Combining Texts

Ideas for 'Thinking About Mathematics', 'On Husserl' and 'The Nature of Mathematical Knowledge'

expand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

21 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 / d. Logicism critique
12423 Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher]
8744 Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
8749 Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
8750 Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
8752 Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
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]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8753 Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [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]
8731 Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8730 'Impredicative' definitions refer to the thing being described [Shapiro]