11 ideas
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths). |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1 | |
| A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries. |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2 | |
| A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy. |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3 | |
| A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field. |
| 5500 | Biologists see many organic levels, 'abstract' if seen from below, 'structural' if seen from above [Lycan] |
| Full Idea: Biologists don't split living things into a 'structural' level and an 'abstract' level; ..rather, they are organised at many levels, each level 'abstract' with respect to those beneath it, but 'structural' as it realises those levels above it. | |
| From: William Lycan (Introduction - Ontology [1999], p.9) | |
| A reaction: This is a very helpful distinction. Compare Idea 4601. It seems to fit well with the 'homuncular' picture of a hierarchical mind, and explains why there are so many levels of description available for mental life. |
| 5494 | 'Lightning is electric discharge' and 'Phosphorus is Venus' are synthetic a posteriori identities [Lycan] |
| Full Idea: There is such a thing as synthetic and a posteriori identity that is nonetheless genuine identity, as in lightning being electrical discharge, and the Morning Star being Venus. | |
| From: William Lycan (Introduction - Ontology [1999], p.5) | |
| A reaction: It is important to note that although these identities are synthetic a posteriori, that doesn't make them contingent. The early identity theorists like Smart seemed to think that it did. Kripke must be right that they are necessary identities. |
| 5496 | Functionalism has three linked levels: physical, functional, and mental [Lycan] |
| Full Idea: Functionalism has three distinct levels of description: a neurophysiological description, a functional description (relative to a program which the brain is realising), and it may have a further mental description. | |
| From: William Lycan (Introduction - Ontology [1999], p.6) | |
| A reaction: I have always thought that the 'levels of description' idea was very helpful in describing the mind/brain. I feel certain that we are dealing with a single thing, so this is the only way we can account for the diverse ways in which we discuss it. |
| 5499 | A mental state is a functional realisation of a brain state when it serves the purpose of the organism [Lycan] |
| Full Idea: Some theorists have said that the one-to-one correspondence between the organism and parts of its 'program' is too liberal, and suggest that the state and its functional role are seen teleologically, as functioning 'for' the organism. | |
| From: William Lycan (Introduction - Ontology [1999], p.9) | |
| A reaction: This seems an inevitable development, once the notion of a 'function' is considered. It has to be fitted into some sort of Aristotelian teleological picture, even if the functions are seen subjectively (by what?). Purpose is usually seen as evolutionary. |
| 7861 | Libet says the processes initiated in the cortex can still be consciously changed [Libet, by Papineau] |
| Full Idea: Libet himself points out that the conscious decisions still have the power to 'endorse' or 'cancel', so to speak, the processes initiated by the earlier cortical activity: no action will result if the action's execution is consciously countermanded. | |
| From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by David Papineau - Thinking about Consciousness 1.4 | |
| A reaction: This is why Libet's findings do not imply 'epiphenomenalism'. It seems that part of a decisive action is non-conscious, undermining the all-or-nothing view of consciousness. Searle tries to smuggle in free will at this point (Idea 3817). |
| 6660 | Libet found conscious choice 0.2 secs before movement, well after unconscious 'readiness potential' [Libet, by Lowe] |
| Full Idea: Libet found that a subject's conscious choice to move was about a fifth of a second before movement, and thus later than the onset of the brain's so-called 'readiness potential', which seems to imply that unconscious processes initiates action. | |
| From: report of Benjamin Libet (Unconscious Cerebral Initiative [1985]) by E.J. Lowe - Introduction to the Philosophy of Mind Ch.9 | |
| A reaction: Of great interest to philosophers! It seems to make conscious choices epiphenomenal. The key move, I think, is to give up the idea of consciousness as being all-or-nothing. My actions are still initiated by 'me', but 'me' shades off into unconsciousness. |
| 5501 | People are trying to explain biological teleology in naturalistic causal terms [Lycan] |
| Full Idea: There is now a small but vigorous industry whose purpose is to explicate biological teleology in naturalistic terms, typically in terms of causes. | |
| From: William Lycan (Introduction - Ontology [1999], p.10) | |
| A reaction: This looks like a good strategy. In some sense, it seems clear that the moon has no purpose, but an eyeball has one. Via evolution, one would expect to reduce this to causation. Purposes are real (not subjective), but they are reducible. |