86 ideas
5278 | Philosophy is no more than abstractions concerning observations of human historical development [Marx/Engels] |
10633 | 'Some critics admire only one another' cannot be paraphrased in singular first-order [Linnebo] |
9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
10779 | A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo] |
9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
18151 | Could we replace sets by the open sentences that define them? [Chihara, by Bostock] |
9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
10638 | A pure logic is wholly general, purely formal, and directly known [Linnebo] |
10781 | A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo] |
9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
10778 | Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo] |
10783 | Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo] |
10635 | Second-order quantification and plural quantification are different [Linnebo] |
10636 | Plural plurals are unnatural and need a first-level ontology [Linnebo] |
10639 | Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo] |
10640 | Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo] |
10641 | Traditionally we eliminate plurals by quantifying over sets [Linnebo] |
23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |
5287 | Philosophical problems are resolved into empirical facts [Marx/Engels] |
10643 | We speak of a theory's 'ideological commitments' as well as its 'ontological commitments' [Linnebo] |
9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
10637 | Ordinary speakers posit objects without concern for ontology [Linnebo] |
14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
10782 | The modern concept of an object is rooted in quantificational logic [Linnebo] |
5303 | For the proletariate, law, morality and religion are just expressions of bourgeois interests [Marx/Engels] |
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] |
9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
5280 | Language co-exists with consciousness, and makes it social [Marx/Engels] |
9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
10634 | Predicates are 'distributive' or 'non-distributive'; do individuals do what the group does? [Linnebo] |
5281 | Consciousness is a social product [Marx/Engels] |
5276 | The nature of an individual coincides with what they produce and how they produce it [Marx/Engels] |
21998 | Bourgeois interests create our morality, law and religion [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] |
5302 | Modern governments are just bourgeois management committees [Marx/Engels] |
5304 | Communism aims to abolish not all property, but bourgeois property [Marx/Engels] |
5307 | Many of the bourgeois rights grievances are a form of self-defence [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] |
5306 | The free development of each should be the condition for the free development of all [Marx/Engels] |
5291 | The law says private property is the result of the general will [Marx/Engels] |
5305 | Communists want to rescue education from the ruling class [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] |
5301 | The history of all existing society is the history of class struggles [Marx/Engels] |
9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |