20 ideas
2510 | Traditionally philosophy is an a priori enquiry into general truths about reality [Katz] |
2516 | Most of philosophy begins where science leaves off [Katz] |
7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
13827 | Logical consequence isn't a black box (Tarski's approach); we should explain how arguments work [Prawitz] |
13826 | Model theory looks at valid sentences and consequence, but not how we know these things [Prawitz] |
9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
2521 | 'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz] |
9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
17265 | Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder] |
2513 | We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz] |
2522 | Experience cannot teach us why maths and logic are necessary [Katz] |
9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
2517 | Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz] |
2519 | It is generally accepted that sense is defined as the determiner of reference [Katz] |
2520 | Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz] |
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] |
2518 | Sentences are abstract types (like musical scores), not individual tokens [Katz] |
12233 | The ground of a pure conceptual truth is only in other conceptual truths [Bolzano] |