Combining Texts

All the ideas for 'The Philosophy of Mathematics', 'Plural Quantification' and 'On Body and Force, Against the Cartesians'

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22 ideas

2. Reason / D. Definition / 12. Paraphrase
10633 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo]
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 / A. Overview of Logic / 4. Pure Logic
10638 A pure logic is wholly general, purely formal, and directly known [Linnebo]
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 / G. Quantification / 6. Plural Quantification
10636 Plural plurals are unnatural and need a first-level ontology [Linnebo]
10639 Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo]
10640 Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo]
10635 Second-order quantification and plural quantification are different [Linnebo]
10641 Traditionally we eliminate plurals by quantifying over sets [Linnebo]
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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
10643 We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
10637 Ordinary speakers posit objects without concern for ontology [Linnebo]
14. Science / D. Explanation / 2. Types of Explanation / h. Explanations by function
13195 To explain a house we must describe its use, as well as its parts [Leibniz]
15. Nature of Minds / C. Capacities of Minds / 10. Conatus/Striving
13193 Active force is not just potential for action, since it involves a real effort or striving [Leibniz]
19. Language / C. Assigning Meanings / 3. Predicates
10634 Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
13194 God's laws would be meaningless without internal powers for following them [Leibniz]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
13196 All qualities of bodies reduce to forces [Leibniz]
13192 Power is passive force, which is mass, and active force, which is entelechy or form [Leibniz]