Combining Texts

All the ideas for 'Identity and Spatio-Temporal Continuity', 'The Metaphysics of Modality' and 'Set Theory and Its Philosophy'

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40 ideas

1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
12027 There must be a plausible epistemological theory alongside any metaphysical theory [Forbes,G]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / a. Symbols of PL
12005 The symbol 'ι' forms definite descriptions; (ιx)F(x) says 'the x which is such that F(x)' [Forbes,G]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10702 Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10713 Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13044 Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10708 Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13546 The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10707 Mereology elides the distinction between the cards in a pack and the suits [Potter]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10704 We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
12010 Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
10703 Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
10712 If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17882 It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
12023 Vagueness problems arise from applying sharp semantics to vague languages [Forbes,G]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
13043 A relation is a set consisting entirely of ordered pairs [Potter]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
12017 In all instances of identity, there must be some facts to ensure the identity [Forbes,G]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
13128 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
13042 If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
12024 If we combined two clocks, it seems that two clocks may have become one clock. [Forbes,G]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13041 Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
9. Objects / D. Essence of Objects / 3. Individual Essences
11885 Only individual essences will ground identities across worlds in other properties [Forbes,G, by Mackie,P]
12014 An individual essence is a set of essential properties which only that object can have [Forbes,G]
12015 Non-trivial individual essence is properties other than de dicto, or universal, or relational [Forbes,G]
9. Objects / D. Essence of Objects / 5. Essence as Kind
12013 Essential properties depend on a category, and perhaps also on particular facts [Forbes,G]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
12012 Essential properties are those without which an object could not exist [Forbes,G]
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
12022 Same parts does not ensure same artefact, if those parts could constitute a different artefact [Forbes,G]
12025 Artefacts have fuzzy essences [Forbes,G]
9. Objects / E. Objects over Time / 12. Origin as Essential
12020 An individual might change their sex in a world, but couldn't have differed in sex at origin [Forbes,G]
9. Objects / F. Identity among Objects / 1. Concept of Identity
11888 Identities must hold because of other facts, which must be instrinsic [Forbes,G, by Mackie,P]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
10. Modality / A. Necessity / 4. De re / De dicto modality
12003 De re modal formulae, unlike de dicto, are sensitive to transworld identities [Forbes,G]
10. Modality / C. Sources of Modality / 4. Necessity from Concepts
12028 De re necessity is a form of conceptual necessity, just as de dicto necessity is [Forbes,G]
10. Modality / E. Possible worlds / 1. Possible Worlds / c. Possible worlds realism
12008 Unlike places and times, we cannot separate possible worlds from what is true at them [Forbes,G]
12009 The problem with possible worlds realism is epistemological; we can't know properties of possible objects [Forbes,G]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
12007 Possible worlds are points of logical space, rather like other times than our own [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
12011 Transworld identity concerns the limits of possibility for ordinary things [Forbes,G]
12016 The problem of transworld identity can be solved by individual essences [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
12004 Counterpart theory is not good at handling the logic of identity [Forbes,G]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
12021 Haecceitism attributes to each individual a primitive identity or thisness [Forbes,G]
12029 We believe in thisnesses, because we reject bizarre possibilities as not being about that individual [Forbes,G]