Saturday, March 25, 2006

Logic As Too Commonly Used

(I realize this wouldn't have a broad appeal, but I am amused by it so please indulge me. Click at bottom of post to see the whole thing. P is a stand in for any premise someone is trying to prove.)

Proofs that p

Davidson's proof that p:
Let us make the following bold conjecture: p

Wallace's proof that 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
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.

Sellars' proof that p:
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 P (1):
Saul Kripke
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.
(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.

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

It is a model theorem that p -> p. Surely its possible that p must be true. Thus p. But it is a model theorem that p -> p. Therefore p.

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

If not p, what? q maybe?


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