Combining Philosophers

Ideas for Plato, Epicurus and B Hale / C Wright

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20 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
8726 Geometry can lead the mind upwards to truth and philosophy [Plato]
9867 It is absurd to define a circle, but not be able to recognise a real one [Plato]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
13155 If you add one to one, which one becomes two, or do they both become two? [Plato]
9865 Daily arithmetic counts unequal things, but pure arithmetic equalises them [Plato]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
10624 The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
8784 Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
8787 The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10629 If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
10628 The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
9863 We aim for elevated discussion of pure numbers, not attaching them to physical objects [Plato]
9864 In pure numbers, all ones are equal, with no internal parts [Plato]
8727 Geometry is not an activity, but the study of unchanging knowledge [Plato]
10216 We master arithmetic by knowing all the numbers in our soul [Plato]
16150 One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
9861 The same thing is both one and an unlimited number at the same time [Plato]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8788 Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
10622 The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
8783 Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
12225 Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
12224 Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright]