Monday, 26 May 2014

Liar Paradox

In the Epimenides Paradox post,  I looked at the easily refuted "This statement is false," where obviously enough it is seen that there is no statement, and so the line is intellectual gibberish. If the line is changed to "This sentence is false," the same refutation basically applies as there is no claim here which justifies this sentence being described as true or false, and so it is a false construct and despite appearances not a valid sentence.

Not that I remember but when I did a number of posts on alleged paradoxes way back, maybe I hadn't initially even formulated to myself the inner motivation behind the refutations, and on a surface level was perhaps simply struck by the faulty logic of the individual cases, but after a while it becoming clear that a general truth was involved which was that language used properly cannot result in meaningless conclusions, while the paradox acolytes like Borges were claiming otherwise - that language and even by extension life were inconsistent, faulty systems. But all that has happened with the 'paradoxes' is, without noticing it, people have intellectually gone wrong.

So now onto the Liar Paradox, which is closely related it seems to Epimenides paradox but far more clever or tricky to unravel. To add, I'm not really going to look into the history of these 'paradoxes' and whether the Epimenides Paradox truly is "This statement is false" isn't the point or just considered an equivalent of it. It is the inner logic of the given sentence that I am dealing with, and even if just for the sake of demarcation we'll call that the Epimenides and the following the Liar.

So lifting from elsewhere:

The Liar Paradox is among the simplest of paradoxes. It can be traced back at least as far as Eubulides of Miletus, a fourth-century B.C. Greek philosopher.
Eubulides’ version of the paradox is this: A man says that he is lying; is what he says true or false?
However we answer this question, difficulties arise.
If we suggest that what the man says is true, then we end in contradiction: if the man’s claim that he is lying is true, then he is lying, in which case what he says is false.
If we suggest that what the man says is false, then we are no better off: if the man’s claim that he is lying is false, then he is not lying, in which case what he says is true.

So, the relevant line here is "I am lying." Again unfortunately like "This statement is false," this is a meaningless construct. About what is he lying? There is no statement which as above can be true or false. So the intended gist of this must be put a little differently to make at least more apparent sense; and so a better variation is the line "All Cretans are liars," said by, it is said, a Cretan. Here we do have an apparent statement. Also it could equally be put, "Everything I say is a lie." Again, rather than just saying "I am lying", this seems at least to be a definite statement about an aspect of reality - that everything I say is a lie. The resulting train of thought then goes or is alleged to go that if everything I say is a lie then this is itself a lie, and everything I say is hence not a lie. Or if the statement is true and so is itself a lie, this this implies everything I say is not false, which contradicts itself. And the wider philosophical implication being that language is capable of being used correctly and yet leading to untenable conclusions; this showing that language is ultimately a flawed system, and so Truth is an illusion, reality is intellectually corrupt, etc.

So with truth and coherence at stake, onwards. It turns out however that this has already been covered in the previous post, with the point that logic follows from true statements, not false ones. An intellectual process is real when every step is true, every line is in accordance with the inner logic of language and accurate representation of external reality. A mathematical or linguistic line, theorem, etc is real on such a basis, and if error occurs the overall construct which follows is unreal, does not in truth exist.  And so to begin with 'Everything I say is a lie', means that the logical process has been immediately flouted at source, and so there is no further justifiable process. It is a degradation of the logical process to go any further, since the line is not real, not in accordance with the truth to which logic must conform. Logic applies to the logical implications of true statements, not false ones.  The line explicitly describes itself an untrue and so unreal, and so reality cannot proceed from unreality.  It is not real but for someone who wrongly follows a supposed train of logic along this illogical pathway, an intellectual hallucination or something which appears to be real ensues, such as a supposed paradox resulting from imagining the false conclusion has been arrived at legitimately. The false conclusion though should be the giveaway that it is the intellectual process that has been degraded or simply gone wrong.


To some degree I imagine the above denying of the validity of the process that supposedly leads to the paradox could be felt to be a bit unfair, and I will now look at the matter from a slightly different angle.

Is it intellectually possible - i.e. can it make sense - for me to say that everything I say is a lie? - which is the essence of the Liar Paradox.  The whole supposed point of a paradox being of such import is that it is allegedly logically coherent and yet leads to illogical conclusions. And we should try being as existential as we can and first realise the 'logical deductions' which follows the line "Everything I say is a lie" are as yet nowhere to be seen; it is that line itself that we should be looking directly at.

Quoting from an earlier piece - "To say anything in a true intellectual sense is to involve oneself necessarily in an acceptance that the language one is using is real and imbued with meaning; that the words one is using- if used correctly, i.e. meaningfully- are meaningful." This is the necessary ground and of course is the ground from which logic proceeds. So to say that everything I say is a lie is immediately a total violation of the ground upon which argument and logic sits. And so it is self-contradictory as a piece of logic. Truth doesn't dwell within falseness or lies, and so, as more or less said earlier, it makes no sense for such a line to be considered to dwell within the world of logic or logical statements. So there is no great truth revealed by this 'paradox' as the line can't be said to exist intellectually.

That it is worthy of any intellectual interest is that it is a truth claim, but here it is clearly self-contradictory for a truth-claim to deny itself as precisely that, to claim itself to be a lie, and so not to fall within the sphere of logic. Even following the supposed logic though doesn't lead to the paradox but simply to the falseness of the line's claim. So, having laboured the point, going back to looking directly at the statement, "Everything I say is a lie," and seeing if it can be legitimately said. The idea of the paradox is that the relevant line can be said but the conclusion of this valid line contradicts truth, thus revealing language's flawed nature. Generally the supposed sophistication of these paradoxes comes out as quite a childish and stupid misunderstanding however - such as with the inane "This statement is false", and its deflating riposte"What statement?"

                                              Everything I say is false.

 Is it possible for everything I say to be without exception false, that is in practical terms, to be with every utterance relentlessly lying? And as this extends philosophically, can Falseness be a consistent cohesive system? And so, the reach of all this has extended with more at stake than what one might have thought.

So the key now is whether it is possible to relentlessly lie. As already shown, to use language is to accept its truth and meaningfulness, and the very fact that we are discussing whether this Liar Paradox is a viable or true language statement shows how impossible it is to escape this. But now we are seeing whether Falseness can exist relativistically, to dwell cohesively at some more minor level within the necessarily admitted greater truth of Truth. Someone can of course within a trivial range lie with everything he says, from what he had for breakfast to who won a football match, what age he is, etc. Such a life of relentless lying could happen. But that's not the issue. Is this unbroken lying possible as an entire system when pushed to its intellectual limits? In a theological sense, could a Satan console himself with the truth of his defiance of Truth, even while reluctantly accepting God's existence and primacy?

Well and perhaps surprisingly, the line itself "Everything I say is false" reveals the impossibility of the coherence of this edifice of falseness. Lying reaches its own limits, trips itself up, as if I am lying with this very statement, then this implies that not everything I say can be false. So falseness as a system collapses in on itself, and has no consolation.

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