17 ideas
7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
17265 | Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder] |
9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
22276 | Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter] |
17264 | Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder] |
12232 | A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano] |
12233 | The ground of a pure conceptual truth is only in other conceptual truths [Bolzano] |
12163 | Literary meaning emerges in comparisons, and tradition shows which comparisons are relevant [Scruton] |
12162 | In literature, word replacement changes literary meaning [Scruton] |
12159 | Without intentions we can't perceive sculpture, but that is not the whole story [Scruton] |
12160 | In aesthetic interest, even what is true is treated as though it were not [Scruton] |
12161 | We can be objective about conventions, but love of art is needed to understand its traditions [Scruton] |