61 ideas
18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
18789 | Intuitionist logic looks best as natural deduction [Mares] |
18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
18793 | Material implication (and classical logic) considers nothing but truth values for implications [Mares] |
18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares] |
18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
18782 | The connectives are studied either through model theory or through proof theory [Mares] |
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] |
10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
18783 | Many-valued logics lack a natural deduction system [Mares] |
18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
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] |
18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
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] |
10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
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] |
1619 | There is an attempt to give a verificationist account of meaning, without the error of reducing everything to sensations [Dennett on Quine] |
1617 | The word 'meaning' is only useful when talking about significance or about synonymy [Quine] |
1609 | I do not believe there is some abstract entity called a 'meaning' which we can 'have' [Quine] |
18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |
19159 | Quine relates predicates to their objects, by being 'true of' them [Quine, by Davidson] |