Combining Texts

Ideas for 'fragments/reports', 'The Nature of Mathematical Knowledge' and 'Constructibility and Mathematical Existence'

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17 ideas

6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
12393 Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher]
18061 Mathematical intuition is not the type platonism needs [Kitcher]
12420 If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
12387 Mathematical knowledge arises from basic perception [Kitcher]
12412 My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher]
18065 We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher]
18077 The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10265 Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
8759 We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12423 Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
18069 Arithmetic is an idealizing theory [Kitcher]
18068 Arithmetic is made true by the world, but is also made true by our constructions [Kitcher]
18070 We develop a language for correlations, and use it to perform higher level operations [Kitcher]
18072 Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher]
10264 Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
18063 Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher]
18064 If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher]