Combining Texts

Ideas for 'Tropes', 'Philosophy of Mathematics' and 'On Hippocrates and Plato'

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8 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 / 10. Constructivism / a. Constructivism

10254

Can the ideal constructor also destroy objects? [Shapiro]

10255

Presumably nothing can block a possible dynamic operation? [Shapiro]