86 ideas
| 9108 | From an impossibility anything follows [William of Ockham] |
| 16676 | Why use more things when fewer will do? [William of Ockham] |
| 6806 | Do not multiply entities beyond necessity [William of Ockham] |
| 9107 | A proposition is true if its subject and predicate stand for the same thing [William of Ockham] |
| 16300 | Ockham had an early axiomatic account of truth [William of Ockham, by Halbach] |
| 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] |
| 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] |
| 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] |
| 9106 | The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham] |
| 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] |
| 10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
| 10975 | Compactness does not deny that an inference can have infinitely many premisses [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] |
| 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] |
| 9113 | Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham] |
| 9110 | The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham] |
| 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] |
| 16608 | Ockham was an anti-realist about the categories [William of Ockham, by Pasnau] |
| 16654 | Our words and concepts don't always correspond to what is out there [William of Ockham] |
| 18529 | Relations are expressed either as absolute facts, or by a relational concept [William of Ockham] |
| 22132 | Species and genera are individual concepts which naturally signify many individuals [William of Ockham] |
| 9103 | A universal is not a real feature of objects, but only a thought-object in the mind [William of Ockham] |
| 15388 | Universals are single things, and only universal in what they signify [William of Ockham] |
| 10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
| 16779 | Cut wood doesn't make a new substance, but seems to make separate subjects [William of Ockham] |
| 16757 | Hot water naturally cools down, which is due to the substantial form of the water [William of Ockham] |
| 16599 | Ockham says matter must be extended, so we don't need Quantity [William of Ockham, by Pasnau] |
| 16681 | Matter gets its quantity from condensation and rarefaction, which is just local motion [William of Ockham] |
| 9109 | If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham] |
| 16792 | If parts change, the whole changes [William of Ockham] |
| 11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| 10989 | The standard view of conditionals is that they are truth-functional [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] |
| 9089 | Knowledge is a quality existing subjectively in the soul [William of Ockham] |
| 9091 | Sometimes 'knowledge' just concerns the conclusion, sometimes the whole demonstration [William of Ockham] |
| 9100 | Our intellect only assents to what we believe to be true [William of Ockham] |
| 9090 | Knowledge is certain cognition of something that is true [William of Ockham] |
| 9101 | Abstractive cognition knows universals abstracted from many singulars [William of Ockham] |
| 9102 | If an animal approached from a distance, we might abstract 'animal' from one instance [William of Ockham] |
| 10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
| 9114 | There are no secure foundations to prove the separate existence of mind, in reason or experience [William of Ockham] |
| 9104 | A universal is the result of abstraction, which is only a kind of mental picturing [William of Ockham] |
| 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] |
| 9105 | Some concepts for propositions exist only in the mind, and in no language [William of Ockham] |
| 6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |
| 16675 | Every extended material substance is composed of parts distant from one another [William of Ockham] |
| 19381 | The past has ceased to exist, and the future does not yet exist, so time does not exist [William of Ockham] |
| 9111 | God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham] |
| 8010 | William of Ockham is the main spokesman for God's commands being the source of morality [William of Ockham] |
| 9112 | We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham] |
| 9115 | To love God means to love whatever God wills to be loved [William of Ockham] |
| 16679 | Even an angel must have some location [William of Ockham, by Pasnau] |