64 ideas
12330 | In ontology, logic dominated language, until logic was mathematized [Badiou] |
7950 | Philosophy tries to explain how the actual is possible, given that it seems impossible [Macdonald,C] |
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] |
7923 | 'Did it for the sake of x' doesn't involve a sake, so how can ontological commitments be inferred? [Macdonald,C] |
12324 | Consensus is the enemy of thought [Badiou] |
7933 | Don't assume that a thing has all the properties of its parts [Macdonald,C] |
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] |
18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
12341 | Logic is a mathematical account of a universe of relations [Badiou] |
18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
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] |
18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
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] |
7944 | Reduce by bridge laws (plus property identities?), by elimination, or by reducing talk [Macdonald,C] |
12320 | Ontology is (and always has been) Cantorian mathematics [Badiou] |
7938 | Relational properties are clearly not essential to substances [Macdonald,C] |
7967 | Being taller is an external relation, but properties and substances have internal relations [Macdonald,C] |
7965 | Does the knowledge of each property require an infinity of accompanying knowledge? [Macdonald,C] |
7934 | Tropes are abstract (two can occupy the same place), but not universals (they have locations) [Macdonald,C] |
7958 | Properties are sets of exactly resembling property-particulars [Macdonald,C] |
7972 | Tropes are abstract particulars, not concrete particulars, so the theory is not nominalist [Macdonald,C] |
7959 | How do a group of resembling tropes all resemble one another in the same way? [Macdonald,C] |
7960 | Trope Nominalism is the only nominalism to introduce new entities, inviting Ockham's Razor [Macdonald,C] |
7951 | Numerical sameness is explained by theories of identity, but what explains qualitative identity? [Macdonald,C] |
7964 | How can universals connect instances, if they are nothing like them? [Macdonald,C] |
7971 | Real Nominalism is only committed to concrete particulars, word-tokens, and (possibly) sets [Macdonald,C] |
7955 | Resemblance Nominalism cannot explain either new resemblances, or absence of resemblances [Macdonald,C] |
7961 | A 'thing' cannot be in two places at once, and two things cannot be in the same place at once [Macdonald,C] |
7926 | We 'individuate' kinds of object, and 'identify' particular specimens [Macdonald,C] |
7936 | Unlike bundles of properties, substances have an intrinsic unity [Macdonald,C] |
7930 | The bundle theory of substance implies the identity of indiscernibles [Macdonald,C] |
7932 | A phenomenalist cannot distinguish substance from attribute, so must accept the bundle view [Macdonald,C] |
7937 | When we ascribe a property to a substance, the bundle theory will make that a tautology [Macdonald,C] |
7939 | Substances persist through change, but the bundle theory says they can't [Macdonald,C] |
7940 | A substance might be a sequence of bundles, rather than a single bundle [Macdonald,C] |
7948 | A statue and its matter have different persistence conditions, so they are not identical [Macdonald,C] |
7929 | A substance is either a bundle of properties, or a bare substratum, or an essence [Macdonald,C] |
7941 | Each substance contains a non-property, which is its substratum or bare particular [Macdonald,C] |
7942 | The substratum theory explains the unity of substances, and their survival through change [Macdonald,C] |
7943 | A substratum has the quality of being bare, and they are useless because indiscernible [Macdonald,C] |
7927 | At different times Leibniz articulated three different versions of his so-called Law [Macdonald,C] |
7928 | The Identity of Indiscernibles is false, because it is not necessarily true [Macdonald,C] |
7947 | In continuity, what matters is not just the beginning and end states, but the process itself [Macdonald,C] |
18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
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] |
12317 | The God of religion results from an encounter, not from a proof [Badiou] |