Combining Texts

All the ideas for 'Exigency to Exist in Essences', 'Geometrical Method and Metaphysics' and 'Review of Chihara 'Struct. Accnt of Maths''

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10 ideas

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
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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
19400 Possibles demand existence, so as many of them as possible must actually exist [Leibniz]
19401 God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
19402 The actual universe is the richest composite of what is possible [Leibniz]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
19398 Minds are best explained by their ends, and bodies by efficient causes [Leibniz]