30 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] |
18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
18216 | Abstractions can form useful counterparts to concrete statements [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] |
5078 | Kant and Mill both try to explain right and wrong, without a divine lawgiver [Taylor,R] |
5067 | Morality based on 'forbid', 'permit' and 'require' implies someone who does these things [Taylor,R] |
5079 | Pleasure can have a location, and be momentary, and come and go - but happiness can't [Taylor,R] |
5068 | 'Eudaimonia' means 'having a good demon', implying supreme good fortune [Taylor,R] |
5076 | To Greeks it seemed obvious that the virtue of anything is the perfection of its function [Taylor,R] |
5077 | The modern idea of obligation seems to have lost the idea of an obligation 'to' something [Taylor,R] |
5065 | The ethics of duty requires a religious framework [Taylor,R] |
5066 | If we are made in God's image, pursuit of excellence is replaced by duty to obey God [Taylor,R] |
15877 | The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré] |
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] |