Combining Philosophers

Ideas for Lynch,MP/Glasgow,JM, Stewart Shapiro and Jean-Paul Sartre

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18 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10200 We distinguish realism 'in ontology' (for objects), and 'in truth-value' (for being either true or false) [Shapiro]
10210 If mathematical objects are accepted, then a number of standard principles will follow [Shapiro]
10215 Platonists claim we can state the essence of a number without reference to the others [Shapiro]
10233 Platonism must accept that the Peano Axioms could all be false [Shapiro]
6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
10244 Intuition is an outright hindrance to five-dimensional geometry [Shapiro]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10280 A stone is a position in some pattern, and can be viewed as an object, or as a location [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
13664 Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
13625 Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro]
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
10254 Can the ideal constructor also destroy objects? [Shapiro]
10255 Presumably nothing can block a possible dynamic operation? [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
13663 Some reject formal properties if they are not defined, or defined impredicatively [Shapiro]
8730 'Impredicative' definitions refer to the thing being described [Shapiro]