7 ideas
| 4298 | All items of possible human knowledge are interconnected, and can be reached by inference [Descartes] |
| Full Idea: All the items of knowledge that lie within the reach of the human mind are linked together with a marvellous bond, and can be derived from each other by necessary inferences. | |
| From: René Descartes (unfinished dialogue [1649]) | |
| A reaction: It does seem that God ought to be able to infer all empirical facts from first principles. But how do you get started? |
| 18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
| Full Idea: Tarski made a division of logical and non-logical vocabulary. He then defined a model as a non-logical assignment satisfying the corresponding sentential function. Then a conclusion follows logically if every model of the premises models the conclusion. | |
| From: report of Alfred Tarski (The Concept of Logical Consequence [1936]) by Ian Rumfitt - The Boundary Stones of Thought 3.2 | |
| A reaction: [compressed] This is Tarski's account of logical consequence, which follows on from his account of truth. 'Logical validity' is then 'true in every model'. Rumfitt doubts whether Tarski has given the meaning of 'logical consequence'. |
| 13344 | X follows from sentences K iff every model of K also models X [Tarski] |
| Full Idea: The sentence X follows logically from the sentences of the class K if and only if every model of the class K is also a model of the sentence X. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417) | |
| A reaction: [see Idea 13343 for his account of a 'model'] He is offering to define logical consequence in general, but this definition fits what we now call 'semantic consequence', written |=. This it is standard practice to read |= as 'models'. |
| 13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
| Full Idea: An arbitrary sequence of objects which satisfies every sentential function of the sentences L' will be called a 'model' or realization of the class L of sentences. There can also be a model of a single sentence is this way. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.417) | |
| A reaction: [L' is L with the constants replaced by variables] Tarski is the originator of model theory, which is central to modern logic. The word 'realization' is a helpful indicator of what he has in mind. A model begins to look like a possible world. |
| 3158 | Theories of intentionality presuppose rationality, so can't explain it [Dennett] |
| Full Idea: Intentional theory is vacuous as psychology because it presupposes and does not explain rationality or intelligence. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.15?) | |
| A reaction: Virtually every philosophical theory seems to founder because it presupposes something like the thing it is meant to explain. I agree that 'intentionality' is a slightly airy concept that would probably reduce to something better. |
| 3159 | Beliefs and desires aren't real; they are prediction techniques [Dennett] |
| Full Idea: Intentional systems don't really have beliefs and desires, but one can explain and predict their behaviour by ascribing beliefs and desires to them. This strategy is pragmatic, not right or wrong. | |
| From: Daniel C. Dennett (Brainstorms:Essays on Mind and Psychology [1978], p.7?) | |
| A reaction: If the ascription of beliefs and desires explains behaviour, then that is good grounds for thinking they might be real features of the brain, and even if that is not so, they are real enough as abstractions from brain events, like the 'economic climate'. |
| 13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
| Full Idea: A class of sentences can be called 'analytical' if every sequence of objects is a model of it. | |
| From: Alfred Tarski (The Concept of Logical Consequence [1936], p.418) | |
| A reaction: See Idea 13344 and Idea 13343 for the context of this assertion. |