30 ideas
| 22153 | Quine rejects Carnap's view that science and philosophy are distinct [Quine, by Boulter] |
| Full Idea: Quine rejects Carnap's view that the methods of science and philosophy are distinct. | |
| From: report of Willard Quine (On Carnap's Views on Ontology [1951]) by Stephen Boulter - Why Medieval Philosophy Matters 5 | |
| A reaction: I can't decide this one. Leibniz agreed with Carnap, but rated philosophy more highly. I like the view of philosophy as continuous with science, but that doesn't make it a branch of science. I incline towards science being a branch of philosophy. |
| 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? |
| 19485 | Names have no ontological commitment, because we can deny that they name anything [Quine] |
| Full Idea: I think there is no commitment to entities through use of alleged names of them; other things being equal, we can always deny the allegation that the words in question are names. | |
| From: Willard Quine (On Carnap's Views on Ontology [1951], p.205) | |
| A reaction: Hm. So why can't you deny that variables actually refer to existing entities? If I say 'I just saw James', it's a bit cheeky to then deny that James refers to anyone. He uses Russell's technique to paraphrase names. |
| 19486 | We can use quantification for commitment to unnameable things like the real numbers [Quine] |
| Full Idea: Through our variables of quantification we are quite capable of committing ourselves to entities which cannot be named individually at all in the resources of our language; witness the real numbers. | |
| From: Willard Quine (On Carnap's Views on Ontology [1951], p.205) | |
| A reaction: The real numbers are uncountable, and thus cannot all be named. This is quite an impressive point. I've always had doubts about the existence of real numbers, on the grounds that they could never all be named. |
| 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? |
| 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. |
| 19487 | Without the analytic/synthetic distinction, Carnap's ontology/empirical distinction collapses [Quine] |
| Full Idea: If there is no proper distinction between analytic and synthetic, then no basis at all remains for the contrast which Carnap urges between ontological statements and empirical statements of existence. Ontology then ends up on a par with natural science. | |
| From: Willard Quine (On Carnap's Views on Ontology [1951], p.211) | |
| A reaction: Carnap says ontology is relative to a linguistic framework. 'External' ontology is empty. This quotation gives Quine's main motivation for denying the analytic/synthetic distinction. |
| 21093 | Friendship without community spirit misses out on the main part of virtue [Hume] |
| Full Idea: A man who is only susceptible of friendship, without public spirit or a regard to the community, is deficient in the most material part of virtue. | |
| From: David Hume (That Politics may be reduced to a Science [1750], p.21) | |
| A reaction: I think this is aimed at the epicureans. If the highest virtues are focused on one's friends that can easily lead to injustice, because it can tolerate prejudice against people who are very unlike one's friends. |
| 21091 | It would be absurd if even a free constitution did not impose restraints, for the public good [Hume] |
| Full Idea: A republican and free form of government would be an obvious absurdity, if the particular checks and controls, provided by the constitution, had really no influence, and made it not the interest, even of bad men, to act for the public good. | |
| From: David Hume (That Politics may be reduced to a Science [1750], p.14) | |
| A reaction: Presumably if you attain absolute power you can write any old constitution you like (Clause 1: the presidency is for life). But there does seem much point in doing it - unless it is to facilitate the use of the law for persecutions. |
| 21092 | Nobility either share in the power of the whole, or they compose the power of the whole [Hume] |
| Full Idea: A nobility may possess power in two different ways. Either every nobleman shares the power as part of the whole body, or the whole body enjoys the power as composed of parts, which each have a distinct power and authority. | |
| From: David Hume (That Politics may be reduced to a Science [1750], p.15) | |
| A reaction: He says the first type is found in Venice, and is preferable to the second type, which is found in Poland. Presumably in the shared version there is some restraint on depraved nobles. The danger is each noble being an autocrat. |