Kripkenstein Attacks!

The last post was referring to Saul Kripke's book, "Wittgenstein: On Rules and Private Language". The first half of this book is Kirpke's attempt to reconstruct Wittgenstein's "argument" against the traditional view that meaning comes from a referent, either mental or physical, and that one can show that one understands something, say, for example, the concept of addition, through the appeal to or interpretation of or application of some kind of general or universal 'rule'. The question is how can I justify my belief that I am 'using the same rule of addition' when I add the two numbers before me right now that I used yesterday when I was adding two different numbers. If I have never before added numbers larger than 57, but I have successfully added smaller numbers in the past, how can I tell that I am applying the same rule? What if 'addition' meant that for every number smaller than 57, proceed in such-and-such a way, but if you ever try to add numbers larger than 57, remember that the answer is always going to be 5? This sounds crazy, I know, and I am probably retelling it wrong, but I think that the important point is that we cannot point to any facts about our previous behavior or our previous 'mental states' to prove that we know when we are 'acting in accord with such-and-such rule'. We can't appeal to our previous behavior because part of the idea of a rule is that it can apply to an infinite number of possibilities, whereas we have only encountered a finite number, and we cannot appeal to the 'mental picture' of the rule (in this case, the rule of addition) because then we would need some other 'mental rule-concept' to appeal in order to be sure that we were interpreting the previous rule-concept correctly. [ex: "How do you know you're reading this map right?" Because I can use this legend that I have here. "But how do you know that you're reading that legend right?"] Kripke says, "Each new application we make is a leap in the dark; any present intention could be interpreted so as to accord with anything we may choose to do." Kripke's answer to this 'skeptical paradox' is through appealing to the fact that we are always engaged in a community of speakers who teach us these concepts and correct us when we use them incorrectly, which is true and good I think, but also I think that there is something to the fact that there is not one way to add, that we use this concept in many different ways in many different parts of our lives, and that mathematics as a whole ought to be viewed not as a set of universal truisms but as an evolving network of tools that we have invented and that we use on a daily basis to help build houses and roads and cakes and to explain the behavior of atomic particles and the populations of fruitflies. But I'm not sure, lots of people tell me that I'm wrong here.

On a personal note: I had a meeting with Prof. James Conant yesterday to talk about my Kierkegaard and Wittgenstein paper. The entire 50 minutes were spent having him list essays and books that I needed to read if I wanted to this paper right. So at the end of the day, there is always something I should be reading.