The Philosopher's Zone (pardon them their name) has recently had a discussion of "the liar's paradox and other philosophical absurdities". (In brief: "I am lying", says a liar, which means that he's not! Etc.)
It occurs to me that the point to be made about these things is that in order to see the liar's paradox as paradoxical, one has to be a logician; the error lies within logic, so to speak -- because any average-minded adult can see instantly that the liar's paradox is nonsense; what's more: that it is -- irrelevant. Ordinary men and women shrug at the liar's paradox. They know it's garbage.
Now, noble souls like Russell have justly spent their lifetimes trying to fix the liar's paradox: for, if we are to trust logic (and math) in those outlying areas of reality which they seem to penetrate while our minds don't -- things like the shape of the universe at time one times ten to minus ten billionth of a second following the big bang, spacial distortions at the edge of the anomaly, behavior of things in seven-dimensional space, strange matter, why, indeed, things far closer to earth, such as fat tail risk of credit derivatives) - then the instruments of logic and math better be rid of anomalies themselves. All power to them who set out to fix them.
But here is an area of research that is just as intriguing; why, it may have within it the seed to the solution: nearly everyone who hears the liar's paradox (unless they are mentally retarded or a professionally trained logician) knows instantly that the thing is hogwash. I mean, knows to shrug and ignore it. Knows it is an anomaly. Knows something's wrong and also knows that -- well, it does not matter. Knows to sidestep it.
So, here is my question: how does everyone know it? There must be an algorithm; a mental procedure; some sort of a trick, a matrix perhaps, within our brain that instantly reveals the nonsensical nature of the liar's paradox. In some sense, therefore -- in this sense -- we are more intelligent than our logic -- and our logicians. How do we manage that?
If we can figure this one out -- the liar's paradox will have been solved and the likes of Russell will be able to finally rest in their graves.
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4 comments:
Sir G, I think you are a bit unfair to the liar's paradox! It has been solved, but the question it raised cut to the core of the Leibnizian idea of "Calculuare!", that we could devise an algorithm that could solve all our arguments.
The reality of subject and object languages that the liar's paradox points to served as a necessary reminder when thinking one could create such an algorithm, which we now now is impossible!
But you are right, it is a game for the mind, not important, but then, how is that different from all the beautiful stuff you show us here?
Sir A
your just upbraiding is probably what I deserve for writing in haste: i did not mean to diss the liar's paradox: there are parts of reality in which we are utterly lost unless we can rely on logic; so fixing problems with logic is essential! rather, what i wanted to suggest is that the solution to the paradox may not lie in complex manoevres like object languages and so forth but in trying to figure out how it comes that most of us shrug when we hear it -- i.e. how it comes that we automatically know there is something wrong and -- well -- take it in our stride; i honestly think that by shrugging our shoulders thus we do perform some sort of logical calculation, and it probably does not involve anything as massive and complicated as object/metalanguages; think of this intuition as -- well, not "ordinary language philosophy" but -- shall we dare to coin a term? - "ordinary life logic", I suppose; anyway, just wanted to share with you a hunch on where the solution to the problem may lie; if, however, as you say, the paradox has really been solved, then the hunch is as worthless as the rest of this blog :)
glad it entertains you for all its worthlessness!
Sir G, I think you're right about the "shrugging as calculation" bit. What I think is really interesting about this is the relationship between these calculations and the real world.
By this I mean things like decision making. There's actually quite a bit of evidence to show that people aren't great at making certain kinds of decisions, but that they're consistent about their badness.
We see this kind of stuff in the papers all the time, but I think one of the values of stuff like logic is that it lets us close the gap between our evolutionary decision making processes and what might actually be best for us.
As for the worthlessness of this blog, I certainly didn't say that, I find it very valuable!
I've never heard of this paradox before. I certainly wouldn't know how to quantify it. Trying to prove the truth of a statement whose essence includes a falsehood is futile. What makes us dismiss it so easily at first glance is our humanity - our understanding that there exists no perfect human, and no perfect (or rather, consistent) liar. "Liar" can be used as a description of a human being, but never as a definition. A person would see the paradox and know that it exists in a realm apart from reality. As logic excludes emotion, no human interpretation of information is logical entirely, and no explanation of the world can be scientific entirely. It is our humanity that tells us this. There is no explaining the paradox within logic.
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