15 ideas
| 8251 | The logical space of reasons is a natural phenomenon, and it is the realm of freedom [McDowell] |
| Full Idea: The logical space of reasons is just part of the logical space of nature. ...And, in a Kantian slogan, the space of reasons is the realm of freedom. | |
| From: John McDowell (Mind and World [1994], Intro 7) | |
| A reaction: [second half on p.5] This is a modern have-your-cake-and-eat-it view of which I am becoming very suspicious. The modern Kantians (Davidson, Nagel, McDowell) are struggling to naturalise free will, but it won't work. Just dump it! |
| 10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
| Full Idea: A logic is a collection of closely related artificial languages, and its older meaning is the study of the rules of sound argument. The languages can be used as a framework for studying rules of argument. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.1) | |
| A reaction: [Hodges then says he will stick to the languages] The suspicion is that one might confine the subject to the artificial languages simply because it is easier, and avoids the tricky philosophical questions. That approximates to computer programming. |
| 10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
| Full Idea: To have a truth-value, a first-order formula needs an 'interpretation' (I) of its constants, and a 'valuation' (ν) of its variables. Something in the world is attached to the constants; objects are attached to variables. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) |
| 10284 | There are three different standard presentations of semantics [Hodges,W] |
| Full Idea: Semantic rules can be presented in 'Tarski style', where the interpretation-plus-valuation is reduced to the same question for simpler formulas, or the 'Henkin-Hintikka style' in terms of games, or the 'Barwise-Etchemendy style' for computers. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) | |
| A reaction: I haven't yet got the hang of the latter two, but I note them to map the territory. |
| 10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
| Full Idea: I |= φ means that the formula φ is true in the interpretation I. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.5) | |
| A reaction: [There should be no space between the vertical and the two horizontals!] This contrasts with |-, which means 'is proved in'. That is a syntactic or proof-theoretic symbol, whereas |= is a semantic symbol (involving truth). |
| 10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
| Full Idea: Downward Löwenheim-Skolem (the weakest form): If L is a first-order language with at most countably many formulas, and T is a consistent theory in L. Then T has a model with at most countably many elements. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
| Full Idea: Upward Löwenheim-Skolem: every first-order theory with infinite models has arbitrarily large models. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
| Full Idea: Compactness Theorem: suppose T is a first-order theory, ψ is a first-order sentence, and T entails ψ. Then there is a finite subset U of T such that U entails ψ. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) | |
| A reaction: If entailment is possible, it can be done finitely. |
| 10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
| Full Idea: A 'set' is a mathematically well-behaved class. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.6) |
| 8128 | Representation must be propositional if it can give reasons and be epistemological [McDowell, by Burge] |
| Full Idea: McDowell has claimed that one cannot make sense of representation that plays a role in epistemology unless one takes the representation to be propositional, and thus capable of yielding reasons. | |
| From: report of John McDowell (Mind and World [1994]) by Tyler Burge - Philosophy of Mind: 1950-2000 p.456 | |
| A reaction: A transcendental argument leads back to a somewhat implausible conclusion. I suspect that McDowell has a slightly inflated (Kantian) notion of the purity of the 'space of reasons'. Do philosophers just imagine their problems? |
| 19092 | There is no pure Given, but it is cultured, rather than entirely relative [McDowell, by Macbeth] |
| Full Idea: McDowell argues that the Myth of the Given shows not that there is no content to a concept that is not a matter of its inferential relations to other concepts but only that awareness of the sort that we enjoy ...is acquired in the course of acculturation. | |
| From: report of John McDowell (Mind and World [1994]) by Danielle Macbeth - Pragmatism and Objective Truth p.185 | |
| A reaction: The first view is of Wilfred Sellars, who derives pragmatic relativism from his rejection of the Myth. This idea is helpful is seeing why McDowell has a good proposal. As I look out of my window, my immediate experience seems 'cultured'. |
| 8253 | Sense impressions already have conceptual content [McDowell] |
| Full Idea: The world's impressions on our senses are already possessed of conceptual content. | |
| From: John McDowell (Mind and World [1994], I.6) | |
| A reaction: This is a key idea of McDowell's, which challenges most traditional empiricist views, and (maybe) offers a solution to the rationalist/empiricist debate. His commitment to the 'space of reasons' strikes me as an optional extra. |
| 8254 | Forming concepts by abstraction from the Given is private definition, which the Private Lang. Arg. attacks [McDowell] |
| Full Idea: The idea that concepts can be formed by abstraction from the Given just is the idea of private ostensive definition. So the Private Language Argument just is the rejection of the Given, in so far as it bears on the possibilities for language. | |
| From: John McDowell (Mind and World [1994], I.7) | |
| A reaction: I'm not clear why the process of abstraction from raw impressions shouldn't be a matter of public, explicit, community negotiation. We seem to be able to share and compare fairly raw impressions without much trouble (discussing sunsets). |
| 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. |