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All the ideas for 'The Evolution of Modern Metaphysics', 'First-Order Modal Logic' and 'Philosophy of Logic'

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71 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
21959 Metaphysics is the most general attempt to make sense of things [Moore,AW]
2. Reason / B. Laws of Thought / 3. Non-Contradiction
9023 If you say that a contradiction is true, you change the meaning of 'not', and so change the subject [Quine]
3. Truth / F. Semantic Truth / 2. Semantic Truth
9012 Talk of 'truth' when sentences are mentioned; it reminds us that reality is the point of sentences [Quine]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
9011 Truth is redundant for single sentences; we do better to simply speak the sentence [Quine]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
9013 We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)' [Quine]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
9738 Each line of a truth table is a model [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / a. Symbols of ML
9727 Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn]
9726 We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn]
9737 The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn]
13136 The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / b. Terminology of ML
13727 A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn]
9741 Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn]
9734 Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn]
9736 A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn]
9735 A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / c. Derivation rules of ML
13149 S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn]
9740 If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn]
9739 If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn]
13137 Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn]
13140 Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn]
13139 Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn]
13143 Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn]
13141 Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn]
13138 Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn]
13142 Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn]
13144 T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn]
13145 D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn]
13146 B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn]
13147 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn]
13148 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / b. System K
9742 The system K has no accessibility conditions [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / c. System D
13114 □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn]
9743 The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / d. System T
9744 The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / e. System K4
9746 The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / f. System B
9745 The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / g. System S4
9747 The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
9748 System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
9404 Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 5. Epistemic Logic
13112 In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn]
13111 Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 6. Temporal Logic
13113 F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
13728 The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn]
13729 The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
9020 My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
9028 Maybe logical truth reflects reality, but in different ways in different languages [Quine]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10014 Quine rejects second-order logic, saying that predicates refer to multiple objects [Quine, by Hodes]
10828 Quantifying over predicates is treating them as names of entities [Quine]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
9024 Excluded middle has three different definitions [Quine]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
10012 Quantification theory can still be proved complete if we add identity [Quine]
5. Theory of Logic / F. Referring in Logic / 1. Naming / f. Names eliminated
9016 Names are not essential, because naming can be turned into predication [Quine]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
9725 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn]
5. Theory of Logic / G. Quantification / 1. Quantification
9015 Universal quantification is widespread, but it is definable in terms of existential quantification [Quine]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9025 You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine]
9026 Some quantifications could be false substitutionally and true objectually, because of nameless objects [Quine]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10705 Putting a predicate letter in a quantifier is to make it the name of an entity [Quine]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
9027 A sentence is logically true if all sentences with that grammatical structure are true [Quine]
8. Modes of Existence / B. Properties / 12. Denial of Properties
9017 Predicates are not names; predicates are the other parties to predication [Quine]
9. Objects / A. Existence of Objects / 1. Physical Objects
9018 A physical object is the four-dimensional material content of a portion of space-time [Quine]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
9019 Four-d objects helps predication of what no longer exists, and quantification over items from different times [Quine]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
13730 The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn]
10. Modality / B. Possibility / 8. Conditionals / b. Types of conditional
9014 Some conditionals can be explained just by negation and conjunction: not(p and not-q) [Quine]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
13725 □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn]
13731 Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
13726 Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
21958 Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW]
19. Language / A. Nature of Meaning / 8. Synonymy
9009 Single words are strongly synonymous if their interchange preserves truth [Quine]
19. Language / D. Propositions / 6. Propositions Critique
9007 It makes no sense to say that two sentences express the same proposition [Quine]
9008 There is no rule for separating the information from other features of sentences [Quine]
9010 We can abandon propositions, and just talk of sentences and equivalence [Quine]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
9021 A good way of explaining an expression is saying what conditions make its contexts true [Quine]