91 ideas
12330 | In ontology, logic dominated language, until logic was mathematized [Badiou] |
9808 | Philosophy aims to reveal the grandeur of mathematics [Badiou] |
12318 | The female body, when taken in its entirety, is the Phallus itself [Badiou] |
19275 | You cannot understand what exists without understanding possibility and necessity [Hale] |
12325 | Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology [Badiou] |
10308 | Questions about objects are questions about certain non-vacuous singular terms [Hale] |
12324 | Consensus is the enemy of thought [Badiou] |
19291 | A canonical defintion specifies the type of thing, and what distinguish this specimen [Hale] |
10314 | An expression is a genuine singular term if it resists elimination by paraphrase [Hale] |
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] |
12337 | There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou] |
12321 | The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou] |
12342 | Topos theory explains the plurality of possible logics [Badiou] |
19296 | If second-order variables range over sets, those are just objects; properties and relations aren't sets [Hale] |
12341 | Logic is a mathematical account of a universe of relations [Badiou] |
19289 | Maybe conventionalism applies to meaning, but not to the truth of propositions expressed [Hale] |
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] |
9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
12335 | Numbers are for measuring and for calculating (and the two must be consistent) [Badiou] |
12334 | There is no single unified definition of number [Badiou] |
12333 | Each type of number has its own characteristic procedure of introduction [Badiou] |
12322 | Must we accept numbers as existing when they no longer consist of units? [Badiou] |
10632 | The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright] |
9813 | Mathematics shows that thinking is not confined to the finite [Badiou] |
12327 | The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory [Badiou] |
12329 | If mathematics is a logic of the possible, then questions of existence are not intrinsic to it [Badiou] |
12328 | Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic [Badiou] |
19295 | Add Hume's principle to logic, to get numbers; arithmetic truths rest on the nature of the numbers [Hale] |
12331 | Logic is definitional, but real mathematics is axiomatic [Badiou] |
9809 | Mathematics inscribes being as such [Badiou] |
12340 | There is no Being as a whole, because there is no set of all sets [Badiou] |
12323 | Existence is Being itself, but only as our thought decides it [Badiou] |
12332 | The modern view of Being comes when we reject numbers as merely successions of One [Badiou] |
12326 | The primitive name of Being is the empty set; in a sense, only the empty set 'is' [Badiou] |
9811 | It is of the essence of being to appear [Badiou] |
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] |
10520 | Token-letters and token-words are concrete objects, type-letters and type-words abstract [Hale] |
10519 | The abstract/concrete distinction is in the relations in the identity-criteria of object-names [Hale] |
10524 | There is a hierarchy of abstraction, based on steps taken by equivalence relations [Hale] |
12320 | Ontology is (and always has been) Cantorian mathematics [Badiou] |
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] |
10318 | Realists take universals to be the referrents of both adjectives and of nouns [Hale] |
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] |
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] |
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] |
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] |
15080 | 'Relative' necessity is just a logical consequence of some statements ('strong' if they are all true) [Hale] |
15081 | A strong necessity entails a weaker one, but not conversely; possibilities go the other way [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] |
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] |
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] |
12436 | Concept-identities explain how we know necessities, not why they are necessary [Hale] |
15087 | Conceptual necessities are made true by all concepts [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] |
19300 | The molecules may explain the water, but they are not what 'water' means [Hale] |
12338 | We must either assert or deny any single predicate of any single subject [Badiou] |
9814 | All great poetry is engaged in rivalry with mathematics [Badiou] |
7350 | The Torah just says: do not do to your neighbour what is hateful to you [Hillel the Elder] |
12316 | For Enlightenment philosophers, God was no longer involved in politics [Badiou] |
12317 | The God of religion results from an encounter, not from a proof [Badiou] |