54 ideas
18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
12430 | Classical logic is our preconditions for assessing empirical evidence [Kitcher] |
12431 | I believe classical logic because I was taught it and use it, but it could be undermined [Kitcher] |
1507 | We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea] |
5109 | The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle] |
1512 | Zeno is wrong that one grain of millet makes a sound; why should one grain achieve what the whole bushel does? [Aristotle on Zeno of Elea] |
1508 | Zeno's arrow paradox depends on the assumption that time is composed of nows [Aristotle on Zeno of Elea] |
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] |
12428 | Many necessities are inexpressible, and unknowable a priori [Kitcher] |
12429 | Knowing our own existence is a priori, but not necessary [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] |
12790 | Generalisations must be invariant to explain anything [Leuridan] |
12789 | Biological functions are explained by disposition, or by causal role [Leuridan] |
14388 | Mechanisms must produce macro-level regularities, but that needs micro-level regularities [Leuridan] |
14386 | Mechanisms are ontologically dependent on regularities [Leuridan] |
12787 | Mechanisms can't explain on their own, as their models rest on pragmatic regularities [Leuridan] |
14384 | We can show that regularities and pragmatic laws are more basic than mechanisms [Leuridan] |
14389 | There is nothing wrong with an infinite regress of mechanisms and regularities [Leuridan] |
18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
454 | If there are many things they must have a finite number, but there must be endless things between them [Zeno of Elea] |
14387 | Rather than dispositions, functions may be the element that brought a thing into existence [Leuridan] |
14382 | Pragmatic laws allow prediction and explanation, to the extent that reality is stable [Leuridan] |
14385 | Strict regularities are rarely discovered in life sciences [Leuridan] |
14383 | A 'law of nature' is just a regularity, not some entity that causes the regularity [Leuridan] |
455 | That which moves, moves neither in the place in which it is, nor in that in which it is not [Zeno of Elea] |
1511 | If everything is in a place, what is the place in? Place doesn't exist [Zeno of Elea, by Simplicius] |