25 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] |
4020 | The modern self has disengaged reason, self-exploration, and personal commitment [Taylor,C] |
4002 | My aim is to map the connections between our sense of self and our moral understanding [Taylor,C] |
4006 | I can only be aware of myself as a person who changes by means of my personal history [Taylor,C] |
4003 | Selfhood and moral values are inextricably intertwined [Taylor,C] |
4021 | Willingness to risk life was the constitutive quality of the man of honour [Taylor,C] |
4005 | To have respect for people, you must feel their claims, or their injustices, or hold them in awe [Taylor,C] |
4004 | Consistency presupposes intrinsic description [Taylor,C] |
4010 | In later utilitarianism the modern stress on freedom leads to the rejection of paternalism [Taylor,C] |
15313 | By 'force' I mean the sources of all actions - sometimes called 'powers' by their outcomes [Breheny] |
4009 | Nominalists defended the sovereignty of God against the idea of natural existing good and evil [Taylor,C] |