Combining Texts

All the ideas for 'fragments/reports', 'The Logic of What Might Have Been' and 'Set Theory and Its Philosophy'

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42 ideas

4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / b. Terminology of ML
14684 A world is 'accessible' to another iff the first is possible according to the second [Salmon,N]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
14669 For metaphysics, T may be the only correct system of modal logic [Salmon,N]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
14667 System B has not been justified as fallacy-free for reasoning on what might have been [Salmon,N]
14668 In B it seems logically possible to have both p true and p is necessarily possibly false [Salmon,N]
14692 System B implies that possibly-being-realized is an essential property of the world [Salmon,N]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
14671 What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
14686 S5 modal logic ignores accessibility altogether [Salmon,N]
14691 S5 believers say that-things-might-have-been-that-way is essential to ways things might have been [Salmon,N]
14693 The unsatisfactory counterpart-theory allows the retention of S5 [Salmon,N]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
14670 Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..) [Salmon,N]
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 / 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]
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 / 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 / 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 / 15. Against Essentialism
14678 Any property is attached to anything in some possible world, so I am a radical anti-essentialist [Salmon,N]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
10. Modality / A. Necessity / 3. Types of Necessity
14680 Logical possibility contains metaphysical possibility, which contains nomological possibility [Salmon,N]
10. Modality / A. Necessity / 5. Metaphysical Necessity
14690 In the S5 account, nested modalities may be unseen, but they are still there [Salmon,N]
14677 Metaphysical necessity is said to be unrestricted necessity, true in every world whatsoever [Salmon,N]
14679 Bizarre identities are logically but not metaphysically possible, so metaphysical modality is restricted [Salmon,N]
14688 Without impossible worlds, the unrestricted modality that is metaphysical has S5 logic [Salmon,N]
14685 Metaphysical necessity is NOT truth in all (unrestricted) worlds; necessity comes first, and is restricted [Salmon,N]
10. Modality / A. Necessity / 6. Logical Necessity
14681 Logical necessity is free of constraints, and may accommodate all of S5 logic [Salmon,N]
10. Modality / A. Necessity / 7. Natural Necessity
14676 Nomological necessity is expressed with intransitive relations in modal semantics [Salmon,N]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
14689 Necessity and possibility are not just necessity and possibility according to the actual world [Salmon,N]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
14674 Impossible worlds are also ways for things to be [Salmon,N]
14682 Denial of impossible worlds involves two different confusions [Salmon,N]
14687 Without impossible worlds, how things might have been is the only way for things to be [Salmon,N]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
14683 Possible worlds rely on what might have been, so they can' be used to define or analyse modality [Salmon,N]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
14672 Possible worlds are maximal abstract ways that things might have been [Salmon,N]
14675 Possible worlds just have to be 'maximal', but they don't have to be consistent [Salmon,N]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
14673 You can't define worlds as sets of propositions, and then define propositions using worlds [Salmon,N]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]