35 ideas
| 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? |
| 10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
| Full Idea: Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter. | |
| From: Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6 | |
| A reaction: This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well. |
| 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. |
| 19527 | We don't acquire evidence and then derive some knowledge, because evidence IS knowledge [Williamson] |
| Full Idea: When we acquire new evidence in perception, we do not first acquire unknown evidence and then somehow base knowledge on it later. Rather, acquiring new is evidence IS acquiring new knowledge. | |
| From: Timothy Williamson (Knowledge First (and reply) [2014], p.4) | |
| A reaction: This makes his point much better than Idea 19526 does. |
| 19528 | Knowledge is prior to believing, just as doing is prior to trying to do [Williamson] |
| Full Idea: Knowing corresponds to doing, believing to trying. Just as trying is naturally understood in relation to doing, so believing is naturally understood in relation to knowing. | |
| From: Timothy Williamson (Knowledge First (and reply) [2014], p.4) | |
| A reaction: An interesting analogy. You might infer that there can be no concept of 'belief' without the concept of 'knowledge', but we could say that it is 'truth' which is indispensible, and leave out knowledge entirely. Belief is to truth as trying is to doing? |
| 19529 | Belief explains justification, and knowledge explains belief, so knowledge explains justification [Williamson] |
| Full Idea: If justification is the fundamental epistemic norm of belief, and a belief ought to constitute knowledge, then justification should be understood in terms of knowledge too. | |
| From: Timothy Williamson (Knowledge First (and reply) [2014], p.5) | |
| A reaction: If we are looking for the primitive norm which motivates the whole epistemic game, then I am thinking that truth might well play that role better than knowledge. TW would have to reply that it is the 'grasped truth', rather than the 'theoretical truth'. |
| 19530 | A neutral state of experience, between error and knowledge, is not basic; the successful state is basic [Williamson] |
| Full Idea: A neutral state covering both perceiving and misperceiving (or remembering and misrembering) is not somehow more basic than perceiving, for what unifies the case of each neutral state is their relation to the successful state. | |
| From: Timothy Williamson (Knowledge First (and reply) [2014], p.5-6) | |
| A reaction: An alternative is Disjunctivism, which denies the existence of a single neutral state, so that there is nothing to unite the two states, and they don't have a dependence relation. Why can't there be a prior family of appearances, some of them successful? |
| 19531 | Internalism about mind is an obsolete view, and knowledge-first epistemology develops externalism [Williamson] |
| Full Idea: A postulated underlying layer of narrow mental states is a myth, whose plausibility derives from a comfortingly familiar but obsolescent philosophy of mind. Knowledge-first epistemology is a further step in the development of externalism. | |
| From: Timothy Williamson (Knowledge First (and reply) [2014], p.6) | |
| A reaction: Williamson is a real bruiser, isn't he? I don't take internalism about mind to be obsolescent at all, but now I feel so inferior for clinging to such an 'obsolescent' belief. ...But then I cling to Aristotle, who is (no doubt) an obsolete philosopher. |
| 19536 | Knowledge-first says your total evidence IS your knowledge [Williamson] |
| Full Idea: Knowledge-first equate one's total evidence with one's total knowledge. | |
| From: Timothy Williamson (Knowledge First (and reply) [2014], p.8) | |
| A reaction: Couldn't lots of evidence which merely had a high probability be combined together to give a state we would call 'knowledge'? Many dubious witnesses confirm the truth, as long as they are independent, and agree. |
| 19526 | Surely I am acquainted with physical objects, not with appearances? [Williamson] |
| Full Idea: When I ask myself what I am acquainted with, the physical objects in front of me are far more natural candidates than their appearances. | |
| From: Timothy Williamson (Knowledge First (and reply) [2014], p.3) | |
| A reaction: Not very impressive. The word 'acquainted' means the content of the experience, not the phenomena. Do I 'experience' the objects, or the appearances? The answer there is less obvious. If you apply it to colours, it is even less obvious. |
| 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? |
| 19534 | How does inferentialism distinguish the patterns of inference that are essential to meaning? [Williamson] |
| Full Idea: Inferentialism faces the grave problem of separating patterns of inference that are to count as essential to the meaning of an expression from those that will count as accidental (a form of the analytic/synthetic distinction). | |
| From: Timothy Williamson (Knowledge First (and reply) [2014], p.6) | |
| A reaction: This sounds like a rather persuasive objection to inferentialism, though I don't personally take that as a huge objection to all internalist semantics. |
| 19535 | Internalist inferentialism has trouble explaining how meaning and reference relate [Williamson] |
| Full Idea: The internalist version of inferentialist semantics has particular difficulty in establishing an adequate relation between meaning and reference. | |
| From: Timothy Williamson (Knowledge First (and reply) [2014], p.6) | |
| A reaction: I would have thought that this was a big problem for referentialist semantics too, though evidently Williamson doesn't think so. If he is saying that the meaning is in the external world, dream on. |
| 19533 | Inferentialist semantics relies on internal inference relations, not on external references [Williamson] |
| Full Idea: On internalist inferential (or conceptual role) semantics, the inferential relations of an expression do not depend on what, if anything, it refers to, ...rather, the meaning is something like its place in a web of inferential relations. | |
| From: Timothy Williamson (Knowledge First (and reply) [2014], p.6) | |
| A reaction: Williamson says the competition is between externalist truth-conditional referential semantics (which he favours), and this internalist inferential semantics. He is, like, an expert, of course, but I doubt whether that is the only internalist option. |
| 19532 | Truth-conditional referential semantics is externalist, referring to worldly items [Williamson] |
| Full Idea: Truth-conditional referential semantics is an externalist programme. In a context of utterance the atomic expressions of a language refer to worldly items, from which the truth-conditions of sentences are compositionally determined. | |
| From: Timothy Williamson (Knowledge First (and reply) [2014], p.6) | |
| A reaction: I just don't see how a physical object can be part of the contents of a sentence. 'Dragons fly' is atomic, and meaningful, but its reference fails. 'The cat is asleep' is just words - it doesn't contain a live animal. |
| 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. |