18 ideas
7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |
13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
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] |
21971 | Transcendental philosophy is the subject becoming the originator of unified reality [Kant] |
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] |