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All the ideas for 'Philosophy of Mathematics', 'A World of Dispositions' and 'Modality'

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25 ideas

2. Reason / A. Nature of Reason / 1. On Reason
5750 Consistency is modal, saying propositions are consistent if they could be true together [Melia]
2. Reason / D. Definition / 8. Impredicative Definition
10882 Predicative definitions only refer to entities outside the defined collection [Horsten]
4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC
5737 Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets [Melia]
4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
5744 First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) [Melia]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
5740 Second-order logic needs second-order variables and quantification into predicate position [Melia]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
5741 If every model that makes premises true also makes conclusion true, the argument is valid [Melia]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10884 A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10885 Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10881 The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
7. Existence / D. Theories of Reality / 8. Facts / a. Facts
5736 No sort of plain language or levels of logic can express modal facts properly [Melia]
5735 Maybe names and predicates can capture any fact [Melia]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / e. Dispositions as potential
15797 All structures are dispositional, objects are dispositions sets, and events manifest dispositions [Fetzer]
9. Objects / C. Structure of Objects / 1. Structure of an Object
15800 All events and objects are dispositional, and hence all structural properties are dispositional [Fetzer]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
5746 The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities [Melia]
10. Modality / A. Necessity / 2. Nature of Necessity
5738 We may be sure that P is necessary, but is it necessarily necessary? [Melia]
10. Modality / A. Necessity / 4. De re / De dicto modality
5732 'De re' modality is about things themselves, 'de dicto' modality is about propositions [Melia]
10. Modality / B. Possibility / 1. Possibility
5739 Sometimes we want to specify in what ways a thing is possible [Melia]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
5734 Possible worlds make it possible to define necessity and counterfactuals without new primitives [Melia]
5742 In possible worlds semantics the modal operators are treated as quantifiers [Melia]
5743 If possible worlds semantics is not realist about possible worlds, logic becomes merely formal [Melia]
5749 Possible worlds could be real as mathematics, propositions, properties, or like books [Melia]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / b. Worlds as fictions
5751 The truth of propositions at possible worlds are implied by the world, just as in books [Melia]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
5748 We accept unverifiable propositions because of simplicity, utility, explanation and plausibility [Melia]
26. Natural Theory / B. Natural Kinds / 2. Defining Kinds
15798 Kinds are arrangements of dispositions [Fetzer]
26. Natural Theory / D. Laws of Nature / 3. Laws and Generalities
15799 Lawlike sentences are general attributions of disposition to all members of some class [Fetzer]