27 ideas
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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
23805 | Some explanations offer to explain a mystery by a greater mystery [Schulte] |
23793 | On the whole, referential content is seen as broad, and sense content as narrow [Schulte] |
23796 | Naturalists must explain both representation, and what is represented [Schulte] |
23806 | Naturalist accounts of representation must match the views of cognitive science [Schulte] |
23792 | Phenomenal and representational character may have links, or even be united [Schulte] |
23795 | Naturalistic accounts of content cannot rely on primitive mental or normative notions [Schulte] |
23804 | Maybe we can explain mental content in terms of phenomenal properties [Schulte] |
23802 | Conceptual role semantics says content is determined by cognitive role [Schulte] |
23797 | Cause won't explain content, because one cause can produce several contents [Schulte] |
23800 | Teleosemantic explanations say content is the causal result of naturally selected functions [Schulte] |
23799 | Teleosemantics explains content in terms of successful and unsuccessful functioning [Schulte] |
23798 | Information theories say content is information, such as smoke making fire probable [Schulte] |