42 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] |
18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
18182 | The extension of concepts is not important to me [Maddy] |
18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
23044 | All knowledge rests on a fundamental unity between the knower and what is known [Green,TH, by Muirhead] |
23034 | The ultimate test for truth is the systematic interdependence in nature [Green,TH, by Muirhead] |
8130 | Qualities of experience are just representational aspects of experience ('Representationalism') [Harman, by Burge] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
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] |