59 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] |
| 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] |
| 10373 | Logical form can't dictate metaphysics, as it may propose an undesirable property [Schaffer,J] |
| 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] |
| 10367 | There is only one fact - the True [Schaffer,J] |
| 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] |
| 10359 | In causation there are three problems of relata, and three metaphysical problems [Schaffer,J] |
| 10372 | Causation may not be transitive; the last event may follow from the first, but not be caused by it [Schaffer,J] |
| 10374 | There are at least ten theories about causal connections [Schaffer,J] |
| 10366 | Causation transcends nature, because absences can cause things [Schaffer,J] |
| 10377 | Causation may not be a process, if a crucial part of the process is 'disconnected' [Schaffer,J] |
| 10378 | A causal process needs to be connected to the effect in the right way [Schaffer,J] |
| 10382 | Causation can't be a process, because a process needs causation as a primitive [Schaffer,J] |
| 10375 | At least four rivals have challenged the view that causal direction is time direction [Schaffer,J] |
| 10389 | Causal order must be temporal, or else causes could be blocked, and time couldn't be explained [Schaffer,J] |
| 10390 | Causal order is not temporal, because of time travel, and simultanous, joint or backward causes [Schaffer,J] |
| 10380 | Causation is primitive; it is too intractable and central to be reduced; all explanations require it [Schaffer,J] |
| 10385 | If causation is just observables, or part of common sense, or vacuous, it can't be primitive [Schaffer,J] |
| 10387 | The notion of causation allows understanding of science, without appearing in equations [Schaffer,J] |
| 10388 | Causation is utterly essential for numerous philosophical explanations [Schaffer,J] |
| 10384 | If two different causes are possible in one set of circumstances, causation is primitive [Schaffer,J] |
| 10386 | If causation is primitive, it can be experienced in ourselves, or inferred as best explanation [Schaffer,J] |
| 10361 | Events are fairly course-grained (just saying 'hello'), unlike facts (like saying 'hello' loudly) [Schaffer,J] |
| 10360 | Causal relata are events - or facts, features, tropes, states, situations or aspects [Schaffer,J] |
| 10362 | One may defend three or four causal relata, as in 'c causes e rather than e*' [Schaffer,J] |
| 10368 | If causal relata must be in nature and fine-grained, neither facts nor events will do [Schaffer,J] |
| 10383 | The relata of causation (such as events) need properties as explanation, which need causation! [Schaffer,J] |
| 10393 | Our selection of 'the' cause is very predictable, so must have a basis [Schaffer,J] |
| 10394 | Selecting 'the' cause must have a basis; there is no causation without such a selection [Schaffer,J] |
| 10376 | The actual cause may make an event less likely than a possible more effective cause [Schaffer,J] |
| 10381 | All four probability versions of causation may need causation to be primitive [Schaffer,J] |