18 ideas
7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
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] |
9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
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] |