14 ideas
| 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. |
| 2526 | Philosophers regularly confuse failures of imagination with insights into necessity [Dennett] |
| Full Idea: The besetting foible of philosophers is mistaking failures of imagination for insights into necessity. | |
| From: Daniel C. Dennett (Brainchildren [1998], Ch.25) |
| 2523 | That every mammal has a mother is a secure reality, but without foundations [Dennett] |
| Full Idea: Naturalistic philosophers should look with favour on the finite regress that peters out without foundations or thresholds or essences. That every mammal has a mother does not imply an infinite regress. Mammals have secure reality without foundations. | |
| From: Daniel C. Dennett (Brainchildren [1998], Ch.25) | |
| A reaction: I love this thought, which has permeated my thinking quite extensively. Logicians are terrified of regresses, but this may be because they haven't understood the vagueness of language. |
| 2528 | Does consciousness need the concept of consciousness? [Dennett] |
| Full Idea: You can't have consciousness until you have the concept of consciousness. | |
| From: Daniel C. Dennett (Brainchildren [1998], Ch.6) | |
| A reaction: If you read enough Dennett this begins to sound vaguely plausible, but next day it sounds like an absurd claim. 'You can't see a tree until you have the concept of a tree?' When do children acquire the concept of consciousness? Are apes non-conscious? |
| 2525 | Maybe language is crucial to consciousness [Dennett] |
| Full Idea: I continue to argue for a crucial role of natural language in generating the central features of consciousness. | |
| From: Daniel C. Dennett (Brainchildren [1998], Ch.25) | |
| A reaction: 'Central features' might beg the question. Dennett does doubt the consciousness of animals (1996). As I stare out of my window, his proposal seems deeply counterintuitive. How could language 'generate' consciousness? Would loss of language create zombies? |
| 2527 | Unconscious intentionality is the foundation of the mind [Dennett] |
| Full Idea: It is on the foundation of unconscious intentionality that the higher-order complexities developed that have culminated in what we call consciousness. | |
| From: Daniel C. Dennett (Brainchildren [1998], Ch.25) | |
| A reaction: Sounds right to me. Pace Searle, I have no problem with unconscious intentionality, and the general homuncular picture of low levels building up to complex high levels, which suddenly burst into the song and dance of consciousness. |
| 2530 | Could a robot be made conscious just by software? [Dennett] |
| Full Idea: How could you make a robot conscious? The answer, I think, is to be found in software. | |
| From: Daniel C. Dennett (Brainchildren [1998], Ch.6) | |
| A reaction: This seems to be a commitment to strong AI, though Dennett is keen to point out that brains are the only plausible implementation of such software. Most find his claim baffling. |
| 2524 | A language of thought doesn't explain content [Dennett] |
| Full Idea: Postulating a language of thought is a postponement of the central problems of content ascription, not a necessary first step. | |
| From: Daniel C. Dennett (Brainchildren [1998], Ch.25) | |
| A reaction: If the idea of content is built on the idea of representation, then you need some account of what the brain does with its representations. |
| 2529 | Maybe there can be non-conscious concepts (e.g. in bees) [Dennett] |
| Full Idea: Concepts do not require consciousness. As Jaynes says, the bee has a concept of a flower, but not a conscious concept. | |
| From: Daniel C. Dennett (Brainchildren [1998], Ch.6) | |
| A reaction: Does the flower have a concept of rain? Rain plays a big functional role in its existence. It depends, alas, on what we mean by a 'concept'. |
| 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. |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |