51 ideas
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 1618 | We study bound variables not to know reality, but to know what reality language asserts [Quine] |
| 8455 | Canonical notation needs quantification, variables and predicates, but not names [Quine, by Orenstein] |
| 8456 | Quine extended Russell's defining away of definite descriptions, to also define away names [Quine, by Orenstein] |
| 1611 | Names can be converted to descriptions, and Russell showed how to eliminate those [Quine] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 1613 | Logicists cheerfully accept reference to bound variables and all sorts of abstract entities [Quine] |
| 1616 | Formalism says maths is built of meaningless notations; these build into rules which have meaning [Quine] |
| 1615 | Intuitionism says classes are invented, and abstract entities are constructed from specified ingredients [Quine] |
| 1614 | Conceptualism holds that there are universals but they are mind-made [Quine] |
| 10241 | For Quine, there is only one way to exist [Quine, by Shapiro] |
| 4064 | The idea of a thing and the idea of existence are two sides of the same coin [Quine, by Crane] |
| 19277 | Quine rests existence on bound variables, because he thinks singular terms can be analysed away [Quine, by Hale] |
| 12210 | Quine's ontology is wrong; his question is scientific, and his answer is partly philosophical [Fine,K on Quine] |
| 8496 | What actually exists does not, of course, depend on language [Quine] |
| 1610 | To be is to be the value of a variable, which amounts to being in the range of reference of a pronoun [Quine] |
| 8459 | Fictional quantification has no ontology, so we study ontology through scientific theories [Quine, by Orenstein] |
| 8497 | An ontology is like a scientific theory; we accept the simplest scheme that fits disorderly experiences [Quine] |
| 16261 | If commitment rests on first-order logic, we obviously lose the ontology concerning predication [Maudlin on Quine] |
| 7698 | If to be is to be the value of a variable, we must already know the values available [Jacquette on Quine] |
| 1612 | Realism, conceptualism and nominalism in medieval universals reappear in maths as logicism, intuitionism and formalism [Quine] |
| 15402 | There is no entity called 'redness', and that some things are red is ultimate and irreducible [Quine] |
| 4443 | Quine has argued that predicates do not have any ontological commitment [Quine, by Armstrong] |
| 8498 | Treating scattered sensations as single objects simplifies our understanding of experience [Quine] |
| 8856 | Quine's indispensability argument said arguments for abstracta were a posteriori [Quine, by Yablo] |
| 12443 | Can an unactualized possible have self-identity, and be distinct from other possibles? [Quine] |
| 18209 | We can never translate our whole language of objects into phenomenalism [Quine] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 1619 | There is an attempt to give a verificationist account of meaning, without the error of reducing everything to sensations [Dennett on Quine] |
| 1609 | I do not believe there is some abstract entity called a 'meaning' which we can 'have' [Quine] |
| 1617 | The word 'meaning' is only useful when talking about significance or about synonymy [Quine] |
| 19159 | Quine relates predicates to their objects, by being 'true of' them [Quine, by Davidson] |
| 3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |