over the years — including two of Descartes’s contemporaries, Princess Elizabeth of Bohemia and Antoine Arnauld — Descartes’ own arguments are rife with circularity.

    Most seriously: I know that my clear and distinct ideas are true because I know that my intellect was created by a veracious God, but how do I know that my intellect was created by a veracious God? It is because I have a clear and distinct idea of Him; from inspecting this idea I have of Him, I know He must exist. So it seems that I know that my intellect was created by a veracious God because I know that my clear and distinct ideas are true and that my clear and distinct ideas are true because I know that my intellect was created by a veracious God.

    Thus from Descartes’s attempted refutation of Montaigne, we get Hume’s renewal of skepticism against Descartes, then Kant’s attempted response to Humean skepticism, and Nietzsche in response to Kant . . .

  21. Hi, KN. A couple of my profs at Brown were particularly interested in ‘The Problem of the Criterion”. Chishom wrote a famous pamphlet on it, and Van Cleve has a terrific paper that I’ve mentioned before, called ‘The Cartesian Circle.’.

    In a word, I think the problem with Pyrrhoism, is that it requires us to know that we know, in order for us to know anything.

  22. walto,

    Ken Westphal has a really superb paper arguing that Chisholm misunderstands the Problem of the Criterion and that Hegel has the correct response to Pyrrhonian Skepticism; see “Hegel’s Solution to the Dilemma of the Criterion“, also “Rational Justification & Mutual Recognition in Substantive Domains“. I’ll post more on this later on today, because I think that Westphal actually does capture the correct view — whether or not he is correct in attributing it to Hegel.

  23. walto: In a word, I think the problem with Pyrrhoism, is that it requires us to know that we know, in order for us to know anything.

    Interesting point. But relaxing the KK requirement doesn’t help, does it? Suppose knowledge isn’t JTB but any settled cognitive state produced by reliable means. Great, so now animals can know stuff. But they don’t know that they know. But maybe we’re in the same boat as nonlinguistic critters — for all we can tell, if the Dilemma of the Criterion is left open, it could be that we do in fact know but cannot know that we know.

  24. Mark Frank:

    A) X is self-evident if anyone who understands it must also see that it is true

    B) X is self-evident if it is true and it is not possible to provide any evidence for it

    C) X is self-evident if it is true and it is not necessary to provide any evidence for it

    D) X is self-evident if denying its truth leads to utter absurdity

    Typically, there are two distinct meanings for self-evident. In logic, it means a necessary truth; 2+2=4, which follows from the agreed meanings of the symbols. In other discourse, it means a precept that most can accept; all men are created equal. If they do accept the precept, then further argument can be made.

    These are very distinct uses of the term, and it has led to continued confusion on Uncommon Descent, where the denizens are not capable of seeing the equivocation involved.

    A,B&C are frequently held together. The problem with this position is that there is no argument that can convince someone of the truth of another person’s self-evident truth. You can only point and exclaim.

    D is a claim from logic. Interestingly, we can provide evidence of a logical truth, such as proof through arithmetic.

    Colin: A=A

    The axiom of equality is a definition derived from Leibniz’s Law.

  25. Kantian Naturalist: for all we can tell, if the Dilemma of the Criterion is left open, it could be that we do in fact know but cannot know that we know.

    Yes, I think we can know without knowing that we know. There’s nothing paradoxical about that. Suppose there’s a red ball in front of me that I’m looking at in good light, there’s nothing wrong with my eyes, no occlusion, etc. Now suppose too, that I have never learned what knowledge is. I think I might well know that the ball is red without having the capacity to know that I know anything whatever. I don’t see any problem with that.

    There just has to actually BE evidence for propositions. We don’t have to know that it’s evidence or even know what evidence is.

  26. Self-evident? 1+1 =2

    How does that square with Trinitarian viewpoints espoused by StephenB and KF?

    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!

    Not only that, when dealing with infinite terms, that sort of reasoning breaks down.

    What is reasonable in finitistic realm

    0 + 0 = 0

    breaks down in the infinitistic realm

    0 +….. 0 + 0 = ??????

    Self-evident? HA!

    0 + 0 = 0

    and

    1 + (-1) = 0

    thus

    0 + 0 …..+ 0 = 0

    so self evidently

    (1 + (-1) ) + (1+ (-1) + …. = 0

    but self evidently since we can just rearrange terms we ought to (but won’t be) able to make this assertion

    (1 + (-1) ) + (1+ (-1) + …. = 1 + ((-1) + 1+ ((-1) + 1) ….

    Because the right hand side reduces this way

    1 + ((-1) + 1+ ((-1) + 1) …. = 1 + 0 + 0 = 1

    thus we show

    0 = 1

    through the Grandi series.

    😯

    Self-evident, my eye! When we deal with question for all possible reality which includes question of the infinite, the mode of reasoning that works for finite questions doesn’t work so well for systems that touch upon the infinite.

    Self evident is thus irrelevant to some of the great questions that go beyond trivial.

    1 + 1 = 2

    So 1 ball plus another makes two balls? Or alternatively 1 ball can’t equal two balls? If we deal in the non-material realm, self-evident breaks down.

    See: Banach-Tarski paradox:

    https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

    A stronger form of the theorem implies that given any two “reasonable” solid objects (such as a small ball and a huge ball), either one can be reassembled into the other. This is often stated informally as “a pea can be chopped up and reassembled into the Sun” and called the “pea and the Sun paradox”.

    The reason the Banach–Tarski theorem is called a paradox is that it contradicts basic geometric intuition. “Doubling the ball” by dividing it into parts and moving them around by rotations and translations, without any stretching, bending, or adding new points, seems to be impossible, since all these operations ought to, intuitively speaking, preserve the volume. The intuition that such operations preserve volumes is not mathematically absurd and it is even included in the formal definition of volumes

    Trinitarian viewpoints ironically have to argue the self-evident 1+1 =2 does not apply.

    That’s why both from an ID standpoint and even basic Christian theology, “self-evident” theology has problems.

    Additionally, the Bible teaches human minds are usually blinded and can only see by the grace of God. Ears to hear, eyes to see, minds to think — they are given by God because truth is not self-evident, it must be illumed by God, not by human perception. So even on those grounds, arguing for self-evidence and the ability to reason to God does not work so well with many accepted Christian theological traditions.

    The heart is deceitful above all things, and desperately sick; who can understand it?

    Jeremiah 17:9

    but apparently some think pondering self-evident truths will lead them to the most important conclusions about reality. I beg to differ. Truth is evident by God’s grace, not because it is self-evident!

    I’ve said the line of reasoning of “self-evident” truths is not productive and may even be harmful. That didn’t go over well at UD.

  27. Barry at UD: “Over at The Skeptical Zone LH says he cannot be infallibly certain that A=A.”

    Come and participate, Barry. Be brave. Nothing to fear if you’re correct and capable, right?

  28. keiths: Exactly. I’ve lost track of how many times Mung and others, in response to my claim that absolute certainty is unattainable, have asked “Are you absolutely certain of that?” as if it were a rebuttal.

    My answer is “No, of course not.”

    Barry at UD:

    ““Error exists.”

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

    http://www.uncommondescent.com/intelligent-design/self-evident-does-not-mean-apparent/#comment-578491

  29. One of the deep problems with all talk of “self-evident truths” — I keep on hammering this point — is that it conflates two quite different epistemological states: what is known without inference and what is known without presuppositions.

    It is self-evident that 2+2=4, or that a red object is red (if conditions are normal, light is good, my eyes are normal, etc.) in the sense that no process of inference — neither deduction, induction, abduction (= ‘inference to the best explanation) is necessary in order for me to entitled to the assertion. If I say, “that’s a red ball!” and someone says, “how do you know?”, what can I say? A trained epistemologist might say, “because I know how to determine whether I am in the right position to see the colors as what they are,” but that is a theorist’s response. The person on the street would say, “I just do” — and that’s the end of it.

    But just because the person on the street lacks a justification, doesn’t mean that there’s one — and it certainly doesn’t mean that what is self-evident to the layperson is either necessary or sufficient to solve Agrippa’s Trilemma.

    As Descartes was the first to suggest, the Trilemma requires that a self-evident truth be one that cannot be doubted by anyone, not one that is not doubted by most people. It’s a modal claim that can’t be grounded in a survey.

    The heart of the problem, of course, is that in order to be infallibly certain that A=A, one would need to know that one’s own cognitive abilities are infallible — but could one know that?

    It’s not for nothing that Descartes claims that refuting skepticism requires proving that his cognitive abilities are not the result of chance and necessity!

  30. Rich:

    Barry at UD:

    ““Error exists.”

    That’s KF’s favorite, and I agree that it’s true, but I’m not absolutely certain of it.

    How could I be? To be absolutely certain of it, I would have to be absolutely certain of the rules of logic and absolutely certain that I was applying them infallibly.

    If that is an example of a “self-evident truth”, by KF’s and Barry’s standards, then self-evident truths are not absolutely certain.

  31. I’m surprised BA77 didn’t weigh in with quantum mechanics!

    If A is a photon and Charlie observes it as a particle, then is it self evidently a particle since Marcia later decided to perceive it as a wave through quantum erasure methods?

    life = not dead

    But schrodinger’s cat can be both dead and alive. Hence

    (dead cat) = not (dead cat)

    or

    A = not A
    in a manner of speaking. So much for self-evident.

    Whether the cat is dead or alive depends on the observer. So the cat will be alive in one virtual universe, dead in another. One could still axiomatically declare that A=A in either virtual universe, and hence maintain the principle of non-contradiction. But this only shows, it casts doubt on how far arguing “self-evident” arguments will go. If one thinks Shrodinger’s cat is a mere thought exercise, I refer the reader to this as it has relevance to quantum computing:
    https://www.newscientist.com/article/dn22336-quantum-measurements-leave-schrodingers-cat-alive/

    Truth isn’t necessarily self-evident, nor inherent, it may even be observer dependent. How one chooses to perceive something may influence what it is!

    I gave examples in the realm of mathematics (grand series, conditionally convergent series), and can also support it through quantum mechanics.

    What good do these discussion do for ID? It’s a pointless philosophical distraction at best, and not very informed by cutting edge knowledge in math and science.

  32. KN,

    It’s not for nothing that Descartes claims that refuting skepticism requires proving that his cognitive abilities are not the result of chance and necessity!

    It’s worse than that, because even divinely created cognitive faculties needn’t be reliable.

  33. Barry’s seems to be arguing:

    X is self-evidently true
    If you cannot see that X is self-evidently true you are a fool.

    From which follows, it seems to me:

    Therefore X is only self-evidently true to non-fools.

    Which would seem to have a relativity that he would probably not want to own.

  34. even divinely created cognitive faculties needn’t be reliable.

    In fact they can be divinely induced to give unreliable perceptions.

    God sends them a strong delusion, so that they may believe what is false,

    2 Thes 2:11

    So much for self-evident truths rescuing the day.

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