42 ideas
18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
4975 | A thought can be split in many ways, so that different parts appear as subject or predicate [Frege] |
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] |
9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
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] |
18995 | Frege mistakenly takes existence to be a property of concepts, instead of being about things [Frege, by Yablo] |
10317 | It is unclear whether Frege included qualities among his abstract objects [Frege, by Hale] |
18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
10535 | Frege's 'objects' are both the referents of proper names, and what predicates are true or false of [Frege, by Dummett] |
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] |
18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
9839 | Frege equated the concepts under which an object falls with its properties [Frege, by Dummett] |
4973 | As I understand it, a concept is the meaning of a grammatical predicate [Frege] |
9167 | Frege felt that meanings must be public, so they are abstractions rather than mental entities [Frege, by Putnam] |
4974 | For all the multiplicity of languages, mankind has a common stock of thoughts [Frege] |
5492 | How can essences generate the right powers to vary with distance between objects? [Armstrong] |