Combining Texts

All the ideas for 'The Philosophy of Mathematics', 'Dispositions and Powers' and 'Belief Truth and Knowledge'

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24 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9193 ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
9194 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
9195 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
9186 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
9187 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
9191 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
9192 The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
8. Modes of Existence / B. Properties / 1. Nature of Properties
23708 Humeans see properties as having no more essential features and relations than their distinctness [Friend/Kimpton-Nye, by PG]
23709 Dispositions are what individuate properties, and they constitute their essence [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
23707 Powers are properties which necessitate dispositions [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
23714 Dispositional essentialism (unlike the grounding view) says only fundamental properties are powers [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
23711 A power is a property which consists entirely of dispositions [Friend/Kimpton-Nye]
23712 Powers are qualitative properties which fully ground dispositions [Friend/Kimpton-Nye]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / a. Dispositions
23698 Dispositions have directed behaviour which occurs if triggered [Friend/Kimpton-Nye]
23699 'Masked' dispositions fail to react because something intervenes [Friend/Kimpton-Nye]
23700 A disposition is 'altered' when the stimulus reverses the disposition [Friend/Kimpton-Nye]
23701 A disposition is 'mimicked' if a different cause produces that effect from that stimulus [Friend/Kimpton-Nye]
23702 A 'trick' can look like a stimulus for a disposition which will happen without it [Friend/Kimpton-Nye]
23703 Some dispositions manifest themselves without a stimulus [Friend/Kimpton-Nye]
23704 We could analyse dispositions as 'possibilities', with no mention of a stimulus [Friend/Kimpton-Nye]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
23710 Dispositionalism says modality is in the powers of this world, not outsourced to possible worlds [Friend/Kimpton-Nye]
12. Knowledge Sources / B. Perception / 7. Causal Perception
3900 Maybe experience is not essential to perception, but only to the causing of beliefs [Armstrong, by Scruton]
13. Knowledge Criteria / C. External Justification / 1. External Justification
4253 Externalism says knowledge involves a natural relation between the belief state and what makes it true [Armstrong]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
23706 Hume's Dictum says no connections are necessary - so mass and spacetime warping could separate [Friend/Kimpton-Nye]