560 | Mathematical precision is only possible in immaterial things [Aristotle] |
9076 | Mathematics studies the domain of perceptible entities, but its subject-matter is not perceptible [Aristotle] |
12377 | Mathematics is concerned with forms, not with superficial properties [Aristotle] |
2252 | Surely maths is true even if I am dreaming? [Descartes] |
2430 | I can learn the concepts of duration and number just from observing my own thoughts [Descartes] |
17185 | Mathematics deals with the essences and properties of forms [Spinoza] |
16918 | Mathematics cannot proceed just by the analysis of concepts [Kant] |
12427 | All of mathematics is properties of the whole numbers [Kronecker] |
15910 | Cantor named the third realm between the finite and the Absolute the 'transfinite' [Lavine on Cantor] |
16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Friend on Hilbert] |
10059 | In mathematic we are ignorant of both subject-matter and truth [Russell] |
18119 | Mathematics is a mental activity which does not use language [Bostock on Brouwer] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [George/Velleman on Gödel] |
18281 | In mathematics everything is algorithm and nothing is meaning [Wittgenstein] |
9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Resnik on Kitcher] |
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] |
9226 | If mathematical theories conflict, it may just be that they have different subject matter [Field,H] |
6304 | Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik] |
10201 | Virtually all of mathematics can be modeled in set theory [Shapiro] |
9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
4240 | It might be argued that mathematics does not, or should not, aim at truth [Lowe] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |