Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'The Philosophy of Mathematics' and 'The Epistemology of Essence (draft)'

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12 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / a. Conceivable as possible
If conceivability is a priori coherence, that implies possibility [Tahko]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
Essences are used to explain natural kinds, modality, and causal powers [Tahko]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Scientific essentialists tend to characterise essence in terms of modality (not vice versa) [Tahko]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / b. Scientific necessity
If essence is modal and laws are necessary, essentialist knowledge is found by scientists [Tahko]