36 ideas
| 11103 | We aren't stuck with our native conceptual scheme; we can gradually change it [Quine] |
| Full Idea: We must not leap to the fatalistic conclusion that we are stuck with the conceptual scheme that we grew up in. We can change it bit by bit, plank by plank. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 5) | |
| A reaction: This is an interesting commitment to Strawson's 'revisionary' metaphysics, rather than its duller cousin 'descriptive' metaphysics. Good for Quine. Remember, though, Davidson's 'On the Very Idea of Conceptual Scheme'. |
| 13252 | Some truths have true negations [Beall/Restall] |
| Full Idea: Dialetheism is the view that some truths have true negations. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.4) | |
| A reaction: The important thing to remember is that they are truths. Thus 'Are you feeling happy?' might be answered 'Yes and no'. |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| Full Idea: The truthmaker thesis is that an object is a truthmaker for a sentence if and only if its existence entails the sentence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.3) | |
| A reaction: The use of the word 'object' here is even odder than usual, and invites many questions. And the 'only if' seems peculiar, since all sorts of things can make a sentence true. 'There is someone in the house' for example. |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| Full Idea: The inference of 'distribution' (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically. It is straightforward to construct a 'stage' at which the LHS is true but the RHS is not. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 6.1.2) | |
| A reaction: This seems to parallel the iterative notion in set theory, that you must construct your hierarchy. All part of the general 'constructivist' approach to things. Is some kind of mad platonism the only alternative? |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| Full Idea: Relevant logic endorses excluded middle, ..but says instances of the law may fail. Bv¬B is true in every situation that settles the matter of B. It is necessary that there is some such situation. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: See next idea for the unusual view of necessity on which this rests. It seems easier to assert something about all situations than just about 'some' situation. |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| Full Idea: The argument from P to A is 'relevantly' valid if and only if, for every situation in which each premise in P is true, so is A. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: I like the idea that proper inference should have an element of relevance to it. A falsehood may allow all sorts of things, without actually implying them. 'Situations' sound promising here. |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| Full Idea: We have not abandoned classical logic in our acceptance of relevant logic. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.4) | |
| A reaction: It appears that classical logic is straightforwardly accepted, but there is a difference of opinion over when it is applicable. |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| Full Idea: Relevant consequence says the conclusion of a relevantly invalid argument is not 'carried in' the premises - it does not follow from the premises. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.3.3) | |
| A reaction: I find this appealing. It need not invalidate classical logic. It is just a tougher criterion which is introduced when you want to do 'proper' reasoning, instead of just playing games with formal systems. |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| Full Idea: We could reject the inference from A to itself (on grounds of circularity). | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [Martin-Meyer System] 'It's raining today'. 'Are you implying that it is raining today?' 'No, I'm SAYING it's raining today'. Logicians don't seem to understand the word 'implication'. Logic should capture how we reason. Nice proposal. |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| Full Idea: Some relevant logics reject transitivity, but we defend the classical view. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: [they cite Neil Tennant for this view] To reject transitivity (A?B ? B?C ? A?C) certainly seems a long way from classical logic. But in everyday inference Tennant's idea seems good. The first premise may be irrelevant to the final conclusion. |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| Full Idea: A logic is 'free' to the degree it refrains from existential import of its singular and general terms. Classical logic must have non-empty domain, and each name must denote in the domain. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 7.1) | |
| A reaction: My intuition is that logic should have no ontology at all, so I like the sound of 'free' logic. We can't say 'Pegasus does not exist', and then reason about Pegasus just like any other horse. |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| Full Idea: Nowadays we think of the consequence relation itself as the primary subject of logic, and view logical truths as degenerate instances of this relation. Logical truths follow from any set of assumptions, or from no assumptions at all. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: This seems exactly right; the alternative is the study of necessities, but that may not involve logic. |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| Full Idea: According to the Peripatetics (Aristotelians), only syllogistic laws stated in variables belong to logic, and not their applications to concrete terms. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: [from Lukasiewicz] Seems wrong. I take it there are logical relations between concrete things, and the variables are merely used to describe these relations. Variables lack the internal powers to drive logical necessities. Variables lack essence! |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| Full Idea: Through much of the 20th century the conception of logic was inherited from Frege and Russell, as knowledge of a body of logical truths, as arithmetic or geometry was a knowledge of truths. This is odd, and a historical anomaly. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Interesting. I have always taken this idea to be false. I presume logic has minimal subject matter and truths, and preferably none at all. |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| Full Idea: Logic does not study formal languages for their own sake, which is formal grammar. Logic evaluates arguments, and primarily considers formal languages as interpreted. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: Hodges seems to think logic just studies formal languages. The current idea strikes me as a much more sensible view. |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| Full Idea: The model theory of classical predicate logic is mathematics if anything is. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 4.2.1) | |
| A reaction: This is an interesting contrast to the claim of logicism, that mathematics reduces to logic. This idea explains why students of logic are surprised to find themselves involved in mathematics. |
| 13253 | There are several different consequence relations [Beall/Restall] |
| Full Idea: We are pluralists about logical consequence because we take there to be a number of different consequence relations, each reflecting different precisifications of the pre-theoretic notion of deductive logical consequence. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 8) | |
| A reaction: I don't see how you avoid the slippery slope that leads to daft logical rules like Prior's 'tonk' (from which you can infer anything you like). I say that nature imposes logical conquence on us - but don't ask me to prove it. |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| 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: JC Beall / G Restall (Logical Pluralism [2006], 3.2) | |
| A reaction: This why the symbol |= is often referred to as 'models'. |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| Full Idea: If mathematical truth reduces to logical truth then it is important what counts as logically true, …but if logicism is not a going concern, then the body of purely logical truths will be less interesting. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.2) | |
| A reaction: Logicism would only be one motivation for pursuing logical truths. Maybe my new 'Necessitism' will derive the Peano Axioms from broad necessary truths, rather than from logic. |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| Full Idea: The Paradox of the Preface is an apology, that you are committed to each proposition in the book, but admit that collectively they probably contain a mistake. There is a contradiction, of affirming and denying the conjunction of propositions. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.4) | |
| A reaction: This seems similar to the Lottery Paradox - its inverse perhaps. Affirm all and then deny one, or deny all and then affirm one? |
| 11092 | A river is a process, with stages; if we consider it as one thing, we are considering a process [Quine] |
| Full Idea: A river is a process through time, and the river stages are its momentary parts. Identification of the river bathed in once with the river bathed in again is just what determines our subject matter to be a river process as opposed to a river stage. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 1) | |
| A reaction: So if we take a thing which has stages, but instead of talking about the stages we talk about a single thing that endures through them, then we are talking about a process. Sounds very good to me. |
| 11093 | We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape [Quine] |
| Full Idea: 'Red' is surely not going to be opposed to 'Cayster' [name of a river], as abstract to concrete, merely because of discontinuity in geometrical shape? | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2) | |
| A reaction: I've been slow to grasp the truth of this. However, Quine assumes that 'red' is concrete because 'Cayster' is, but it is perfectly arguable that 'Cayster' is an abstraction, despite all that water. |
| 11101 | General terms don't commit us ontologically, but singular terms with substitution do [Quine] |
| Full Idea: The use of general terms does not commit us to admitting a corresponding abstract entity into our ontology, but an abstract singular term, including the law of putting equals for equals, flatly commits us to an abstract entity named by the term. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 4) | |
| A reaction: Does this mean that in 'for the sake of the children', I have to believe in 'sakes' if I can find a synonym which will substitute for it? |
| 11096 | Discourse generally departmentalizes itself to some degree [Quine] |
| Full Idea: Discourse generally departmentalizes itself to some degree. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2) | |
| A reaction: I pick this out because I think it is important. There is a continually shifting domain in any conversation ('what we are talking about'), and speech cannot be understand if the shifting domain or department has not been grasped. |
| 11099 | Understanding 'is square' is knowing when to apply it, not knowing some object [Quine] |
| Full Idea: No more need be demanded of 'is square' than that our listener learn when to expect us to apply it to an object and when not; there is no need for the phrase itself to be the name in turn of a separate object of any kind. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 4) |
| 11094 | 'Red' is a single concrete object in space-time; 'red' and 'drop' are parts of a red drop [Quine] |
| Full Idea: Why not view 'red' as naming a single concrete object extended in space and time? ..To say a drop is red is to say that the one object, the drop, is a spatio-temporal part of the other, red, as a waterfall is part of a river. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2) |
| 11097 | Red is the largest red thing in the universe [Quine] |
| Full Idea: Red is the largest red thing in the universe - the scattered total thing whose parts are all the red things. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 3) |
| 17595 | To unite a sequence of ostensions to make one object, a prior concept of identity is needed [Quine] |
| Full Idea: The concept of identity is central in specifying spatio-temporally broad objects by ostension. Without identity, n acts of ostension merely specify up to n objects. ..But when we affirm identity of object between ostensions, they refer to the same object. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 1) | |
| A reaction: Quine says that there is an induction involved. On the whole, Quine seems to give a better account of identity than Geach or Wiggins can offer. |
| 11095 | We should just identify any items which are indiscernible within a given discourse [Quine] |
| Full Idea: We might propound the maxim of the 'identification of indiscernibles': Objects indistinguishable from one another within the terms of a given discourse should be construed as identical for that discourse. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2) | |
| A reaction: This increasingly strikes me as the correct way to discuss such things. Identity is largely contextual, and two things can be viewed as type-identical for practical purposes (e.g. teaspoons), but distinguished if it is necessary. |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| Full Idea: In relevant logic, the necessary truths are not those which are true in every situation; rather, they are those for which it is necessary that there is a situation making them true. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.2) | |
| A reaction: This seems to rest on the truthmaker view of such things, which I find quite attractive (despite Merricks's assault). Always ask what is making some truth necessary. This leads you to essences. |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| Full Idea: All judgement, for Kant, is essentially the predication of some property to some subject. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.5) | |
| A reaction: Presumably the denial of a predicate could be a judgement, or the affirmation of ambiguous predicates? |
| 11104 | Concepts are language [Quine] |
| Full Idea: Concepts are language. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 5) | |
| A reaction: Hm. This seems to mean that animals and pre-linguistic children have no concepts. I just don't believe that. |
| 11102 | Apply '-ness' or 'class of' to abstract general terms, to get second-level abstract singular terms [Quine] |
| Full Idea: Applying the operator '-ness' or 'class of' to abstract general terms, we get second-level abstract singular terms. | |
| From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 5) | |
| A reaction: This is the derivation of abstract concepts by naming classes, rather than by deriving equivalence classes. Any theory which doesn't allow multi-level abstraction is self-evidently hopeless. Quine says Frege and Russell get numbers this way. |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| Full Idea: Situation semantics is a variation of the truth-conditional approach, taking the salient unit of analysis not to be the possible world, or some complete consistent index, but rather the more modest 'situation'. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 5.5.4) | |
| A reaction: When I read Davidson (and implicitly Frege) this is what I always assumed was meant. The idea that worlds are meant has crept in to give truth conditions for modal statements. Hence situation semantics must cover modality. |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| Full Idea: Our talk of propositions expresses commitment to the general notion of content, without a commitment to any particular way of spelling this out. | |
| From: JC Beall / G Restall (Logical Pluralism [2006], 2.1) | |
| A reaction: As a fan of propositions I like this. It leaves open the question of whether the content belongs to the mind or the language. Animals entertain propositions, say I. |
| 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? |