Philosophers’ Proofs that p    

Let us make the following bold conjecture: p.

Davidson has made the following bold conjecture: p.

As I have asserted again and again in previous publications, p.

Some philosophers have argued that not-p, on the grounds that q. It would be an interesting exercise to count all the fallacies in this “argument.” (It’s really awful, isn’t it?) Therefore p.

It would be nice to have a deductive argument that p from self-evident premises. Unfortunately I am unable to provide one. So I will have to rest content with the following intuitive considerations in its support: p.

Suppose it were the case that not-p. It would follow from this that someone knows that q. But on my view, no one knows anything whatsoever. Therefore p. (Unger believes that the louder you say this argument, the more persuasive it becomes.)

I have seventeen arguments for the claim that p, and I know of only four for the claim that not-p. Therefore p.

Most people find the claim that not-p completely obvious and when I assert p they give me an incredulous stare. But the fact that they find not-p obvious is no argument that it is true; and I do not know how to refute an incredulous stare. Therefore, p.

My argument for p is based on three premises:

(1) q
(2) r, and
(3) p

From these, the claim that p deductively follows. Some people may find the third premise controversial, but it is clear that if we replaced that premise by any other reasonable premise, the argument would go through just as well.

Unfortunately limitations of space prevent it from being included here, but important parts of the proof can be found in each of the articles in the attached bibliography.

There are solutions to the field equations of general relativity in which space-time has the structure of a four-dimensional Klein bottle and in which there is no matter. In each such space-time, the claim that not-p is false. Therefore p.

Zabludowski has insinuated that my thesis that p is false, on the basis of alleged counterexamples. But these so-called “counterexamples” depend on construing my thesis that p in a way that it was obviously not intended -- for I intended my thesis to have no counterexamples. Therefore p.

Outline of a Proof That p¹

Some philosophers have argued that not-p. But none of them seems to me to have made a convincing argument against the intuitive view that this is not the case. Therefore, p.

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         1. This outline was prepared hastily--at the editor’s insistence--from a taped manuscript of a lecture. Since I was not even given the opportunity to revise the first draft before publication, I cannot be held responsible for any lacunae in the (published version of the) argument, or for any fallacious or garbled inferences resulting from faulty preparation of the typescript. Also, the argument now seems to me to have problems which I did not know when I wrote it, but which I can’t discuss here, and which are completely unrelated to any criticisms that have appeared in the literature (or that I have seen in manuscript); all such criticisms misconstrue my argument. It will be noted that the present version of the argument seems to presuppose the (intuitionistically unacceptable) law of double negation. But the argument can easily be reformulated in a way that avoids employing such an inference rule. I hope to expand on these matters further in a separate monograph.

If (q & not-q) is true, then there is a model for p. Therefore, p.

It is a theorem of modal logic that ♢☐p → ☐p. Surely it’s possible that p must be true. Thus, ☐p. But it is a theorem that ☐p → p. Therefore, p.

p-ness is self-presenting. Therefore, p.

If not p, what? q maybe?

Unfortunately, by the very nature of logical codationalism I cannot offer a proof that p along the elegant lines of BonJour’s coherentist proof. Indeed, I cannot offer a PROOF that p at all, and for two reasons; first, because PROOF (as opposed to proof) embodies a linear foundationalist conception of justification that cannot survive the “up, up and away” argument, and second because BonJour’s own account of justification falls prey to the “drunken students” argument. Nor can I offer a proof that p, as I seem (like Fodor) to have mislaid my theory of the a priori.

Yet a case can be made -- in modest, fallibly naturalistic terms -- for p. And if the criteria embodied in codationalism are in fact truth-conducive (and if they are not, then every other theory of justification is likewise a failure since codational criteria are used by coherentists and foundationalists without proper appreciation of their interconnections), then this will amount not to a PROOF nor yet a proof that p, but simply a proof that p, based on the explanatory integration of p with the rest of my beliefs that are explanatorily integrated with each other.

The explanatory integration at work in this proof is rather like that found in a crossword puzzle. . . . [Remainder of the proof is left as an exercise for the reader. For the solution, consult next Sunday’s London Times.]

The assumption that p -- indeed, the belief that p is so natural and obvious as to be beyond dispute -- is so deeply woven into Western thought that any attempt to question it, much less to overthrow it, is likely to be met with disbelief, scorn, and ridicule. The denial of p is a deep thesis, a theme of courage, a profound insight into the fundamental nature of things. (Or at any rate it would be if there were a fundamental nature of things, which there isn’t.) Anyone unfamiliar with the hidden brutalities of professional philosophy cannot imagine all the nasty things that will be said about someone who dares to mount an assault on p. (Just look at how neglected Protagoras is now -- they even cut his writings up into tiny little bits!)

It has repeatedly been alleged that the denial of p is self-refuting. Extraordinary! As if one bold enough to deny p would feel bound by the conventions of dialethism on which alone any charge of self-refutation rests! Once we have seen through this delusion, we are free to dismiss as nonsense our current vision not only of philosophy and science but also that quaint notion of ‘the good life.’ We are also free to discard antiquated Hellenic prejudices as to what counts as proof and disproof, whilst retaining (of course) a proper sense of logical rigor. Hence, the foregoing constitutes a disproof of p.

Some people have claimed that not-p. How can that be? I just don’t get it. When I think about not-p, it makes me sick to my stomach, and I lie awake at night worrying about the future of philosophy. Therefore, p.

I can entertain an idea of the most perfect state of affairs inconsistent with not-p. If this state of affairs does not obtain then it is less than perfect, for an obtaining state of affairs is better than a non-obtaining one; so the state of affairs inconsistent with not-p obtains; therefore it is proved, etc.

Certain of my opponents claim to think that not-p; but it is precisely my thesis that they do not. Therefore p.

The theory p, though “refuted” by the anomaly q and a thousand others, may nevertheless be adhered to by a scientist for any length of time; and “rationally” adhered to. For did not the most “absurd” of theories, heliocentrism, stage a come-back after two thousand years? And is not Voodoo now emerging from a long period of unmerited neglect?

SOCRATES: Is it not true that p?
GLAUCON: I agree.
CEPHALUS: It would seem so.
POLEMARCHUS: Necessarily.
THRASYMACHUS: Yes, Socrates.
ALCIBIADES: Certainly, Socrates.
PAUSANIAS: Quite so, if we are to be consistent.
ARISTOPHANES: Assuredly.
ERYXIMACHUS: The argument certainly points that way.
PHAEDO: By all means.
PHAEDRUS: What you say is true, Socrates.

Dammit all! p.

While everyone knows deep down that p, some philosophers feel curiously compelled to assert that not-p, as a result of being closet Marxists. I shall label this phenomenon “the blithering idiot effect”. As I have shown that all assertions of not-p by anyone worth speaking of, and several by people who aren’t, are due to the blithering idiot effect, there remains no reason to deny p, which everyone knows deep down anyway. I won’t even waste my time arguing for it any further.

Some philosophers have argued that not-p, on the grounds that q. To show that p, I must therefore refute q. How can I do this? I think there really is no better or more rigorous argument than the following. I know that p. But I could not know this, if q were true. Therefore, q is false. How ridiculous it would be to say that I didn’t know p, but only believed it and that perhaps it was not true! You might as well say that I don’t know I’m not dreaming now!