62 ideas
162 | Can we understand an individual soul without knowing the soul in general? [Plato] |
160 | The highest ability in man is the ability to discuss unity and plurality in the nature of things [Plato] |
166 | A speaker should be able to divide a subject, right down to the limits of divisibility [Plato] |
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] |
7953 | Reasoning needs to cut nature accurately at the joints [Plato] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
16121 | I revere anyone who can discern a single thing that encompasses many things [Plato] |
153 | It takes a person to understand, by using universals, and by using reason to create a unity out of sense-impressions [Plato] |
154 | We would have an overpowering love of knowledge if we had a pure idea of it - as with the other Forms [Plato] |
151 | True knowledge is of the reality behind sense experience [Plato] |
165 | If the apparent facts strongly conflict with probability, it is in everyone's interests to suppress the facts [Plato] |
9296 | The soul is self-motion [Plato] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
23997 | Plato saw emotions and appetites as wild horses, in need of taming [Plato, by Goldie] |
159 | Only a good philosopher can be a good speaker [Plato] |
5946 | 'Phaedrus' pioneers the notion of philosophical rhetoric [Lawson-Tancred on Plato] |
158 | An excellent speech seems to imply a knowledge of the truth in the mind of the speaker [Plato] |
7352 | Jesus said learning was unnecessary, and only the spirit of the Law was needed [Jesus, by Johnson,P] |
155 | Beauty is the clearest and most lovely of the Forms [Plato] |
143 | The two ruling human principles are the natural desire for pleasure, and an acquired love of virtue [Plato] |
6289 | Love your enemies [Jesus] |
6292 | Love thy neighbour as thyself [Jesus] |
157 | Most pleasure is release from pain, and is therefore not worthwhile [Plato] |
5356 | Treat others as you would have them treat you [Jesus] |
6286 | Blessed are the merciful: for they shall obtain mercy [Jesus] |
144 | Reason impels us towards excellence, which teaches us self-control [Plato] |
6290 | Except ye become as little children, ye shall not enter heaven [Jesus] |
6287 | If you lust after a woman, you have committed adultery [Jesus] |
6285 | Blessed are the meek; for they shall inherit the earth [Jesus] |
6288 | Don't resist evil, but turn the other cheek [Jesus] |
6293 | It is almost impossible for the rich to go to heaven [Jesus] |
156 | Bad people are never really friends with one another [Plato] |
148 | If the prime origin is destroyed, it will not come into being again out of anything [Plato] |
152 | The mind of God is fully satisfied and happy with a vision of reality and truth [Plato] |
6291 | No one is good except God [Jesus] |
150 | We cannot conceive of God, so we have to think of Him as an immortal version of ourselves [Plato] |
149 | There isn't a single reason for positing the existence of immortal beings [Plato] |
7351 | Jesus turned the ideas of Hillel into a theology reduced to its moral elements [Jesus, by Johnson,P] |
146 | Soul is always in motion, so it must be self-moving and immortal [Plato] |