23 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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
6624 | Dennett denies the existence of qualia [Dennett, by Lowe] |
9264 | Persons are distinguished by a capacity for second-order desires [Frankfurt] |
9266 | A person essentially has second-order volitions, and not just second-order desires [Frankfurt] |
9267 | Free will is the capacity to choose what sort of will you have [Frankfurt] |
9265 | The will is the effective desire which actually leads to an action [Frankfurt] |
20015 | Freedom of action needs the agent to identify with their reason for acting [Frankfurt, by Wilson/Schpall] |
9270 | A 'wanton' is not a person, because they lack second-order volitions [Frankfurt] |
9269 | A person may be morally responsible without free will [Frankfurt] |