57 ideas
21405 | Cicero sees wisdom in terms of knowledge, but earlier Stoics saw it as moral [Cicero, by Long] |
20871 | Unfortunately we choose a way of life before we are old enough to think clearly [Cicero] |
6267 | A culture needs to admit that knowledge is more extensive than just 'science' [Putnam] |
6272 | 'True' and 'refers' cannot be made scientically precise, but are fundamental to science [Putnam] |
6276 | 'The rug is green' might be warrantedly assertible even though the rug is not green [Putnam] |
6266 | We need the correspondence theory of truth to understand language and science [Putnam] |
6277 | Correspondence between concepts and unconceptualised reality is impossible [Putnam] |
6264 | In Tarski's definition, you understand 'true' if you accept the notions of the object language [Putnam] |
6265 | Tarski has given a correct account of the formal logic of 'true', but there is more to the concept [Putnam] |
6269 | Only Tarski has found a way to define 'true' [Putnam] |
18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
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] |
6280 | Realism is a theory, which explains the convergence of science and the success of language [Putnam] |
18067 | Abstract objects were a bad way of explaining the structure in mathematics [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] |
6284 | If a tautology is immune from revision, why would that make it true? [Putnam] |
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] |
6273 | Knowledge depends on believing others, which must be innate, as inferences are not strong enough [Putnam] |
6274 | Empathy may not give knowledge, but it can give plausibility or right opinion [Putnam] |
17084 | You can't decide which explanations are good if you don't attend to the interest-relative aspects [Putnam] |
18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
6282 | Theory of meaning presupposes theory of understanding and reference [Putnam] |
6281 | Truth conditions can't explain understanding a sentence, because that in turn needs explanation [Putnam] |
6278 | We should reject the view that truth is prior to meaning [Putnam] |
6271 | How reference is specified is not what reference is [Putnam] |
6268 | The claim that scientific terms are incommensurable can be blocked if scientific terms are not descriptions [Putnam] |
6279 | A private language could work with reference and beliefs, and wouldn't need meaning [Putnam] |
6270 | The correct translation is the one that explains the speaker's behaviour [Putnam] |
6283 | Language maps the world in many ways (because it maps onto other languages in many ways) [Putnam] |
6275 | You can't say 'most speaker's beliefs are true'; in some areas this is not so, and you can't count beliefs [Putnam] |
6031 | The essence of propriety is consistency [Cicero] |