20 ideas
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| Full Idea: Late nineteenth century mathematicians said that, although plus, minus and 0 could not be precisely defined, they could be partially 'implicitly defined' as a group. This nonsense was rejected by Frege and others, as expressed in Russell 1903. | |
| From: Wilfrid Hodges (Model Theory [2005], 2) | |
| A reaction: [compressed] This is helpful in understanding what is going on in Frege's 'Grundlagen'. I won't challenge Hodges's claim that such definitions are nonsense, but there is a case for understanding groups of concepts together. |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
| A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
| 10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
| Full Idea: In first-order languages the completeness theorem tells us that T |= φ holds if and only if there is a proof of φ from T (T |- φ). Since the two symbols express the same relationship, theorist often just use |- (but only for first-order!). | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: [actually no spaces in the symbols] If you are going to study this kind of theory of logic, the first thing you need to do is sort out these symbols, which isn't easy! |
| 10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
| Full Idea: If every structure which is a model of a set of sentences T is also a model of one of its sentences φ, then this is known as the model-theoretic consequence relation, and is written T |= φ. Not to be confused with |= meaning 'satisfies'. | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: See also Idea 10474, which gives the other meaning of |=, as 'satisfies'. The symbol is ALSO used in propositional logical, to mean 'tautologically implies'! Sort your act out, logicians. |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
| From: Ian Rumfitt ("Yes" and "No" [2000]) | |
| A reaction: This is the standard view which Rumfitt sets out to challenge. |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
| A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
| 10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
| Full Idea: The symbol in 'I |= S' reads that if the interpretation I (about word meaning) happens to make the sentence S state something true, then I 'is a model for' S, or I 'satisfies' S. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: Unfortunately this is not the only reading of the symbol |= [no space between | and =!], so care and familiarity are needed, but this is how to read it when dealing with models. See also Idea 10477. |
| 10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
| Full Idea: Model theory is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures, with Tarski's truth definition as a paradigm. | |
| From: Wilfrid Hodges (Model Theory [2005], Intro) | |
| A reaction: My attention is caught by the fact that natural languages are included. Might we say that science is model theory for English? That sounds like Quine's persistent message. |
| 10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
| Full Idea: A 'structure' in model theory is an interpretation which explains what objects some expressions refer to, and what classes some quantifiers range over. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: He cites as examples 'first-order structures' used in mathematical model theory, and 'Kripke structures' used in model theory for modal logic. A structure is also called a 'universe'. |
| 10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
| Full Idea: The models in model-theory are structures, but there is also a common use of 'model' to mean a formal theory which describes and explains a phenomenon, or plans to build it. | |
| From: Wilfrid Hodges (Model Theory [2005], 5) | |
| A reaction: Hodges is not at all clear here, but the idea seems to be that model-theory offers a set of objects and rules, where the common usage offers a set of descriptions. Model-theory needs homomorphisms to connect models to things, |
| 10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
| Full Idea: First-order logic is hopeless for discriminating between one infinite cardinal and another. | |
| From: Wilfrid Hodges (Model Theory [2005], 4) | |
| A reaction: This seems rather significant, since mathematics largely relies on first-order logic for its metatheory. Personally I'm tempted to Ockham's Razor out all these super-infinities, but mathematicians seem to make use of them. |
| 7630 | Ryle's dichotomy between knowing how and knowing that is too simplistic [Maund] |
| Full Idea: There is a convincing claim that we need to leave behind Ryle's dichotomy between knowing how and knowing that as being too simplistic. | |
| From: Barry Maund (Perception [2003], Ch. 2) | |
| A reaction: [John Campbell is mentioned as source of this idea] I find this proposal immediately appealing. I was taught that riding a bicycle shows the division, as hardly anyone knows the theory, but I am sure children need some propositional information. |
| 7632 | Perception is sensation-then-concept, or direct-concepts, or sensation-saturated-in-concepts [Maund] |
| Full Idea: Three forms of (cognitive) direct realism are: two stages - non-conceptual sensory experience, then a non-sensory conceptual state; directly acquiring non-sensuous conceptual states; and sensuous states saturated with concepts. | |
| From: Barry Maund (Perception [2003], Ch. 3) | |
| A reaction: [First: Reid, Dretske, Evans, Sellars. Second: Armstrong, Heil, Pitcher, Clark. Third: Kant, McDowell, Strawson, McGinn, Searle]. I find the first one plausible, because of the ambiguity in language, and because unusual experiences separate them. |
| 7635 | Sense-data have an epistemological purpose (foundations) and a metaphysical purpose (explanation) [Maund] |
| Full Idea: Sense-data have an epistemological purpose (to serve as foundations on which the edifice of knowledge is to be constructed), and a metaphysical purpose (to provide an accurate account of the phenomenology of perceptual experience). | |
| From: Barry Maund (Perception [2003], Ch. 6) | |
| A reaction: This is very important, because there is a real danger (e.g. in Russell) that the epistemological convenience of sense-data for giving reliability in knowledge means that we are too quick in making the assumption that they actually exist. |
| 7638 | One thesis says we are not aware of qualia, but only of objects and their qualities [Maund] |
| Full Idea: The representationalist/intentionalist thesis about perception is that we are not aware of the intrinsic qualities of experience in normal perception; we are instead aware of those objects and their qualities that are specified in the content. | |
| From: Barry Maund (Perception [2003], Ch. 9) | |
| A reaction: If secondary qualities are in the mind, not in objects, how come people always thought they were in objects? Answer: because this thesis is right? The primary mode of the mind is projected outwards, though we can introspect about colours. [Dretske] |
| 7642 | The Myth of the Given claims that thought is rationally supported by non-conceptual experiences [Maund] |
| Full Idea: The so-called 'myth of the given' is the view that conceptual content can be rationally supported by experiences construed as states with non-conceptual content. | |
| From: Barry Maund (Perception [2003], Ch.10) | |
| A reaction: The myth is attacked by Sellars and McDowell, the latter claiming that concepts must be embedded in the experiences. Maybe only realism is required to make the Given work. The experiences are definitely of something, and off we go... |
| 7640 | Mountains are adverbial modifications of the earth, but still have object-characteristics [Maund] |
| Full Idea: Metaphysically, mountains are only adverbial modifications of the Earth's belt. They have no existence independent of being part of the earth. Yet for all that, they have some rather strong 'object'-characteristics. | |
| From: Barry Maund (Perception [2003], Ch.10) | |
| A reaction: The point being that you don't give up all the advantages of a sense-data view if you switch to adverbialism. I'm not convinced by the analogy, but we can only be aware of adverbial qualities if they have causal powers. |
| 7641 | Adverbialism tries to avoid sense-data and preserve direct realism [Maund] |
| Full Idea: The two primary motivations of the adverbialist analysis are thought to be to avoid commitment to sensory particulars such as sense-data, and to allow us to hold on to a version of direct realism. | |
| From: Barry Maund (Perception [2003], Ch.10) | |
| A reaction: Maund says that the adverbialist's fears about indirect/representative theories are unfounded. My feeling is that neither account will do the job properly once we get a better account of consciousness. Maybe adverbialism is only for secondary qualities. |
| 7637 | Thought content is either satisfaction conditions, or exercise of concepts [Maund, by PG] |
| Full Idea: The content of thought can either be expressed as satisfaction conditions (e.g. truth-conditions for beliefs), or as the exercise of at least two concepts. | |
| From: report of Barry Maund (Perception [2003], Ch. 8) by PG - Db (ideas) | |
| A reaction: I think I favour the first view, because not all conjunctions of concepts would count as thoughts (e.g. rhubarb-plus-contradiction). A bunch of concepts becomes a thought when it connects in some way to reality? |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
| From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
| A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |