67 ideas
5988 | Anaximander produced the first philosophy book (and maybe the first book) [Anaximander, by Bodnár] |
1496 | The earth is stationary, because it is in the centre, and has no more reason to move one way than another [Anaximander, by Aristotle] |
19215 | Arguers often turn the opponent's modus ponens into their own modus tollens [Merricks] |
19205 | 'Snow is white' only contingently expresses the proposition that snow is white [Merricks] |
10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
19209 | Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem [Merricks] |
11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
19208 | The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists' [Merricks] |
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] |
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] |
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] |
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] |
19207 | Sentence logic maps truth values; predicate logic maps objects and sets [Merricks] |
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] |
14874 | Anaximander saw the contradiction in the world - that its own qualities destroy it [Anaximander, by Nietzsche] |
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] |
10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
19214 | In twinning, one person has the same origin as another person [Merricks] |
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] |
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] |
19217 | I don't accept that if a proposition is directly about an entity, it has a relation to the entity [Merricks] |
19203 | A sentence's truth conditions depend on context [Merricks] |
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] |
19200 | Propositions are standardly treated as possible worlds, or as structured [Merricks] |
19206 | 'Cicero is an orator' represents the same situation as 'Tully is an orator', so they are one proposition [Merricks] |
19202 | Propositions are necessary existents which essentially (but inexplicably) represent things [Merricks] |
19204 | True propositions existed prior to their being thought, and might never be thought [Merricks] |
19210 | The standard view of propositions says they never change their truth-value [Merricks] |
19201 | Propositions can be 'about' an entity, but that doesn't make the entity a constituent of it [Merricks] |
19211 | Early Russell says a proposition is identical with its truthmaking state of affairs [Merricks] |
19212 | Unity of the proposition questions: what unites them? can the same constituents make different ones? [Merricks] |
19213 | We want to explain not just what unites the constituents, but what unites them into a proposition [Merricks] |
405 | The essential nature, whatever it is, of the non-limited is everlasting and ageless [Anaximander] |
13222 | The Boundless cannot exist on its own, and must have something contrary to it [Aristotle on Anaximander] |
404 | Things begin and end in the Unlimited, and are balanced over time according to justice [Anaximander] |
1495 | Anaximander introduced the idea that the first principle and element of things was the Boundless [Anaximander, by Simplicius] |
1746 | The parts of all things are susceptible to change, but the whole is unchangeable [Anaximander, by Diog. Laertius] |