33 ideas
23027 | Ideals and metaphysics are practical, not imaginative or speculative [Green,TH, by Muirhead] |
23030 | Truth is a relation to a whole of organised knowledge in the collection of rational minds [Green,TH, by Muirhead] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
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] |
16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
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] |
23044 | All knowledge rests on a fundamental unity between the knower and what is known [Green,TH, by Muirhead] |
16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
23034 | The ultimate test for truth is the systematic interdependence in nature [Green,TH, by Muirhead] |
23032 | What is distinctive of human life is the desire for self-improvement [Green,TH, by Muirhead] |
23033 | Hedonism offers no satisfaction, because what we desire is self-betterment [Green,TH, by Muirhead] |
23045 | Politics is compromises, which seem supported by a social contract, but express the will of no one [Green,TH] |
23050 | The ideal is a society in which all citizens are ladies and gentlemen [Green,TH] |
23052 | Enfranchisement is an end in itself; it makes a person moral, and gives a basis for respect [Green,TH] |
23036 | The good is identified by the capacities of its participants [Green,TH, by Muirhead] |
23039 | A true state is only unified and stabilised by acknowledging individuality [Green,TH, by Muirhead] |
23038 | People only develop their personality through co-operation with the social whole [Green,TH, by Muirhead] |
23040 | If something develops, its true nature is embodied in its end [Green,TH] |
23031 | God is the ideal end of the mature mind's final development [Green,TH] |
23041 | God is the realisation of the possibilities of each man's self [Green,TH] |