24 ideas
8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
19125 | If we define truth, we can eliminate it [Halbach/Leigh] |
19128 | If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh] |
19120 | Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh] |
19127 | The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh] |
19124 | A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh] |
19126 | If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh] |
19129 | The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh] |
19130 | KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh] |
13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
19121 | We can reduce properties to true formulas [Halbach/Leigh] |
19122 | Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh] |
20921 | How can we state relativism of sweet and sour, if they have no determinate nature? [Theophrastus] |
5990 | Theophrastus doubted whether nature could be explained teleologically [Theophrastus, by Gottschalk] |