33 ideas
291 | Don't assume that wisdom is the automatic consequence of old age [Plato] |
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] |
3756 | Perception, introspection, testimony, memory, reason, and inference can give us knowledge [Bernecker/Dretske] |
3757 | Causal theory says true perceptions must be caused by the object perceived [Bernecker/Dretske] |
3759 | You can acquire new knowledge by exploring memories [Bernecker/Dretske] |
3752 | Justification can be of the belief, or of the person holding the belief [Bernecker/Dretske] |
3753 | Foundationalism aims to avoid an infinite regress [Bernecker/Dretske] |
3754 | Infallible sensations can't be foundations if they are non-epistemic [Bernecker/Dretske] |
3755 | Justification is normative, so it can't be reduced to cognitive psychology [Bernecker/Dretske] |
3761 | Modern arguments against the sceptic are epistemological and semantic externalism, and the focus on relevance [Bernecker/Dretske] |
3760 | Predictions are bound to be arbitrary if they depend on the language used [Bernecker/Dretske] |
18222 | Beneath every extrinsic explanation there is an intrinsic explanation [Field,H] |
3758 | Semantic externalism ties content to the world, reducing error [Bernecker/Dretske] |
9917 | 'Abstract' is unclear, but numbers, functions and sets are clearly abstract [Field,H] |
293 | Being unafraid (perhaps through ignorance) and being brave are two different things [Plato] |
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] |