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There are several interviews in Quine in Dialogue that are worth reading. A 1978 interview with Magee has a bit that made me stop.

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I was thinking about the Tractatus recently and came up with a question about it that I was unsure about the answer to. (This is not that hard to do really.) The question is whether Wittgenstein thinks that it is a logical impossibility that there could be no objects.

Why would one think that this is not an option that there could be no objects? In the 2’s, Wittgenstein talks about how there must be a substance to the world, and this substance is comprised of Tractarian objects. This makes it seem like it is not a logical possibility for there to be no objects. Granted, this would only be a logical possibility if the world were connected tightly to language or logic or if objects were similarly tightly connected to language. I’m not terribly comfortable with the 2’s, either alone or together with what comes later. Luckily, I don’t think that we need to appeal to them specifically in order to come up with an answer, which point I’ll get to below.

Why would one think that it is an option? In 5.453 Wittgenstein says: “All numbers in logic must be capable of justification. Or rather, it must become plain that there are no numbers in logic. There are no pre-eminent numbers.”
If it is a matter of logic that it is impossible for there to be no objects, this would seem to make zero a distinguished or pre-eminent number, which seems to be ruled out by the above. It might look like I’m running together objects and names, and all that logic will deal with is the names. In the Tractatus, however, every name designates an object.

Alternatively, one might ask why there must be at least one thing. Is this asking for logic to give a justification? Thinking about the way that the TLP is set up, it seems not. Rather, this issue is left implicit in the propositions. Propositions consist of concatenations of names. Names designate Tractarian objects. Thus, for there to be Tractarian propositions at all, there must be names and so objects. In order to be talking about logic at all, we must presuppose that there are at least some objects. It looks like the question of why there is something rather than nothing is barred from the outset, which is probably something that Wittgenstein would’ve approved of.

I do want to note that things are complicated with Tractarian claims about possibility. In TLP, the objects are the same in all possible worlds. Indeed, the possible worlds, if we want to use that language, are constituted by those things in various arrangements of facts. It seems like claims such as “there could have been more or fewer things than there are,” if formulable in a Tractarian proposition, must come out false. The possibilities are completely determined by the Tractarian objects that there actually are. Of course, the way that the above claim is formulated, in terms of generic things, is probably the source of this seeming weirdness. “Thing” and “object” are formal concepts in the TLP. A claim like “there could have been more espresso cups than there actually are” needn’t turn out necessarily false because “espresso cup” is a proper concept, which can be expressed with a propositional function.

Throughout MIE, we are told what incompatibility is. Two claims are incompatible when commitment to one precludes entitlement to the other. We are also told that incompatibility is a modal notion. In fact, it plays are rather central and rather modal role in the later part of MIE and Brandom’s later work. Now, my problem is I don’t understand where the modality comes from. Commitment and entitlement are normative but they aren’t, at least at this point in the story, modal. The preclusion isn’t modal either; it is just straightforward non-modal precluding.

There is a modal sense of incompatibility that is used in other philosophical papers. This is, I think, a sense in which two propositions are not jointly possible; non-compossible is the term I think. This is clearly modal. If that is what Brandom means, then there should be some demonstration that this sort of incompatibility and the kind defined in MIE coincide. There isn’t any such demonstration, which makes me think that this is not on the right track. However, if it isn’t on the right track, then I don’t know how in the world incompatibility is modal. If it is on the right track though, then I’m also not sure how the argument is supposed to run since these two notions don’t seem coextensional. I’m doubtful that the latter implies the former either, but then this is just denying that I’m on the right track.

Here’s another post on something that Karen Bennett said, which will hopefully be more substantive than the last one. In one of the discussions, Bennett said that Lewis’s semantics for modal logic runs into trouble when talking about the “moving parts of his system”. This means, roughly, when it starts talking about matters metalinguistic, like the domain of worlds, truth, domains of individuals, etc. Her particular example was: necessarily there are many worlds. Apparently Lewis’s semantics mess this up. I don’t know the details since I don’t know what sort of language Lewis was using and the particular semantics. That’s not really the point. It got me wondering how prevalent this sort of thing is. When do semantics go astray for things that are naturally situated in the metalangauge? The truth predicate can cause some problems. Does the reference predicate? I’m not really sure I’ve read anything about logics that include an object language reference predicate.

The idea dovetailed nicely with some stuff I was working on for Nuel Belnap’s modal logic class. Aldo Bressan’s quantified modal logic includes a construction of terms that represent worlds. This construction works at least as long as the number of worlds is countable. I’m not sure what happens when there are uncountably many worlds since that requires me to get much clearer on a few other things. This allows the construction of nominal-like things and quantification over them. The language lets you say that for any arbitrary number of worlds, necessarily there are at least that many worlds. The neat point is that the semantics works out correctly. [The following might need to be changed because I’m worried that I glossed over something important in the handwaving. I think the basic point is still correct.] For example, (finessing and handwaving some details for the post) the sentence “necessarily there are at least 39 worlds” will be true iff for all worlds, the sentence “there are at least 39 worlds” is true, which will be just in case there are at least 39 worlds. This is because you can prove that there is a one-one correspondence between worlds and the terms that represent worlds. Bressan uses S5. The way “worlds” is defined uses a diamond, so the specific world at which we are evaluating does not really matter. So, the semantics gets it right. Of course, this doesn’t say that there are only models with at least 39 worlds. If that is what we want to say, we can’t. It does say that within a model, it’s true at all worlds that there are at least 39 worlds, which is all the object language necessity says. This gives us a way to talk about a bit of the metalanguage in the object language, albeit in a slightly restricted way.

[A word of warning, this is not the clearest post.] In a paper called “Could there be Unicorns?” Dummett goes into Kripke’s argument in Naming and Necessity that there could not be unicorns. Dummett presents three ways of understanding Kripke’s argument and on two of those ways, the argument doesn’t work. I didn’t understand that part of the paper (nor do I remember it well), so I won’t talk about that. In the conclusion Dummett doesn’t sound terribly convinced of it either. What is more interesting is some of the background discussion. First, Dummett talks about the revival of modality among philosophers. As the story goes, modal concepts like possible worlds fell into ill-repute among philosophers in the first half of the 20th century, due in large part to arguments by Quine. Modal notions were “spooky” intensional notions and so modal logic was a “spooky” intensional logic. The only good notion was an extensional one, so modal notions were right out. Modal logic and possible worlds were revived, and made palatable, in the 60s and 70s by Kripke’s giving a completeness proof and a semantics for modal logic in addition to his Naming and Necessity lectures. Dummett thinks that this story does not get things right. Whatever the reasons for modal logic becoming popular among philosophers again, he thinks that Kripke’s work is not relevant. One of the big advances was that the Leibnizian idea of possible worlds could be extended to weaker logics by relativizing the accessibility. Also, Kripke’s big proof was for K. However, K is not the logic that most philosophers use. They use an unrestricted accessibility relation, which is what is used in S5. This leads Dummett to say that philosophers don’t put any structure into their accessibility relation (which is sort of odd since it is fairly structured, in an equivalence relation kind of way). I think what he means is made clearer when he says that in S5, there is nothing special about the actual world. In general in K or S4, the actual world is special in virtue of what is accessible from it and what is accessible to. At least, that is what I think he means. So, since Kripke’s work didn’t do anything to make S5 any clearer than it already was, philosophers shouldn’t use it as a justification for using possible worlds talk in the sense of S5. This is not to say that S5 is obscure. Dummett seems to think that Leibniz and others made unrestricted modality and possible worlds somewhat respectable, although not completely clear.

The other bit of background that was neat was Dummett’s attempt to make sense of the relative accessibility relation. He says that no one has made philosophical sense of relative accessibility. Nuel Belnap seems to agree with him. Mathematically it is clear and elegant, but it is philosophically a bit flaccid. What is Dummett’s proposal? While he doesn’t explain exactly what the relative accessibility relation could be, he tries to give an example that would motivate having an accessibility relation that is not an equivalence relation. He does this by casting things in terms of states of affairs. Dummett’s example motivates rejecting symmetry. A state of affairs S is accessible if a state of affairs T which is presupposed or required by S is in the world under consideration. Suppose we are in a world w that has T and S and is related to a world u that has S that is related to a world v that has neither. The relation is transitive so w is related to v. However, v is not related to w since v does not have S. It could still be related to u, but it is necessary for a world to have S to be related to a world with T. This seemed
somewhat convincing, although he admits the difficulties in extending this to something that would motivate abandoning transitivity.

Finally, Dummett expresses some worries about possible worlds talk in general. To quote, “I believe that the use by philosophers of possible-worlds semantics has done, on balance, more harm than good.” In regards to his arguments in the article, Sir Michael says they “may possibly not be watertight”.

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Shawn Standefer, recent Ph.D. in philosophy from Pitt. (More about me)

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