49 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] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 12337 | There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 12321 | The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou] |
| 12342 | Topos theory explains the plurality of possible logics [Badiou] |
| 12341 | Logic is a mathematical account of a universe of relations [Badiou] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 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] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 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] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 12329 | If mathematics is a logic of the possible, then questions of existence are not intrinsic to it [Badiou] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 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] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 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] |
| 12317 | The God of religion results from an encounter, not from a proof [Badiou] |