Outlines of a Formalist Philosophy of Mathematics

a₁ abstract acceptability autonymous axiom schemes axı axı axı beweisbar binary operation Carnap Chapter character Church-Rosser Theorem classical analysis consider considerations consistency proof constructive criterion defined definition of mathematical derived discussion elementary algebra elementary propositions elementary theorems essentially Example 9 expressions fact finite formal system formalist definition Gödel green cheese Heyting Hilbert idealistic intuitionism intuitionist intuitive evidence involved let us call linguistic mathe mathematical induction mathematical truth mathematicians matics meaning metaphysical metaproposition metatheoretic mode of speech Moreover morphological notions number of arguments O-expressions O-language O-sentence O-symbols object language occurs free ordinary P₁ p₁₁ paper parentheses philosophical PHILOSOPHY OF MATHEMATICS point of view polynomials postulates primitive frame priori quasi-quotes recursive definitions reference regard relation replace representation rules of procedure sense sentence specifications subject matter Subst symbols syntactical system of logic t₂ theory tokens unary predicate variables word