107 ideas
| 15357 | Philosophy is the most general intellectual discipline [Horsten] |
| 15352 | A definition should allow the defined term to be eliminated [Horsten] |
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
| 18889 | Ostensive definitions needn't involve pointing, but must refer to something specific [Salmon,N] |
| 15324 | Semantic theories of truth seek models; axiomatic (syntactic) theories seek logical principles [Horsten] |
| 15323 | Truth is a property, because the truth predicate has an extension [Horsten] |
| 15374 | Truth has no 'nature', but we should try to describe its behaviour in inferences [Horsten] |
| 15348 | Propositions have sentence-like structures, so it matters little which bears the truth [Horsten] |
| 15333 | Modern correspondence is said to be with the facts, not with true propositions [Horsten] |
| 15337 | The correspondence 'theory' is too vague - about both 'correspondence' and 'facts' [Horsten] |
| 15334 | The coherence theory allows multiple coherent wholes, which could contradict one another [Horsten] |
| 15336 | The pragmatic theory of truth is relative; useful for group A can be useless for group B [Horsten] |
| 15354 | Tarski's hierarchy lacks uniform truth, and depends on contingent factors [Horsten] |
| 15340 | Tarski Bi-conditional: if you'll assert φ you'll assert φ-is-true - and also vice versa [Horsten] |
| 15345 | Semantic theories have a regress problem in describing truth in the languages for the models [Horsten] |
| 15373 | Axiomatic approaches avoid limiting definitions to avoid the truth predicate, and limited sizes of models [Horsten] |
| 15346 | Axiomatic approaches to truth avoid the regress problem of semantic theories [Horsten] |
| 15371 | An axiomatic theory needs to be of maximal strength, while being natural and sound [Horsten] |
| 15332 | 'Reflexive' truth theories allow iterations (it is T that it is T that p) [Horsten] |
| 15361 | A good theory of truth must be compositional (as well as deriving biconditionals) [Horsten] |
| 15350 | The Naďve Theory takes the bi-conditionals as axioms, but it is inconsistent, and allows the Liar [Horsten] |
| 15351 | Axiomatic theories take truth as primitive, and propose some laws of truth as axioms [Horsten] |
| 15367 | By adding truth to Peano Arithmetic we increase its power, so truth has mathematical content! [Horsten] |
| 15330 | Friedman-Sheard theory keeps classical logic and aims for maximum strength [Horsten] |
| 15331 | Kripke-Feferman has truth gaps, instead of classical logic, and aims for maximum strength [Horsten] |
| 15325 | Inferential deflationism says truth has no essence because no unrestricted logic governs the concept [Horsten] |
| 15344 | Deflationism skips definitions and models, and offers just accounts of basic laws of truth [Horsten] |
| 15356 | Deflationism concerns the nature and role of truth, but not its laws [Horsten] |
| 15368 | This deflationary account says truth has a role in generality, and in inference [Horsten] |
| 15358 | Deflationism says truth isn't a topic on its own - it just concerns what is true [Horsten] |
| 15359 | Deflation: instead of asserting a sentence, we can treat it as an object with the truth-property [Horsten] |
| 14684 | A world is 'accessible' to another iff the first is possible according to the second [Salmon,N] |
| 14669 | For metaphysics, T may be the only correct system of modal logic [Salmon,N] |
| 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] |
| 14671 | What is necessary is not always necessarily necessary, so S4 is fallacious [Salmon,N] |
| 14627 | S4, and therefore S5, are invalid for metaphysical modality [Salmon,N, by Williamson] |
| 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] |
| 14670 | Metaphysical (alethic) modal logic concerns simple necessity and possibility (not physical, epistemic..) [Salmon,N] |
| 15329 | Nonclassical may accept T/F but deny applicability, or it may deny just T or F as well [Horsten] |
| 15326 | Doubt is thrown on classical logic by the way it so easily produces the liar paradox [Horsten] |
| 15341 | Deduction Theorem: ψ only derivable from φ iff φ→ψ are axioms [Horsten] |
| 15328 | A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten] |
| 15349 | It is easier to imagine truth-value gaps (for the Liar, say) than for truth-value gluts (both T and F) [Horsten] |
| 15366 | Satisfaction is a primitive notion, and very liable to semantical paradoxes [Horsten] |
| 10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
| 15353 | The first incompleteness theorem means that consistency does not entail soundness [Horsten] |
| 15355 | Strengthened Liar: 'this sentence is not true in any context' - in no context can this be evaluated [Horsten] |
| 15364 | English expressions are denumerably infinite, but reals are nondenumerable, so many are unnameable [Horsten] |
| 10885 | Computer proofs don't provide explanations [Horsten] |
| 10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
| 15360 | ZFC showed that the concept of set is mathematical, not logical, because of its existence claims [Horsten] |
| 15369 | Set theory is substantial over first-order arithmetic, because it enables new proofs [Horsten] |
| 15370 | Predicativism says mathematical definitions must not include the thing being defined [Horsten] |
| 458 | Nothing could come out of nothing, and existence could never completely cease [Empedocles] |
| 5112 | Empedocles says things are at rest, unless love unites them, or hatred splits them [Empedocles, by Aristotle] |
| 15338 | We may believe in atomic facts, but surely not complex disjunctive ones? [Horsten] |
| 15363 | In the supervaluationist account, disjunctions are not determined by their disjuncts [Horsten] |
| 15362 | If 'Italy is large' lacks truth, so must 'Italy is not large'; but classical logic says it's large or it isn't [Horsten] |
| 14742 | It can't be indeterminate whether x and y are identical; if x,y is indeterminate, then it isn't x,x [Salmon,N] |
| 13209 | There is no coming-to-be of anything, but only mixing and separating [Empedocles, by Aristotle] |
| 18888 | Essentialism says some properties must be possessed, if a thing is to exist [Salmon,N] |
| 14678 | Any property is attached to anything in some possible world, so I am a radical anti-essentialist [Salmon,N] |
| 457 | Substance is not created or destroyed in mortals, but there is only mixing and exchange [Empedocles] |
| 14680 | Logical possibility contains metaphysical possibility, which contains nomological possibility [Salmon,N] |
| 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] |
| 14681 | Logical necessity is free of constraints, and may accommodate all of S5 logic [Salmon,N] |
| 14676 | Nomological necessity is expressed with intransitive relations in modal semantics [Salmon,N] |
| 14689 | Necessity and possibility are not just necessity and possibility according to the actual world [Salmon,N] |
| 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] |
| 14683 | Possible worlds rely on what might have been, so they can' be used to define or analyse modality [Salmon,N] |
| 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] |
| 14673 | You can't define worlds as sets of propositions, and then define propositions using worlds [Salmon,N] |
| 15372 | Some claim that indicative conditionals are believed by people, even though they are not actually held true [Horsten] |
| 462 | One vision is produced by both eyes [Empedocles] |
| 22765 | Wisdom and thought are shared by all things [Empedocles] |
| 1524 | For Empedocles thinking is almost identical to perception [Empedocles, by Theophrastus] |
| 18886 | Frege's 'sense' solves four tricky puzzles [Salmon,N] |
| 18887 | The perfect case of direct reference is a variable which has been assigned a value [Salmon,N] |
| 18885 | Kripke and Putnam made false claims that direct reference implies essentialism [Salmon,N] |
| 15347 | A theory of syntax can be based on Peano arithmetic, thanks to the translation by Gödel coding [Horsten] |
| 552 | Empedocles said good and evil were the basic principles [Empedocles, by Aristotle] |
| 589 | 'Nature' is just a word invented by people [Empedocles] |
| 21823 | The principle of 'Friendship' in Empedocles is the One, and is bodiless [Empedocles, by Plotinus] |
| 2680 | Empedocles said that there are four material elements, and two further creative elements [Empedocles, by Aristotle] |
| 6002 | Empedocles says bone is water, fire and earth in ratio 2:4:2 [Empedocles, by Inwood] |
| 13207 | Fire, Water, Air and Earth are elements, being simple as well as homoeomerous [Empedocles, by Aristotle] |
| 459 | All change is unity through love or division through hate [Empedocles] |
| 13218 | The elements combine in coming-to-be, but how do the elements themselves come-to-be? [Aristotle on Empedocles] |
| 13225 | Love and Strife only explain movement if their effects are distinctive [Aristotle on Empedocles] |
| 460 | If the one Being ever diminishes it would no longer exist, and what could ever increase it? [Empedocles] |
| 18891 | Nothing in the direct theory of reference blocks anti-essentialism; water structure might have been different [Salmon,N] |
| 5090 | Maybe bodies are designed by accident, and the creatures that don't work are destroyed [Empedocles, by Aristotle] |
| 466 | God is pure mind permeating the universe [Empedocles] |
| 461 | God is a pure, solitary, and eternal sphere [Empedocles] |
| 1719 | In Empedocles' theory God is ignorant because, unlike humans, he doesn't know one of the elements (strife) [Aristotle on Empedocles] |
| 1522 | It is wretched not to want to think clearly about the gods [Empedocles] |