45 ideas
6294 | In the beginning was the Word, and the Word was with God, and the word was God [John] |
8821 | Jesus said he bore witness to the truth. Pilate asked, What is truth? [John] |
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] |
18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
20189 | Belief is a feeling, independent of the will, which arises from uncontrolled and unknown causes [Hume] |
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] |
21309 | A proposition cannot be intelligible or consistent, if the perceptions are not so [Hume] |
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] |
15755 | Hume needs a notion which includes degrees of resemblance [Shoemaker on Hume] |
5323 | Experiences are logically separate, but factually linked by simultaneity or a feeling of continuousness [Ayer on Hume] |
21311 | Are self and substance the same? Then how can self remain if substance changes? [Hume] |
21312 | Perceptions are distinct, so no connection between them can ever be discovered [Hume] |
21308 | We have no impression of the self, and we therefore have no idea of it [Hume] |
21310 | Does an oyster with one perception have a self? Would lots of perceptions change that? [Hume] |
23115 | We have no natural love of mankind, other than through various relationships [Hume] |
16946 | Causation is just invariance, as long as it is described in general terms [Quine on Hume] |
15250 | If impressions, memories and ideas only differ in vivacity, nothing says it is memory, or repetition [Whitehead on Hume] |