Combining Texts

Ideas for 'Thinking About Mathematics', 'On Formally Undecidable Propositions' and 'Laches'

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

display all the ideas for this combination of texts

---

8 ideas

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

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 / 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

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

8747	Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro]

8730	'Impredicative' definitions refer to the thing being described [Shapiro]