By Professor Hao Wang (auth.)
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Extra resources for Computation, Logic, Philosophy: A Collection of Essays
Since it is usually impossible to explain clearly and exactly even the technical usages, a formal or 10 Computation, Logic, Philosophy exact theory can almost always be defended against charges that it does not conform to fact. As long as there is a sufficiently complicated system and a fairly big and energetic group of people who, for one reason or another, en joy elaborating the system, we have a powerful school oflearning, be it the theory of meaning, the sociology of knowledge, or the logic of induction.
6 Effective methods Kleene gives a more or less standard explanation of the notion of constructive proofs in the following words: "Therefore an intuitionistic proof of the proposition there exists an n such that P(n) must be constructive in the following (strict) sense. " (Kleene 1952, p. ) Here, of course, the problem is shifted to knowing exactly what kind of method is acceptable. With regard to the case which concerns us, we do have a method of finding the corresponding equation for given n.
There are different kinds of answers to questions of this sort. Gauss and Wessel gave interesting and definite answers to the question: What are complex numbers? These answers are still preserved in textbooks, while speculative discourses by their contemporaries on the same topic have been quickly forgotten. The answers by Gauss and Wessel are usually not considered philosophy. What Kant had to say on time is often taken as philosophy, and probably interesting philosophy. " is perhaps also philosophy.