42 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. |
| 9065 | S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith] |
| Full Idea: S5 collapses iterated modalities (so ◊□P → □P, and ◊◊P → ◊P). | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §5) | |
| A reaction: It is obvious why this might be controversial, and there seems to be a general preference for S4. There may be confusions of epistemic and ontic (and even semantic?) possibilities within a single string of modalities. |
| 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? |
| 9064 | Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature [Keefe/Smith] |
| Full Idea: A common intuition is that a vague object has indeterminate or fuzzy spatio-temporal boundaries, such as a cloud. Mount Everest can only have arbitrary boundaries placed around it, so in nature it must have fuzzy boundaries. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §5) | |
| A reaction: We would have to respond by questioning whether Everest counts precisely as an 'object'. At the microscopic or subatomic level it seems that virtually everything has fuzzy boundaries. Maybe boundaries don't really exist. |
| 9044 | If someone is borderline tall, no further information is likely to resolve the question [Keefe/Smith] |
| Full Idea: If Tek is borderline tall, the unclarity does not seem to be epistemic, because no amount of further information about his exact height (or the heights of others) could help us decide whether he is tall. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: One should add also that information about social conventions or conventions about the usage of the word 'tall' will not help either. It seems fairly obvious that God would not know whether Tek is tall, so the epistemic view is certainly counterintuitive. |
| 9048 | The simplest approach, that vagueness is just ignorance, retains classical logic and semantics [Keefe/Smith] |
| Full Idea: The simplest approach to vagueness is to retain classical logic and semantics. Borderline cases are either true or false, but we don't know which, and, despite appearances, vague predicates have well-defined extensions. Vagueness is ignorance. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: It seems to me that you must have a rather unhealthy attachment to the logicians' view of the world to take this line. It is the passion of the stamp collector, to want everything in sets, with neatly labelled properties, and inference lines marked out. |
| 9055 | The epistemic view of vagueness must explain why we don't know the predicate boundary [Keefe/Smith] |
| Full Idea: A key question for the epistemic view of vagueness is: why are we ignorant of the facts about where the boundaries of vague predicates lie? | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §2) | |
| A reaction: Presumably there is a range of answers, from laziness, to inability to afford the instruments, to limitations on human perception. At the limit, with physical objects, how do we tell whether it is us or the object which is afflicted with vagueness? |
| 9049 | Supervaluationism keeps true-or-false where precision can be produced, but not otherwise [Keefe/Smith] |
| Full Idea: The supervaluationist view of vagueness is that 'tall' comes out true or false on all the ways in which we can make 'tall' precise. There is a gap for borderline cases, but 'tall or not-tall' is still true wherever you draw a boundary. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: [Kit Fine is the spokesperson for this; it preserves classical logic, but not semantics] This doesn't seem to solve the problem of vagueness, but it does (sort of) save the principle of excluded middle. |
| 9056 | Vague statements lack truth value if attempts to make them precise fail [Keefe/Smith] |
| Full Idea: The supervaluationist view of vagueness proposes that a sentence is true iff it is true on all precisifications, false iff false on all precisifications, and neither true nor false otherwise. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: This seems to be just a footnote to the Russell/Unger view, that logic works if the proposition is precise, but otherwise it is either just the mess of ordinary life, or the predicate doesn't apply at all. |
| 9058 | Some of the principles of classical logic still fail with supervaluationism [Keefe/Smith] |
| Full Idea: Supervaluationist logic (now with a 'definite' operator D) fails to preserve certain classical principles about consequence and rules of inference. For example, reduction ad absurdum, contraposition, the deduction theorem and argument by cases. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: The aim of supervaluationism was to try to preserve some classical logic, especially the law of excluded middle, in the face of problems of vagueness. More drastic views, like treating vagueness as irrelevant to logic, or the epistemic view, do better. |
| 9059 | The semantics of supervaluation (e.g. disjunction and quantification) is not classical [Keefe/Smith] |
| Full Idea: The semantics of supervaluational views is not classical. A disjunction can be true without either of its disjuncts being true, and an existential quantification can be true without any of its substitution instances being true. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: There is a vaguely plausible story here (either red or orange, but not definitely one nor tother; there exists an x, but which x it is is undecidable), but I think I will vote for this all being very very wrong. |
| 9060 | Supervaluation misunderstands vagueness, treating it as a failure to make things precise [Keefe/Smith] |
| Full Idea: Why should we think vague language is explained away by how things would be if it were made precise? Supervaluationism misrepresents vague expressions, as vague only because we have not bothered to make them precise. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3) | |
| A reaction: The theory still leaves a gap where vagueness is ineradicable, so the charge doesn't seem quite fair. Logicians always yearn for precision, but common speech enjoys wallowing in a sea of easy-going vagueness, which works fine. |
| 9050 | A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1 [Keefe/Smith] |
| Full Idea: One approach to predications in borderline cases is to say that they have a third truth value - 'neutral', 'indeterminate' or 'indefinite', leading to a three-valued logic. Or a degree theory, such as fuzzy logic, with infinite values between 0 and 1. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: This looks more like a strategy for computer programmers than for metaphysicians, as it doesn't seem to solve the difficulty of things to which no one can quite assign any value at all. Sometimes you can't be sure if an entity is vague. |
| 9061 | People can't be placed in a precise order according to how 'nice' they are [Keefe/Smith] |
| Full Idea: There is no complete ordering of people by niceness, and two people could be both fairly nice, nice to intermediate degrees, while there is no fact of the matter about who is the nicer. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
| A reaction: This is a difficulty if you are trying to decide vague predicates by awarding them degrees of truth. Attempts to place a precise value on 'nice' seem to miss the point, even more than utilitarian attempts to score happiness. |
| 9062 | If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall' [Keefe/Smith] |
| Full Idea: Many-valued theories still seem to have a sharp boundary between sentences taking truth-value 1 and those taking value less than 1. So there is a last man in our sorites series who counts as 'completely tall'. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
| A reaction: Lovely. Completely nice, totally red, perfectly childlike, an utter mountain, one hundred per cent amused. The enterprise seems to have the same implausibility found in Bayesian approaches to assessing evidence. |
| 9063 | How do we decide if my coat is red to degree 0.322 or 0.321? [Keefe/Smith] |
| Full Idea: What could determine which is the correct function, settling that my coat is red to degree 0.322 rather than 0.321? | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §4) | |
| A reaction: It is not just the uncertainty of placing the coat on the scale. The two ends of the scale have all the indeterminacy of being red rather than orange (or, indeed, pink). You are struggling to find a spot on the ruler, when the ruler is placed vaguely. |
| 9045 | Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change [Keefe/Smith] |
| Full Idea: Three interrelated features of vague predicates such as 'tall', 'red', 'heap', 'child' are that they have borderline cases (application is uncertain), they lack well-defined extensions (objects are uncertain), and they're susceptible to sorites paradoxes. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: The issue will partly depend on what you think an object is: choose from bundles of properties, total denial, essential substance, or featureless substance with properties. The fungal infection of vagueness could creep in at any point, even the words. |
| 9047 | Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement [Keefe/Smith] |
| Full Idea: Many vague predicates are multi-dimensional. 'Big' of people depends on both height and volume; 'nice' does not even have clear dimensions; whether something is a 'heap' depends both the number of grains and their arrangement. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: Anyone who was hoping for a nice tidy theory for this problem should abandon hope at this point. Huge numbers of philosophical problems can be simplified by asking 'what exactly do you mean here?' (e.g. tall or bulky?). |
| 9053 | If there is a precise borderline area, that is not a case of vagueness [Keefe/Smith] |
| Full Idea: If a predicate G has a sharply-bounded set of cases falling in between the positive and negative, this shows that merely having borderline cases is not sufficient for vagueness. | |
| From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §1) | |
| A reaction: Thus you might have 'pass', 'fail' and 'take the test again'. But there seem to be two cases in the border area: will decide later, and decision seems impossible. And the sharp boundaries may be quite arbitrary. |
| 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. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |