111 ideas
13860 | We can only learn from philosophers of the past if we accept the risk of major misrepresentation [Wright,C] |
19275 | You cannot understand what exists without understanding possibility and necessity [Hale] |
10308 | Questions about objects are questions about certain non-vacuous singular terms [Hale] |
13883 | The best way to understand a philosophical idea is to defend it [Wright,C] |
19291 | A canonical defintion specifies the type of thing, and what distinguish this specimen [Hale] |
10142 | The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K] |
10314 | An expression is a genuine singular term if it resists elimination by paraphrase [Hale] |
19504 | My modus ponens might be your modus tollens [Pritchard,D] |
19297 | The two Barcan principles are easily proved in fairly basic modal logic [Hale] |
19301 | With a negative free logic, we can dispense with the Barcan formulae [Hale] |
19296 | If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale] |
19289 | Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale] |
9868 | An expression refers if it is a singular term in some true sentences [Wright,C, by Dummett] |
10316 | We should decide whether singular terms are genuine by their usage [Hale] |
10312 | Often the same singular term does not ensure reliable inference [Hale] |
10313 | Plenty of clear examples have singular terms with no ontological commitment [Hale] |
10322 | If singular terms can't be language-neutral, then we face a relativity about their objects [Hale] |
19298 | Unlike axiom proofs, natural deduction proofs needn't focus on logical truths and theorems [Hale] |
13861 | Number theory aims at the essence of natural numbers, giving their nature, and the epistemology [Wright,C] |
13892 | One could grasp numbers, and name sizes with them, without grasping ordering [Wright,C] |
10632 | The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright] |
13867 | Instances of a non-sortal concept can only be counted relative to a sortal concept [Wright,C] |
17441 | Wright thinks Hume's Principle is more fundamental to cardinals than the Peano Axioms are [Wright,C, by Heck] |
13862 | There are five Peano axioms, which can be expressed informally [Wright,C] |
17853 | Number truths are said to be the consequence of PA - but it needs semantic consequence [Wright,C] |
17854 | What facts underpin the truths of the Peano axioms? [Wright,C] |
13894 | Sameness of number is fundamental, not counting, despite children learning that first [Wright,C] |
10140 | We derive Hume's Law from Law V, then discard the latter in deriving arithmetic [Wright,C, by Fine,K] |
8692 | Frege has a good system if his 'number principle' replaces his basic law V [Wright,C, by Friend] |
17440 | Wright says Hume's Principle is analytic of cardinal numbers, like a definition [Wright,C, by Heck] |
13893 | It is 1-1 correlation of concepts, and not progression, which distinguishes natural number [Wright,C] |
13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C] |
13869 | Number platonism says that natural number is a sortal concept [Wright,C] |
13870 | We can't use empiricism to dismiss numbers, if numbers are our main evidence against empiricism [Wright,C] |
13873 | Treating numbers adjectivally is treating them as quantifiers [Wright,C] |
13899 | The Peano Axioms, and infinity of cardinal numbers, are logical consequences of how we explain cardinals [Wright,C] |
13896 | The aim is to follow Frege's strategy to derive the Peano Axioms, but without invoking classes [Wright,C] |
19295 | Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale] |
7804 | Wright has revived Frege's discredited logicism [Wright,C, by Benardete,JA] |
13863 | Logicism seemed to fail by Russell's paradox, Gödel's theorems, and non-logical axioms [Wright,C] |
13895 | The standard objections are Russell's Paradox, non-logical axioms, and Gödel's theorems [Wright,C] |
13884 | The idea that 'exist' has multiple senses is not coherent [Wright,C] |
19281 | Interesting supervenience must characterise the base quite differently from what supervenes on it [Hale] |
10512 | The abstract/concrete distinction is based on what is perceivable, causal and located [Hale] |
10517 | Colours and points seem to be both concrete and abstract [Hale] |
10519 | The abstract/concrete distinction is in the relations in the identity-criteria of object-names [Hale] |
10520 | Token-letters and token-words are concrete objects, type-letters and type-words abstract [Hale] |
10524 | There is a hierarchy of abstraction, based on steps taken by equivalence relations [Hale] |
19278 | There is no gap between a fact that p, and it is true that p; so we only have the truth-condtions for p [Hale] |
13877 | Singular terms in true sentences must refer to objects; there is no further question about their existence [Wright,C] |
10521 | If F can't have location, there is no problem of things having F in different locations [Hale] |
10511 | It is doubtful if one entity, a universal, can be picked out by both predicates and abstract nouns [Hale] |
10318 | Realists take universals to be the referrents of both adjectives and of nouns [Hale] |
10310 | Objections to Frege: abstracta are unknowable, non-independent, unstatable, unindividuated [Hale] |
10518 | Shapes and directions are of something, but games and musical compositions are not [Hale] |
10513 | Many abstract objects, such as chess, seem non-spatial, but are not atemporal [Hale] |
10514 | If the mental is non-spatial but temporal, then it must be classified as abstract [Hale] |
10523 | Being abstract is based on a relation between things which are spatially separated [Hale] |
9878 | Contextually defined abstract terms genuinely refer to objects [Wright,C, by Dummett] |
10307 | The modern Fregean use of the term 'object' is much broader than the ordinary usage [Hale] |
10315 | We can't believe in a 'whereabouts' because we ask 'what kind of object is it?' [Hale] |
13868 | Sortal concepts cannot require that things don't survive their loss, because of phase sortals [Wright,C] |
19302 | If a chair could be made of slightly different material, that could lead to big changes [Hale] |
10522 | The relations featured in criteria of identity are always equivalence relations [Hale] |
10321 | We sometimes apply identity without having a real criterion [Hale] |
15086 | Absolute necessity might be achievable either logically or metaphysically [Hale] |
19290 | Absolute necessities are necessarily necessary [Hale] |
8261 | Maybe not-p is logically possible, but p is metaphysically necessary, so the latter is not absolute [Hale] |
15081 | A strong necessity entails a weaker one, but not conversely; possibilities go the other way [Hale] |
15080 | 'Relative' necessity is just a logical consequence of some statements ('strong' if they are all true) [Hale] |
19286 | 'Absolute necessity' is when there is no restriction on the things which necessitate p [Hale] |
19288 | Logical and metaphysical necessities differ in their vocabulary, and their underlying entities [Hale] |
15082 | Metaphysical necessity says there is no possibility of falsehood [Hale] |
12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge] |
15085 | 'Broadly' logical necessities are derived (in a structure) entirely from the concepts [Hale] |
15088 | Logical necessities are true in virtue of the nature of all logical concepts [Hale] |
19285 | Logical necessity is something which is true, no matter what else is the case [Hale] |
19287 | Maybe each type of logic has its own necessity, gradually becoming broader [Hale] |
19503 | An improbable lottery win can occur in a nearby possible world [Pritchard,D] |
12432 | Explanation of necessity must rest on something necessary or something contingent [Hale] |
12434 | Why is this necessary, and what is necessity in general; why is this necessary truth true, and why necessary? [Hale] |
12435 | The explanation of a necessity can be by a truth (which may only happen to be a necessary truth) [Hale] |
19282 | It seems that we cannot show that modal facts depend on non-modal facts [Hale] |
12433 | If necessity rests on linguistic conventions, those are contingent, so there is no necessity [Hale] |
15087 | Conceptual necessities are made true by all concepts [Hale] |
12436 | Concept-identities explain how we know necessities, not why they are necessary [Hale] |
19276 | The big challenge for essentialist views of modality is things having necessary existence [Hale] |
19293 | Essentialism doesn't explain necessity reductively; it explains all necessities in terms of a few basic natures [Hale] |
19294 | If necessity derives from essences, how do we explain the necessary existence of essences? [Hale] |
19279 | What are these worlds, that being true in all of them makes something necessary? [Hale] |
19299 | Possible worlds make every proposition true or false, which endorses classical logic [Hale] |
19505 | Moore begs the question, or just offers another view, or uses 'know' wrongly [Pritchard,D, by PG] |
19499 | We can have evidence for seeing a zebra, but no evidence for what is entailed by that [Pritchard,D] |
19500 | Favouring: an entailment will give better support for the first belief than reason to deny the second [Pritchard,D] |
19502 | Maybe knowledge just needs relevant discriminations among contrasting cases [Pritchard,D] |
19498 | Epistemic internalism usually says justification must be accessible by reflection [Pritchard,D] |
19506 | Externalism is better than internalism in dealing with radical scepticism [Pritchard,D] |
19496 | Disjunctivism says perceptual justification must be both factual and known by the agent [Pritchard,D] |
19497 | Metaphysical disjunctivism says normal perceptions and hallucinations are different experiences [Pritchard,D] |
19495 | Epistemic externalism struggles to capture the idea of epistemic responsibility [Pritchard,D] |
19501 | We assess error against background knowledge, but that is just what radical scepticism challenges [Pritchard,D] |
19507 | Radical scepticism is merely raised, and is not a response to worrying evidence [Pritchard,D] |
19300 | The molecules may explain the water, but they are not what 'water' means [Hale] |
13866 | A concept is only a sortal if it gives genuine identity [Wright,C] |
13865 | 'Sortal' concepts show kinds, use indefinite articles, and require grasping identities [Wright,C] |
13890 | Entities fall under a sortal concept if they can be used to explain identity statements concerning them [Wright,C] |
13898 | If we can establish directions from lines and parallelism, we were already committed to directions [Wright,C] |
13882 | A milder claim is that understanding requires some evidence of that understanding [Wright,C] |
7320 | Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A] |
13885 | If apparent reference can mislead, then so can apparent lack of reference [Wright,C] |
17857 | We can accept Frege's idea of object without assuming that predicates have a reference [Wright,C] |