I’ve been getting back into Wittgenstein lately. For my proseminar at Wash U we had to read the Tractatus Logico-Philosophicus for a weekly assignment. I had never really studied it in depth before, but I now have a new found appreciation for early Wittgenstein. I’m fascinated by the metaphysical claims in the book. For example, 2.02-2.0212 might be charitably understood as endorsing the following reductio ad absurdum argument for the idea that any meaningful language must presuppose the existence of metaphysically simple objects:
1. Assume that a meaningful language does not necessarily presuppose there being metaphysically simple objects i.e. objects that are not composed of further objects.
2. Assume that in this language you can successfully refer to ordinary middle-sized objects (which are not simple).Accordingly, assume the statement “The cat is orange” is meaningful.
3. If “The cat is orange” is meaningful, it’s because, at the very least, in saying it a speaker presupposes that the cat is an object.
4. If (1) is true, and if the statement “The cat is orange” presupposes a distinct cat exists, then it also presupposes that the cat is a metaphysically nonsimple object (i.e. it is composed of further objects)
5. If statements about a cat presuppose that it is composed of further objects, and (1) is true, then those objects it is presupposed to be composed of are also presupposed to be nonsimple and composed of further objects, ad infinitum.
6. Thus, if (1) is true, the presuppositions built into the statement “The cat is orange” are infinite in complexity.
7. By the same reasoning, the presuppositions about the cat built into the opposing statement “The cat is not orange” are also infinite in complexity.
8. It seems natural to think that if talk about objects like cats has an infinite complexity in its presuppositions about how the cat is composed, then the statement “The cat is orange” can only be logically distinguished from the statement “The cat is not orange” if the most elementary parts of the presupposed infinite complexes of objects are different in some distinctive manner. [2.0201, 2.0211-2, 4.221]
9. By (1), the language is not committed to there being such things as “most elementary parts”; everything is composed of further things ad infinitum, for any posited basic entity would not be basic if it was assumed there were no basic entities. In other words, there would be no “substratum” for the regress to bottom out at; no substance [2.021]
10. Therefore, by (8) and (9), two opposing statements in the language about a complex object with infinite presuppositional complexity cannot be logically distinguished from each other simply on the basis of their elementary presuppositions because it seems strange to say two infinite complexes are different unless their (basic) members are different, but this is ruled out by (1), which assumes there are no basic members.
11. If two opposing statements are logically indistinguishable in the totality of their presuppositions, then they cannot refer to different states of affairs.[2.02331]
12. If two opposing statements cannot refer to different states of affairs, then the statements are not meaningful, for each statement could not be true or false.
13. The statements “The cat is orange” and “The cat is not orange” are obviously meaningful, so we must reject (1), since that is what got us into the infinite regress.
14. Thus, any meaningful language that refers to objects at all must be logically committed to the existence of metaphysically simple objects i.e. objects that are not composed of further objects.
Arguably premise (8) is the most problematic and controversial, for it might be begging the question. For this I don’t know how to repair the argument. Either you get it or you don’t. This might be a clash of intuition between people who have a gut feeling that it’s “parts all the way down” or that it bottoms out somewhere. I used to not have a strong opinion on this, but I am now inclined to think it bottoms out somewhere. I take this to be a logical fact, and not a fact of the universe, for only science can tell us what the actual bottom to reality is, be that quarks or whatever physics tells us. The intuition that reality bottoms out is driven by the inner logic of the idea of finite objects being composed of parts. It just seems downright strange, almost mystical, to say that a finite object like a coffee mug is composed of an infinite number of smaller objects. Surely it makes sense to say it is composed of a great many smaller objects, but I see no reason for thinking this amount infinite. Objects must bottom out according to the sheer logic of our ways of talking about composition. If this is right, then we arrive at a different interpretation of Wittgenstein’s argument for metaphysical simples than is commonly given. The concept of simple objects is not arrived at by seeing it in our language and then saying because language mirrors reality there really are metaphysical objects. Rather, the argument is transcendental in the sense that Wittgenstein shows that if we are going to talk about objects at all, we must presuppose metaphysically simple objects. So the Wittgensteinian point is not that language mirrors reality therefore simple objects exist (“One cannot, e.g. say “There are objects” 4.1272). The point is that language use logically commits us to the idea of there being simple objects when discussing objects. As Wittgenstein says, “Logic is transcendental” [6.13].