51 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] |
12325 | Philosophy has been relieved of physics, cosmology, politics, and now must give up ontology [Badiou] |
12324 | Consensus is the enemy of thought [Badiou] |
15375 | If terms change their designations in different states, they are functions from states to objects [Fitting] |
15376 | Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting] |
15378 | Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting] |
15379 | Justication logics make explicit the reasons for mathematical truth in proofs [Fitting] |
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] |
13479 | Given that thinking aims at truth, logic gives universal rules for how to do it [Burge] |
11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
12341 | Logic is a mathematical account of a universe of relations [Badiou] |
8132 | We now have a much more sophisticated understanding of logical form in language [Burge] |
11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
17622 | We come to believe mathematical propositions via their grounding in the structure [Burge] |
9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
9159 | You can't simply convert geometry into algebra, as some spatial content is lost [Burge] |
12334 | There is no single unified definition of number [Badiou] |
12335 | Numbers are for measuring and for calculating (and the two must be consistent) [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] |
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] |
16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
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] |
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] |
12320 | Ontology is (and always has been) Cantorian mathematics [Badiou] |
15377 | Definite descriptions pick out different objects in different possible worlds [Fitting] |
16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
9382 | Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge] |
8126 | Anti-individualism says the environment is involved in the individuation of some mental states [Burge] |
8127 | Broad concepts suggest an extension of the mind into the environment (less computer-like) [Burge] |
8129 | Anti-individualism may be incompatible with some sorts of self-knowledge [Burge] |
8131 | Some qualities of experience, like blurred vision, have no function at all [Burge] |
3115 | Are meaning and expressed concept the same thing? [Burge, by Segal] |
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] |
12316 | For Enlightenment philosophers, God was no longer involved in politics [Badiou] |
14349 | If there are no finks or antidotes at the fundamental level, the laws can't be ceteris paribus [Burge, by Corry] |
12317 | The God of religion results from an encounter, not from a proof [Badiou] |