Wednesday, June 04, 2008

Must there be Tractarian objects?

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.


Colin Caret said...

I have no idea what Wittgenstein is talking about, but it is a notorious feature of two 20th century research programs that they agree with him on this point. Classical first-order logic has Ex(x=x) as a theorem, which requires as a logical truth that something exists. David Lewis' modal realist theory of possible worlds also implies that it is impossible for there to be nothing. One thing we can say is that these two projects probably arrived at this conclusion for the same reasons Wittgenstein did: elegance or simplicity of the theory.

N. N. said...

In the Philosophical Remarks Wittgenstein writes,

"What I once called 'objects', simples, were simply what I could refer to without running the risk of their possible non-existence; i.e. that for which there is neither existence nor non-existence, and that means: what we can speak about no matter what may be the case."

According to the early Wittgenstein, for any proposition to have sense, it must be analyzable into a proposition consisting of logically simple parts that have immediate reference to objects. If the parts of every proposition were logically complex, then the sense of any proposition would depend on the truth of another, viz., the proposition that asserts the existence of the relevant complexes. Of course, the sense of the latter proposition would in turn depend on the truth of another, ad infinitum.

Shawn said...

I didn't realize David Lewis thought that it was impossible for there to be nothing. If I had given this some more thought, it would've been clear that in order for there to be nothing, there couldn't be necessary existents.

Now that you mention it, what you attribute to the early Wittgenstein sounds familiar. I think one of the grad students at Pitt gave a presentation on some of that material recently. In retrospect it should've been fairly clear that Wittgenstein wouldn't think there could be nothing. The post was mainly for working out the tension I felt between that view and 5.453. The passage from the Philosophical Remarks is interesting. Do you have any further thoughts on it?

Shawn said...

Looking at 4.1272, it appears that Wittgenstein thinks that the Tractarian strictures bar the expression of a sentence along the lines of "there are n objects" since it involves only formal concepts.

N. N. said...

Wittgenstein wouldn't think there could be nothing.

I think I'd rather put it this way: Wittgenstein wouldn't think that it could be said that there could be no objects. Such a statement would be nonsense.

I take the PR passage to be an exposition of TLP 2.027: "the existent [Bestehende] and the object are one." I think that Wittgenstein's point is that his doctrine in the Tractatus is more sophisticated than the metaphysical thesis that objects are necessary existents. Here are some good comments from the secondary literature on this question.

Hacker (Wittgenstein’s Place in Twentieth-Century Analytic Philosophy, p. 30):

"Objects cannot be said either to exist or not to exist. … This is reflected in the fact that 'a exists' ('([existential quantifier]x) (x = a)') does not express a proposition if 'a' is a simple name; for in that case it is not bipolar inasmuch as its negation 'a does not exist' must be nonsense."

The Hintikkas (Investigating Wittgenstein, p. 48): "Just as we cannot say that a particular object exists or does not exist, so it makes little sense (according to Wittgenstein) to say that it might not exist or could exist even though it does not actually do so. And this Wittgenstein takes to mean that we have to deal with the objects that actually are as if each of them existed necessarily and as if collectively they were exhaustive by necessity."

Pears (False Prison, Vol. 1, p. 108): "It is not even accurate to say that the objects of the Tractatus necessarily exist. Wittgenstein's doctrine is more subtle: their existence cannot be questioned, asserted, or denied."