16 ideas
15833 | Tell cleverness from answers, but wisdom from questions [Mahfouz] |
5784 | In its primary and formal sense, 'true' applies to propositions, not beliefs [Russell] |
5777 | The truth or falsehood of a belief depends upon a fact to which the belief 'refers' [Russell] |
5783 | Propositions of existence, generalities, disjunctions and hypotheticals make correspondence tricky [Russell] |
17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
5780 | The three questions about belief are its contents, its success, and its character [Russell] |
5778 | If we object to all data which is 'introspective' we will cease to believe in toothaches [Russell] |
5779 | There are distinct sets of psychological and physical causal laws [Russell] |
5781 | Our important beliefs all, if put into words, take the form of propositions [Russell] |
5782 | A proposition expressed in words is a 'word-proposition', and one of images an 'image-proposition' [Russell] |
5776 | A proposition is what we believe when we believe truly or falsely [Russell] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |