27 ideas
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] |
7949 | Varied descriptions of an event will explain varied behaviour relating to it [Davidson, by Macdonald,C] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
20020 | If one action leads directly to another, they are all one action [Davidson, by Wilson/Schpall] |
20072 | We explain an intention by giving an account of acting with an intention [Davidson, by Stout,R] |
20045 | Acting for a reason is a combination of a pro attitude, and a belief that the action is appropriate [Davidson] |
20075 | Early Davidson says intentional action is caused by reasons [Davidson, by Stout,R] |
23734 | The best explanation of reasons as purposes for actions is that they are causal [Davidson, by Smith,M] |
23737 | Reasons can give purposes to actions, without actually causing them [Smith,M on Davidson] |
6664 | Reasons must be causes when agents act 'for' reasons [Davidson, by Lowe] |
3395 | Davidson claims that what causes an action is the reason for doing it [Davidson, by Kim] |
5049 | Intelligent pleasure is the perception of beauty, order and perfection [Leibniz] |
5048 | Perfection is simply quantity of reality [Leibniz] |
5050 | Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz] |