27 ideas
14600 | Analysis aims at secure necessary and sufficient conditions [Schaffer,J] |
8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
14603 | 'Reification' occurs if we mistake a concept for a thing [Schaffer,J] |
13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
14607 | T adds □p→p for reflexivity, and is ideal for modeling lawhood [Schaffer,J] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
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] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
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] |
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] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
14604 | If a notion is ontologically basic, it should be needed in our best attempt at science [Schaffer,J] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
14599 | Three types of reduction: Theoretical (of terms), Definitional (of concepts), Ontological (of reality) [Schaffer,J] |
14605 | Tropes are the same as events [Schaffer,J] |
14601 | Individuation aims to count entities, by saying when there is one [Schaffer,J] |
14606 | Only ideal conceivability could indicate what is possible [Schaffer,J] |