• Amalac
    489
    Being tired of seeing that a significant number of philosophers and other people tend to think that the problems raised by philosophical scepticism can be solved by just saying: “Well, if the arguments/claims of sceptics are valid/true, then they would refute themselves, therefore they can't be valid/true”, (and that's it! They think that's all it takes to solve the problems of scepticism that have troubled many of the greatest philosophers for so many years!) which seems to me to be a lazy and simplistic response, I have written this thread:

    One of the arguments used against skeptics since the times of ancient Greece and down to the present day, starts from the following implication: "If there is no proof, there is proof" (¬p → p)

    They say that it must necessarily be true, because if the skeptics affirm without proof that there is no proof, they would be as untrustworthy as those who affirm without proof that proof exists. And if they affirm it with a demonstration, they are contradicting themselves, because then there would be at least one demonstration: the one proving that there is no proof.

    The ancient skeptics themselves have already responded to this argument in Adversus Mathematicos and in Outlines of Pyrrhonism.

    I for my part will give a somewhat different answer to that argument:

    Let p be: "Proof exists" (Meaning: “There is at least one proof”).

    1: ¬p (Sceptical hypothesis)

    2:¬p is equivalent to ¬ (p v p) (1, Idempotent Law)

    3: ¬(p v p) is equivalent to ¬(¬¬p v p) (2, Double negation)

    4: ¬(¬¬p v p) is equivalent to ¬ (¬p → p) (3, Implication)

    5: ¬p is equivalent to ¬(¬p → p) (1,2,3,4 Transitivity)

    6: p v ¬p (Law of the Excluded Middle)

    7: ¬p → ¬p (6, Implication)

    8: ¬p → ¬(¬p → p) (5,7 Substitution)

    9: ¬p ^ [¬p → ¬(¬p → p)] (1,8 Conjunction)



    This shows that there is no logical contradiction in denying the implication ¬p → p if proof does not exist, and therefore those who disagree with the sceptics cannot hold that the implication ¬p → p is true to show that p is true without begging the question, since this implication is only true if p, that is: "Proof exists", is true.

    It will be answered: "But what you have just done here is certainly a demonstration, therefore there is at least one demonstration." Then the skeptic will answer: But if what I just did is a proof, then its conclusion: ¬p^ [¬p →¬(¬p → p)] must be true, therefore ¬p is true, therefore ¬(¬p→p) is true, therefore (¬p→p) is false, therefore ¬p is true and p is false.

    The problem is that logic seems to self-destruct, and the skeptic then asks: Where is the error in [Insert here a seemingly valid argument that has “therefore there is no proof” as its conclusion, that the opponent of the sceptic has criticised by saying that ¬p→p] then? Since if the conclusion follows from the premises, and the premises are admited to be true, then the conclusion, “proof does not exist”, must also be admited.

    He would continue: “I myself admit that I do not know if there is an error or not, nor if what I have just stated is a proof , but my argument is that by not being able to determine even if proof is more likely to exist than for it not to exist, we should suspend judgment”

    David Hume, in the conclusion of section I of his Treatise of Human Nature, understood the problem quite well:

    If the sceptical reasonings be strong, say they, ’tis a proof, that reason may have some force and authority: if weak, they can never be sufficient to invalidate all the conclusions of our understanding. This argument is not just; because the sceptical reasonings, were it possible for them to exist, and were they not destroy’d by their subtility, wou’d be successively both strong and weak, according to the successive dispositions of the mind. Reason first appears in possession of the throne, prescribing laws, and imposing maxims, with an absolute sway and authority. Her enemy, therefore, is oblig’d to take shelter under her protection, and by making use of rational arguments to prove the fallaciousness and imbecility of reason, produces, in a manner, a patent under her hand and seal. This patent has at first an authority, proportion’d to the present and immediate authority of reason, from which it is deriv’d. But as it is suppos’d to be contradictory to reason, it gradually diminishes the force of that governing power, and its own at the same time; till at last they both vanish away into nothing, by a regular and just diminution. The sceptical and dogmatical reasons are of the same kind, tho’ contrary in their operation and tendency; so that where the latter is strong, it has an enemy of equal force in the former to encounter; and as their forces were at first equal, they still continue so, as long as either of them subsists; nor does one of them lose any force in the contest, without taking as much from its antagonist. ’Tis happy, therefore, that nature breaks the force of all sceptical arguments in time, and keeps them from having any considerable influence on the understanding. Were we to trust entirely to their self-destruction, that can never take place, ’till they have first subverted all conviction, and have totally destroy’d human reason.

    Yet even Hume appears not to have been thoroughgoing enough: Just because in the past our nature has been such that sceptical reasonings haven't had a considerable influence on our understanding, that doesn't mean that in the future they won't have a considerable influence in our minds. As Bertrand Russell pointed out:

    (...)the law of habit is itself a causal law.
    Therefore if we take Hume seriously we must say: Although in the past the sight of an apple has been conjoined with expectation of a certain kind of taste, there is no reason why it should continue to be so conjoined: perhaps the next time I see an apple I shall expect it to taste like roast beef. You may, at the moment, think this unlikely; but that is no reason for expecting that you will think it unlikely five minutes hence. If Hume's objective doctrine is right, we have no better reason for expectations in psychology than in the physical world.
  • Zophie
    176
    Cool but.. can't you prove anything from a negation?

    If these philosophers believe the truth is a real thing, aren't they trying to refute a tautology? Why bother?
  • Amalac
    489


    Cool but.. can't you prove anything from a negation?Zophie

    I suppose you are talking about the Principle of Explosion (Ex Falso Quodlibet). Indeed, if the statement “there is no proof” were false, then you could prove anything from it. But that's only if it is false (that has to be proven first). The problem is that some try to argue that it is false by saying that if it were true, then it would be false, which contradicts what seemingly valid logical reasoning tells us.

    If these philosophers believe the truth is a real thing, aren't they trying to refute a tautology? Why bother?Zophie

    Which philosophers are you refering to here, the sceptics or the non-sceptics? Also, which tautology are you refering to?
  • Zophie
    176
    I notice your explanation of there being proof prequires provability, which, like all deduction, involves a signal conversion to new rules that isn't licenced by the prior system. It is just given.

    Those are the kind of tautologies I mean.
  • ernest meyer
    100

    I can understand there being concern about it, because there are obvious cases when skeptics are hypocritical. For example, Chomsky was a prolific user of media in saying that media deliberately falsifies explanations as propaganda, making himself a propagandist. But I dont think there should be any doubt that logic would reach the conclusion that skepticism does not refute its own existence, because it's predicated on the existence of negation in the first place, lol. Skeptics just feel there are more cases where conclusions are false.
  • Zophie
    176
    Chomsky was a prolific user of media in saying that media deliberately falsifies explanations as propaganda, making himself a propagandist.ernest meyer
    If so, does this not just further demonstrate what he said was true? He would be the one to know.
  • ernest meyer
    100
    to Chomsky what he said was true. To others he should be a propagandist by his own definition. lol.
  • Zophie
    176
    Should -- if you presume an argument from commitment is relevant.
  • Amalac
    489
    I notice your explanation of there being proof prequires provability, which, like all deduction, involves a signal conversion to new rules that isn't licenced by the prior system. It is just given.Zophie


    Hmmm, not entirely sure what you are saying here.

    Are you saying that the argument/ proof proving that there is no proof assumes that proof is reliable, and therefore refutes itself?

    If so, what would be your response to the passage by Hume I quoted in the OP?
  • Amalac
    489


    Chomsky was a prolific user of media in saying that media deliberately falsifies explanations as propaganda, making himself a propagandisternest meyer

    You are generalizing a bit too much. Chomsky says many people in the media falsify explanations, not that everybody does. Some people do not only care about propaganda.

    But anyway, we're already getting off topic.
  • ernest meyer
    100
    well, in that case, he should have defined what is different about his view that doesn't make it propaganda, but he didn't, he just complained all the time. But I agree, how much should one care whether the opinions of populist philosophers are coherent. I just stated that it is a natural tendency to think that skepticism is self-falsifying, because many skeptics are similarly hypocritical, but it doesn't seem to me to need much more than to say skeptics just believe more conclusions are false, and there's nothing wrong with that.
  • Zophie
    176
    I'm assuming the modern, deductive meaning of proof, and yeah. Ultimately, it provides no new information. It rearranges what is already known. It's a method of translation, not of truth in the traditional sense. Speaking of translation, I don't know what Hume is talking about.
  • Amalac
    489


    Speaking of translation, I don't know what Hume is talking about.Zophie

    Really now... I thought he was quite clear.

    What about this passage of Sextus Empiricus?:

    (...) just as it is not impossible for the man who has ascended to a high place by a ladder to overturn the ladder with his foot after his ascent, so also it is not unlikely that the Sceptic after he has arrived at the demonstration of his thesis by means of the argument proving the non-existence of proof, as it were by a step-ladder, should then abolish this very argument.
  • Amalac
    489
    It rearranges what is already known. It's a method of translation, not of truth in the traditional sense.Zophie

    I should clarify that the argument in the OP is not one for the conclusion that “proof does not exist”, but rather for the claim that it is not necessarily inconsistent to deny the proposition “proof does not exist, implies that proof exists”, if indeed “proof does not exist” were true.
  • Zophie
    176
    I should clarify that the argument in the OP is not one for the conclusion that “proof does not exist”Amalac
    I'm merely suggesting that the method of deductive proof is generally trivial. In my humble opinion a skeptic may be better served by moving to a relativist model since that allows the following phrasing:

    Skepticism says the truth of everything is doubtable to a skeptic, but if that is true, the truth of skepticism is doubtable to a skeptic, therefore skepticism says the truth of skepticism is doubtable to a skeptic because skepticism is doubtable to a skeptic (and that is a something, and every something is doubtable). All of this is trivially true. A positive phrasing reveals the absurdity of that kind of argument.
  • Amalac
    489
    All of this is trivially true.Zophie

    Do you think it is trivially true that logic should seemingly allow anyone (not just the sceptic) to validly conclude something that contradicts logic itself, and that in case the argument that proved that which contradicts logic were invalid, it was also such that we have difficulties pointing out where its error is? Well, I don't agree with that. If you do, then there is nothing else I can reply to you.
  • Zophie
    176
    You misunderstand. The question is not 'logic?' but 'which logic? (and for what?)'. :)
  • Amalac
    489


    'which logic? (and for what?)'Zophie

    Let's take a logic that has as its basis: The Law of Contradiction, The Law of the Excluded Middle, The Law of Identity, and principles of inference such as Modus Ponens, De Morgan's Law, etc. And also one that believes that some statements can always be validly proven by using those laws and principles.

    For example: aristotelian logic, mathematical logic, etc. Not a paraconsistent logic.

    Don't you think the arguments of sceptics give important objections to those systems, even if their arguments were invalid?
  • Zophie
    176
    I think the arguments of skeptics -- using those systems at least -- give trivial subjections to those systems that resolve to the thesis that not even logic can disprove logic, and that this is expected because it's a sign that the logic of those systems is true.
  • Amalac
    489
    I think the arguments of skeptics -- using those systems at least -- give trivial subjections to those systems that resolve to the thesis that not even logic can disprove logic, and that this is expected because it's a sign that the logic is true.Zophie

    Ok, let's try this approach instead: Surely you'd say that sceptical arguments such as the argument that uses Agrippa's Trilemma to conclude “therefore there are no proofs” are invalid/unsound.

    But why is it invalid/unsound? Is one of the premises false? Does the conclusion not follow from the premises? At least one of those must surely be true according to those systems. If not, then according to logic it must be valid and sound, and therefore its conclusion “Therefore there are no proofs” must be true (since otherwise it would not be valid and sound). According to logic, we should be able to pinpoint the error in that argument, and also in the argument which concludes that if not p (p= There is at least one proof), then it's not the case that not p implies p.

    You say the sceptical arguments resolve to the thesis that not even logic can disprove logic, but how do you know this? How did you come to that conclusion? How do you know that it is not instead how Sextus or Hume say it is?:

    (...) just as it is not impossible for the man who has ascended to a high place by a ladder to overturn the ladder with his foot after his ascent, so also it is not unlikely that the Sceptic after he has arrived at the demonstration of his thesis by means of the argument proving the non-existence of proof, as it were by a step-ladder, should then abolish this very argument.
  • Zophie
    176
    Surely you'd say that sceptical arguments such as the argument that uses Agrippa's Trilemma to conclude “therefore there are no proofs” is invalid.Amalac
    At face value, no. I would say it needs another element to make it properly analyzable, though.
    How did you come to that conclusion?Amalac
    I didn't. It's set by the definitions of every well-defined system.
  • Amalac
    489
    At face value, no. I would say it needs another element to make it properly analyzable, though.Zophie

    Ok, what is wrong with the argument that has the horns of the Trilemma as its premises and “Therefore no claim is justified” as its conclusion? According to those systems of logic, it must be either invalid or unsound (either at least one of the premises is false, or the conclusion does not follow from the premises). There is no third option.

    I didn't. It's set by the definitions of every well-defined system.Zophie

    Really now, which set of definitions are you refering to? Why should one accept the implicit premises in those definitions, such as those which already assume, right off the bat, that nothing can ever disprove logic, not even logic itself? Such definitions would in that case just assume that the sceptic can't refute logic using logic, but why should the sceptic accept them then?
  • Zophie
    176
    what is wrong with the argument that has the horns of the Trilemma as its premises and “Therefore no claim is justified” as it's conclusion?Amalac
    It's unrealistic. Propositions may be true/false but any actual proposition is defeasible.
    why should the sceptic accept them then?Amalac
    I don't know, why should they? Because they do? Because they can?
  • Banno
    25k
    One of the arguments used against skeptics since the times of ancient Greece and down to the present day, starts from the following implication: "If there is no proof, there is proof" (¬p → p)Amalac

    Wouldn't it have been simpler to point out that this leads directly to a contradiction, and hence is invalid?

    More interestingly, who are the Greeks and others who used such a silly argument?
  • Bartricks
    6k
    It seems to me that you are arguing that there is no contradiction involved in the sceptical thesis and thus that the sceptical thesis is not self-refuting. (Unless I have misunderstood).

    But although I accept that there is no contradiction involved in the thesis, I take it that a theory is 'self-refuting' when there would be a practical contradiction involved in believing it. So, for instance, "I do not exist" would be a self-refuting theory for anyone to hold, even though there is no contradiction involved in the thesis. If I hold it, I do exist. And "It is raining, but no one believes it is raining" would be another, as although it is possibly true - there seems nothing impossible about the scenario described - to believe it is to render it false.

    The charge against radical scepticism is surely that it is self-refuting in this way. That is, it is not that the thesis describes an impossible scenario. Rather, it is that anyone who believes it is justified, is confused: for if it is indeed justified (as it could be), then it is false.

    I suppose you might respond that this does not establish that radical scepticism is false, just that believing it is something we can never have epistemic reason to do. (For if it is true, then we have no epistemic reason to believe it; and if it is false, then we have no epistemic reason to believe it, because one can only have epistemic reason to believe a proposition if it is true).

    However, I take one of Descartes' lessons to be that self-refuting positions are more certainly false than those that contain contradictions. For I know more certainly that I exist, than that the law of non-contradiction is true. And so when we have shown that it would be self-refuting to hold a particular view, we have established that to hold it would be to hold a false view.
  • Amalac
    489
    [

    Wouldn't it have been simpler to point out that this leads directly to a contradiction, and hence is invalid?Banno

    Their argument is that the argument the sceptic uses proves the sceptic's conclusion “therefore, there are no proofs”, and therefore refutes itself, because if there is no proof, then the sceptic's argument is not a proof either. They then conclude that it's impossible for the statement “No statement can be proven” to be true, since if it were, then that would imply a logical contradiction.

    More interestingly, who are the Greeks and others who used such a silly argument?Banno

    They are refered to as “the dogmatists” by Sextus Empiricus. I assume he means, based on the people he references in “Outlines of Pyrrhonism”, philosophers from the school of Plato, Aristotle, and/or stoic philosophers, of his time and of earlier times.
  • Banno
    25k
    “the dogmatists”Amalac

    Where?

    Here's a of Outlines of Pyrronism; where is this argument?
  • Amalac
    489


    Where?Banno

    Pages 88-89 (185) in the pdf you linked, it starts saying: It will suffice to have said this much...at the end of page 88
  • Amalac
    489


    Pages 88-89 (185) in the pdf you linked, it starts saying: It will suffice to have said this much...Amalac

    That's where it starts I mean, Sextus finishes talking about it in page 90.
  • Banno
    25k
    Thanks.

    So we have this:
    If there is a proof, there is a proof.
    If there is no proof, there is a proof.
    Either there is a proof or there is no proof.
    Therefore, there is a proof.

    The second premiss is surely a contradiction, no?

    SO yes, it is a bad argument. But it's far from the only argument against scepticism.
  • Amalac
    489


    The second premiss is surely a contradiction, no?Banno

    Well, ¬p→p is equivalent to: ¬¬p v p, which is just p (Proof exists), according to the rules of material Implication, double negation and the idempotent law. So in that sense, I suppose it's not a contradiction.

    SO yes, it is a bad argument. But it's far from the only argument against scepticism.Banno

    I didn't say it's the only one, but it's one very commonly used in the internet and by many philosophers. If you don't believe me, lookup videos on that subject and what philosophers have said about scepticism, and I'm sure you'll find many people using it.
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