An Extended Tractarian Argument for the Simplicity of Objects

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].



Filed under Philosophy

4 responses to “An Extended Tractarian Argument for the Simplicity of Objects

  1. Alternatively, if language is circular, there could be no basic entities, no bottom, while objects are not necessarily composed of an infinite number of parts. An object would be the node of a network of objects.
    For example, I’m not sure that one’s concept of a cat can be reduced to different parts composing the cat without any reference to the cat’s environment. These relations to the environment are thus “part” of the concept of cat. Further, such environmental objects could as well refer to the concept of cat as “part” of them. It does not follow that an infinite number of objects is required, while no object is itself simple.
    As far as I remember, this kind of circular view of language has been defended by Merleau-Ponty

    • Gary Williams


      I’m inclined to agree with you that there is more to the concept of cat than just composition of parts. I agree with you that the environment is part of the concept. However, I take this to be a result of a kind of dual-process view of concepts. On the lower end of the scale, you have affordance-reactivity concepts that are shared with nonhuman animals. The affordance concept of a cat to a mouse surely includes reference to the environment. However, on the higher end of the scale, you have linguistic concepts that include a framework for interpreting objects qua objects. Early Wittgenstein might be interpreted as only talking about the inner logic of linguistic concepts, and not affordance concepts. It seems plausible to me that affordance concepts could have no reference to composition, whereas linguistic concepts could. Hope that makes sense.

  2. vicp

    Objects form the substance of the world. Therefore they cannot be compound.
    If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.

    It would then be impossible to form a picture of the world (true or false).

    One must conclude that Wittgenstein could not conceive of Zombies.

  3. Increasingly I have been wondering if the bottom is not created by the sheer limitations of human attention spans. Sure, we could imagine breaking the cat into two pieces, and then breaking each of those into two pieces, and then each of those, and then… then we get bored and start talking about the cat again.

    I don’t mean that to sound trite. One feature of William James and E. B. Holt style metaphysics was that they thought relations were real, and that mental things were real relations. One criticism of this approach was that it could fall into infinite regress: Well, my thinking about the cat is real, and my thinking about the thinking is real, and my thinking about the thinking is real… and thus (the argument goes) even one knower and one known thing creates an infinity of real relations: imagine the carnage in a world of many knowers and many known things!

    And yet, it seems to me that the simplest reply to such an argument is that there are as many real relations in such a situation as you are willing to sit there and thinking them — no more, no less, and definitely nothing near infinite.

    To return to Wittgenstein, I am tempted to say “Yes, I grant you all your claims, and therefore grant you that a person willing to spend eternity breaking the cat into ever smaller pieces will never finish even one sentence…. but since no such person exists, will exist, or ever could exist… who cares?”

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