29 ideas
| 7396 | Hobbes created English-language philosophy [Hobbes, by Tuck] |
| 19048 | Contextual definition shifted the emphasis from words to whole sentences [Quine] |
| 19047 | Bentham's contextual definitions preserved terms after their denotation became doubtful [Quine] |
| 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] |
| 16638 | The qualities of the world are mere appearances; reality is the motions which cause them [Hobbes] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 16688 | Evidence is conception, which is imagination, which proceeds from the senses [Hobbes] |
| 7405 | Experience can't prove universal truths [Hobbes] |
| 19049 | In scientific theories sentences are too brief to be independent vehicles of empirical meaning [Quine] |
| 19046 | Empiricism improvements: words for ideas, then sentences, then systems, then no analytic, then naturalism [Quine] |
| 19050 | Holism in language blurs empirical synthetic and empty analytic sentences [Quine] |
| 7408 | It is an error that reason should control the passions, which give right guidance on their own [Hobbes, by Tuck] |
| 7407 | Good and evil are what please us; goodness and badness the powers causing them [Hobbes] |
| 7410 | Self-preservation is basic, and people judge differently about that, implying ethical relativism [Hobbes, by Tuck] |
| 7409 | Hobbes shifted from talk of 'the good' to talk of 'rights' [Hobbes, by Tuck] |
| 7411 | The attributes of God just show our inability to conceive his nature [Hobbes] |