50 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. |
| 9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
| Full Idea: Until the 1960s standard truth-table semantics were the only ones that there were. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.10.1) | |
| A reaction: The 1960s presumably marked the advent of possible worlds. |
| 9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
| Full Idea: 'dom R' indicates the 'domain' of a relation, that is, the set of all objects that are members of ordered pairs and that have that relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
| Full Idea: 'fld R' indicates the 'field' of a relation, that is, the set of all objects that are members of ordered pairs on either side of the relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
| Full Idea: 'ran R' indicates the 'range' of a relation, that is, the set of all objects that are members of ordered pairs and that are related to by the first objects. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
| Full Idea: We write F : A → B to indicate that A maps into B, that is, the domain of relating things is set A, and the things related to are all in B. If we add that F = B, then A maps 'onto' B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
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Full Idea:
F(x) is a 'function', which indicates the unique value which y takes in |
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| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
| Full Idea: A relation is 'symmetric' on a set if every ordered pair in the set has the relation in both directions. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
| Full Idea: A relation is 'transitive' on a set if the relation can be carried over from two ordered pairs to a third. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
| Full Idea: The 'powerset' of a set is all the subsets of a given set. Thus: PA = {x : x ⊆ A}. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
| Full Idea: Two sets are 'disjoint' iff their intersection is empty (i.e. they have no members in common). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
| Full Idea: The 'domain' of a relation is the set of all objects that are members of ordered pairs that are members of the relation. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9701 | A 'relation' is a set of ordered pairs [Enderton] |
| Full Idea: A 'relation' is a set of ordered pairs. The ordering relation on the numbers 0-3 is captured by - in fact it is - the set of ordered pairs {<0,1>,<0,2>,<0,3>,<1,2>,<1,3>,<2,3>}. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) | |
| A reaction: This can't quite be a definition of order among numbers, since it relies on the notion of a 'ordered' pair. |
| 9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
| Full Idea: A 'function' is a relation which is single-valued. That is, for each object, there is only one object in the function set to which that object is related. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
| Full Idea: A function 'maps A into B' if the domain of relating things is set A, and the things related to are all in B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
| Full Idea: A function 'maps A onto B' if the domain of relating things is set A, and the things related to are set B. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
| Full Idea: A relation is 'reflexive' on a set if every member of the set bears the relation to itself. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
| Full Idea: A relation satisfies 'trichotomy' on a set if every ordered pair is related (in either direction), or the objects are identical. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
| Full Idea: A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
| Full Idea: An 'equivalence relation' is a binary relation which is reflexive, and symmetric, and transitive. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
| Full Idea: Equivalence classes will 'partition' a set. That is, it will divide it into distinct subsets, according to each relation on the set. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], Ch.0) |
| 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. |
| 9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
| Full Idea: The process is dubbed 'conversational implicature' when the inference is not from the content of what has been said, but from the fact that it has been said. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.7.3) |
| 9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
| Full Idea: The point of logic is to give an account of the notion of validity,..in two standard ways: the semantic way says that a valid inference preserves truth (symbol |=), and the proof-theoretic way is defined in terms of purely formal procedures (symbol |-). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.3..) | |
| A reaction: This division can be mirrored in mathematics, where it is either to do with counting or theorising about things in the physical world, or following sets of rules from axioms. Language can discuss reality, or play word-games. |
| 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. |
| 9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
| Full Idea: A is a logical truth (tautology) (|= A) iff it is a semantic consequence of the empty set of premises (φ |= A), that is, every interpretation makes A true. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.3.4) | |
| A reaction: So the final column of every line of the truth table will be T. |
| 9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
| Full Idea: A truth assignment 'satisfies' a formula, or set of formulae, if it evaluates as True when all of its components have been assigned truth values. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.2) | |
| A reaction: [very roughly what Enderton says!] The concept becomes most significant when a large set of wff's is pronounced 'satisfied' after a truth assignment leads to them all being true. |
| 9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
| Full Idea: If every proof-theoretically valid inference is semantically valid (so that |- entails |=), the proof theory is said to be 'sound'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.7) |
| 9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
| Full Idea: If every semantically valid inference is proof-theoretically valid (so that |= entails |-), the proof-theory is said to be 'complete'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.7) |
| 9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
| Full Idea: If a wff is tautologically implied by a set of wff's, it is implied by a finite subset of them; and if every finite subset is satisfiable, then so is the whole set of wff's. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 2.5) | |
| A reaction: [Enderton's account is more symbolic] He adds that this also applies to models. It is a 'theorem' because it can be proved. It is a major theorem in logic, because it brings the infinite under control, and who doesn't want that? |
| 9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
| Full Idea: A set of expressions is 'decidable' iff there exists an effective procedure (qv) that, given some expression, will decide whether or not the expression is included in the set (i.e. doesn't contradict it). | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.7) | |
| A reaction: This is obviously a highly desirable feature for a really reliable system of expressions to possess. All finite sets are decidable, but some infinite sets are not. |
| 9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
| Full Idea: The Enumerability Theorem says that for a reasonable language, the set of valid wff's can be effectively enumerated. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 2.5) | |
| A reaction: There are criteria for what makes a 'reasonable' language (probably specified to ensure enumerability!). Predicates and functions must be decidable, and the language must be finite. |
| 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. |
| 9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
| Full Idea: Not all sentences using 'if' are conditionals. Consider 'if you want a banana, there is one in the kitchen'. The rough test is that a conditional can be rewritten as 'that A implies that B'. | |
| From: Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.6.4) |
| 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. |
| 5122 | Maybe consequentialism is a critique of ordinary morality, rather than describing it [Harman] |
| Full Idea: Consequentialism may be put forward not as an attempt to capture intuitive folk morality but rather as a critique of ordinary tuitions. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.1) | |
| A reaction: It is certainly true that most people are concerned with why an action was performed, and (after initial anger) are prepared to forgive an unintended disaster. We have no moral objections to earthquakes, which have bad consequences. |
| 5123 | Maybe there is no such thing as character, and the virtues and vices said to accompany it [Harman] |
| Full Idea: It may be the case that there is no such thing as character, no ordinary character traits of the sort people think there are, none of the usual moral virtues and vices. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.1) | |
| A reaction: This would be a devastating fact for virtue theory, if it were true. I don't believe it. He thinks patterns of behaviour result from circumstances, but we give accurate and detailed pictures of people's characters (esp. in novels). |
| 5124 | If a person's two acts of timidity have different explanations, they are not one character trait [Harman] |
| Full Idea: If Herbert is disposed to not speak in history class (but not other subjects), and explanation of this is different from his avoidance of roller coaster rides, then these two dispositions are not special cases of a single character trait. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.2) | |
| A reaction: A basic Harman argument for denying the existence of character (and hence of virtues). I just say that character traits are more complex than his caricature of them. If I keep imagining disaster and humiliation for myself, that is a character trait. |
| 5125 | Virtue ethics might involve judgements about the virtues of actions, rather than character [Harman] |
| Full Idea: There are variants of virtue ethics that do not require character traits in the ordinary sense. For example, moral thinking might be explicated by appeal to judgements about whether particular actions are just or courageous or whatever. | |
| From: Gilbert Harman (Moral Philosophy meets social psychology [1999], 10.7.1.1) | |
| A reaction: A very interesting proposal (from Judith Jarvis Thomson). This would flatly reject Aristotle, and one presumes that the judgement about the virtue of the action would largely be a matter of pondering cultural conventions (or, perhaps, consequences). |