50 ideas
7623 | For ancient Greeks being wise was an ethical value [Putnam] |
4714 | Putnam's epistemic notion of truth replaces the realism of correspondence with ontological relativism [Putnam, by O'Grady] |
7617 | Before Kant, all philosophers had a correspondence theory of truth [Putnam] |
4716 | The correspondence theory is wrong, because there is no one correspondence between reality and fact [Putnam, by O'Grady] |
7616 | Truth is an idealisation of rational acceptability [Putnam] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
9570 | In Field's Platonist view, set theory is false because it asserts existence for non-existent things [Field,H, by Chihara] |
10260 | Logical consequence is defined by the impossibility of P and ¬q [Field,H, by Shapiro] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
14203 | Intension is not meaning, as 'cube' and 'square-faced polyhedron' are intensionally the same [Putnam] |
14207 | If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth [Putnam] |
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] |
8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
8757 | The Indispensability Argument is the only serious ground for the existence of mathematical entities [Field,H] |
18212 | Nominalists try to only refer to physical objects, or language, or mental constructions [Field,H] |
10261 | The application of mathematics only needs its possibility, not its truth [Field,H, by Shapiro] |
18218 | Hilbert explains geometry, by non-numerical facts about space [Field,H] |
9623 | Field needs a semantical notion of second-order consequence, and that needs sets [Brown,JR on Field,H] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
18215 | It seems impossible to explain the idea that the conclusion is contained in the premises [Field,H] |
18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
14214 | If we try to cure the abundance of theories with causal links, this is 'just more theory' [Putnam, by Lewis] |
14205 | The sentence 'A cat is on a mat' remains always true when 'cat' means cherry and 'mat' means tree [Putnam] |
7610 | A fact is simply what it is rational to accept [Putnam] |
18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
7618 | Very nominalistic philosophers deny properties, though scientists accept them [Putnam] |
8959 | Field presumes properties can be eliminated from science [Field,H, by Szabó] |
18213 | Abstract objects are only applicable to the world if they are impure, and connect to the physical [Field,H] |
4718 | If necessity is always relative to a description in a language, then there is only 'de dicto' necessity [Putnam, by O'Grady] |
7620 | Some kind of objective 'rightness' is a presupposition of thought itself [Putnam] |
14204 | Naïve operationalism would have meanings change every time the tests change [Putnam] |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
7611 | Rationality is one part of our conception of human flourishing [Putnam] |
14200 | 'Water' on Twin Earth doesn't refer to water, but no mental difference can account for this [Putnam] |
7612 | Reference is social not individual, because we defer to experts when referring to elm trees [Putnam] |
7613 | Concepts are (at least in part) abilities and not occurrences [Putnam] |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
14202 | Neither individual nor community mental states fix reference [Putnam] |
14201 | Maybe the total mental state of a language community fixes the reference of a term [Putnam] |
14206 | There are infinitely many interpretations of a sentence which can all seem to be 'correct' [Putnam] |
7624 | The word 'inconsiderate' nicely shows the blurring of facts and values [Putnam] |
18223 | In theories of fields, space-time points or regions are causal agents [Field,H] |
18220 | Both philosophy and physics now make substantivalism more attractive [Field,H] |
18219 | Relational space is problematic if you take the idea of a field seriously [Field,H] |