Can anyone or has anyone proven the law of contradiction to be invalid?

Question

Please explain your (or someone elses) reasoning behind the rejection of this law as best as possible.

Answer 1

Of course no one has ever proved that it is not valid -- because it is valid.

That hasn't kept some people from saying that they don't like it and prefer direct proofs as more elegant. There were a number of prominant logicians in the early 20th century who decided that they would only accept proofs that were proved directly. Ironically, one of them was Brower -- whose famous fixed point theorem has never been proven directly.

No one will ever remember any of the others.

Answer 2

Most "reasoning" you give is going to assume the axiom.

Wikipedia fuzzy logic.

If we define A as an apple, and then I bite into one, the apple has changed. So it's not A. But that's crazy, I still have an apple in my hand. If it's still an apple, when does it Stop being an apple?

Totalizing categories over particulars causes more aporia than just this case. Maybe I'll elaborate more later.

For the time being, this is BOTH an answer and not an answer!

Answer 3

Someone thought he had proven that theory, but another someone contradicted him.

Answer 4

The law of contradiction means that two antithetical propositions cannot both be true at the same time and in the same sense. X cannot be non-X. A thing cannot be and not be simultaneously. And nothing that is true can be self-contradictory or inconsistent with any other truth.
Debate:---.
'I am anxious to be sure whether I understand or misunderstand your Assumption of Nothing.' The answer is, as I have said before (and as your letter amply confirms) that you do understand but that, up to the present at least, you do not accept the logical consequences of that understanding.

In the paragraph you have labelled (1) you say that by assuming nothing one 'is postulating that nothing has at least one quality, namely assumability.' Quite so. Further, you go on: 'If nothing has no qualities (being absolutely nothing) then the statement I assume nothing contains an inner self-contradiction.' Quite so. I agree. Let me add some more examples of self-contradiction. 'If nothing has no qualities' to qualify it, then it is completely unqualified. But this utter lack of qualities is itself a qualification of nothing. It is, indeed, a distinguishing quality. Thus it contains another self-contradiction. We must therefore reject it as unthinkable, absurd and self-contradictory. Reject it? But how can we reject 'it' when there is no 'it' to reject? In order to be referred to as 'it', nothing must have an identity. But this is just what nothing lacks. Yet, in regarding nothing as having completely no identity, we are distinguishing nothing from all those things which have identity and so giving it an identity. Another self-contradiction.

Again, nothing can have no limits whatever; nothing must be entirely without limitation. But this quality of 'being entirely without limits' is itself a limitation. Self-contradiction again. Further, nothing is completely indefinable. But this is a species of definition. More self-contradiction.

And so we could go on: (a) Nothing is completely meaningless - but this is giving it a unique meaning (Self-contradiction) (b) Nothing is entirely unthinkable - but 'entirely unthinkable' is a thought in terms of which we have thought of nothing. (Self-contradiction. ) - (c) Nothing is wholly unknowable - but knowing this is knowing something about nothing (Self-contradiction) (d) Nothing is the comple e negation of everything - but if it is the complete negation of everything then it cannot be nothing (it must be the complete negation of itself.) Self-contradiction. Etc., etc., etc., ad infinitum. If I had unlimited time, energy, life, paper, ink, income, etc., etc., I could go on forever showing that whatever statement is made about nothing, it leads to self-contradiction. Nothing is inherently self-contradictory and self-negating. Moreover, any statement to this effect also leads to self-contradiction (otherwise it would not be a complete or infinite self-contradiction). A complete self-contradiction is a complete negation of negation. A complete selfcontradiction is a complete contradiction of contradiction.

So you see, Seton, your statement that the assumption of nothing contains a self-contradiction is not new to me. I should have been disconcerted were it simply not so. Indeed, I have claimed that nothing is purely self contradiction. But let us examine the consequences of your argument. You say in para. (1) 'If nothing has no qualities (being absolutely nothing) then the statement I assume nothing contains an inner self-contradiction, - for it proves that nothing cannot be assumed.' (Your emphasis). If this conclusion is valid then it certainly shows that you can know something about nothing, - namely that 'nothing is entirely unassumable,' and moreover that nothing has the quality of 'complete unassumability.' So that your statement that 'nothing cannot be assumed' contains the same self-contradiction as the one you pointed out. But despite this you reject the one statement ('I assume nothing' or 'nothing is [not] completely unassumable') without so much as a single blush. Do you not see that in the process of proving that 'nothing cannot be assumed' you prove the contrary? You must assume nothing in order to show it has the quality or being utterly unassumable. If you did not assume nothing, how did you know that it was that which could not be assumed? 'But', you might say, if it is an error to reject the statement "I assume nothing" and to accept "nothing cannot be assumed", surely it is an error to accept 'I assume nothing' and reject 'nothing cannot be assumed'? My answer would be: 'It certainly is. But I do not make that error for I have already said that by "assuming nothing" I mean that I make no fundamental assumption at all.' Thus 'assuming nothing as fundamental' and 'not assuming nothing as fundamental' are the same thing: i.e. they are the same assumption - viz. the assumption of fundamental non-assumption.

In para. (2) you say: 'If the statement: I assume nothing is regarded as primary... it is based upon a false assumption. For behind the "primary" assumption lies another which logically precedes it, namely: I assume that it is possible ... to make a primary assumption.'

Similar considerations apply to this paragraph as to the other: namely, that if you attempt to prove it you will succeed in proving the contrary. If nothing is assumed as primary, it just as much assumes the impossibility of primary assumption as the possibility of primary assumption. We are thus brought to the absurd position where the 'assumption of nothing' itself assumes (a) 'that it is possible to make a primary assumption' and (b) that: it is impossible to make a primary assumption.' These two contradictory assumptions can only be reconciled as the outcome of the self-contradiction of nothing. As a compound assumption they cancel one another out entirely and thus make nothing. They can only be brought together in the self-contradictory nature of nothing; i.e. as one of the infinite self-contradictory properties of nothing. Thus the logically prior assumption of nothing is nothing - and the and the logically prior assumption of that is nothing - and the logically prior assumption of that is nothing, and so on, ad infinitum.

You then go on to say that paragraphs 1 and 2 appear to make the assumption of nothing illegitimate 'unless that assumption is regarded as an ellipsis meaning: When a, b, c, ... n are severally presented to me for assumption as primary or absolute I do not assume them.' Now let us get: this 'ellipsis' business in its proper perspective. If I say 'No man can be God,' I mean by 'no man' not any man or, if you like, 'not Socrates, Plato, Julius Caesar, John Brown ... etc., etc.' If I say 'Nothing can be God' I mean by 'nothing' not any thing or, if you like, 'not a, b, c... n.' If 'nothing' is elliptical, then so is 'No man.' and if 'no man' is elliptical, then so is 'man', and if 'man' is elliptical, then so is 'thing'; and if 'thing' is elliptical, then so is 'a, b, c, ... n' - and so is 'not a, b, c ... n,' whatever a, b, c, etc., may be.

By insisting that 'nothing' has only an elliptical meaning you put yourself in the same position as the materialist who asserts that there is only an objective reality. In other words, the materialist, by qualifying 'reality with 'objective' distinguishes a species of reality (namely 'objective reality') from some other kind of reality which is not objective. If there is only one reality, then he should say just 'reality' and it can neither be 'objective' nor 'not-objective'. The same considerations apply to your characterisation of 'nothing' as having only an elliptical meaning. By saying that 'nothing' is an ellipsis, or,has elliptical meaning, you presuppose some ocher meaning of which 'nothing' is the ellipsis. 'But since this other meaning cannot be found or does not exist, then there is no point in stating that its meaning is wholly elliptical. IF nothing has wholly elliptical meaning, then, ipso facto, it has wholly non-elliptical meaning.

The trouble is, I think, that you are try ng to treat 'nothing' as an ordinary, relatively rational thing. You are trying to get sense out of it (or put sense into it) without accepting it first as essentially irrational and nonsensical. You are trying to deal with it as you deal with the things and matters of everyday life. With everyday things, the Law of Contradiction holds: A thing cannot both be and not be. You cannot make contradictory propositions about everyday matters, you cannot predicate contradictory properties, attributes or qualities of things, without one of the contradictories being false. With nothing it is different. The Law of Contradiction states in its obverse form: 'Nothing can both be and not be.' Thus the Law holds in relation to nothing only by negating itself. In short: Nothing is entirely governed by the Law of Contradiction and at the same time it is entirely not governed by the Law of Contradiction.

I think you are trying to escape its wholly irrational, self-contradictory nature by just not firstly accepting it as necessarily self-contradictory and irrational. The refusal to accept that nothing is completely irrational assumes that it should be other than completely irrational without, at the same time, being completely irrational.

Next, you say: 'If the proposition: There is an Absolute is presented to me, I do not accept it. If the proposition: There is not an Absolute, is presented, I still do not accept it. Both propositions go beyond my competence. If the proposition: There must either be or not be an Absolute, I cannot accept it, for the introduction of any notion of the Absolute leads to self-contradiction and only serves to demonstrate that I have made a false start.' But that is a useful demonstration; it is moreover a completely necessary demonstration. And if it is a completely necessary demonstration.

Let us examine this. One thing, at least, is clear: You do not accept 'the introduction of any notion of the Absolute' in any shape or form. From which it follows that the Absolute is that, any notion of which, you do not accept - i.e. the Absolute is that which, in any form, you utterly reject (since non-acceptance by definition is rejection). But your complete non-acceptance or rejection 'of any notion of the Absolute' is logically equivalent to the acceptance of its complete negation. In short, you must fully accept that you fully reject 'any notion of the Absolute.' If I offer you something and you do not accept it, then you must be aware that it is the offering which you are refusing to accept; you must accept that offering as the offering that you reject. If you refuse to accept it, if you reject it, then you must accept it AT LEAST as that which you are refusing. You therefore cannot be refusing to accept it in any shape or form whatever.

The reason that you give for your statement of complete non-acceptance is that it 'leads to self-contradiction and only serves to demonstrate that I have made a false start.' Now, I think I have said enough to show that I agree with 'complete non-acceptance' of the Absolute. Where we differ is in this: that complete non-acceptance leads just as much to self-contradiction (as I have just shown) as complete acceptance. If we find self-contradiction in the Absolute, let us not be afraid of it, let us accept it. Let us accept that it is self-contradictory and irrational. As you say, 'it serves to demonstrate that we have made a false start.' But that is a useful demonstration; it is moreover a completely necessary demonstration. And if it is a completely necessary demonstration, then it is not 'only' a false, start. In being a wholly false start (and it being completely necessary to demonstrate this) it becomes the only true start. In brief: until this demonstration has been made, one cannot make a true beginning. Thus it becomes the only true start, i.e. the only true, logical start.

Your remarks on the analogy of Nothing with Heisenberg's principle of Indeterminacy are most interesting, for I have long regarded the principle of Indetereminacy as a special case of the principle of Nothing. I think I have said enough to show that I agree with your statement that 'if we could experience that from which experience is born we should ipso facto distort that which we experience so that it would cease to be that which we experience.' This statement leads, as you say, to self-contradiction. But if it leads, as it must, to self-contradiction, then you cannot logically hold to it without also, at the same time, holding to its negation. That is the logical consequence of the statement. Both the statement and the logical consequence flow from the principle (or assumption) of Nothing and its completely illogical (and completely logical) properties.

Summing up, I think it would be generally true to say I can agree nth your positive statements even when they lead to self-contradiction (for I no longer 'take flight' from self-contradiction). Where we differ is that, whereas I press on with the self-contradiction and accept that too, and make sense of it deliberately and systematically, you decline to do this. Thus my disagreement with you is not so much with what you hold, but with what you reect or refuse to hold; namely, the other side of the self-contradiction which emerges when the contradiction is pressed to its logical conclusion. I hold that in order to be logically consistent one must 'hold to' (or accept) both sides of a wholly logical inconsistency. Otherwise it is not a wholly logical inconsistency. If one does not accept both sides, but attempts to accept the one and reject the other, then, although this leads to self-contradiction, it leads only to partial self-contradiction. It is not until the self-contradiction has been fully realised and taken to its logical conclusion, that we can use it most efficiently as a general principle for eliminating (or resolving) logical inconsistencies in our own thinking about other matters - matters of great practical importance.

When taken to its logical conclusion, the self-contradiction from from being partial and incomplete, becomes whole and complete. It thus negates and resolves itself. Until this full 'negation of negation' has been effected, we cannot use the self-contradiction most effectively, and efficiently. Until this happens we 'take flight' whenever self-contradiction appears; we 'retreat' from it whenever we see it emerging; we endeavour to 'avoid' it at all costs! Why? The reason is that, as Freud has pointed out, self-contradiction resides quite self-consistently in the unconscious, i.e. in the primal omnipotence. The repression of the assumption of omnipotence (i.e. 'limitation by nothing') which is a necessary conqition of use becoming sane, rational, civilised social beings, produces this dread of conscious self-contradiction. We dread it and fear its emergence into the full light of consciousness. We avoid it like the plague and will do, or think, anything to prevent the full realisation of self-contradiction from manifesting itself to us. Thus the barrier is largely an emotional one. We must avoid self-contradiction at all costs - and, of course, convince ourselves and others that this avoidance gely an emotional one. We must avoid self-contradiction at all costs - and, of course, convince ourselves and others that this avoidance is solely for rational reasons and not for irrational and emotional ones! We may even smile with tolerant amusement when this is first suggested to us. But the dread is there just the same.

We must avoid self-contradiction. We must avoid anything which leads to self-contradiction! But we must especially not be brought face to face with self-contradiction! Self-contradiction is something which sane people do not consider. Rational people have no truck with. it. And if an argument or set of ideas leads to self-contradiction - well, that is sufficient to condemn it out of hand! Forget it! Turn to something else which does not lead to self-contradiction. Start again. But whatever you do, don't pursue anything which leads to self-contradiction. Any path which leads to that is forbidden. For self-contradiction is banned, Verboten and out-of-bounds - it is taboo! One does not treat it seriously, but dismisses it with amused tolerance and discreetly passes on to something else. Need I say more?