93 ideas
8558 | One system has properties, powers, events, similarity and substance [Shoemaker] |
8559 | Analysis aims at internal relationships, not reduction [Shoemaker] |
10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
11011 | Same say there are positive, negative and neuter free logics [Read] |
10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
10986 | Not all validity is captured in first-order logic [Read] |
10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
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] |
10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
10973 | A theory is logically closed, which means infinite premisses [Read] |
11007 | Quantifiers are second-order predicates [Read] |
10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
10900 | Logically true sentences are true in all structures [Zalabardo] |
10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
10988 | Any first-order theory of sets is inadequate [Read] |
10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
10975 | Compactness does not deny that an inference can have infinitely many premisses [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] |
11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
11016 | Would a language without vagueness be usable at all? [Read] |
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] |
15092 | Formerly I said properties are individuated by essential causal powers and causing instantiation [Shoemaker, by Shoemaker] |
8543 | Genuine properties are closely related to genuine changes [Shoemaker] |
8551 | Properties must be essentially causal if we can know and speak about them [Shoemaker] |
8557 | To ascertain genuine properties, examine the object directly [Shoemaker] |
15761 | We should abandon the idea that properties are the meanings of predicate expressions [Shoemaker] |
15756 | Some truths are not because of a thing's properties, but because of the properties of related things [Shoemaker] |
15758 | Things have powers in virtue of (which are entailed by) their properties [Shoemaker] |
8547 | One power can come from different properties; a thing's powers come from its properties [Shoemaker] |
8549 | Properties are functions producing powers, and powers are functions producing effects [Shoemaker] |
12678 | Shoemaker says all genuine properties are dispositional [Shoemaker, by Ellis] |
8545 | A causal theory of properties focuses on change, not (say) on abstract properties of numbers [Shoemaker] |
15757 | 'Square', 'round' and 'made of copper' show that not all properties are dispositional [Shoemaker] |
15759 | The identity of a property concerns its causal powers [Shoemaker] |
15760 | Properties are clusters of conditional powers [Shoemaker] |
15762 | Could properties change without the powers changing, or powers change without the properties changing? [Shoemaker] |
8552 | If properties are separated from causal powers, this invites total elimination [Shoemaker] |
4040 | The notions of property and of causal power are parts of a single system of related concepts [Shoemaker] |
15765 | Actually, properties are individuated by causes as well as effects [Shoemaker] |
8548 | Dispositional predicates ascribe powers, and the rest ascribe properties [Shoemaker] |
9485 | Universals concern how things are, and how they could be [Shoemaker, by Bird] |
8550 | Triangular and trilateral are coextensive, but different concepts; but powers and properties are the same [Shoemaker] |
10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
8555 | There is no subset of properties which guarantee a thing's identity [Shoemaker] |
11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
8554 | Possible difference across worlds depends on difference across time in the actual world [Shoemaker] |
10989 | The standard view of conditionals is that they are truth-functional [Read] |
11017 | Some people even claim that conditionals do not express propositions [Read] |
10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
15764 | 'Conceivable' is either not-provably-false, or compatible with what we know? [Shoemaker] |
8562 | It is possible to conceive what is not possible [Shoemaker] |
10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
8556 | Grueness is not, unlike green and blue, associated with causal potential [Shoemaker] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
8542 | If causality is between events, there must be reference to the properties involved [Shoemaker] |
8560 | If causal laws describe causal potentialities, the same laws govern properties in all possible worlds [Shoemaker] |
15763 | If properties are causal, then causal necessity is a species of logical necessity [Shoemaker] |
8561 | If a world has different causal laws, it must have different properties [Shoemaker] |
8553 | It looks as if the immutability of the powers of a property imply essentiality [Shoemaker] |