77 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] |
| 12223 | It is a fallacy to explain the obscure with the even more obscure [Hale/Wright] |
| 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] |
| 12341 | Logic is a mathematical account of a universe of relations [Badiou] |
| 12230 | Singular terms refer if they make certain atomic statements true [Hale/Wright] |
| 10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
| 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] |
| 10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
| 8784 | Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright] |
| 8787 | The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright] |
| 12329 | If mathematics is a logic of the possible, then questions of existence are not intrinsic to it [Badiou] |
| 10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
| 10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
| 12328 | Platonists like axioms and decisions, Aristotelians like definitions, possibilities and logic [Badiou] |
| 8788 | Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright] |
| 10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
| 8783 | Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright] |
| 12225 | Neo-Fregeanism might be better with truth-makers, rather than quantifier commitment [Hale/Wright] |
| 12224 | Are neo-Fregeans 'maximalists' - that everything which can exist does exist? [Hale/Wright] |
| 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] |
| 12226 | The identity of Pegasus with Pegasus may be true, despite the non-existence [Hale/Wright] |
| 16661 | There are two sorts of category - referring to things, and to circumstances of things [Boethius] |
| 12229 | Maybe we have abundant properties for semantics, and sparse properties for ontology [Hale/Wright] |
| 18443 | A successful predicate guarantees the existence of a property - the way of being it expresses [Hale/Wright] |
| 15035 | If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio] |
| 10626 | Objects just are what singular terms refer to [Hale/Wright] |
| 14665 | We can call the quality of Plato 'Platonity', and say it is a quality which only he possesses [Boethius] |
| 23308 | Reasoning relates to understanding as time does to eternity [Boethius, by Sorabji] |
| 5771 | Knowledge of present events doesn't make them necessary, so future events are no different [Boethius] |
| 5767 | Rational natures require free will, in order to have power of judgement [Boethius] |
| 5769 | Does foreknowledge cause necessity, or necessity cause foreknowledge? [Boethius] |
| 5768 | God's universal foreknowledge seems opposed to free will [Boethius] |
| 10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
| 8786 | One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright] |
| 12227 | Abstractionism needs existential commitment and uniform truth-conditions [Hale/Wright] |
| 12228 | Equivalence abstraction refers to objects otherwise beyond our grasp [Hale/Wright] |
| 12231 | Reference needs truth as well as sense [Hale/Wright] |
| 10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
| 12338 | We must either assert or deny any single predicate of any single subject [Badiou] |
| 5762 | The wicked want goodness, so they would not be wicked if they obtained it [Boethius] |
| 9814 | All great poetry is engaged in rivalry with mathematics [Badiou] |
| 5770 | Rewards and punishments are not deserved if they don't arise from free movement of the mind [Boethius] |
| 5764 | When people fall into wickedness they lose their human nature [Boethius] |
| 5756 | Happiness is a good which once obtained leaves nothing more to be desired [Boethius] |
| 5763 | The bad seek the good through desire, but the good through virtue, which is more natural [Boethius] |
| 5759 | Varied aims cannot be good because they differ, but only become good when they unify [Boethius] |
| 5754 | You can't control someone's free mind, only their body and possessions [Boethius] |
| 12316 | For Enlightenment philosophers, God was no longer involved in politics [Badiou] |
| 16692 | Divine eternity is the all-at-once and complete possession of unending life [Boethius] |
| 5752 | Where does evil come from if there is a god; where does good come from if there isn't? [Boethius] |
| 5757 | God is the supreme good, so no source of goodness could take precedence over God [Boethius] |
| 5758 | God is the good [Boethius] |
| 5760 | The power through which creation remains in existence and motion I call 'God' [Boethius] |
| 5753 | The regular events of this life could never be due to chance [Boethius] |
| 12317 | The God of religion results from an encounter, not from a proof [Badiou] |
| 5765 | The reward of the good is to become gods [Boethius] |
| 5761 | God can do anything, but he cannot do evil, so evil must be nothing [Boethius] |
| 5766 | If you could see the plan of Providence, you would not think there was evil anywhere [Boethius] |