46 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. |
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| Full Idea: 'Equivocation' is when the terms do not mean the same thing in the premises and in the conclusion. | |
| From: JC Beall / G Restall (Logical Consequence [2005], Intro) |
| 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. |
| 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
| Full Idea: Logic is purely formal either when it is invariant under permutation of object (Tarski), or when it has totally abstracted away from all contents, or it is the constitutive norms for thought. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: [compressed] The third account sounds rather woolly, and the second one sounds like a tricky operation, but the first one sounds clear and decisive, so I vote for Tarski. |
| 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. |
| 10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
| Full Idea: Technical work on logical consequence has either focused on proofs, where validity is the existence of a proof of the conclusions from the premises, or on models, which focus on the absence of counterexamples. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 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'. |
| 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
| Full Idea: Two different views of logical consequence are necessary truth-preservation (based on modelling possible worlds; favoured by Realists), or truth-preservation based on the meanings of the logical vocabulary (differing in various models; for Anti-Realists). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) | |
| A reaction: Thus Dummett prefers the second view, because the law of excluded middle is optional. My instincts are with the first one. |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
| Full Idea: A logical step is a 'material consequence' and not a formal one, if we need the contents as well as the structure or form. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 2) |
| 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
| Full Idea: If a conclusion follows from an empty collection of premises, it is true by logic alone, and is a 'logical truth' (sometimes a 'tautology'), or, in the proof-centred approach, 'theorems'. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 4) | |
| A reaction: These truths are written as following from the empty set Φ. They are just implications derived from the axioms and the rules. |
| 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. |
| 10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
| Full Idea: Models are abstract mathematical structures that provide possible interpretations for each of the non-logical primitives in a formal language. | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 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? |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| Full Idea: There are many proof-systems, the main being Hilbert proofs (with simple rules and complex axioms), or natural deduction systems (with few axioms and many rules, and the rules constitute the meaning of the connectives). | |
| From: JC Beall / G Restall (Logical Consequence [2005], 3) |
| 16554 | Activities have place, rate, duration, entities, properties, modes, direction, polarity, energy and range [Machamer/Darden/Craver] |
| Full Idea: Activities can be identified spatiotemporally, and individuated by rate, duration, and types of entity and property that engage in them. They also have modes of operation, directionality, polarity, energy requirements and a range. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3) | |
| A reaction: This is their attempt at making 'activity' one of the two central concepts of ontology, along with 'entity'. A helpful analysis. It just seems to be one way of slicing the cake. |
| 16556 | Penicillin causes nothing; the cause is what penicillin does [Machamer/Darden/Craver] |
| Full Idea: It is not the penicillin that causes the pneumonia to disappear, but what the penicillin does. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3.1) | |
| A reaction: This is a very neat example for illustrating how we slip into 'entity' talk, when the reality we are addressing actually concerns processes. Without the 'what it does', penicillin can't participate in causation at all. |
| 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. |
| 16285 | A possible world can be seen as a complete and consistent novel [Jeffrey] |
| Full Idea: A novel describes a possible world in as much detail as is possible without exceeding the resources of the agent's language. But if talk of possible worlds seems dangerously metaphysical, focus on the novels themselves, when complete and consistent. | |
| From: Richard Jeffrey (The Logic of Decision [1965], 12.8), quoted by David Lewis - On the Plurality of Worlds | |
| A reaction: Lewis seems to cite this remark from Jeffrey as the source of the idea that ersatz linguistic worlds are like novels. Why won't a novel with one tiny inconsistency count as a possible world? People seem to live in it. |
| 16562 | We understand something by presenting its low-level entities and activities [Machamer/Darden/Craver] |
| Full Idea: The intelligibility of a phenomenon consists in the mechanisms being portrayed in terms of a field's bottom out entities and activities. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 7) | |
| A reaction: In other words, we understand complex things by reducing them to things we do understand. It would, though, be illuminating to see a nest of interconnected activities, even if we understood none of them. |
| 19155 | Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey, by Davidson] |
| Full Idea: Jeffrey produced a version of Bayesianism that made no direct use of gambling (as Ramsey had), but treats the objects of preference ...as propositions. | |
| From: report of Richard Jeffrey (The Logic of Decision [1965]) by Donald Davidson - Truth and Predication 3 | |
| A reaction: I'm guessing that Jeffreys launched modern Bayesian theory with this idea. It suggest that one can consider degrees of truth, rather than mere winning or losing. |
| 16563 | The explanation is not the regularity, but the activity sustaining it [Machamer/Darden/Craver] |
| Full Idea: It is not regularities that explain but the activities that sustain the regularities. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 7) | |
| A reaction: Good, but we had better not characterise the 'activities' in terms of regularities. |
| 16555 | Functions are not properties of objects, they are activities contributing to mechanisms [Machamer/Darden/Craver] |
| Full Idea: It is common to speak of functions as properties 'had by' entities, …but they should rather be understood in terms of the activities by virtue of which entities contribute to the workings of a mechanism. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3) | |
| A reaction: I'm certainly quite passionately in favour of cutting down on describing the world almost entirely in terms of entities which have properties. An 'activity', though, is a bit of an elusive concept. |
| 16528 | Mechanisms are not just push-pull systems [Machamer/Darden/Craver] |
| Full Idea: One should not think of mechanisms as exclusively mechanical (push-pull) systems. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 1) | |
| A reaction: The difficulty seems to be that you could broaden the concept of 'mechanism' indefinitely, so that it covered history, mathematics, populations, cultural change, and even mathematics. Where to stop? |
| 16529 | Mechanisms are systems organised to produce regular change [Machamer/Darden/Craver] |
| Full Idea: Mechanisms are entities and activities organized such that they are productive of regular change from start or set-up to finish or termination conditions. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 1) | |
| A reaction: This is their initial formal definition of a mechanism. Note that a mere 'activity' can be included. Presumably the mechanism might have an outcome that was not the intended outcome. Does a random element disqualify it? Are hands mechanisms? |
| 16530 | A mechanism explains a phenomenon by showing how it was produced [Machamer/Darden/Craver] |
| Full Idea: To give a description of a mechanism for a phenomenon is to explain that phenomenon, i.e. to explain how it was produced. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 1) | |
| A reaction: To 'show how' something happens needs a bit of precisification. It is probably analytic that 'showing how' means 'revealing the mechanism', though 'mechanism' then becomes the tricky concept. |
| 16553 | Our account of mechanism combines both entities and activities [Machamer/Darden/Craver] |
| Full Idea: We emphasise the activities in mechanisms. This is explicitly dualist. Substantivalists speak of entities with dispositions to act. Process ontologists reify activities and try to reduce entities to processes. We try to capture both intuitions. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3) | |
| A reaction: [A quotation of selected fragments] The problem here seems to be the raising of an 'activity' to a central role in ontology, when it doesn't seem to be primitive, and will typically be analysed in a variety of ways. |
| 16559 | Descriptions of explanatory mechanisms have a bottom level, where going further is irrelevant [Machamer/Darden/Craver] |
| Full Idea: Nested hierachical descriptions of mechanisms typically bottom out in lowest level mechanisms. …Bottoming out is relative …the explanation comes to an end, and description of lower-level mechanisms would be irrelevant. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 5.1) | |
| A reaction: This seems to me exactly the right story about mechanism, and it is a story I am associating with essentialism. The relevance is ties to understanding. The lower level is either fully understood, or totally baffling. |
| 16564 | There are four types of bottom-level activities which will explain phenomena [Machamer/Darden/Craver] |
| Full Idea: There are four bottom-out kinds of activities: geometrico-mechanical, electro-chemical, electro-magnetic and energetic. These are abstract means of production that can be fruitfully applied in particular cases to explain phenomena. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 7) | |
| A reaction: I like that. It gives a nice core for a metaphysics for physicalists. I suspect that 'mechanical' can be reduced to something else, and that 'energetic' will disappear in the final story. |
| 16561 | We can abstract by taking an exemplary case and ignoring the detail [Machamer/Darden/Craver] |
| Full Idea: Abstractions may be constructed by taking an exemplary case or instance and removing detail. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 5.3) | |
| A reaction: I love 'removing detail'. That's it. Simple. I think this process is the basis of our whole capacity to formulate abstract concepts. Forget Frege - he's just describing the results of the process. How do we decide what is 'detail'? Essentialism! |
| 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? |
| 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. |
| 16558 | Laws of nature have very little application in biology [Machamer/Darden/Craver] |
| Full Idea: The traditional notion of a law of nature has few, if any, applications in neurobiology or molecular biology. | |
| From: Machamer,P/Darden,L/Craver,C (Thinking About Mechanisms [2000], 3.2) | |
| A reaction: This is a simple and self-evident fact, and bad news for anyone who want to build their entire ontology around laws of nature. I take such a notion to be fairly empty, except as a convenient heuristic device. |