28 ideas
| 15118 | A successful Aristotelian 'definition' is what sciences produces after an investigation [Koslicki] |
| 15116 | Essences cause necessary features, and definitions describe those necessary features [Koslicki] |
| 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] |
| 15110 | An essence and what merely follow from it are distinct [Koslicki] |
| 15113 | Individuals are perceived, but demonstration and definition require universals [Koslicki] |
| 15112 | If an object exists, then its essential properties are necessary [Koslicki] |
| 18969 | How do you distinguish three beliefs from four beliefs or two beliefs? [Quine] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 15111 | In demonstration, the explanatory order must mirror the causal order of the phenomena [Koslicki] |
| 15115 | In a demonstration the middle term explains, by being part of the definition [Koslicki] |
| 15117 | Greek uses the same word for 'cause' and 'explanation' [Koslicki] |
| 15114 | Discovering the Aristotelian essence of thunder will tell us why thunder occurs [Koslicki] |
| 18967 | A 'proposition' is said to be the timeless cognitive part of the meaning of a sentence [Quine] |
| 18968 | The problem with propositions is their individuation. When do two sentences express one proposition? [Quine] |
| 18970 | The concept of a 'point' makes no sense without the idea of absolute position [Quine] |