37 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] |
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] |
23044 | All knowledge rests on a fundamental unity between the knower and what is known [Green,TH, by Muirhead] |
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] |
7127 | If men are good you should keep promises, but they aren't, so you needn't [Machiavelli] |
23045 | Politics is compromises, which seem supported by a social contract, but express the will of no one [Green,TH] |
6309 | The principle foundations of all states are good laws and good armies [Machiavelli] |
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] |
6306 | People are vengeful, so be generous to them, or destroy them [Machiavelli] |
6305 | To retain a conquered state, wipe out the ruling family, and preserve everything else [Machiavelli] |
6308 | A sensible conqueror does all his harmful deeds immediately, because people soon forget [Machiavelli] |
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] |
6307 | A desire to conquer, and men who do it, are always praised, or not blamed [Machiavelli] |
7486 | Machiavelli emancipated politics from religion [Machiavelli, by Watson] |
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] |