Combining Philosophers

Ideas for Anaxarchus, Tyler Burge and Frank P. Ramsey

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6 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

16901

The equivalent algebra model of geometry loses some essential spatial meaning [Burge]

9159	You can't simply convert geometry into algebra, as some spatial content is lost [Burge]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

16902

Peano arithmetic requires grasping 0 as a primitive number [Burge]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory

6409	The 'simple theory of types' distinguishes levels among properties [Ramsey, by Grayling]

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

13426

Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey]

6. Mathematics / C. Sources of Mathematics / 7. Formalism

13425

Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey]