From Mathematics to Philosophy by Hao Wang

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By Hao Wang

First released in 1974. regardless of the tendency of up to date analytic philosophy to place common sense and arithmetic at a important place, the writer argues it didn't enjoy or account for his or her wealthy content material. via discussions of such mathematical innovations as quantity, the continuum, set, evidence and mechanical approach, the writer presents an advent to the philosophy of arithmetic and an inner feedback of the then present educational philosophy. the fabric offered is additionally an indication of a brand new, extra normal approach to process referred to as monstrous factualism which the writer asserts makes it possible for the improvement of a extra accomplished philosophical place via no longer trivialising or distorting mammoth evidence of human wisdom.

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It is not denied that alternative extensions of the current axioms of set theory may be experimented with, and in fact one does study mutually incompatible axioms such as the axiom of choice and the axiom of determinateness, or the existence of measur­ able cardinals and the axiom of constructibility. What the objectivists would like to say is that we have in our intention an equally fixed model of sets as with natural numbers. Only we do not perceive it as clearly. Consequently, when the dust settles down, one expects to recognize only one of the incompatible alternatives as conforming to the intended concept of set.

What is meant is local clarity comparable to the listing of historical dates rather than global clarity as one would speak of a clear overview of history. Many of us have been brought up to think of such clarity as a minor virtue which becomes a primary concern only after we have given up looking for the important, either because we are in despair or because we have succeeded and are currently engaged in a careful exposition o f what we have. To elevate local clarity to the status o f the dominating goal of philosophy can appeal only to those who have been successfully indoctrinated.

Some are pleased that philosophy is now tied up to a science, viz. linguistics, and sometimes refute competing philosophical views by an appeal to the relevance to linguistics. Others are hard at work arguing that linguistic philosophy is like a science but not a science and, therefore, different from linguistics. For a number o f people, the simultaneous interest in logic and language leads to a gratifying field o f operation on account of the many points of contact between the foundations of linguistics and the philosophy of logic.

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