19 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) |
| 5806 | Belief is the power of metarepresentation [Dretske] |
| Full Idea: Belief is the power of metarepresentation. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2.3) | |
| A reaction: Hm. I have always defined belief as 'commitment to truth', and this definition leaves out both parts. Where is the commitment? If hope is another metarepresentation, how does it differ from belief? I imagine things, not believing them to be true. |
| 5801 | A mouse hearing a piano played does not believe it, because it lacks concepts and understanding [Dretske] |
| Full Idea: A mouse can see and hear a piano being played, but believing is something else; it requires the concept of a piano, and understanding. Mice who hear pianos being played do not believe pianos are being played. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §1.3) | |
| A reaction: Are we to say that when a mouse hears a piano it has no beliefs at all? Might not a belief involve images, so that a mouse calls up appropriate images from previous experiences, which are in a grey area on the edge of belief? |
| 5802 | Representations are in the head, but their content is not, as stories don't exist in their books [Dretske] |
| Full Idea: Representations are in the head, but their content is not; in this sense, the mind isn't in the head any more than stories (i.e. story contents) are in books. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §1.6) | |
| A reaction: This is the final consequence of Putnam's idea that meanings ain't in the head. Intentionality is an extraordinary bridge between the brain and the external world. The ontology of stories, and musical compositions, is one philosophy's deepest problems. |
| 5809 | Some activities are performed better without consciousness of them [Dretske] |
| Full Idea: Some tasks (playing the piano, speaking foreign languages, playing fast sports) are best performed when the agent is largely unconscious of the details. | |
| From: Fred Dretske (Naturalizing the Mind [1997], Ch.4 n16) | |
| A reaction: A significant point, but it supports the evolutionary view, which is that what matters is success, and consciousness will switch on or off, whichever promotes the activity best. |
| 5808 | Qualia are just the properties objects are represented as having [Dretske] |
| Full Idea: The Representational Thesis of mind identifies the qualities of experience - qualia - with the properties objects are represented as having. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §3.2) | |
| A reaction: This seems to challenge the distinction between primary and secondary qualities, of which I am very fond. Is 'looks beautiful' a property of an object? Is the feeling of anger a property of an object? Qualia are properties of brains? |
| 5807 | Introspection is the same as the experience one is introspecting [Dretske] |
| Full Idea: Introspection has no phenomenology or, if it does, it always has the same phenomenology as the experience one is introspecting. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2.4) | |
| A reaction: There is a difference between looking at a tree, and being aware of yourself looking at a tree. You can be faintly depressed, and then become aware that you are faintly depressed. He is nearly right. |
| 5803 | In a representational theory of mind, introspection is displaced perception [Dretske] |
| Full Idea: On a representational theory of the mind, introspection becomes an instance of displaced perception - knowledge of internal (mental) facts via an awareness of external (physical) objects. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2) | |
| A reaction: This sounds close to a behaviourist (e.g. Ryle) account of introspection, via observing one's own behaviour. The word 'displaced' is an easy one, concealing a multitude of questions. |
| 5805 | Introspection does not involve looking inwards [Dretske] |
| Full Idea: The 'problem' of introspection evaporates once one understands that it is not a process in which one looks inward. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2) | |
| A reaction: I take it that when we introspect we look at the contents of thoughts, which are representations of the external world, on the whole. But surely only the connections of those contents with memories can be seen inwardly? |
| 5804 | A representational theory of the mind is an externalist theory of the mind [Dretske] |
| Full Idea: A representational theory of the mind is an externalist theory of the mind. | |
| From: Fred Dretske (Naturalizing the Mind [1997], §2) | |
| A reaction: Presumably brain events bring the world into the mind, so the world must be mentioned in explaining the mind. Maybe 'externalism' sounds grand, but is stating the boringly obvious. Explanations of mind need no mention of external particulars. |
| 5800 | All mental facts are representation, which consists of informational functions [Dretske] |
| Full Idea: My thesis is that all mental facts are representational facts, and that all representational facts are facts about informational functions. | |
| From: Fred Dretske (Naturalizing the Mind [1997], Prol) | |
| A reaction: The first half of the thesis seems a bit difficult to disagree with, but that a fact is 'represented' may not be the essence of that fact. The biggest mystery is the content, not its representation. And everything is 'information' about everything else. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |