29 ideas
19370 | 'Blind thought' is reasoning without recognition of the ingredients of the reasoning [Leibniz, by Arthur,R] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
19391 | We can assign a characteristic number to every single object [Leibniz] |
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] |
19390 | Everything is subsumed under number, which is a metaphysical statics of the universe, revealing powers [Leibniz] |
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] |
22227 | For Sartre there is only being for-itself, or being in-itself (which is beyond experience) [Sartre, by Daigle] |
20743 | Appearances do not hide the essence; appearances are the essence [Sartre] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
6151 | Sartre says consciousness is just directedness towards external objects [Sartre, by Rowlands] |
6164 | Sartre rejects mental content, and the idea that the mind has hidden inner features [Sartre, by Rowlands] |
7074 | Man is a useless passion [Sartre] |
6687 | Man is the desire to be God [Sartre] |
22228 | Sartre's freedom is not for whimsical action, but taking responsibility for our own values [Sartre, by Daigle] |
22233 | Love is the demand to be loved [Sartre] |
20755 | Fear concerns the world, but 'anguish' comes from confronting my self [Sartre] |
20760 | Sincerity is not authenticity, because it only commits to one particular identity [Sartre, by Aho] |
22231 | We flee from the anguish of freedom by seeing ourselves objectively, as determined [Sartre] |