63 ideas
| 6891 | Quine's naturalistic and empirical view is based entirely on first-order logic and set theory [Quine, by Mautner] |
| 6310 | Enquiry needs a conceptual scheme, so we should retain the best available [Quine] |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| 12798 | Plurals can in principle be paraphrased away altogether [Quine] |
| 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] |
| 17905 | Any progression will do nicely for numbers; they can all then be used to measure multiplicity [Quine] |
| 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] |
| 9556 | Nearly all of mathematics has to quantify over abstract objects [Quine] |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| 18069 | Arithmetic is an idealizing theory [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] |
| 16462 | The quest for ultimate categories is the quest for a simple clear pattern of notation [Quine] |
| 15723 | Either dispositions rest on structures, or we keep saying 'all things being equal' [Quine] |
| 15490 | Explain unmanifested dispositions as structural similarities to objects which have manifested them [Quine, by Martin,CB] |
| 8504 | Quine aims to deal with properties by the use of eternal open sentences, or classes [Quine, by Devitt] |
| 7924 | The notion of a physical object is by far the most useful one for science [Quine] |
| 8464 | Physical objects in space-time are just events or processes, no matter how disconnected [Quine] |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| 8482 | Mathematicians must be rational but not two-legged, cyclists the opposite. So a mathematical cyclist? [Quine] |
| 12136 | Cyclist are not actually essentially two-legged [Brody on Quine] |
| 17594 | We can paraphrase 'x=y' as a sequence of the form 'if Fx then Fy' [Quine] |
| 15725 | Normal conditionals have a truth-value gap when the antecedent is false. [Quine] |
| 15722 | Conditionals are pointless if the truth value of the antecedent is known [Quine] |
| 15719 | We feign belief in counterfactual antecedents, and assess how convincing the consequent is [Quine] |
| 15721 | Counterfactuals are plausible when dispositions are involved, as they imply structures [Quine] |
| 15724 | Counterfactuals have no place in a strict account of science [Quine] |
| 15720 | What stays the same in assessing a counterfactual antecedent depends on context [Quine] |
| 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] |
| 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] |
| 4630 | Two theories can be internally consistent and match all the facts, yet be inconsistent with one another [Quine, by Baggini /Fosl] |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| 3131 | Quine expresses the instrumental version of eliminativism [Quine, by Rey] |
| 3988 | Indeterminacy of translation also implies indeterminacy in interpreting people's mental states [Dennett on Quine] |
| 6311 | The firmer the links between sentences and stimuli, the less translations can diverge [Quine] |
| 6312 | We can never precisely pin down how to translate the native word 'Gavagai' [Quine] |
| 6313 | Stimulus synonymy of 'Gavagai' and 'Rabbit' does not even guarantee they are coextensive [Quine] |
| 6317 | Dispositions to speech behaviour, and actual speech, are never enough to fix any one translation [Quine] |
| 6315 | We should be suspicious of a translation which implies that a people have very strange beliefs [Quine] |
| 6314 | Weird translations are always possible, but they improve if we impose our own logic on them [Quine] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |