40 ideas
4456 | Epistemological Ockham's Razor demands good reasons, but the ontological version says reality is simple [Moreland] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
6368 | If my ticket won't win the lottery (and it won't), no other tickets will either [Kyburg, by Pollock/Cruz] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
4474 | Existence theories must match experience, possibility, logic and knowledge, and not be self-defeating [Moreland] |
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] |
4449 | Evidence for universals can be found in language, communication, natural laws, classification and ideals [Moreland] |
4450 | The traditional problem of universals centres on the "One over Many", which is the unity of natural classes [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] |
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] |
4468 | How could 'being even', or 'being a father', or a musical interval, exist naturally in space? [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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
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] |
4473 | 'Presentism' is the view that only the present moment exists [Moreland] |