73 ideas
5278 | Philosophy is no more than abstractions concerning observations of human historical development [Marx/Engels] |
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] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
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] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
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] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
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] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
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] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
5287 | Philosophical problems are resolved into empirical facts [Marx/Engels] |
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] |
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] |
23872 | 'Society determines consciousness' is contradictory; society only exists in minds [Weil on Marx/Engels] |
5277 | Life is not determined by consciousness, but consciousness by life [Marx/Engels] |
10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
5280 | Language co-exists with consciousness, and makes it social [Marx/Engels] |
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] |
5276 | The nature of an individual coincides with what they produce and how they produce it [Marx/Engels] |
5281 | Consciousness is a social product [Marx/Engels] |
5289 | When aristocracy or the bourgeoisie dominate, certain values dominate with them [Marx/Engels] |
5274 | Young Hegelians proposed changing our present consciousness for liberating critical consciousness [Marx/Engels] |
21992 | Producing their own subsistence distinguishes men from animals [Marx/Engels] |
5275 | Men distinguish themselves from animals when they begin to produce their means of subsistence [Marx/Engels] |
5292 | Individuals are mutually hostile unless they group together in competition with other groups [Marx/Engels] |
5293 | Only in community are people able to cultivate their gifts, and therefore be free [Marx/Engels] |
5273 | Young Hegelians think consciousness is chains for men, where old Hegelians think it the bond of society [Marx/Engels] |
5283 | In communist society we are not trapped in one activity, but can act freely [Marx/Engels] |
5282 | If the common interest imposes on the individual, his actions become alienated and enslaving [Marx/Engels] |
5288 | The class controlling material production also controls mental production [Marx/Engels] |
5290 | The revolutionary class is opposed to 'class', and represents all of society [Marx/Engels] |
5294 | To assert themselves as individuals, the proletarians must overthrow the State [Marx/Engels] |
5285 | Slavery cannot be abolished without the steam-engine [Marx/Engels] |
5284 | Communism abolishes private property and dissolves the powerful world market [Marx/Engels] |
5291 | The law says private property is the result of the general will [Marx/Engels] |
5279 | Human history must always be studied in relation to industry and exchange [Marx/Engels] |
5286 | Most historians are trapped in the illusions of their own epoch [Marx/Engels] |