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My view is that 'Moses existed' can be seen as a reiteration of the general existential statement under which the name 'Moses' was (must have been) introduced. And that general existential would have said that someone existed. Likewise the denial 'It is not the case that Moses existed' does not have the form ~Fa which would have the unfortunate implication Astute supplies. Instead we take it as a denial of the general existential (which I'm saying has to be present for the argument to be valid) under which the name 'Moses' was introduced. In informal English we can say 'There never was such a man as this so-called 'Moses''.
Hello Bill, Astute and I have discussed this and we disagree. I have hopes of winning him round because what I'm suggesting is hugely simplifying. In the PC there is just one way of introducing a name. This is the rule of Existential Elimination (EE). Argument (A) as it stands flouts EE. EE says that in the context of an existential claim such as ∃x.P(x) one can introduce a new name, 'c', say, and infer P(c). 'c' names one of the entities that satisfy P(). Entity c is said to 'witness' the existential. Names cannot arise in any other way. Textbooks often gloss over this point, with examples that use names without introduction. They will launch intoMan(Socrates) rather than the more formal ∃x.Man(x) Man(Socrates)One can translate this into informal English as There is a man called Socrates,which is, of course, how every story begins! Can I refer you back to Deducing John McCain from the Principle of Identity? Your solution (B) to this puzzle is essentially what I am saying here.
But is the argument A1. Stromboli exists. Ergo, A2. Something exists,in fact valid? If it were it would be so by virtue of its logical form. This is B1. name exists. Ergo, B2. Something exists.But if this were a valid form then C1. Oberfringelhorn exists. Ergo, C2. Something exists,would be a valid argument. I say it's not because (C1) informs us of nothing whereas (C2) informs us of something and information cannot arise from no information. So by reductio ad absurdum the (A) argument and the (B) form are invalid. However, I think we can say that argument (A) is enthymematic for a valid argument. And when the missing steps are put back in we get an argument that can be expressed in predicate calculus language.
Hello Bill, It’s often said that the physics of the very small cannot be accommodated within the terms of the DF---one runs up against violations of LEM. Yet we do have some mathematics which gives us a grasp of such physics. Now I imagine that we would want to include the whole of mathematics inside the DF. If so, we would seem to have a paradox. On the other hand, what would it mean for our understanding of the reach of the DF if we were to exclude (the relevant) mathematics? This strikes me as a genuine puzzle and I wonder what your take on it is.
I suspect Ed's argument would be effective against any theory that proposes a truth-making correspondent in the world. But suppose we say that the correspondent of sentence S is not a fact or object in the world, but a way or mode, M, in which the world might possibly be. Then what makes S true is M's being actual.
Apologies if this example has come up before but it does seem apropos. Suppose Harry worships Hesperus conceived as the heavenly body that's visible only at dusk, and Phil worships Phosphorus conceived as the heavenly body visible only at dawn. Do Harry and Phil worship the same thing? Yes, because they both worship Venus. No, because their conceptions of their object of worship are mutually exclusive.
Bill, >> As devoid of forms, it is devoid of actuality. So it is pure potency. But potency is grounded in actuality. Contradiction in one step. Agreed. But only if the matter--form principle is subject to and subordinated to the potency--actuality principle. There are good reasons for not doing this, not the least of which are the contradictions you derive. So why does Thomism insist on it?
Bill, I also have an objection to your Argument for limb (2). You declare right at the outset that prime matter is pure potency. I'm afraid I can't make sense of this. My understanding is that matter--form and potency--actuality are distinct axes onto which we can decompose substance. Seeking to decompose matter into potency--actuality has the feel of a category error. It's a little like agreeing that a piece of music can be understood in terms of melody, harmony, and rhythm, say, and then asking how much melody is in the rhythm. I'm not surprised a contradiction can be teased out of this.
Hello Bill, Could the defender of prime matter say something like this? That prime matter is indeterminate with respect to form but determinate with respect to quantity and number and that form is determinate with respect to, well, form, and indeterminate with respect to quantity and number. There is a pleasing symmetry here. Their combination is fully determinate substance. Quantification in (g) is over substances not principles.
Morning Bill, It seems quite natural to say that D1 changes into D2 and D3, in which case we can hardly assign the role of the unchanging substratum of this instance of change to D1. It seems equally natural, to me at least, to assign this role to the water, or perhaps more specifically, to the water of D1.
Bill, I often find these metaphysical arguments very difficult to follow. You say, for example, that the following statements issue in contradiction.1. Prime matter is the substrate of substantial change. 2. Prime matter does not exist in reality except as divided among individual material substances. 3. The substratum of a substantial change cannot be identified with any of the substances involved in the change, or with any other substance, or with any accident of any substance. 4. There is substantial change and it requires a really existent substrate.I don't understand how you get this result. Let's think of 'prime matter' and 'substance' as undefined terms and (1)--(4) as axioms. If there is a contradiction hidden here then it should be impossible to find a model for these sentences. But if we say 'prime matter' means water and that 'substance' means (water) droplet we get something like the following,1. Water is the substrate of droplet change. 2. Water does not exist in reality except as divided among individual droplets. 3. The substratum of a droplet change cannot be identified with any of the droplets involved in the change, or with any other droplet, or with any accident of any droplet. 4. There is droplet change and it requires a really existent substrate.This seems perfectly consistent. A world of eternal fission and fusion of water droplets obtained by abstracting away all other compounds and the other phases of water.
Bill, With regard to the first point, I guess I'm so impressed by the enormity of the chasm between the concrete and the abstract that I can't conceive of some concrete thing and some abstract thing being in relation to one another, unless that 'relation' is instantiation. >> then we seem to ignite Bradley's regress Yes, or something very similar. I'm struggling to articulate what I think the issue is. Perhaps we could say something like this: The idea of instantiation is part and parcel with the concrete/abstract distinction. If a is abstracted from concrete c then c instantiates abstraction a. Abstraction and instantiation are inverses. Instantiation = concretisation. We need the concrete/abstract distinction fully to explicate the idea of 'relation'. Having established what relation is, it then seems otiose to go back and redefine instantiation in terms of something that succeeds it. Whether this 'pulling up the ladder' manifests in paradox or explanatory regress, I'm not certain. But it looks fishy! For example, it seems to lead to the absurdity of your conclusion (B). On PVI's view all properties are relations. An 'intrinsic property' is a monadic relation, and a 'relational property' is a dyadic or higher arity relation, I think. The relation 'being black' is monadic and hence an intrinsic property. Nothing absurd here, PVI would say.
Bill, You characterise the instantiation connection between ordinary particulars like Max and his properties as, under PVI's scheme, an external and abstract relation. This worries me. Firstly, because this relation is cross-category. And secondly, because I think the notion of instantiation, as a connection between the concrete and the abstract, must be logically prior to the notion of relation. We use the cross-category notions of instantiation and extension to explicate abstract relations, not the other way about. For if we try the other way about we have to say that the extension of a relation is the set of its instances. And what are its instances? Well, they are (embedded in) the extension of the instantiation relation, and I think we have here the beginnings of an infinite regress.
>> Are you saying that just as there is univocity across 'Cats run' and 'Max runs,' there is likewise univocity across 'Cats exist' and 'Max exists'? No. I'm saying that the general existential 'something runs' (↔ there is something that runs) is equivalent to 'the property *runs* is instantiated', but that the singular existential 'Max runs', though sufficient for 'the property *runs* is instantiated', is not necessary.
I think we are focusing too narrowly on 'exists'. Something very similar arises for general predicates:something runs ↔ *runs* is instantiated, Max runs → *runs* is instantiated.But*runs* is instantiated ⇸ Max runsand I think you would say a fortiori that there is no (necessary?) property P such that P is instantiated → Max runsBut from this we would not conclude that 'runs' is not univocal. Rather we would put this asymmetry down to the singular/general distinction.
Bill, One last submission then, if I may. >> You seem to be denying the very possibility of coherent fictional discourse! How so? In some other possible world 'Once upon a time there was a philosopher named 'Socrates'' is the beginning of a work of fiction. It's false, of course. I stand corrected on 'enthymematic'. >> I don't see the need for your brand of logical hygiene. Well, it eliminates 99% of the confusion in evidence here, for example. It works for mathematics. What baby goes out with the bathwater?
Bill, Ed, All three of the arguments that we have just put forward are 'conversationally inept'. They all use a proper name without first introducing it via an existential claim. To make sense of an initial 'Max is a cat' we have to supply the existential: 'There is a cat named 'Max''. We could call this the 'mention before use' rule for proper names. Thereafter 'Max exists' is true but uninformative, and 'Cats exist' follows by existential generalisation. Likewise an initial 'Frodo is a hobbit' has to be understood as making the existential claim 'There is a hobbit called 'Frodo''. A subsequent 'Frodo does not exist' simply denies this existential claim. It's another way of saying 'There are no such things as hobbits'. So 'Frodo does not exist' and 'Frodo is a hobbit' are in contradiction, and absurdities follow. Similarly, the initial 'Stromboli is an island volcano' is enthymematic for 'There is an island volcano called 'Stromboli'', from which we infer the uninformative 'Stromboli exists'. What I am doing here is extending into natural language the rules observed by mathematicians in their proofs. A new name may be introduced only on the back of a general existential claim: ∃x.P(x) ⊢ P(a), where 'a' is a new logical constant. This is the rule somewhat confusingly called 'existential elimination'. Singular existential denials occur as the conclusions of reductio ad absurdum arguments. 'a does not exist' is colloquial for ~∃x.P(x) where ∃x.P(x) is the existential hypothesis under which the name 'a' was introduced. It's my contention that if we follow the mathematicians in these simple rules of logical hygiene some of the puzzles in this area evaporate. As far as I can see the rules are consistent with Ed's 'story-relative' theory of reference.
Is this a sound argument? 1. Max exists 2. Max is a cat ----------------- 3. Some cat exists 4. Cats exist If it is, how do we prise 'exists' in (1) away from 'exist' in (4)?
Ed, Yes, I think Geach's sentence and my formulation are consistent with both Nob knowing about Bob's mare (and telling Geach or not telling Geach) and with Nob's not knowing about her sorry state. If he did know and wondered if the witch was responsible and he told Geach his misgivings then Geach might have said Hob thinks that a witch has blighted Bob’s mare, and Nob wonders whether she killed Cob’s sow too.There are many scenarios to which Geach's sentence is faithful.
John, Can we not say that Visiting relatives can be annoyinghas an unambiguous and unique meaning, viz,Visiting relatives can be annoying ∨ Visiting relatives can be annoying, where Visiting relatives can be annoying → Visiting can be annoying, Visiting relatives can be annoying → Relatives can be annoying.Which of the disjuncts we take depends on the context, of course. Bill, I think it's true to say that once we have learned to speak and read the meaning of a clearly enunciated utterance or clearly written inscription simply shines through it unbidden. The question you are asking is what credence we should give this meaning. Knowledge of the source and history of the words helps in deciding this. For we know we can be deceived.
There are several scenarios which make Geach's HobNob sentence true. The simplest might be that both Hob and Nob believe there is a single witch in the village. (There may be multiple witches in existence but their powers are localised, say) Hob thinks that the witch blighted Bob's mare and Nob wonders whether the witch killed Cob's sow. Hob's thought: ∃x. unique-witch(x) ∧ blighted(x, Bob's mare) Nob's wondering: ∃x. unique-witch(x) ∧ killed(x, Cob's sow), where unique-witch(x) ⇔ ∀y. witch(y) → y=xGeach could faithfully report these two attitudes with the HobNob sentence. The predicate calculus lacks a quotation/disquotation mechanism so though the individual attitudes can be rendered their attribution cannot. English is, of course, more powerful. Is that the problem?
Just to expand on the last. Tom has two predicates to distribute over two objects. He can always do this consistently. In representing Tom's belief we take his two predicates but distribute them over just one object. If the two predicates are mutually exclusive we have a contradiction.
This is by way of a follow up to my comment on the What exactly is Kripke's puzzle about belief thread. We are supposing that Tom believes (b) and (c). We believe that at least one of (b) and (c) is false but that (a) is true, and the girl in question has the name 'Susan'. Bill says, After all, if Susan is the tallest and cleverest girl, and the beliefs in question are irreducibly de re, then Tom believes, of Susan, that she is both 18 and not 18...This misrepresents Tom's belief. He knows nothing of Susan. He believes the tallest girl and the cleverest girl are distinct, believing one thing of one and the opposite thing of the other. This 'de re belief' attributed to Tom is a curious amalgam of Tom's belief and our belief that ends up representing nobody's belief! How on earth did we get led so badly astray? The answer, I suspect, has to do with the existential commitments underlying Tom's beliefs and our beliefs. Tom must believe in at least two girls. We can get by with just one. But we are trying to represent Tom's beliefs in terms of our own existential commitments. The two are incompatible.