Combining Texts

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

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85 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]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
11832 We learn a concept's relations by using it, without reducing it to anything [Wiggins]
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]
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]
9741 Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn]
4. Formal Logic / D. Modal Logic ML / 2. Tools of Modal Logic / c. Derivation rules of ML
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]
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]
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]
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 / F. Referring in Logic / 3. Property (λ-) Abstraction
11863 (λx)[Man x] means 'the property x has iff x is a man'. [Wiggins]
9725 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
14746 What exists can't depend on our conceptual scheme, and using all conceptual schemes is too liberal [Sider on Wiggins]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
11900 We can accept criteria of distinctness and persistence, without making the counterfactual claims [Mackie,P on Wiggins]
11870 Activity individuates natural things, functions do artefacts, and intentions do artworks [Wiggins]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
11866 The idea of 'thisness' is better expressed with designation/predication and particular/universal [Wiggins]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
11896 A sortal essence is a thing's principle of individuation [Wiggins, by Mackie,P]
15835 Wiggins's sortal essentialism rests on a thing's principle of individuation [Wiggins, by Mackie,P]
11841 The evening star is the same planet but not the same star as the morning star, since it is not a star [Wiggins]
10679 'Sortalism' says parts only compose a whole if it falls under a sort or kind [Wiggins, by Hossack]
14363 Identity a=b is only possible with some concept to give persistence and existence conditions [Wiggins, by Strawson,P]
14364 A thing is necessarily its highest sortal kind, which entails an essential constitution [Wiggins, by Strawson,P]
11851 Many predicates are purely generic, or pure determiners, rather than sortals [Wiggins]
11865 The possibility of a property needs an essential sortal concept to conceive it [Wiggins]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
14744 Objects can only coincide if they are of different kinds; trees can't coincide with other trees [Wiggins, by Sider]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
11852 Is the Pope's crown one crown, if it is made of many crowns? [Wiggins]
11875 Boundaries are not crucial to mountains, so they are determinate without a determinate extent [Wiggins]
9. Objects / C. Structure of Objects / 5. Composition of an Object
14749 Identity is an atemporal relation, but composition is relative to times [Wiggins, by Sider]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
11844 If I destroy an item, I do not destroy each part of it [Wiggins]
9. Objects / D. Essence of Objects / 3. Individual Essences
11861 We can forget about individual or particularized essences [Wiggins]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
11871 Essences are not explanations, but individuations [Wiggins]
9. Objects / D. Essence of Objects / 9. Essence and Properties
11879 Essentialism is best represented as a predicate-modifier: □(a exists → a is F) [Wiggins, by Mackie,P]
9. Objects / D. Essence of Objects / 13. Nominal Essence
11835 The nominal essence is the idea behind a name used for sorting [Wiggins]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
11876 It is easier to go from horses to horse-stages than from horse-stages to horses [Wiggins]
9. Objects / E. Objects over Time / 9. Ship of Theseus
11858 The question is not what gets the title 'Theseus' Ship', but what is identical with the original [Wiggins]
9. Objects / F. Identity among Objects / 1. Concept of Identity
11843 Identity over a time and at a time aren't different concepts [Wiggins]
11864 Hesperus=Hesperus, and Phosphorus=Hesperus, so necessarily Phosphorus=Hesperus [Wiggins]
9. Objects / F. Identity among Objects / 2. Defining Identity
11831 The formal properties of identity are reflexivity and Leibniz's Law [Wiggins]
9. Objects / F. Identity among Objects / 3. Relative Identity
14362 Relative Identity is incompatible with the Indiscernibility of Identicals [Wiggins, by Strawson,P]
11838 Relativity of Identity makes identity entirely depend on a category [Wiggins]
11847 To identify two items, we must have a common sort for them [Wiggins]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
13730 The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
11839 Do both 'same f as' and '=' support Leibniz's Law? [Wiggins]
11845 Substitutivity, and hence most reasoning, needs Leibniz's Law [Wiggins]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
11869 Possible worlds rest on the objects about which we have suppositions [Wiggins]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / b. Worlds as fictions
11850 Not every story corresponds to a possible world [Wiggins]
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]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
11848 Asking 'what is it?' nicely points us to the persistence of a continuing entity [Wiggins]
18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
11859 The mind conceptualizes objects; yet objects impinge upon the mind [Wiggins]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
11836 We can use 'concept' for the reference, and 'conception' for sense [Wiggins]
26. Natural Theory / B. Natural Kinds / 3. Knowing Kinds
11860 Lawlike propensities are enough to individuate natural kinds [Wiggins]