47 ideas
12124 | Metaphysics is the best knowledge, because it is the simplest [Bacon] |
12123 | Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon] |
12119 | Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon] |
12120 | Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon] |
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] |
12121 | We don't assume there is no land, because we can only see sea [Bacon] |
12117 | Science moves up and down between inventions of causes, and experiments [Bacon] |
12127 | Many different theories will fit the observed facts [Bacon] |
12126 | People love (unfortunately) extreme generality, rather than particular knowledge [Bacon] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
23814 | Every human yearns for an unattainable transcendent good [Weil] |
23824 | Where human needs are satisfied we find happiness, friendship and beauty [Weil] |
23815 | We cannot equally respect what is unequal, so equal respect needs a shared ground [Weil] |
23823 | Life needs risks to avoid sickly boredom [Weil] |
23822 | We all need to partipate in public tasks, and take some initiative [Weil] |
23817 | We need both equality (to attend to human needs) and hierarchy (as a scale of responsibilities) [Weil] |
23819 | Deliberate public lying should be punished [Weil] |
23818 | We have liberty in the space between nature and accepted authority [Weil] |
23820 | People need personal and collective property, and a social class lacking property is shameful [Weil] |
23821 | Crime should be punished, to bring the perpetrator freely back to morality [Weil] |
12125 | Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon] |
12118 | Essences are part of first philosophy, but as part of nature, not part of logic [Bacon] |
23816 | Attention to a transcendent reality motivates a duty to foster the good of humanity [Weil] |