25 ideas
21855 | Only in the 1780s did it become acceptable to read Spinoza [Lord] |
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] |
21866 | Hobbes and Spinoza use 'conatus' to denote all endeavour for advantage in nature [Lord] |
2590 | Dispositions need mental terms to define them [Putnam] |
2591 | Total paralysis would mean that there were mental states but no behaviour at all [Putnam] |
2592 | Functional states correlate with AND explain pain behaviour [Putnam] |
2589 | Functionalism is compatible with dualism, as pure mind could perform the functions [Putnam] |
2588 | Is pain a functional state of a complete organism? [Putnam] |
2587 | Temperature is mean molecular kinetic energy, but they are two different concepts [Putnam] |
6376 | Neuroscience does not support multiple realisability, and tends to support identity [Polger on Putnam] |
2330 | If humans and molluscs both feel pain, it can't be a single biological state [Putnam, by Kim] |