48 ideas
4456 | Epistemological Ockham's Razor demands good reasons, but the ontological version says reality is simple [Moreland] |
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] |
9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
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] |
9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
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] |
10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
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] |
10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
4474 | Existence theories must match experience, possibility, logic and knowledge, and not be self-defeating [Moreland] |
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] |
4461 | Tropes are like Hume's 'impressions', conceived as real rather than as ideal [Moreland] |
4462 | A colour-trope cannot be simple (as required), because it is spread in space, and so it is complex [Moreland] |
4463 | In 'four colours were used in the decoration', colours appear to be universals, not tropes [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] |
4468 | How could 'being even', or 'being a father', or a musical interval, exist naturally in space? [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] |
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] |
4476 | Most philosophers think that the identity of indiscernibles is false [Moreland] |
13165 | Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus] |
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] |
9569 | The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus] |
9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |
4473 | 'Presentism' is the view that only the present moment exists [Moreland] |