31 ideas
| 4901 | Truth has to be correspondence to facts, and a match between relations of ideas and relations in the world [Perry] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 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] |
| 12712 | Substance is that which can act [Leibniz] |
| 4885 | Identity is a very weak relation, which doesn't require interdefinability, or shared properties [Perry] |
| 4899 | Possible worlds thinking has clarified the logic of modality, but is problematic in epistemology [Perry] |
| 4898 | Possible worlds are indices for a language, or concrete realities, or abstract possibilities [Perry] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 12737 | Nature can be fully explained by final causes alone, or by efficient causes alone [Leibniz] |
| 4887 | We try to cause other things to occur by causing mental events to occur [Perry] |
| 4884 | Brain states must be in my head, and yet the pain seems to be in my hand [Perry] |
| 4888 | It seems plausible that many animals have experiences without knowing about them [Perry] |
| 4891 | If epiphenomenalism just says mental events are effects but not causes, it is consistent with physicalism [Perry] |
| 4900 | Prior to Kripke, the mind-brain identity theory usually claimed that the identity was contingent [Perry] |
| 4892 | If physicalists stick with identity (not supervenience), Martian pain will not be like ours [Perry] |
| 4889 | Although we may classify ideas by content, we individuate them differently, as their content can change [Perry] |
| 4896 | The intension of an expression is a function from possible worlds to an appropriate extension [Perry] |
| 4897 | A proposition is a set of possible worlds for which its intension delivers truth [Perry] |
| 4890 | A sharp analytic/synthetic line can rarely be drawn, but some concepts are central to thought [Perry] |