45 ideas
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] |
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] |
1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
8388 | Causation is either direct realism, Humean reduction, non-Humean reduction or theoretical realism [Tooley] |
8389 | Causation distinctions: reductionism/realism; Humean/non-Humean states; observable/non-observable [Tooley] |
8393 | We can only reduce the direction of causation to the direction of time if we are realist about the latter [Tooley] |
8390 | Causation is directly observable in pressure on one's body, and in willed action [Tooley] |
8392 | Probabilist laws are compatible with effects always or never happening [Tooley] |
8399 | The actual cause may not be the most efficacious one [Tooley] |
8391 | In counterfactual worlds there are laws with no instances, so laws aren't supervenient on actuality [Tooley] |
8394 | Explaining causation in terms of laws can't explain the direction of causation [Tooley] |
8398 | Causation is a concept of a relation the same in all worlds, so it can't be a physical process [Tooley] |
1555 | People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus] |
1543 | He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus] |
535 | The gods are just personified human benefits [Prodicus] |