38 ideas
| 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] |
| 8958 | In Field's version of science, space-time points replace real numbers [Field,H, by Szabó] |
| 18221 | 'Metric' axioms uses functions, points and numbers; 'synthetic' axioms give facts about space [Field,H] |
| 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] |
| 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] |
| 18211 | You can reduce ontological commitment by expanding the logic [Field,H] |
| 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] |
| 18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
| 9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
| 1554 | Contradiction is impossible, since only one side of the argument refers to the true facts [Prodicus, by Didymus the Blind] |
| 3926 | The human heart has a natural concern for public good [Hume] |
| 3929 | No moral theory is of any use if it doesn't serve the interests of the individual concerned [Hume] |
| 3925 | Personal Merit is the possession of useful or agreeable mental qualities [Hume] |
| 3922 | Justice only exists to support society [Hume] |
| 23560 | If we all naturally had everything we could ever desire, the virtue of justice would be irrelevant [Hume] |
| 3918 | Moral philosophy aims to show us our duty [Hume] |
| 3919 | Conclusions of reason do not affect our emotions or decisions to act [Hume] |
| 3928 | Virtue just requires careful calculation and a preference for the greater happiness [Hume] |
| 3923 | No one would cause pain to a complete stranger who happened to be passing [Hume] |
| 3924 | Nature makes private affections come first, because public concerns are spread too thinly [Hume] |
| 3921 | The safety of the people is the supreme law [Hume] |
| 3927 | Society prefers helpful lies to harmful truth [Hume] |
| 3920 | If you equalise possessions, people's talents will make them unequal again [Hume] |
| 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] |
| 1555 | People used to think anything helpful to life was a god, as the Egyptians think the Nile a god [Prodicus] |
| 1543 | He denied the existence of the gods, saying they are just exaltations of things useful for life [Prodicus] |
| 535 | The gods are just personified human benefits [Prodicus] |