Kripke's exposition of the Wittgensteinian "paradox" (in his Wittgenstein: on Rules and Private Language) is beginning to bug me. It reminds me of the primordial fear that seems to be built into humans: what if I am crazy and I don't know it? In fact, it is the same problem for crazy person to know he is crazy as it is for a sane person to know he is sane. It seems that the only difference is that the sane person doesn't get all psychotic over the "paradox." Like Zeno, W. has important questions to ask, but the answers are not necessary to life as we know it. The answers are, instead, more like Zen Koans. The Zen master is one who can embrace them without losing his/her mind and the ability to function in the mundane world.
To me, some argument toward utility rises here. A rule is far more important at the scale we need it than at some artificially small scale that no longer makes sense. By this I mean the reductionist tendency to say we can't know something until we know all the sub-parts of the thing, and then all the sub-parts of the sub-parts. We need to apparently define all the defining words and their sub-defining words. To me this gets you to the level of nonsense-- we make up stuff about stuff we don't know anything about just because we want a starting point irreducibly small. Why is that, I wonder? Occam's Razor perhaps.
But let's look at the simple example W. and Kripke use from mathematics: addition. How do we know that 2+2 is always 4 and not 3 or 7, or 5 on Fridays? We are told that "thinking we know" is not enough if we can provide no verifiable proof that anything called addition exists in our mind. Enough for whom-- skeptics who cannot prove their own sanity, or mathematicians who collectively share this rule, and believe that addition is a well-defined and public rule . To the skeptical mind even a mathematical proof would be nothing more than a pageantry based on unprovable sub-parts that are possibly all misunderstood.
We are in the realm of systems of behavior, of the procedure, the recipe. How do ingredients become a meal through the alchemy of a recipe? Where does the proof of the existence of the thing "recipe" exist in our mind? There is a "do this-- get something hopefully good" circuit wired into us that is far more pro-active than any stimulus-response model can account for. We have addition because it helps us get other things that we deem good. Our operational definitions are not just made of symbols, but also of actions that take place in time. Looking at a process whole makes more sense to me than worrying too much over its base ingredients. When you get down into the sub-basements of logic where meaning begins to vanish and paradoxes flourish like hungry rats, well then a comprehensible truth (a usable truth) is likely to reside a level or two higher up.
Can an atom in our brain be said to be thinking? Do we need to know?
To me, some argument toward utility rises here. A rule is far more important at the scale we need it than at some artificially small scale that no longer makes sense. By this I mean the reductionist tendency to say we can't know something until we know all the sub-parts of the thing, and then all the sub-parts of the sub-parts. We need to apparently define all the defining words and their sub-defining words. To me this gets you to the level of nonsense-- we make up stuff about stuff we don't know anything about just because we want a starting point irreducibly small. Why is that, I wonder? Occam's Razor perhaps.
But let's look at the simple example W. and Kripke use from mathematics: addition. How do we know that 2+2 is always 4 and not 3 or 7, or 5 on Fridays? We are told that "thinking we know" is not enough if we can provide no verifiable proof that anything called addition exists in our mind. Enough for whom-- skeptics who cannot prove their own sanity, or mathematicians who collectively share this rule, and believe that addition is a well-defined and public rule . To the skeptical mind even a mathematical proof would be nothing more than a pageantry based on unprovable sub-parts that are possibly all misunderstood.
We are in the realm of systems of behavior, of the procedure, the recipe. How do ingredients become a meal through the alchemy of a recipe? Where does the proof of the existence of the thing "recipe" exist in our mind? There is a "do this-- get something hopefully good" circuit wired into us that is far more pro-active than any stimulus-response model can account for. We have addition because it helps us get other things that we deem good. Our operational definitions are not just made of symbols, but also of actions that take place in time. Looking at a process whole makes more sense to me than worrying too much over its base ingredients. When you get down into the sub-basements of logic where meaning begins to vanish and paradoxes flourish like hungry rats, well then a comprehensible truth (a usable truth) is likely to reside a level or two higher up.
Can an atom in our brain be said to be thinking? Do we need to know?
Comments
I think it quite unfortunate that W. should have resorted to a mathematical example, because that is a realm that is not governed by inferred rules but by definitions. That the paradox must still apply at another level, doesn't help make things clearer at all.
I think that you are completely on the right track with the notion that there is mostly a usable truth to be found. If one can manage to have a steak served prepared precisely to one's heart's desire by simply ordering it, then all there's left to say is paradox schmaradox and prosit.
As I said initially, I still have to do a lot of reading on linguistics and logic, but so far I miss a clear separation of meaning and expression; the unrestrained realization that a word (sentence, treaty, etc.) is but an empty, arbitrary, (as far as meaning is concerned, in spite of the wonderful art of etymology), piece of code.
No expression, I think, carries any meaning at all, unless there is a contract of interpretation that has been established a priori. And that is the ultimate problem, isn't it? How can a contract be established between two would be exchangers of information if it has to be in place before any communication can occur? How can we know whether an event is just a chance occurrence or a signal meant to inform us? My guess is that the contract gets established at a higher or lower level than that of language, which implies that language is not a closed system (why aren't we surprised) and therefore neither consistent nor complete in a logical sense. I think life would be very boring without paradoxes, but one could profit from learning when to wreck one's brain against them, and when to look for answers through a different discipline.
In reply to your two final questions: no, and : for some strange reason we seem to want to.
Edited at 2009-03-04 08:14 am (UTC)
I do not trust Kripke's analysis of W. in general, but it gives me something to react to the same way reading a horoscope can actually lead to finding real truths about oneself by arguing out the strengths or weaknesses of its propositions.
Reading Kant has become far more fascinating to me than I once imagined possible, and I admire the way he constructs neat and orderly houses of logic that he then blows up with bombs like the army testing the effects of nuclear blasts. Or perhaps this is over-stated. I do find, however, at the end of the Critique of Pure Reason, that Kant adopts a "nice try, but no cigar" attitude about his work, setting the stage for act II, the arrival of W. the inquisitor, who asks merely: "if truth were a cigar, what would it be like to smoke one?"
While there are no stupid questions, there may indeed be stupid answers. Despite the wisdom of GIGO, there is still always the possibility of Genius in/Garbage Out. Mia Culpa.
It is very Kantian to try to distinguish between mathematical a priori reasoning and reasoning from the empirical side, but like W. he notes that all thinking of any sort is also a process of pure intuition-- that is, all our logical processes have the same root, being moderated by thought, existing only through our thought, so that perhaps they cannot be said to exist externally, or separately at all.
I am also reading Bergson's The Creative Mind again because I want to factor some metaphysics of time into this broth. I think W. will make a few observations on time, but not enough to satisfy me.
Edited at 2009-03-04 02:30 pm (UTC)