31 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. |
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. |
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. |
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? |
18528 | The single imagined 'interval' between things only exists in the intellect [Auriol] |
Full Idea: It appears that a single thing, which must be imagined as some sort of interval [intervallum] existing between two things, cannot exist in extramental reality, but only in the intellect. | |
From: Peter Auriol (Sentences [1316], I fols318 v a-b), quoted by John Heil - The Universe as We Find It 7 | |
A reaction: This is the standard medieval denial of the existence of real relations. It contrasts with post-Russell ontology, which seems to admit relations as entities. Heil and Auriol and right. |
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. |
10993 | Ramsey's Test: believe the consequent if you believe the antecedent [Ramsey, by Read] |
Full Idea: Ramsey's Test for conditionals is that a conditional should be believed if a belief in its antecedent would commit one to believing its consequent. | |
From: report of Frank P. Ramsey (Law and Causality [1928]) by Stephen Read - Thinking About Logic Ch.3 | |
A reaction: A rather pragmatic approach to conditionals |
14279 | Asking 'If p, will q?' when p is uncertain, then first add p hypothetically to your knowledge [Ramsey] |
Full Idea: If two people are arguing 'If p, will q?' and are both in doubt as to p, they are adding p hypothetically to their stock of knowledge, and arguing on that basis about q; ...they are fixing their degrees of belief in q given p. | |
From: Frank P. Ramsey (Law and Causality [1928], B 155 n) | |
A reaction: This has become famous as the 'Ramsey Test'. Bennett emphasises that he is not saying that you should actually believe p - you are just trying it for size. The presupposition approach to conditionals seems attractive. Edgington likes 'degrees'. |
6894 | Mental terms can be replaced in a sentence by a variable and an existential quantifier [Ramsey] |
Full Idea: Ramsey Sentences are his technique for eliminating theoretical terms in science (and can be applied to mental terms, or to social rights); a term in a sentence is replaced by a variable and an existential quantifier. | |
From: Frank P. Ramsey (Law and Causality [1928]), quoted by Thomas Mautner - Penguin Dictionary of Philosophy p.469 | |
A reaction: The technique is used by functionalists and results in a sort of eliminativism. The intrinsic nature of mental states is eliminated, because everything worth saying can be expressed in terms of functional/causal role. Sounds wrong to me. |
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. |
16589 | Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol] |
Full Idea: Prime matter has no essence, nor a nature that is determinate, distinct, and actual. Instead, it is pure potential, and determinable, so that it is indeterminately and indistinctly a material thing. | |
From: Peter Auriol (Sentences [1316], II.12.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1 | |
A reaction: Pasnau thinks Auriol has the best shot at explaining the vague idea of 'prime matter', with the thought that it exists, but indeterminateness is what gives it a lesser mode of existence. It strikes me as best to treat 'exist' as univocal. |
9418 | All knowledge needs systematizing, and the axioms would be the laws of nature [Ramsey] |
Full Idea: Even if we knew everything, we should still want to systematize our knowledge as a deductive system, and the general axioms in that system would be the fundamental laws of nature. | |
From: Frank P. Ramsey (Law and Causality [1928], §A) | |
A reaction: This is the Mill-Ramsey-Lewis view. Cf. Idea 9420. |
9420 | Causal laws result from the simplest axioms of a complete deductive system [Ramsey] |
Full Idea: Causal laws are consequences of those propositions which we should take as axioms if we knew everything and organized it as simply as possible in a deductive system. | |
From: Frank P. Ramsey (Law and Causality [1928], §B) | |
A reaction: Cf. Idea 9418. |
16651 | God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol] |
Full Idea: If someone says 'God could make straightness without a line, and roughness and lightness in weight without parts', …then show me the reason why God can do whatever does not imply a contradiction, yet cannot do these things. | |
From: Peter Auriol (Sentences [1316], IV.12.2.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 11.4 | |
A reaction: How engagingly bonkers. The key idea preceding this is that God can do all sorts of things that are beyond our understanding. He is then obliged to offer some examples. |