26 ideas
| 12596 | Reasoning aims at increasing explanatory coherence [Harman] |
| Full Idea: In reasoning you try among other things to increase the explanatory coherence of your view. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.2) | |
| A reaction: Harman is a champion of inference to the best explanation (abduction), and I agree with him. I think this idea extends to give us a view of justification as coherence, and that extends from inner individual coherence to socially extended coherence. |
| 12599 | Reason conservatively: stick to your beliefs, and prefer reasoning that preserves most of them [Harman] |
| Full Idea: Conservatism is important; you should continue to believe as you do in the absence of any special reason to doubt your view, and in reasoning you should try to minimize change in your initial opinions in attaining other goals of reasoning. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.6) | |
| A reaction: One of those principles like Ockham's Razor, which feels right but hard to justify. It seems the wrong principle for someone who can reason well, but has been brainwashed into a large collection of daft beliefs. Japanese soldiers still fighting WWII. |
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| Full Idea: Impredicative Definitions are definitions of an object by reference to the totality to which the object itself (and perhaps also things definable only in terms of that object) belong. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], n 13) |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| Full Idea: In the superior realist and simple theory of types, the place of the axiom of reducibility is not taken by the axiom of classes, Zermelo's Aussonderungsaxiom. | |
| From: report of Kurt Gödel (Russell's Mathematical Logic [1944], p.140-1) by Bernard Linsky - Russell's Metaphysical Logic 6.1 n3 | |
| A reaction: This is Zermelo's Axiom of Separation, but that too is not an axiom of standard ZFC. |
| 12595 | We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman] |
| Full Idea: There is as yet no substantial theory of inference or reasoning. To be sure, logic is well developed; but logic is not a theory of inference or reasoning. Logic is a theory of implication and inconsistency. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.2) | |
| A reaction: One problem is that animals can draw inferences without the use of language, and I presume we do so all the time, so it is hard to see how to formalise such an activity. |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| Full Idea: 'Mathematical Logic' is a precise and complete formulation of formal logic, and is both a section of mathematics covering classes, relations, symbols etc, and also a science prior to all others, with ideas and principles underlying all sciences. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.447) | |
| A reaction: He cites Leibniz as the ancestor. In this database it is referred to as 'theory of logic', as 'mathematical' seems to be simply misleading. The principles of the subject are standardly applied to mathematical themes. |
| 12597 | I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman] |
| Full Idea: Principles of implication imply there is not a purely probabilistic rule of acceptance for belief. Otherwise one might accept P and Q, without accepting their conjunction, if the conjuncts have a high probability, but the conjunction doesn't. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.2) | |
| A reaction: [Idea from Scott Soames] I am told that my friend A has just won a very big lottery prize, and am then told that my friend B has also won a very big lottery prize. The conjunction seems less believable; I begin to suspect a conspiracy. |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| Full Idea: One may, on good grounds, deny that reference to a totality necessarily implies reference to all single elements of it or, in other words, that 'all' means the same as an infinite logical conjunction. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.455) |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| Full Idea: In order to be sure that new expression can be translated into expressions not containing them, it is necessary to have a survey of all possible expressions, and this can be furnished only by syntactical considerations. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.448) | |
| A reaction: [compressed] |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
| Full Idea: The generalized Continuum Hypothesis says that there exists no cardinal number between the power of any arbitrary set and the power of the set of its subsets. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| Full Idea: It has turned out that the solution of certain arithmetical problems requires the use of assumptions essentially transcending arithmetic. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.449) | |
| A reaction: A nice statement of the famous result, from the great man himself, in the plainest possible English. |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| Full Idea: Classes and concepts may be conceived of as real objects, ..and are as necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions, with neither case being about 'data'. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.456) | |
| A reaction: Note that while he thinks real objects are essential for mathematics, be may not be claiming the same thing for our knowledge of logic. If logic contains no objects, then how could mathematics be reduced to it, as in logicism? |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| Full Idea: Impredicative definitions are admitted into ordinary mathematics. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) | |
| A reaction: The issue is at what point in building an account of the foundations of mathematics (if there be such, see Putnam) these impure definitions should be ruled out. |
| 12598 | Reality is the overlap of true complete theories [Harman] |
| Full Idea: Reality is what is invariant among true complete theories. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.4) | |
| A reaction: The sort of slogan that gets coined in the age of Quine. The whole manner of starting from your theories and working out to what we think reality is seems to be putting the cart before the horse. |
| 12602 | There is no natural border between inner and outer [Harman] |
| Full Idea: There is no natural border between inner and outer. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.3.4) | |
| A reaction: Perhaps this is the key idea for the anti-individualist view of mind. Subjectively I would have to accept this idea, but looking objectively at another person it seems self-evident nonsense. |
| 12603 | We can only describe mental attitudes in relation to the external world [Harman] |
| Full Idea: No one has ever described a way of explaining what beliefs, desires, and other mental states are except in terms of actual or possible relations to things in the external world. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.3.4) | |
| A reaction: If I pursue my current favourite idea, that how we explain things is the driving force in what ontology we adopt, then this way of seeing the mind, and taking an externalist anti-individualist view of it seems quite attractive. |
| 12601 | The way things look is a relational matter, not an intrinsic matter [Harman] |
| Full Idea: According to functionalism, the way things look to you is a relational characteristic of your experience, not part of its intrinsic character. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.3.3) | |
| A reaction: No, can't make sense of that. How would being in a relation determine what something is? Similar problems with the structuralist account of mathematics. If the whole family love some one cat or one dog, the only difference is intrinsic to the animal. |
| 12592 | Concepts in thought have content, but not meaning, which requires communication [Harman] |
| Full Idea: Concepts and other aspects of mental representation have content but not (normally) meaning (unless they are also expressions in a language used in communication). | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1.2) | |
| A reaction: Given his account of meaning as involving some complex 'role', he has to say this, though it seems a dubious distinction, going against the grain of a normal request to ask what some concept 'means'. What is 'democracy'? |
| 12590 | Take meaning to be use in calculation with concepts, rather than in communication [Harman] |
| Full Idea: (Nonsolipsistic) conceptual role semantics is a version of the theory that meaning is use, where the basic use is taken to be in calculation, not in communication, and where concepts are treated as symbols in a 'language of thought'. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1.1) | |
| A reaction: The idea seems to be to connect the highly social Wittgensteinian view of language with the reductive physicalist account of how brains generate concepts. Interesting, thought I never like meaning-as-use. |
| 12593 | The use theory attaches meanings to words, not to sentences [Harman] |
| Full Idea: A use theory of meaning has to suppose it is words and ways of putting words together that have meaning because of their uses, not sentences. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1.3) | |
| A reaction: He says that most sentences are unique, so cannot have a standard use. Words do a particular job over and over again. How do you distinguish the quirky use of a word from its standard use? |
| 12588 | Meaning from use of thoughts, constructed from concepts, which have a role relating to reality [Harman] |
| Full Idea: Conceptual role semantics involves meanings of expressions determined by used contents of concepts and thoughts, contents constructed from concepts, concepts determined by functional role, which involves relations to things in the world. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1) | |
| A reaction: This essay is the locus classicus for conceptual-role semantics. Any attempt to say what something IS by giving an account of its function always feels wrong to me. |
| 12589 | Some regard conceptual role semantics as an entirely internal matter [Harman] |
| Full Idea: I call my conceptual role semantics 'non-solipsistic' to contrast it with that of authors (Field, Fodor, Loar) who think of conceptual role solipsistically as a completely internal matter. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1) | |
| A reaction: Evidently Harman is influenced by Putnam's Twin Earth, and that meanings ain't in the head, so that the conceptual role has to be extended out into the world to get a good account. I prefer extending into the language community, rather into reality. |
| 12600 | The content of thought is relations, between mental states, things in the world, and contexts [Harman] |
| Full Idea: In (nonsolipsistic) conceptual role semantics the content of thought is not in an 'intrinsic nature', but is rather a matter of how mental states are related to each other, to things in the external world, and to things in a context understood as normal. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.3.3) | |
| A reaction: This is part of Harman's functional view of consciousness, which I find rather dubious. If things only have identity because of some place in a flow diagram, we must ask why that thing has that place in that diagram. |
| 12594 | If one proposition negates the other, which is the negative one? [Harman] |
| Full Idea: A relation of negation might hold between two beliefs without there being anything that determines which belief is the negative one. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1.4) | |
| A reaction: [He attributes this thought to Brian Loar] This seems to give us a reason why we need a semantics for a logic, and not just a structure of inferences and proofs. |
| 12591 | Mastery of a language requires thinking, and not just communication [Harman] |
| Full Idea: If one cannot think in a language, one has not yet mastered it. A symbol system used only for communication, like Morse code, is not a language. | |
| From: Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.1.2) | |
| A reaction: This invites the question of someone who has mastered thinking, but has no idea how to communicate. No doubt we might construct a machine with something like that ability. I think it might support Harman's claim. |
| 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? |