38 ideas
| 12330 | In ontology, logic dominated language, until logic was mathematized [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] |
| 12337 | There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou] |
| 12321 | The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou] |
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| 12342 | Topos theory explains the plurality of possible logics [Badiou] |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| 12341 | Logic is a mathematical account of a universe of relations [Badiou] |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| 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] |
| 12327 | The undecidability of the Continuum Hypothesis may have ruined or fragmented set theory [Badiou] |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| 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] |
| 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] |
| 12320 | Ontology is (and always has been) Cantorian mathematics [Badiou] |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| 12338 | We must either assert or deny any single predicate of any single subject [Badiou] |
| 12316 | For Enlightenment philosophers, God was no longer involved in politics [Badiou] |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| 12317 | The God of religion results from an encounter, not from a proof [Badiou] |
| 6610 | I believe because it is absurd [Tertullian] |