23 ideas
| 18781 | Inconsistency doesn't prevent us reasoning about some system [Mares] |
| Full Idea: We are able to reason about inconsistent beliefs, stories, and theories in useful and important ways | |
| From: Edwin D. Mares (Negation [2014], 1) |
| 18790 | Intuitionism as natural deduction has no rule for negation [Mares] |
| Full Idea: In intuitionist logic each connective has one introduction and one elimination rule attached to it, but in the classical system we have to add an extra rule for negation. | |
| From: Edwin D. Mares (Negation [2014], 5.5) | |
| A reaction: How very intriguing. Mares says there are other ways to achieve classical logic, but they all seem rather cumbersome. |
| 18789 | Intuitionist logic looks best as natural deduction [Mares] |
| Full Idea: Intuitionist logic appears most attractive in the form of a natural deduction system. | |
| From: Edwin D. Mares (Negation [2014], 5.5) |
| 18787 | Three-valued logic is useful for a theory of presupposition [Mares] |
| Full Idea: One reason for wanting a three-valued logic is to act as a basis of a theory of presupposition. | |
| From: Edwin D. Mares (Negation [2014], 3.1) | |
| A reaction: [He cites Strawson 1950] The point is that you can get a result when the presupposition does not apply, as in talk of the 'present King of France'. |
| 18793 | Material implication (and classical logic) considers nothing but truth values for implications [Mares] |
| Full Idea: The problem with material implication, and classical logic more generally, is that it considers only the truth value of formulas in deciding whether to make an implication stand between them. It ignores everything else. | |
| From: Edwin D. Mares (Negation [2014], 7.1) | |
| A reaction: The obvious problem case is conditionals, and relevance is an obvious extra principle that comes to mind. |
| 18784 | In classical logic the connectives can be related elegantly, as in De Morgan's laws [Mares] |
| Full Idea: Among the virtues of classical logic is the fact that the connectives are related to one another in elegant ways that often involved negation. For example, De Morgan's Laws, which involve negation, disjunction and conjunction. | |
| From: Edwin D. Mares (Negation [2014], 2.2) | |
| A reaction: Mares says these enable us to take disjunction or conjunction as primitive, and then define one in terms of the other, using negation as the tool. |
| 18786 | Excluded middle standardly implies bivalence; attacks use non-contradiction, De M 3, or double negation [Mares] |
| Full Idea: On its standard reading, excluded middle tells us that bivalence holds. To reject excluded middle, we must reject either non-contradiction, or ¬(A∧B) ↔ (¬A∨¬B) [De Morgan 3], or the principle of double negation. All have been tried. | |
| From: Edwin D. Mares (Negation [2014], 2.2) |
| 18780 | Standard disjunction and negation force us to accept the principle of bivalence [Mares] |
| Full Idea: If we treat disjunction in the standard way and take the negation of a statement A to mean that A is false, accepting excluded middle forces us also to accept the principle of bivalence, which is the dictum that every statement is either true or false. | |
| From: Edwin D. Mares (Negation [2014], 1) | |
| A reaction: Mates's point is to show that passively taking the normal account of negation for granted has important implications. |
| 18782 | The connectives are studied either through model theory or through proof theory [Mares] |
| Full Idea: In studying the logical connectives, philosophers of logic typically adopt the perspective of either model theory (givng truth conditions of various parts of the language), or of proof theory (where use in a proof system gives the connective's meaning). | |
| From: Edwin D. Mares (Negation [2014], 1) | |
| A reaction: [compressed] The commonest proof theory is natural deduction, giving rules for introduction and elimination. Mates suggests moving between the two views is illuminating. |
| 7755 | Singular terms refer, using proper names, definite descriptions, singular personal pronouns, demonstratives, etc. [Lycan] |
| Full Idea: The paradigmatic referring devices are singular terms, denoting particular items. In English these include proper names, definite descriptions, singular personal pronouns, demonstrative pronouns, and a few others. | |
| From: William Lycan (Philosophy of Language [2000], Ch. 1) | |
| A reaction: This list provides the agenda for twentieth century philosophy of language, since this is the point where language is supposed to hook onto the world. |
| 18783 | Many-valued logics lack a natural deduction system [Mares] |
| Full Idea: Many-valued logics do not have reasonable natural deduction systems. | |
| From: Edwin D. Mares (Negation [2014], 1) |
| 18792 | Situation semantics for logics: not possible worlds, but information in situations [Mares] |
| Full Idea: Situation semantics for logics consider not what is true in worlds, but what information is contained in situations. | |
| From: Edwin D. Mares (Negation [2014], 6.2) | |
| A reaction: Since many theoretical physicists seem to think that 'information' might be the most basic concept of a natural ontology, this proposal is obviously rather appealing. Barwise and Perry are the authors of the theory. |
| 18785 | Consistency is semantic, but non-contradiction is syntactic [Mares] |
| Full Idea: The difference between the principle of consistency and the principle of non-contradiction is that the former must be stated in a semantic metalanguage, whereas the latter is a thesis of logical systems. | |
| From: Edwin D. Mares (Negation [2014], 2.2) |
| 18788 | For intuitionists there are not numbers and sets, but processes of counting and collecting [Mares] |
| Full Idea: For the intuitionist, talk of mathematical objects is rather misleading. For them, there really isn't anything that we should call the natural numbers, but instead there is counting. What intuitionists study are processes, such as counting and collecting. | |
| From: Edwin D. Mares (Negation [2014], 5.1) | |
| A reaction: That is the first time I have seen mathematical intuitionism described in a way that made it seem attractive. One might compare it to a metaphysics based on processes. Apparently intuitionists struggle with infinite sets and real numbers. |
| 7768 | The truth conditions theory sees meaning as representation [Lycan] |
| Full Idea: The truth conditions theory sees meaning as representation. | |
| From: William Lycan (Philosophy of Language [2000], Ch. 9) | |
| A reaction: This suggests a nice connection to Fodor's account of intentional thinking. The whole package sounds right to me (though the representations need not be 'symbolic', or in mentalese). |
| 7766 | Meaning must be known before we can consider verification [Lycan] |
| Full Idea: How could we know whether a sentence is verifiable unless we already knew what it says? | |
| From: William Lycan (Philosophy of Language [2000], Ch. 8) | |
| A reaction: This strikes me as a devastating objection to verificationism. Lycan suggests that you can formulate a preliminary meaning, without accepting true meaningfulness. Maybe verification just concerns truth, and not meaning. |
| 7764 | Could I successfully use an expression, without actually understanding it? [Lycan] |
| Full Idea: Could I not know the use of an expression and fall in with it, mechanically, but without understanding it? | |
| From: William Lycan (Philosophy of Language [2000], Ch. 6) | |
| A reaction: In a foreign country, you might successfully recite a long complex sentence, without understanding a single word. This doesn't doom the 'use' theory, but it means that quite a lot of detail needs to be filled in. |
| 7763 | It is hard to state a rule of use for a proper name [Lycan] |
| Full Idea: Proper names pose a problem for the "use" theorist. Try stating a rule of use for the name 'William G. Lycan'. | |
| From: William Lycan (Philosophy of Language [2000], Ch. 6) | |
| A reaction: Presumably it is normally used in connection with a particular human being, and is typically the subject of a grammatical sentence. Any piece of language could also be used to, say, attract someone's attention. |
| 18791 | In 'situation semantics' our main concepts are abstracted from situations [Mares] |
| Full Idea: In 'situation semantics' individuals, properties, facts, and events are treated as abstractions from situations. | |
| From: Edwin D. Mares (Negation [2014], 6.1) | |
| A reaction: [Barwise and Perry 1983 are cited] Since I take the process of abstraction to be basic to thought, I am delighted to learn that someone has developed a formal theory based on it. I am immediately sympathetic to situation semantics. |
| 7770 | Truth conditions will come out the same for sentences with 'renate' or 'cordate' [Lycan] |
| Full Idea: A Davidsonian truth theory will not be able to distinguish the meaning of a sentence containing 'renate' from that of one containing 'cordate'. | |
| From: William Lycan (Philosophy of Language [2000], Ch. 9) | |
| A reaction: One might achieve the distinction by referring to truth conditions in possible worlds, if there are possible worlds where some cordates are not renate. See Idea 7773. |
| 7773 | A sentence's truth conditions is the set of possible worlds in which the sentence is true [Lycan] |
| Full Idea: A sentence's truth conditions can be taken to be the set of possible worlds in which the sentence is true. | |
| From: William Lycan (Philosophy of Language [2000], Ch.10) | |
| A reaction: Presumably the meaning can't be complete possible worlds, so this must be a supplement to the normal truth conditions view proposed by Davidson. It particularly addresses the problem seen in Idea 7770. |
| 7774 | Possible worlds explain aspects of meaning neatly - entailment, for example, is the subset relation [Lycan] |
| Full Idea: The possible worlds construal affords an elegant algebra of meaning by way of set theory: e.g. entailment between sentences is just the subset relation - S1 entails S2 if S2 is true in any world in which S1 is true. | |
| From: William Lycan (Philosophy of Language [2000], Ch.10) | |
| A reaction: We might want to separate the meanings of sentences from their entailments (though Brandom links them, see Idea 7765). |
| 9425 | Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis] |
| Full Idea: Later Lewis said we must choose between the intersection of the axioms of the tied best systems. He chose for laws the axioms that are in all the tied systems (but then there may be few or no axioms in the intersection). | |
| From: comment on David Lewis (Subjectivist's Guide to Objective Chance [1980], p.124) by Stephen Mumford - Laws in Nature |