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?
