Combining Texts

All the ideas for 'Thinking About Logic', 'The Logic of What Might Have Been' and 'Prolegomena to Ethics'

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72 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL
10987 Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read]
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 / a. Systems of modal logic
11004 Necessity is provability in S4, and true in all worlds in S5 [Read]
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 / E. Nonclassical Logics / 4. Fuzzy Logic
11018 There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read]
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
11011 Same say there are positive, negative and neuter free logics [Read]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets
11020 Realisms like the full Comprehension Principle, that all good concepts determine sets [Read]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10986 Not all validity is captured in first-order logic [Read]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
10972 The non-emptiness of the domain is characteristic of classical logic [Read]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
11024 Semantics must precede proof in higher-order logics, since they are incomplete [Read]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
10985 We should exclude second-order logic, precisely because it captures arithmetic [Read]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10970 A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read]
10984 Logical consequence isn't just a matter of form; it depends on connections like round-square [Read]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
10973 A theory is logically closed, which means infinite premisses [Read]
5. Theory of Logic / G. Quantification / 1. Quantification
11007 Quantifiers are second-order predicates [Read]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10978 In second-order logic the higher-order variables range over all the properties of the objects [Read]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10971 A logical truth is the conclusion of a valid inference with no premisses [Read]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10988 Any first-order theory of sets is inadequate [Read]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10975 Compactness does not deny that an inference can have infinitely many premisses [Read]
10974 Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read]
10977 Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read]
10976 Compactness makes consequence manageable, but restricts expressive power [Read]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
11014 Self-reference paradoxes seem to arise only when falsity is involved [Read]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
11025 Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10979 Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read]
10980 Second-order arithmetic covers all properties, ensuring categoricity [Read]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
10997 Von Neumann numbers are helpful, but don't correctly describe numbers [Read]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
11016 Would a language without vagueness be usable at all? [Read]
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
11019 Supervaluations say there is a cut-off somewhere, but at no particular place [Read]
11012 A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read]
11013 Identities and the Indiscernibility of Identicals don't work with supervaluations [Read]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
10995 A haecceity is a set of individual properties, essential to each thing [Read]
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 / 2. Nature of Necessity
11001 Equating necessity with truth in every possible world is the S5 conception of necessity [Read]
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 / B. Possibility / 8. Conditionals / a. Conditionals
10989 The standard view of conditionals is that they are truth-functional [Read]
10992 The point of conditionals is to show that one will accept modus ponens [Read]
11017 Some people even claim that conditionals do not express propositions [Read]
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 / a. Possible worlds
10983 Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read]
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 / c. Possible worlds realism
10982 How can modal Platonists know the truth of a modal proposition? [Read]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
10996 Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read]
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]
10981 A possible world is a determination of the truth-values of all propositions of a domain [Read]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
11000 If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
10998 The mind abstracts ways things might be, which are nonetheless real [Read]
19. Language / C. Assigning Meanings / 4. Compositionality
11005 Negative existentials with compositionality make the whole sentence meaningless [Read]
19. Language / D. Propositions / 1. Propositions
10966 A proposition objectifies what a sentence says, as indicative, with secure references [Read]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
23035 The good life aims at perfections, or absolute laws, or what is absolutely desirable [Green,TH]
24. Political Theory / D. Ideologies / 6. Liberalism / c. Liberal equality
23037 People are improved by egalitarian institutions and habits [Green,TH]
24. Political Theory / D. Ideologies / 6. Liberalism / e. Liberal community
23043 All talk of the progress of a nation must reduce to the progress of its individual members [Green,TH]