40 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] |
9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
12324 | Consensus is the enemy of thought [Badiou] |
12337 | There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou] |
9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
12321 | The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou] |
9984 | We can have a series with identical members [Tait] |
12342 | Topos theory explains the plurality of possible logics [Badiou] |
12341 | Logic is a mathematical account of a universe of relations [Badiou] |
13416 | Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C] |
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] |
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] |
12331 | Logic is definitional, but real mathematics is axiomatic [Badiou] |
12340 | There is no Being as a whole, because there is no set of all sets [Badiou] |
9809 | Mathematics inscribes being as such [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] |
9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
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] |
6017 | Nomos is king [Pindar] |
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] |