30 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) |
| 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) |
| 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. |
| 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. |
| 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. |
| 14064 | If a statue is identical with the clay of which it is made, that identity is contingent [Gibbard] |
| Full Idea: Under certain conditions a clay statue is identical with the piece of clay of which it is made, and if this is so then the identity is contingent. | |
| From: Allan Gibbard (Contingent Identity [1975], Intro) | |
| A reaction: This initiated the modern debate about statues, and it is an attack on Kripke's claim that if two things are identical, then they are necessarily identical. Kripke seems right about Hesperus and Phosphorus, but not about the statue. |
| 14066 | A 'piece' of clay begins when its parts stick together, separately from other clay [Gibbard] |
| Full Idea: A 'piece' of clay is a portion of clay which comes into existence when all of its parts come to be stuck to each other, and cease to be stuck to any clay which is not a part of the portion. | |
| From: Allan Gibbard (Contingent Identity [1975], I) | |
| A reaction: The sort of gormlessly elementary things that philosophers find themselves having to say, but this is a good basic assertion for a discussion of statue and clay, and I can't think of an objection to it. |
| 14067 | Clay and statue are two objects, which can be named and reasoned about [Gibbard] |
| Full Idea: The piece of clay and the statue are 'objects' - that is to say, they can be designated with proper names, and the logic we ordinarily use will still apply. | |
| From: Allan Gibbard (Contingent Identity [1975], I) | |
| A reaction: An interesting indication of the way that 'object' is used in modern analytic philosophy, which may not be the way that it is used in ordinary English. The number 'seven', for example, seems to be an object by this criterion. |
| 14069 | We can only investigate the identity once we have designated it as 'statue' or as 'clay' [Gibbard] |
| Full Idea: To ask meaningfully what that thing would be, we must designate it either as a statue or as a piece of clay. What that thing would be, apart from the way it is designated, is a question without meaning. | |
| From: Allan Gibbard (Contingent Identity [1975], III) | |
| A reaction: He obviously has a powerful point, but to suggest that we can only investigate a mysterious object once we have designated it as something sounds daft. It would ruin the fun of archaeology. |
| 14076 | Essentialism is the existence of a definite answer as to whether an entity fulfils a condition [Gibbard] |
| Full Idea: Essentialism for a class of entities is that for one entity and a condition which it fulfills, the question of whether it necessarily fulfills the condition has a definite answer apart from the way the entity is specified. | |
| From: Allan Gibbard (Contingent Identity [1975], VII) | |
| A reaction: Yet another definition of essentialism, but resting, as usual in modern discussions, entirely on the notion of necessity. Kit Fine's challenge is that if you investigate the source of the necessity, it turns out to be an essence. |
| 14077 | Essentialism for concreta is false, since they can come apart under two concepts [Gibbard] |
| Full Idea: Essentialism for the class of concrete things is false, since a statue necessarily fulfils a condition as 'Goliath', but only contingently fulfils it as 'lumpl'. On the other hand, essentialism for the class of individual concepts can be true. | |
| From: Allan Gibbard (Contingent Identity [1975], VII) | |
| A reaction: This rests on his definition of essentialism in Idea 14076. He rests his essentialism about concepts on an account given by Carnap ('Meaning and Necessity' §41). The essence of a statue and the essence of a lump of clay do seem distinct. |
| 14070 | A particular statue has sortal persistence conditions, so its origin defines it [Gibbard] |
| Full Idea: A proper name like 'Goliath' denotes a thing in the actual world, and invokes a sortal with certain persistence criteria. Hence its origin makes a statue the statue that it is, and if statues in different worlds have the same beginning, they are the same. | |
| From: Allan Gibbard (Contingent Identity [1975], III) | |
| A reaction: Too neat. There are vague, ambiguous and duplicated origins. Persistence criteria can shift during the existence of a thing (like a club which changes its own constitution). In replicated statues, what is the status of the mould? |
| 14073 | Claims on contingent identity seem to violate Leibniz's Law [Gibbard] |
| Full Idea: The most prominent objection to contingent identity (as in the case of the statue and its clay) is that it violates Leibniz's Law. | |
| From: Allan Gibbard (Contingent Identity [1975], V) | |
| A reaction: Depends what you mean by a property. The trickiest one would be that the statue has (right now) a disposition to be worth a lot, but the clay doesn't. But I don't think that is really a property of the statue. Properties are a muddle. |
| 14065 | Two identical things must share properties - including creation and destruction times [Gibbard] |
| Full Idea: For two things to be strictly identical, they must have all properties in common. That means, among other things, that they must start to exist at the same time and cease to exist at the same time. | |
| From: Allan Gibbard (Contingent Identity [1975], I) | |
| A reaction: I don't accept that coming into existence at time t is a 'property' of a thing. Coincident objects give you the notion of 'existing as' something, which complicates the whole story. |
| 14074 | Leibniz's Law isn't just about substitutivity, because it must involve properties and relations [Gibbard] |
| Full Idea: As a general law of substitutivity of identicals, Leibniz's Law is false. It is a law about properties and relations, that if two things are identical, they have the same properties and relations. It only works in contexts which attribute those. | |
| From: Allan Gibbard (Contingent Identity [1975], V) | |
| A reaction: I'm not convinced about relations, which are not intrinsic properties. Under different descriptions, the relations to human minds might differ. |
| 14072 | Possible worlds identity needs a sortal [Gibbard] |
| Full Idea: Identity across possible worlds makes sense only with respect to a sortal | |
| From: Allan Gibbard (Contingent Identity [1975], IV) | |
| A reaction: See Gibbard's other ideas from this paper. I fear that the sortal invoked is too uncertain and slippery to do any useful job, and I can't see any principled difficulty with naming something before you can think of a sortal for it. |
| 14078 | Only concepts, not individuals, can be the same across possible worlds [Gibbard] |
| Full Idea: It is meaningless to talk of the same concrete thing in different possible worlds, ...but it makes sense to speak of the same individual concept, which is just a function which assigns to each possible world in a set an individual in that world. | |
| From: Allan Gibbard (Contingent Identity [1975], VII) | |
| A reaction: A lovely bold response to the problem of transworld identity, but one which needs investigation. It sounds very promising to me. 'Aristotle' is a cocept, not a name. There is no separate category of 'names'. Wow. (Attach dispositions to concepts?). |
| 14079 | Kripke's semantics needs lots of intuitions about which properties are essential [Gibbard] |
| Full Idea: To use Kripke's semantics, one needs extensive intuitions that certain properties are essential and others accidental. | |
| From: Allan Gibbard (Contingent Identity [1975], X) | |
| A reaction: As usual, we could substitute the word 'necessary' for 'essential' without changing his meaning. If we are always referring to 'our' Hubert Humphrey is speculations about him, then nearly all of his properties will be necessary ones. |
| 14071 | Naming a thing in the actual world also invokes some persistence criteria [Gibbard] |
| Full Idea: The reference of a name in the actual world is fixed partly by invoking a set of persistence criteria which determine what thing it names. | |
| From: Allan Gibbard (Contingent Identity [1975], III) | |
| A reaction: This is offered as a modification to Kripke, to deal with the statue and clay. I fear that the 'persistence criteria' may be too vague, and too subject to possible change after the origin, to do the job required. |
| 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. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |