39 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'. |
| 18996 | A statement S is 'partly true' if it has some wholly true parts [Yablo] |
| Full Idea: A statement S is 'partly true' insofar as it has wholly true parts: wholly true implications whose subject matter is included in that of S. | |
| From: Stephen Yablo (Aboutness [2014], 01.6) | |
| A reaction: He suggests that if we have rival theories, we agree that it is one or the other. And 'we may have pork for dinner, or human flesh' is partly true. |
| 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. |
| 19006 | An 'enthymeme' is an argument with an indispensable unstated assumption [Yablo] |
| Full Idea: An 'enthymeme' is a deductive argument with an unstated assumption that must be true for the premises to lead to the conclusion. | |
| From: Stephen Yablo (Aboutness [2014], 11.1) |
| 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. |
| 18999 | y is only a proper part of x if there is a z which 'makes up the difference' between them [Yablo] |
| Full Idea: The principle of Supplementation says that y is properly part of x, only if a z exists that 'makes up the difference' between them. [note: that is, z is disjoint from y and sums with y to form x] | |
| From: Stephen Yablo (Aboutness [2014], 03.2) |
| 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'. |
| 19001 | 'Pegasus doesn't exist' is false without Pegasus, yet the absence of Pegasus is its truthmaker [Yablo] |
| Full Idea: 'Pegasus does not exist' has a paradoxical, self-undermining flavour. On the one hand, the empty name makes it untrue. But now, why is the name empty? Because Pegasus does not exist. 'Pegasus does not exist' is untrue because Pegasus does not exist. | |
| From: Stephen Yablo (Aboutness [2014], 05.7 n20) | |
| A reaction: Beautiful! This is Yablo's reward for continuing to ask 'why?' after everyone else has stopped in bewilderment at the tricky phenomenon. |
| 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? |
| 19002 | A nominalist can assert statements about mathematical objects, as being partly true [Yablo] |
| Full Idea: If I am a nominalist non-Platonist, I think it is false that 'there are primes over 10', but I want to be able to say it like everyone else. I argue that this because the statement has a part that I do believe, a part that remains interestingly true. | |
| From: Stephen Yablo (Aboutness [2014], 05.8) | |
| A reaction: This is obviously a key motivation for Yablo's book, as it reinforces his fictional view of abstract objects, but aims to capture the phenomena, by investigating what such sentences are 'about'. Admirable. |
| 18998 | Parthood lacks the restriction of kind which most relations have [Yablo] |
| Full Idea: Most relations obtain only between certain kinds of thing. To learn that x is a part of y, however, tells you nothing about x and y taken individually. | |
| From: Stephen Yablo (Aboutness [2014], 03.2) | |
| A reaction: Too sweeping. To be a part of crowd you have to be a person. To be part of the sea you have to be wet. It might depend on whether composition is unrestricted. |
| 18892 | Suppose a world where I'm from different gametes; add my gametes; which one is more me? [McGinn] |
| Full Idea: It seems essential that you come from your gametes. Suppose (for reductio) that I come from Nixon's actual gametes. Now add my actual gametes to that possible world, and suppose they become an adult. Which has the stronger title to be me? | |
| From: Colin McGinn (On the Necessity of Origin [1976], p.132), quoted by Nathan Salmon - Reference and Essence (1st edn) 7.25.5 | |
| A reaction: [See Nathan Salmon 1981:209] Feels like the Ship of Theseus. You say 'that's Theseus Ship', until the rival ship appears around the headland. Confusion. If Nixon's gametes can produce McGinn, the second gametes could produce a Nixon! Then what? |
| 12019 | McGinn falsely claims necessity of origin is a special case of the necessity of identity [Forbes,G on McGinn] |
| Full Idea: McGinn assimilates the origin relation among organisms to the identity relation, so that the necessity of origin becomes a special case of the necessity of identity. We argue that this assimilation is illegitimate. | |
| From: comment on Colin McGinn (On the Necessity of Origin [1976]) by Graeme Forbes - The Metaphysics of Modality 6.1 | |
| A reaction: Not sure about this. I have long suspected what McGinn suspects. Once you have identified the organism with a particular origin, it hardly seems surprising that this particular origin has become inescapable. |
| 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. |
| 19004 | Gettier says you don't know if you are confused about how it is true [Yablo] |
| Full Idea: We know from Gettier that if you are right to regard Q as true, but you are sufficiently confused about HOW it is true - about how things stand with respect to its subject matter - then you don't know that Q. | |
| From: Stephen Yablo (Aboutness [2014], 07.4) | |
| A reaction: I'm inclined to approach Gettier by focusing on the propositions being expressed, where his cases tend to focus on the literal wording of the sentences. What did the utterer mean by the sentences - not what did they appear to say. |
| 19007 | A theory need not be true to be good; it should just be true about its physical aspects [Yablo] |
| Full Idea: A physical theory need not be true to be good, Field has argued, and I agree. All we ask of it truth-wise is that its physical implications should be true, or, in my version, that it should be true about the physical. | |
| From: Stephen Yablo (Aboutness [2014], 12.5) | |
| A reaction: Yablo is, of course, writing a book here about the concept of 'about'. This seems persuasive. The internal terminology of the theory isn't committed to anything - it is only at its physical periphery (Quine) that the ontology matters. |
| 18993 | If sentences point to different evidence, they must have different subject-matter [Yablo] |
| Full Idea: 'All crows are black' cannot say quite the same as 'All non-black things are non-crows', for the two are confirmed by different evidence. Subject matter looks to be the distinguishing feature. One is about crows, the other not. | |
| From: Stephen Yablo (Aboutness [2014], Intro) | |
| A reaction: You might reply that they are confirmed by the same evidence (but only in its unobtainable totality). The point, I think, is that the sentences invite you to start your search in different places. |
| 19003 | Most people say nonblack nonravens do confirm 'all ravens are black', but only a tiny bit [Yablo] |
| Full Idea: The standard response to the raven paradox is to say that a nonblack nonraven does confirm that all ravens are black. But it confirms it just the teeniest little bit - not as much as a black raven does. | |
| From: Stephen Yablo (Aboutness [2014], 06.5) | |
| A reaction: It depends on the proportion between the relevant items. How do you confirm 'all the large animals in this zoo are mammals'? Check for size every animal which is obviously not a mammal? |
| 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? |
| 18992 | Sentence-meaning is the truth-conditions - plus factors responsible for them [Yablo] |
| Full Idea: A sentence's meaning is to do with its truth-value in various possible scenarios, AND the factors responsible for that truth-value. | |
| From: Stephen Yablo (Aboutness [2014], Intro) | |
| A reaction: The thesis of his book, which I welcome. I'm increasingly struck by the way in which much modern philosophy settles for a theory being complete, when actually further explanation is possible. Exhibit A is functional explanations. Why that function? |
| 18994 | The content of an assertion can be quite different from compositional content [Yablo] |
| Full Idea: Assertive content - what a sentence is heard as saying - can be at quite a distance from compositional content. | |
| From: Stephen Yablo (Aboutness [2014], Intro) | |
| A reaction: This is the obvious reason why semantics cannot be entirely compositional, since there is nearly always a contextual component which then has to be added. In the case of irony, the compositional content is entirely reversed. |
| 18997 | Truth-conditions as subject-matter has problems of relevance, short cut, and reversal [Yablo] |
| Full Idea: If the subject-matter of S is how it is true, we get three unfortunate results: S has truth-value in worlds where its subject-matter draws a blank; learning what S is about tells you its truth-value; negating S changes what it's about. | |
| From: Stephen Yablo (Aboutness [2014], 02.8) | |
| A reaction: Together these make fairly devastating objections to the truth-conditions (in possible worlds) theory of meaning. The first-objection concerns when S is false |
| 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. |
| 19005 | Not-A is too strong to just erase an improper assertion, because it actually reverses A [Yablo] |
| Full Idea: The idea that negation is, or can be, a cancellation device raises an interesting question. What does one do to wipe the slate clean after an improper assertion? Not-A is too strong; it reverses our stand on A rather than nullifying it. | |
| From: Stephen Yablo (Aboutness [2014], 09.8) | |
| A reaction: [He is discussing a remark of Strawson 1952] It seems that 'not' has two meanings or uses: a weak use of 'nullifying' an assertion, and a strong use of 'reversing' an assertion. One could do both: 'that's not right; in fact, it's just the opposite'. |