Combining Philosophers

Ideas for Eubulides, Aristotle and John P. Burgess

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11 ideas

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
17851 Number is plurality measured by unity [Aristotle]
17843 The idea of 'one' is the foundation of number [Aristotle]
17850 Each many is just ones, and is measured by the one [Aristotle]
11041 Some quantities are discrete, like number, and others continuous, like lines, time and space [Aristotle]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10185 Set theory is the standard background for modern mathematics [Burgess]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
9793 Mathematics studies abstracted relations, commensurability and proportion [Aristotle]
10184 Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess]
10189 There is no one relation for the real number 2, as relations differ in different models [Burgess]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10186 If set theory is used to define 'structure', we can't define set theory structurally [Burgess]
10187 Abstract algebra concerns relations between models, not common features of all the models [Burgess]
10188 How can mathematical relations be either internal, or external, or intrinsic? [Burgess]