56 ideas
326 | For relaxation one can consider the world of change, instead of eternal things [Plato] |
315 | Philosophy is the supreme gift of the gods to mortals [Plato] |
306 | Nothing can come to be without a cause [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] |
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] |
324 | Before the existence of the world there must have been being, space and becoming [Plato] |
20364 | The apprehensions of reason remain unchanging, but reasonless sensation shows mere becoming [Plato] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
12042 | Plato's Forms were seen as part of physics, rather than of metaphysics [Plato, by Annas] |
307 | Something will always be well-made if the maker keeps in mind the eternal underlying pattern [Plato] |
318 | In addition to the underlying unchanging model and a changing copy of it, there must also be a foundation of all change [Plato] |
321 | For knowledge and true opinion to be different there must be Forms; otherwise we are just stuck with sensations [Plato] |
317 | The universe is basically an intelligible and unchanging model, and a visible and changing copy of it [Plato] |
334 | Only bird-brained people think astronomy is entirely a matter of evidence [Plato] |
8830 | A belief can be justified when the person has forgotten the evidence for it [Goldman] |
8832 | If justified beliefs are well-formed beliefs, then animals and young children have them [Goldman] |
8829 | Justification depends on the reliability of its cause, where reliable processes tend to produce truth [Goldman] |
5962 | Plato says the soul is ordered by number [Plato, by Plutarch] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
8831 | Introspection is really retrospection; my pain is justified by a brief causal history [Goldman] |
330 | No one wants to be bad, but bad men result from physical and educational failures, which they do not want or choose [Plato] |
316 | Music has harmony like the soul, and serves to reorder disharmony within us [Plato] |
332 | One should exercise both the mind and the body, to avoid imbalance [Plato] |
328 | Everything that takes place naturally is pleasant [Plato] |
322 | Intelligence is the result of rational teaching; true opinion can result from irrational persuasion [Plato] |
331 | Bad governments prevent discussion, and discourage the study of virtue [Plato] |
311 | The cosmos must be unique, because it resembles the creator, who is unique [Plato] |
310 | The creator of the cosmos had no envy, and so wanted things to be as like himself as possible [Plato] |
325 | We must consider the four basic shapes as too small to see, only becoming visible in large numbers [Plato] |
327 | There are two types of cause, the necessary and the divine [Plato] |
314 | Heavenly movements gave us the idea of time, and caused us to inquire about the heavens [Plato] |
312 | Time came into existence with the heavens, so that there will be a time when they can be dissolved [Plato] |
309 | Clearly the world is good, so its maker must have been concerned with the eternal, not with change [Plato] |
308 | If the cosmos is an object of perception then it must be continually changing [Plato] |