46 ideas
| 18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
| 14018 | Is Sufficient Reason self-refuting (no reason to accept it!), or is it a legitimate explanatory tool? [Bourne] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 14008 | The redundancy theory conflates metalinguistic bivalence with object-language excluded middle [Bourne] |
| 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] |
| 18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
| 18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
| 18782 | The connectives are studied either through model theory or through proof theory [Mares] |
| 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] |
| 18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
| 14010 | All relations between spatio-temporal objects are either spatio-temporal, or causal [Bourne] |
| 14009 | It is a necessary condition for the existence of relations that both of the relata exist [Bourne] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |
| 14016 | The idea of simultaneity in Special Relativity is full of verificationist assumptions [Bourne] |
| 14019 | Relativity denies simultaneity, so it needs past, present and future (unlike Presentism) [Bourne] |
| 14013 | Special Relativity allows an absolute past, future, elsewhere and simultaneity [Bourne] |
| 14015 | No-Futurists believe in past and present, but not future, and say the world grows as facts increase [Bourne] |
| 14007 | How can presentists talk of 'earlier than', and distinguish past from future? [Bourne] |
| 14011 | Presentism seems to deny causation, because the cause and the effect can never coexist [Bourne] |
| 14017 | Since presentists treat the presentness of events as basic, simultaneity should be define by that means [Bourne] |
| 14003 | Time is tensed or tenseless; the latter says all times and objects are real, and there is no passage of time [Bourne] |
| 14005 | B-series objects relate to each other; A-series objects relate to the present [Bourne] |
| 14006 | Time flows, past is fixed, future is open, future is feared but not past, we remember past, we plan future [Bourne] |