65 ideas
| 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] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 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] |
| 12430 | Classical logic is our preconditions for assessing empirical evidence [Kitcher] |
| 12431 | I believe classical logic because I was taught it and use it, but it could be undermined [Kitcher] |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| 6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik] |
| 12392 | Mathematical a priorism is conceptualist, constructivist or realist [Kitcher] |
| 18078 | The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher] |
| 12426 | The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher] |
| 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] |
| 12395 | Real numbers stand to measurement as natural numbers stand to counting [Kitcher] |
| 12425 | Complex numbers were only accepted when a geometrical model for them was found [Kitcher] |
| 18071 | A one-operation is the segregation of a single object [Kitcher] |
| 18066 | The old view is that mathematics is useful in the world because it describes the world [Kitcher] |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher] |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| 12387 | Mathematical knowledge arises from basic perception [Kitcher] |
| 12412 | My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher] |
| 18065 | We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher] |
| 18077 | The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher] |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| 18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
| 18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
| 18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher] |
| 18064 | If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher] |
| 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] |
| 3353 | If there is no causal interaction with transcendent Platonic objects, how can you learn about them? [Benardete,JA] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 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] |
| 12428 | Many necessities are inexpressible, and unknowable a priori [Kitcher] |
| 12429 | Knowing our own existence is a priori, but not necessary [Kitcher] |
| 3306 | The clearest a priori knowledge is proving non-existence through contradiction [Benardete,JA] |
| 12390 | A priori knowledge comes from available a priori warrants that produce truth [Kitcher] |
| 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] |
| 12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
| 12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher] |
| 12416 | We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher] |
| 12413 | A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher] |
| 20473 | If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 3334 | Rationalists see points as fundamental, but empiricists prefer regions [Benardete,JA] |
| 3308 | In the ontological argument a full understanding of the concept of God implies a contradiction in 'There is no God' [Benardete,JA] |