83 ideas
| 4456 | Epistemological Ockham's Razor demands good reasons, but the ontological version says reality is simple [Moreland] |
| 10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
| 11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
| 11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
| 11011 | Same say there are positive, negative and neuter free logics [Read] |
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| 11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
| 14187 | If logic is topic-neutral that means it delves into all subjects, rather than having a pure subject matter [Read] |
| 10986 | Not all validity is captured in first-order logic [Read] |
| 10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
| 11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
| 10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
| 14188 | Not all arguments are valid because of form; validity is just true premises and false conclusion being impossible [Read] |
| 14182 | If the logic of 'taller of' rests just on meaning, then logic may be the study of merely formal consequence [Read] |
| 14183 | Maybe arguments are only valid when suppressed premises are all stated - but why? [Read] |
| 10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
| 10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
| 14184 | In modus ponens the 'if-then' premise contributes nothing if the conclusion follows anyway [Read] |
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| 14186 | Logical connectives contain no information, but just record combination relations between facts [Read] |
| 10973 | A theory is logically closed, which means infinite premisses [Read] |
| 11007 | Quantifiers are second-order predicates [Read] |
| 10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
| 10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
| 10988 | Any first-order theory of sets is inadequate [Read] |
| 10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
| 10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
| 10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
| 10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
| 11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| 11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
| 10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
| 10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
| 10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| 8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
| 4474 | Existence theories must match experience, possibility, logic and knowledge, and not be self-defeating [Moreland] |
| 11016 | Would a language without vagueness be usable at all? [Read] |
| 11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
| 11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
| 11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
| 4461 | Tropes are like Hume's 'impressions', conceived as real rather than as ideal [Moreland] |
| 4463 | In 'four colours were used in the decoration', colours appear to be universals, not tropes [Moreland] |
| 4462 | A colour-trope cannot be simple (as required), because it is spread in space, and so it is complex [Moreland] |
| 4451 | If properties are universals, what distinguishes two things which have identical properties? [Moreland] |
| 4453 | One realism is one-over-many, which may be the model/copy view, which has the Third Man problem [Moreland] |
| 4464 | Realists see properties as universals, which are single abstract entities which are multiply exemplifiable [Moreland] |
| 4450 | The traditional problem of universals centres on the "One over Many", which is the unity of natural classes [Moreland] |
| 4449 | Evidence for universals can be found in language, communication, natural laws, classification and ideals [Moreland] |
| 4454 | The One-In-Many view says universals have abstract existence, but exist in particulars [Moreland] |
| 4452 | Maybe universals are real, if properties themselves have properties, and relate to other properties [Moreland] |
| 4467 | A naturalist and realist about universals is forced to say redness can be both moving and stationary [Moreland] |
| 4469 | There are spatial facts about red particulars, but not about redness itself [Moreland] |
| 4468 | How could 'being even', or 'being a father', or a musical interval, exist naturally in space? [Moreland] |
| 4472 | Redness is independent of red things, can do without them, has its own properties, and has identity [Moreland] |
| 4459 | Moderate nominalism attempts to embrace the existence of properties while avoiding universals [Moreland] |
| 4458 | Unlike Class Nominalism, Resemblance Nominalism can distinguish natural from unnatural classes [Moreland] |
| 4457 | There can be predicates with no property, and there are properties with no predicate [Moreland] |
| 4471 | We should abandon the concept of a property since (unlike sets) their identity conditions are unclear [Moreland] |
| 10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
| 4476 | Most philosophers think that the identity of indiscernibles is false [Moreland] |
| 11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
| 10989 | The standard view of conditionals is that they are truth-functional [Read] |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| 11017 | Some people even claim that conditionals do not express propositions [Read] |
| 14185 | Conditionals are just a shorthand for some proof, leaving out the details [Read] |
| 10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
| 10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
| 10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
| 10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
| 11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
| 10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
| 4460 | Abstractions are formed by the mind when it concentrates on some, but not all, the features of a thing [Moreland] |
| 4455 | It is always open to a philosopher to claim that some entity or other is unanalysable [Moreland] |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| 11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
| 10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
| 4473 | 'Presentism' is the view that only the present moment exists [Moreland] |