40 ideas
| 16943 | Philosophy is continuous with science, and has no external vantage point [Quine] |
| 8250 | So-called 'free logic' operates without existence assumptions [Meinong, by George/Van Evra] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 16949 | Klein summarised geometry as grouped together by transformations [Quine] |
| 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] |
| 16939 | Mass terms just concern spread, but other terms involve both spread and individuation [Quine] |
| 16948 | Once we know the mechanism of a disposition, we can eliminate 'similarity' [Quine] |
| 16945 | We judge things to be soluble if they are the same kind as, or similar to, things that do dissolve [Quine] |
| 8719 | There can be impossible and contradictory objects, if they can have properties [Meinong, by Friend] |
| 8971 | There are objects of which it is true that there are no such objects [Meinong] |
| 8718 | Meinong says an object need not exist, but must only have properties [Meinong, by Friend] |
| 7756 | Meinong said all objects of thought (even self-contradictions) have some sort of being [Meinong, by Lycan] |
| 15781 | The objects of knowledge are far more numerous than objects which exist [Meinong] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 16944 | Science is common sense, with a sophisticated method [Quine] |
| 16940 | Induction is just more of the same: animal expectations [Quine] |
| 16941 | Induction relies on similar effects following from each cause [Quine] |
| 16933 | Grue is a puzzle because the notions of similarity and kind are dubious in science [Quine] |
| 16934 | General terms depend on similarities among things [Quine] |
| 16938 | To learn yellow by observation, must we be told to look at the colour? [Quine] |
| 8486 | Standards of similarity are innate, and the spacing of qualities such as colours can be mapped [Quine] |
| 16947 | Similarity is just interchangeability in the cosmic machine [Quine] |
| 16932 | Projectible predicates can be universalised about the kind to which they refer [Quine] |
| 7375 | Quine probably regrets natural kinds now being treated as essences [Quine, by Dennett] |
| 16935 | If similarity has no degrees, kinds cannot be contained within one another [Quine] |
| 16936 | Comparative similarity allows the kind 'colored' to contain the kind 'red' [Quine] |
| 16937 | You can't base kinds just on resemblance, because chains of resemblance are a muddle [Quine] |
| 16942 | It is hard to see how regularities could be explained [Quine] |