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David Brightly
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Ed, Bill, My concern is with the assertion status and truth value of the statements that appear in the scope of the hypothesis. A typical RAA looks like this: Suppose p q r s : z ~z ergo, ~pWhen we rehearse the argument we treat p, q, r... in no way different from statements outside the scope of the Suppose. The sequence p, q, r... might be lengthy and while we focus on the inferences between them we see them as asserted and having truth values. Yet when we reach ~z we realise that it's not possible to assign consistent truth values to all of these statements, and I'm not exactly comfortable with that. One way of resolving the difficulty is to abandon assertion and truth value and see the whole business in purely formal terms as a calculus over symbols. But I'm not entirely happy with that, either.
And yet we apply the rules of inference to the statements that appear within the scope of 'suppose that p' just as we would if they were outside. It's as if assertion and truth were irrelevant within the scope of the hypothetical. This has long puzzled me.
Hello Bill, Well, I'd certainly say that from p-->q we can infer neither p nor q. But I'm interested in whether you would say that a statement appearing within the scope of the 'suppose there is...' statement was asserted. For example, the statement 'if an intra-mercurial planet has a diameter greater then D then it is visible' , for some D, may well appear.
Morning Bill, What about statements (are they assertions?) made in the context of a hypothetical slated for reductio? Example:Suppose there is an intra-Mercurial planet---call it Vulcan---whose gravity is responsible for the advance in the perihelion of Mercury. (*) Vulcan's diameter exceeds a certain minimum, d.Statement (*) seems to aim for truth but truth 'in some alternative reality'. It's not clear how to assign it a truth value in this reality.
Hello Bill, and a Happy New Year to you. Ed says, But if I deny what you say, I rule out every possible state of the world that is that way, but allow all else. Surely excluded middle holds. If I deny what you say, I do not rule out anything except what you say, but allow everything else.Suppose you claim the conjunction A∧B. Ed can deny this by asserting ¬B. This rules out B, which is more than the A∧B that you say. And it allows just ¬B, which is less than the everything else to what you say, which is ¬(A∧B), ie, ¬A ∨ ¬B. To deny A∧B does not require asserting its negation. Excluded Middle stands.
Hi Bill, You are right that I'm not buying all the assumptions needed to get the puzzle going. To my mind there has to be something mistaken in our thinking in order for us to arrive at such wildly divergent views. I'm guessing that we are misled by ordinary language into taking Impossible, etc, as properties of things. But I do appreciate that we are talking about particulars. That's why I speak of ideas of things. Perhaps 'intentional object' is closer but this is a term of art that I can't confidently use. Maybe such an idea can be regarded as a unified bundle of properties. This avoids the subjective element inherent in idea. Think of it as a specification for an object. My thought is that such a bundle may itself have properties. I'm influenced here by Ed Zalta's work on encoding/exemplifying. If you tell me 'There is a rational square root of two' then I form the idea of an object that's a number, is rational, and squares to two. That's a bundle that encodes three properties. That's enough to set me searching for such a thing, maybe by working my way through an enumeration of the rationals. A little analysis reveals that such a search would be never-ending. So the property of Impossible attaches to the bundle as an exemplified property, not an encoded one. We have realised that the bundle, the representation, represents nothing. The distinction I'm making between a thing and its idea accounts nicely for your current debate with Ostrich. Socrates himself is irreproducible after his death and dissolution. The idea of Socrates remains contingent (in my sense).
Hello Bill, I'm rather confused. Meyer didn't help at all, I'm afraid. It seems we are given the classes Actual, Merely-possible, and Impossible, but what are they populated with? It can't be with things themselves because then the Impossible class would be empty and redundant. I suggest we are talking about ideas of things, with the proviso that such ideas need not be realisable---they may be inconsistent, like the idea of the rational square root of two, for example. We can say an idea falls in the Actual class if it was, is, or will be realised at some moment in time. Thus the idea of Scollay Square falls under Actual and didn't change its classification when Scollay Square itself passed out of existence. In effect, we are answering Quine's question as to what exists by ascending to an atemporal realm of ideas and classifying them according to their realisation. My guess is that some of the confusion in this topic arises because we readily slide between talking about things themselves (the presentist's modus operandi), and about ideas of things (his opponent's). The presentist prefers to talk about things themselves and when he talks about things of the past he uses the past tense. His opponent is comfortable with tenseless sentences because he is engaged with atemporal ideas. For example, if we want to say of Churchill the man that he both exists and is actual now but lacks the A-property of presentness and instead instantiates the A-property of pastness, I suggest this can better be expressed by saying of the idea of Churchill that it falls under Actual, was once realised but is no longer. That may be because I'm uncomfortable with presentness and pastness as properties of things, suspecting that this leads to contradictions. But the idea of a thing might be said have the property of presentness if it is realised now, or the property of pastness if it was once realised but is no longer.
>> The point, which many find elusive, is that the items in the domain of quantification must be there to be quantified over, where 'there' has not a locative but an existential sense. Yes and No! No, because quantification---how the words 'some' and 'all' operate---works perfectly well in fiction and in history, and there is a definite sense in which the things of fiction are not there, or the things of history are not here now. Yes, because the words 'some' and 'all' make sense only relative to some assumed or understood context or 'domain' of things taken to be the extants that 'are there' in the context. In everyday dialogue there is a default context, namely the actual world or some part of it, though there can be some ambiguity as to whether this includes its past and/or future or not. I suggest it's this context-sensitivity of 'some' and 'all' that make it impossible to capture actual world existence in purely logical terms. After all, the Quine equivalence holds in all contexts. It fails to single out the actual world in any way. Unfortunately, the context-sensitivity of 'all' and 'some' invades the sense of 'being there' and 'exists'. These words make perfect sense in fictional contexts. One(*) can't define a term that 'breaks out', as it were, from its context and becomes absolute. In a fiction such a term would remain relative to the fictional context. All it seems one can do is say, I'm now talking about the actual world, and hope one's interlocutor switches context. But a character in fiction can say this too, of course. Having agreed that the wretched Quine formula is useless, how does its failure justify the distinction between a thing and its existence? And the existence of its existence...? (*) Unless one is Borges, perhaps.
I was struck by Bill's 'You don't see some man or other, but a definite man, ...' If there is a puzzle here isn't it captured in the phrase 'a definite man', which is itself indefinite!?
Toggle Commented Nov 5, 2017 on A Reference Puzzle at Maverick Philosopher
So does ‘valid’ mean ‘having a valid form’ or ‘truth preserving’? The property of primary interest is 'truth-preserving' (TP). It turns out (ie, there is a theorem to the effect) that there is a set of forms we call the 'valid' forms such that every TP argument instantiates a valid form and every argument that instantiates a valid form (call these the 'valid' arguments) is TP. So the valid arguments are exactly the truth-preserving ones.
Ed, you have to understand 'truth-preserving' as 'truth-preserving in the absence of equivocation'. Equivocation is utterly deadly to logic. And it doesn't have to be in the singular term. How can there be any discussion at all possible if the meaning of 'Roman' changes from one token to the next? It can render even 'Cicero is a Roman, ergo Cicero is a Roman' truth-corrupting.
Bill, I prefer to say either, (a) we have a valid three-term syllogism whose truth-preserving property is broken by equivocation, or, (b) we have a four-term syllogism, with no equivocation, but an invalid argument. We must try to not mix these cases up.
Ed is worried about how we are to understand argument form in the presence of equivocation. What is the right form for the argument, Cicero is a Roman ----------------------- Cicero is a Roman when the two tokens 'Cicero' have different meanings? I say this is a needless worry. Logical form is a shallow syntactical business quite independent of the meanings of categorematic terms. It 'floats above' such meanings, as it were. I think we are agreed that we have a notion of valid argument forms, what it means for an argument to instantiate an argument form, and that an argument is valid iff it instantiates a valid form. My next point is one we have not yet brought out. Valid arguments are truth-preserving. Yes, but only in the absence of equivocation in the categorematic terms. We need meanings to reach truth and equivocation on meaning kills truth-preservation. The above argument is valid, instantiating the valid form, P --- P but if we equivocate on the meaning of 'Cicero' (or indeed 'Roman') it may fail to preserve truth. In summary: equivocation impacts truth-preservation but not validity. That's what I meant by 'full stop' in my first comment. Considerations of form and validity do not 'extend down' into considerations of (categorematic) meanings. The two issues are nicely decoupled. I think this answers Ed's underlying problem in his 02:53 PM comment. At 06:57 AM Ed also takes issue with my 'But there is a prerequisite that like terms have like meanings.' I should have been clearer. This is not a prerequisite for ascertaining validity. It is a requirement for a valid argument to be truth-preserving. Note that Ed's account of his resolving 'Judas' in Acts 1 into two distinct meanings is just like the account I give of 'Cicero is a Roman/Cicero is a town' in my first comment.
Is there a puzzle here? I don't see it. The argument, Cicero is a Roman ----------------------- Cicero is a Roman is valid. Full stop. If one wants to say, Cicero-the-man is a Roman ----------------------- Cicero-the-town is a Roman then that is a different, and invalid, argument. Logic expresses the meanings of the logical connectives independently of the meanings of categorematic terms. But there is a prerequisite that like terms have like meanings. This enables us to detect equivocation. Consider, Cicero is a Roman Cicero is a town ----------------------- Some Roman is a town This is valid. With the usual meanings of 'Roman' and 'town' the conclusion is false. Valid arguments are truth-preserving. Hence at least one of the premises is false. Suppose I think the first premise is true (I've heard of the famous Roman orator) and the second is false. If you insist that the second is also true then I will challenge you on the meaning of the second 'Cicero'. I don't think Ed has given us any reason to think that logical form has to do with anything but sentences, perhaps with some shallow notion of grammar thrown in. How do we explain instantiation of logical form except by substitution of grammatically acceptable token strings for placeholders within schematic sentences?
John asks (Sunday, 10:41 AM) about the basis of Oppo's proposed denotation of 'poor'. If one were sympathetic to properties one would likely take the denotation of the word 'poor' to be the property poorness. One might then go on to consider the extension of this property, namely all things having poorness. Oppo could reasonably then say that for him the denotation of 'poor' is exactly this extension. This would be no less well-grounded than the propertyist's denotation. One might go on to reformulate logic in terms of extensions rather than predicates. To do this neatly might require some notion of set and so render the logic less suitable for formalising mathematics. But it might lead to a logic better suited to the analysis of natural language. My brain may have the predicate calculus written through it like a stick of Blackpool Rock, but I have yet to see a good objection to this program.
Toggle Commented Feb 16, 2017 on Against Ostrich Nominalism at Maverick Philosopher
This is just to point out that Oppo's (if I may abbreviate him thus) logic at 06:13 AM is very nearly perfect. Introducing the name 'Poboy' as witness for the existential in [1] gives us [3**] Sam is poor iff Poboy = Sam & denotes ('poor', Poboy)Bill and John are ignoring the second conjunct on the RHS. They thus load all their explanatory requirements on to the identity conjunct, Poboy=Sam. They understandably find this lacking. The explanatory power in Oppo's theory lies almost entirely in the denotes () relation, and we should concentrate our inquiries on this. In the meantime I think we can see Oppo's proposal as an axiomatic theory of truth for predication sentences in which the denotes () relation appears as an undefined term. That denotes () is opaque to us contributes to Bill's sense that Oppo's theory is ungrounded.
Bill, You write, What in the world makes-true 'Sam is a poor man'? [] The answer has to be, on the theory under discussion: the numerical identity of Sam with Poboy.Is said numerical identity an in-the-world fact? I think not. Having observed that 'Sam' denotes exactly one of the denotata of 'poor man', you have declared that 'Poboy' is also to denote this individual. Thus the co-denotation of 'Sam' and 'Poboy' (aka the identity of Sam and Poboy) is an intra-linguistic phenomenon. Hardly the extra-linguistic fact required for a truth-maker.
Bill, Why do you say that Poboy and Richboy are numerically distinct? Do you see the denotations of 'poor' and 'rich' as fixed and exclusive, perhaps? But can't the denotations change so that something denoted by 'poor' at t1 can be denoted by 'rich' at t2?
That your robot lacks conscious states is obvious to me too, Bill. But you are making the stronger statement that any use of language to represent must involve consciousness, on pain of unintelligibility. I'm not convinced of this necessary connection. Obviously linguistic representation and consciousness tend to go together in us. But we don't find the puzzles of consciousness in linguistic representation. If the latter is a way of linearising and manipulating a model which guides behaviour then it need not imply our kind of consciousness at all.
Bill, Addis says, is unintelligible to suppose the existence of beings who are using language in all of its representative functions and who are also lacking in conscious states.What does he mean by all of its representative functions? Would he allow a being using some of the representative functions of language that was lacking in conscious states?
Bill, Is this a question specific to human mortality or is it about the language we use to express the coming in and going out of existence? If the latter consider the following story. There was once a famous diamond called the Noh-i-Koor. It shattered to pieces when being re-cut. Would we say: a. The Noh-i-Koor is not forever. b. The Noh-i-Koor is shattered. c. A diamond is not forever only if there is a future time at which it shatters. d. A diamond cannot shatter twice. I think we would say,a*. The Noh-i-Koor was not forever.
Toggle Commented Jan 26, 2017 on Is a Dead Person Mortal? at Maverick Philosopher
Fair enough. Let me just require that the relation between the state of flux at an earlier time to that at a later time be functional. That is, at worst many-to-one, but never one-to-many. My intuition of an 'indeterministic' flux would allow a one-many relation. I can then revert to my original suggestion that there is no modality in the flux.
Toggle Commented Jan 21, 2017 on On Possibility at Maverick Philosopher
No interesting modality. Just the trivial modality of necessity and impossibility with none of the merely possible that makes modality a puzzle.
Toggle Commented Jan 20, 2017 on On Possibility at Maverick Philosopher
I'd say something like this: In so far as it is deterministic, the flux has no modality. 'Possible' and 'necessary' don't apply. From our human perspective, which partitions the flux into medium-sized objects, events, and circumstances, there is modality for the reason above of coarse-graining, it's just as real as the objects etc are, and, again from our perspective, the world is not deterministic. On top of this there is epistemic modality where we are ignorant of how the world is, even in the terms of our own perspective. I read MA as can --> does and does --> can. I accept only the latter.
Toggle Commented Jan 20, 2017 on On Possibility at Maverick Philosopher
Good Morning, Bill, and thank you for following this up. My brief earlier comment may have too much of an epistemic flavour. Let me see if I can offer an analysis of your light bulb experiment that reduces this. Firstly, yes, I am reluctant to allow a 'disposition to shatter' in B. This loads the modality onto B rather than the circumstances C where I think it lies. Let's think of dropping B onto a hard surface and suppose this system is deterministic and non-chaotic. That is, it displays no extreme sensitivity to initial conditions. Suppose circumstances C are specified almost exactly---floor smooth and homogeneous, height of dropping fixed, zero initial angular velocity---but that the orientation of the bulb is not specified. Suppose also we have circumstance CH in which the bulb is dropped on its head and circumstance CS in which it is dropped on its side as in your illustration. Suppose also that the structure of B is such that in circumstances C&CH the bulb does not shatter but in C&CS it does---something to do with the degree of departure from cylindrical symmetry of the impact, perhaps. Both C&CH and C&CS fix the initial conditions exactly. In C&CH it's impossible that the bulb shatter on pain of breaking the determinism assumption. Likewise in C&CS it's necessary that the bulb shatter. But circumstances C do not fix the initial conditions exactly: C&CH satisfies C and C&CS satisfies C. C is too 'coarse-grained'. It allows initial conditions under which B shatters and initial conditions under which it does not. Hence, under circumstances C, Possibly, the bulb shatters is true. What makes it true is the course- grainedness of C rather than anything that might be thought of as a constituent of B.
Toggle Commented Jan 19, 2017 on On Possibility at Maverick Philosopher