Dr. Kripkenstein: a horror story (Part 1)
And apart of their author being a sort of hybrid monster, the arguments contained in the book mark it as a sort of philosopher's nightmare. They are skeptical arguments, that aim at showing that there is no fact of the matter corresponding to a person "meaning" something when using an expression.
The example Dr. K. uses is addition. In my life so far I have only performed, considered, or thought of, a finite number of sums. Suppose none of them has been greater than 1000 (there must be one number greater than all of them; assume for example it is 1000). Define a function "quus", represented by ++, in the following way: x ++ y is equal to x + y for all x and y smaller or equal than 1000, and equal to 5 whenever x or y is greater than 1000. If now somebody asked me "How much is 1007 plus 24?" I would surely answer 1031. But, Dr. K. asks, what justifies me in answering 1031 instead of 5? How do I know that by the word "plus" as I used it in the past I meant the function plus, and not the function quus?
This is not an ordinary skeptical question of the style "how do you know your memory is reliable?" It is accepted that I remember perfectly well all the past sums I have done, and all the thoughts I had while doing them and while learning about addition in general. The question is, if I never had any concrete thought of a sum greater than 1000 before, how do I know the function I was using and calling "addition" was the plus function (the "real" addition) and not the quus function? Of course that, as a matter of brute fact, I am disposed to answer 1031 instead of 5, but what is my justification for this?
Many of you are surely tempted to say something like: "What I mean by plus is not restricted to a list of particular answers. It is a general rule, that tells me when asked for a sum, to do it applying an algorithm learnt in school (to add 1007 + 24 I have to add 7 + 4, carry the 1, and so on). When meeting a new case I apply this algorithm and get the answer 1031, not 5". But this won't do. It is true, of course -just plain common sense. But it doesn't really answer Dr. K.'s question. Because the algorithm itself I have applied only in a finite number of cases so far, all smaller than 1000. So how do I know how to apply it to greater cases? How do I know that the words in which I express the algorithm don't themselves have meanings like that of "quus", that change when applied to numbers greater than 1000?
The real question is how the mind, being finite, can grasp unambiguously a rule that applies to an infinity of cases. Dr. K. says "It can't. So there is no real fact corresponding to whether we mean plus or quus. We just follow a rule blindly, giving always the plus answer, but there is nothing that justifies us in doing so." And so we are left in a sort of nightmarish uncertainity, all our words and thought suddenly devoid of meaning, and we here at distance the satanic laughter of Dr. K…
Enough of cheap horror movie scenery. Is the argument sound? Well, of course it has not been widely accepted as so. The argument can be read as a challenge: Construct, if you can, an account of meaning and rule-following that does not fall to the skeptical hypothesis. Kripke himself makes some suggestions, only to conclude none of them work; but other philosophers (including this humble amateur philosopher) have not necessarily agreed with him. In following posts I shall discuss some solutions, the objections to them, and try to sketch my own views.
Meanwhile, if you want to read further on Dr. K., try this comprehensive webpage.