55 ideas
| 7791 | The simplest of the logics based on possible worlds is Lewis's S5 [Lewis,CI, by Girle] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 9358 | There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI] |
| 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] |
| 9357 | Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI] |
| 9364 | Names represent a uniformity in experience, or they name nothing [Lewis,CI] |
| 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] |
| 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] |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [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] |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 11002 | Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read] |
| 9362 | Necessary truths are those we will maintain no matter what [Lewis,CI] |
| 7803 | Modal logic began with translation difficulties for 'If...then' [Lewis,CI, by Girle] |
| 12428 | Many necessities are inexpressible, and unknowable a priori [Kitcher] |
| 12429 | Knowing our own existence is a priori, but not necessary [Kitcher] |
| 12390 | A priori knowledge comes from available a priori warrants that produce truth [Kitcher] |
| 12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
| 9365 | We can maintain a priori principles come what may, but we can also change them [Lewis,CI] |
| 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] |
| 21500 | We rely on memory for empirical beliefs because they mutually support one another [Lewis,CI] |
| 21501 | If we doubt memories we cannot assess our doubt, or what is being doubted [Lewis,CI] |
| 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] |
| 6556 | If anything is to be probable, then something must be certain [Lewis,CI] |
| 21498 | Congruents assertions increase the probability of each individual assertion in the set [Lewis,CI] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 5828 | Extension is the class of things, intension is the correct definition of the thing, and intension determines extension [Lewis,CI] |
| 9361 | We have to separate the mathematical from physical phenomena by abstraction [Lewis,CI] |
| 9363 | Science seeks classification which will discover laws, essences, and predictions [Lewis,CI] |