69 ideas
7893 | Our life is the creation of our mind [Anon (Dham)] |
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] |
9456 | Modal logic is multiple systems, shown in the variety of accessibility relations between worlds [Jacquette] |
7689 | The modal logic of C.I.Lewis was only interpreted by Kripke and Hintikka in the 1960s [Jacquette] |
12337 | There is 'transivity' iff membership ∈ also means inclusion ⊆ [Badiou] |
12321 | The axiom of choice must accept an indeterminate, indefinable, unconstructible set [Badiou] |
9457 | The two main views in philosophy of logic are extensionalism and intensionalism [Jacquette] |
7681 | Logic describes inferences between sentences expressing possible properties of objects [Jacquette] |
12342 | Topos theory explains the plurality of possible logics [Badiou] |
9463 | Classical logic is bivalent, has excluded middle, and only quantifies over existent objects [Jacquette] |
12341 | Logic is a mathematical account of a universe of relations [Badiou] |
7682 | Logic is not just about signs, because it relates to states of affairs, objects, properties and truth-values [Jacquette] |
7697 | On Russell's analysis, the sentence "The winged horse has wings" comes out as false [Jacquette] |
9465 | Substitutional universal quantification retains truth for substitution of terms of the same type [Jacquette] |
9466 | Nominalists like substitutional quantification to avoid the metaphysics of objects [Jacquette] |
9458 | Extensionalists say that quantifiers presuppose the existence of their objects [Jacquette] |
9461 | Intensionalists say meaning is determined by the possession of properties [Jacquette] |
7701 | Can a Barber shave all and only those persons who do not shave themselves? [Jacquette] |
9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
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] |
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] |
7707 | To grasp being, we must say why something exists, and why there is one world [Jacquette] |
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] |
7692 | Being is maximal consistency [Jacquette] |
7687 | Existence is completeness and consistency [Jacquette] |
9811 | It is of the essence of being to appear [Badiou] |
12320 | Ontology is (and always has been) Cantorian mathematics [Badiou] |
7679 | Ontology is the same as the conceptual foundations of logic [Jacquette] |
7678 | Ontology must include the minimum requirements for our semantics [Jacquette] |
7683 | Logic is based either on separate objects and properties, or objects as combinations of properties [Jacquette] |
7684 | Reduce states-of-affairs to object-property combinations, and possible worlds to states-of-affairs [Jacquette] |
7703 | If classes can't be eliminated, and they are property combinations, then properties (universals) can't be either [Jacquette] |
7685 | An object is a predication subject, distinguished by a distinctive combination of properties [Jacquette] |
7699 | Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals [Jacquette] |
7691 | The actual world is a consistent combination of states, made of consistent property combinations [Jacquette] |
7688 | The actual world is a maximally consistent combination of actual states of affairs [Jacquette] |
7695 | Do proposition-structures not associated with the actual world deserve to be called worlds? [Jacquette] |
7694 | We must experience the 'actual' world, which is defined by maximally consistent propositions [Jacquette] |
7898 | The world is just the illusion of an appearance [Anon (Dham)] |
7706 | If qualia supervene on intentional states, then intentional states are explanatorily fundamental [Jacquette] |
7704 | Reduction of intentionality involving nonexistent objects is impossible, as reduction must be to what is actual [Jacquette] |
9460 | Extensionalist semantics forbids reference to nonexistent objects [Jacquette] |
9459 | Extensionalist semantics is circular, as we must know the extension before assessing 'Fa' [Jacquette] |
7702 | The extreme views on propositions are Frege's Platonism and Quine's extreme nominalism [Jacquette] |
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] |
7894 | Hate is conquered by love [Anon (Dham)] |
7899 | Even divine pleasure will not satisfy the wise, as it is insatiable, and leads to pain [Anon (Dham)] |
7897 | The wise gradually fill with good, like a slowly-filled water-jar [Anon (Dham)] |
7896 | The foolish gradually fill with evil, like a slowly-filled water-jar [Anon (Dham)] |
7895 | Don't befriend fools; either find superior friends, or travel alone [Anon (Dham)] |
12316 | For Enlightenment philosophers, God was no longer involved in politics [Badiou] |
7900 | Speak the truth, yield not to anger, give what you can to him who asks [Anon (Dham)] |
12317 | The God of religion results from an encounter, not from a proof [Badiou] |