14 ideas
| 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) |
| 19722 | We could know the evidence for our belief without knowing why it is such evidence [Mittag] |
| Full Idea: While one might understand the proposition entailed by one's evidence, one might have no idea how or why one's evidence entails it. This seems to imply one is not justified in believing the proposition on the basis of one's evidence. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Evidential') | |
| A reaction: An example might be seen if a layman tours a physics lab. This looks like a serious problem for evidentialism. Once you see why the evidence entails the proposition, you are getting closer to understanding than to knowledge. Explanation. |
| 19723 | Evidentialism can't explain that we accept knowledge claims if the evidence is forgotten [Mittag] |
| Full Idea: If one came to believe p with good evidence, but has since forgotten that evidence, we might think one can continue to believe justifiably, but evidentialism appears unable to account for this. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Forgotten') | |
| A reaction: We would still think that the evidence was important, and we would need to trust the knower's claim that the forgotten evidence was good. So it doesn't seem to destroy the evidentialist thesis. |
| 19720 | Evidentialism concerns the evidence for the proposition, not for someone to believe it [Mittag] |
| Full Idea: Evidentialism is not a theory about when one's believing is justified; it is a theory about what makes one justified in believing a proposition. It is a thesis regarding 'propositional justification', not 'doxastic justification'. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Preliminary') | |
| A reaction: Thus it is entirely about whether the evidence supports the proposition, and has no interest in who believes it or why. Knowledge is when you believe a true proposition which has good support. This could be internalist or externalist? |
| 19721 | Coherence theories struggle with the role of experience [Mittag] |
| Full Idea: Traditional coherence theories seem unable to account for the role experience plays in justification. | |
| From: Daniel M. Mittag (Evidentialism [2011], 'Evidence') | |
| A reaction: I'm inclined to say that experience only becomes a justification when it has taken propositional (though not necessarily lingistic) form. That is, when you see it 'as' something. Uninterpreted shape and colour can justify virtually nothing. |
| 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. |