27 ideas
| 2945 | Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer] |
| 2946 | You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 15091 | Restrict 'logical truth' to formal logic, rather than including analytic and metaphysical truths [Shoemaker] |
| 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] |
| 15095 | A property's causal features are essential, and only they fix its identity [Shoemaker] |
| 15097 | I claim that a property has its causal features in all possible worlds [Shoemaker] |
| 15094 | I now deny that properties are cluster of powers, and take causal properties as basic [Shoemaker] |
| 15099 | If something is possible, but not nomologically possible, we need metaphysical possibility [Shoemaker] |
| 15101 | Once you give up necessity as a priori, causal necessity becomes the main type of necessity [Shoemaker] |
| 15098 | Empirical evidence shows that imagining a phenomenon can show it is possible [Shoemaker] |
| 15100 | Imagination reveals conceptual possibility, where descriptions avoid contradiction or incoherence [Shoemaker] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 15096 | 'Grue' only has causal features because of its relation to green [Shoemaker] |
| 15093 | We might say laws are necessary by combining causal properties with Armstrong-Dretske-Tooley laws [Shoemaker] |