60 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] |
| 3358 | Metaphysics focuses on Platonism, essentialism, materialism and anti-realism [Benardete,JA] |
| 3312 | There are the 'is' of predication (a function), the 'is' of identity (equals), and the 'is' of existence (quantifier) [Benardete,JA] |
| 3352 | Analytical philosophy analyses separate concepts successfully, but lacks a synoptic vision of the results [Benardete,JA] |
| 3329 | Presumably the statements of science are true, but should they be taken literally or not? [Benardete,JA] |
| 306 | Nothing can come to be without a cause [Plato] |
| 3326 | Set theory attempts to reduce the 'is' of predication to mathematics [Benardete,JA] |
| 3327 | The set of Greeks is included in the set of men, but isn't a member of it [Benardete,JA] |
| 3335 | The standard Z-F Intuition version of set theory has about ten agreed axioms [Benardete,JA, by PG] |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| 3332 | Greeks saw the science of proportion as the link between geometry and arithmetic [Benardete,JA] |
| 3330 | Negatives, rationals, irrationals and imaginaries are all postulated to solve baffling equations [Benardete,JA] |
| 3337 | Natural numbers are seen in terms of either their ordinality (Peano), or cardinality (set theory) [Benardete,JA] |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| 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] |
| 3310 | If slowness is a property of walking rather than the walker, we must allow that events exist [Benardete,JA] |
| 12793 | Early pre-Socratics had a mass-noun ontology, which was replaced by count-nouns [Benardete,JA] |
| 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] |
| 3353 | If there is no causal interaction with transcendent Platonic objects, how can you learn about them? [Benardete,JA] |
| 3304 | Why should packed-together particles be a thing (Mt Everest), but not scattered ones? [Benardete,JA] |
| 3350 | Could a horse lose the essential property of being a horse, and yet continue to exist? [Benardete,JA] |
| 3309 | If a soldier continues to exist after serving as a soldier, does the wind cease to exist after it ceases to blow? [Benardete,JA] |
| 3351 | One can step into the same river twice, but not into the same water [Benardete,JA] |
| 3314 | Absolutists might accept that to exist is relative, but relative to what? How about relative to itself? [Benardete,JA] |
| 3323 | Maybe self-identity isn't existence, if Pegasus can be self-identical but non-existent [Benardete,JA] |
| 3306 | The clearest a priori knowledge is proving non-existence through contradiction [Benardete,JA] |
| 3349 | If we know truths about prime numbers, we seem to have synthetic a priori knowledge of Platonic objects [Benardete,JA] |
| 3341 | Logical positivism amounts to no more than 'there is no synthetic a priori' [Benardete,JA] |
| 3344 | Assertions about existence beyond experience can only be a priori synthetic [Benardete,JA] |
| 3345 | Appeals to intuition seem to imply synthetic a priori knowledge [Benardete,JA] |
| 334 | Only bird-brained people think astronomy is entirely a matter of evidence [Plato] |
| 5962 | Plato says the soul is ordered by number [Plato, by Plutarch] |
| 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] |
| 3334 | Rationalists see points as fundamental, but empiricists prefer regions [Benardete,JA] |
| 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] |
| 3308 | In the ontological argument a full understanding of the concept of God implies a contradiction in 'There is no God' [Benardete,JA] |