43 ideas
19335 | Reasonings have a natural ordering in God's understanding, but only a temporal order in ours [Leibniz] |
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] |
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] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [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] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
19367 | Saying we must will whatever we decide to will leads to an infinite regress [Leibniz] |
19351 | Perfections of soul subordinate the body, but imperfections of soul submit to the body [Leibniz] |
19331 | Will is an inclination to pursue something good [Leibniz] |
19346 | Most people facing death would happily re-live a similar life, with just a bit of variety [Leibniz] |
19340 | Metaphysical evil is imperfection; physical evil is suffering; moral evil is sin [Leibniz] |
19366 | You can't assess moral actions without referring to the qualities of character that produce them [Leibniz] |
15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |
19326 | God must be intelligible, to select the actual world from the possibilities [Leibniz] |
19327 | The intelligent cause must be unique and all-perfect, to handle all the interconnected possibilities [Leibniz] |
19344 | God prefers men to lions, but might not exterminate lions to save one man [Leibniz] |
19330 | If justice is arbitrary, or fixed but not observed, or not human justice, this undermines God [Leibniz] |
19325 | God is the first reason of things; our experiences are contingent, and contain no necessity [Leibniz] |
19329 | The laws of physics are wonderful evidence of an intelligent and free being [Leibniz] |
19437 | Prayers are useful, because God foresaw them in his great plan [Leibniz] |
19337 | How can an all-good, wise and powerful being allow evil, sin and apparent injustice? [Leibniz] |
19345 | Being confident of God's goodness, we disregard the apparent local evils in the visible world [Leibniz] |