The Generality of Logic

At 2.182, Wittgenstein says: “Every picture is also a logical picture. (On the other hand, for example, not every picture is spatial.)”

I can imagine someone worrying that this might be an oversimplification of some kind. For example, people have sometimes debated whether ‘quantum logic’, which is a sort of probability logic, should be the ‘true logic’, since physics tells us that there are some systems in which ‘particle P is at (x,y,z)’ (all of this is itself grossly oversimplified, but never mind) is ‘neither true nor false’ but only probable to such-and-such a degree.

“The cat is on the mat” asserts a spatial relationship between two extended things. If Wittgenstein is right it also asserts a ‘logical’ relationship between them. But in what does that ‘logical’ relationship consist?

The right answer here, surely, is that all it consists in is the cat’s being on the mat. “The proposition is a picture of reality, for I know the state of affairs presented by it, if I understand the proposition.” (4.021)

The geometry, physics, biochemistry, evolution, embedded cognition, etc. of cats on mats might be enormously complicated. Perhaps there are lots of interesting things to study here. But those details don’t really matter to the proposition’s being a logical picture.  

“The proposition shows its sense. The proposition shows how things stand, if it is true. And it says, that they do so stand.” (4.022) Sense, or ‘how things stand if it is true’, is not something which itself has any representation for Wittgenstein in the Tractatus. Likewise the picture’s form of representation: it is not itself represented. There’s nothing ‘in virtue of which’ a proposition is a logical picture of the facts. It is a logical picture of the facts – even, in a way, by virtue of representing them – but there is no ‘representation-relation’, or even a nontrivial second-order fact that such-and-such is a representation, picture, etc.

The key to understanding how this can be so for Wittgenstein is in the way he thinks about sense (Sinn), about which I am preparing a post. Because of the tight link between propositions, thoughts, pictures, and facts they don’t come apart for Wittgenstein in the way that they do for most philosophers. It’s in a way a result of this that there’s nothing to be represented here. But more on that anon.

In any case, it’s a logical picture just because it’s a picture, and the way in which it pictures isn’t relevant to its logical picturing. Logic leaves the facts and our means of representing them off to one side. What matters to logic is just that the picture could apply to reality or fail to do so.

This is connected to something he said later, in 1931:

“When I ‘have done with the world’ I shall have created an amorphous (transparent) mass and the world in all its variety will be left on one side like an uninteresting lumber room. Or perhaps more precisely: the whole outcome of this entire work is for the world to be set on one side. (A throwing-into-the-lumber-room of the whole world.)” (Culture and Value, 9e)

This is quite a striking remark, and in a way cuts against my bit about ‘turning off the TV and going outside’ in the “True but Nonsensical” post from August 31, 2013. The assumption made there is that showing that the terms in which we philosophize are inevitably nonsensical would serve to render the pursuit of philosophy valueless. But this is a bad assumption, privileging product over process. If “the logical clarification of thoughts” (4.112) is what is wanted, then kites and chemical reactions aren’t so much of interest after all.

But let’s get back to quantum logic. We might, as many physicists seem to think, have to employ a notion of ‘chance’ as fundamental in our physical representations of the universe. But even if so this would not make much of a difference for logic as Wittgenstein understood it. We might for example move the probabilities into the propositions, so that “there is a q% chance that particle P is at (x,y,z)” is either true or false, that being the sort of proposition that we can confidently apply to the world on the basis of current theory.

The question which gave rise to this post, though, is – how do we know that’s always something we can do? Can we always reduce the things we say about the world to pictures which either apply or do not apply to reality?

The answer that Wittgenstein gives, roughly, is something like this: if a proposition isn’t a picture, it’s without sense, and we don’t need to worry about it. If it is a picture, it’s also a logical picture, and then it either applies or it doesn’t. No matter how fantastically complex the picture is, this will be the case.

This seems like a plausible claim to me. But do we have to accept it? Are there other options?

When I first started writing this post I was wondering if there were very complicated sorts of facts that were on the one hand so interconnected that you couldn’t break them out cleanly from one another, but on the other hand individually expressible independent of those interconnections. But now that I’ve finished writing the post the sentence I just wrote really reads like nonsense to me. It seems to be asserting that a fact could be atomic and compound at the same time, or that we could have big pictures which both could and couldn’t be broken into smaller pictures. Which, um.

Have I achieved clarity? Or just drunk the kool-aid? Inquiring minds want to know.

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2 comments on “The Generality of Logic

  1. Tom Wood says:

    Kool-aid? Maybe, but you make sense to me. For example, in 4.031 W writes:

    “In a proposition a situation is, as it were, constructed by way of experiment.
    Instead of, ‘This proposition has such and such a sense’, we can simply say, ‘This proposi-
    tion represents such and such a situation’”

    In the Notebooks from 1914-1916 he elaborates: “As when in a law-court in Paris a motor-car accident is represented by means of dolls, etc.: (Notebooks 7e).

    Suppose the dolls, etc. fail to match the states of affairs in the actual accident (e.g. showed the passenger flying out the windshield, when it was the driver that actually did) , then the “experiment” would fail. (For Mythbusters fans this would be a failure at the “proof of concept” stage.) Accordingly, this would show that the experiment/proposition failed to represent.

    Even if this failure to represent were due to some ludicrous arrangement of the dolls, etc. (e.g. having the cars riding around on people) it would not be a failure to be a picture, just a failure of depiction. A “bad” picture is might be false, but it is still a picture.

    Does that make sense. If not, pass the Kool-aid.

  2. seancstidd says:

    This is a good kind of consideration to bring up.

    Another way to ask this question might be: if I say “Travis is wearing a black hat” with understanding then I know what makes it true or false. If it’s true then I’ve got ‘Travis’ and ‘black hat’ referring to objects. Do they still refer if the proposition is false?

    If what you did was look over at hatless Travis you might think (just off the cuff anyway) that ‘Travis’ does refer (there he is!) while ‘black hat’ doesn’t (since there isn’t any black hat such that Travis is wearing it).

    False propositions aren’t nonsensical in general, I thought.

    I am not sure what to say about this in relation to W right now. It is the kind of thing to think about carefully in assessing the text, especially if what we were saying in class last week was right in relation to the mind-world problem.

    3.203 is quite deflationary: “The name means the object. The object is its meaning. (‘A’ is the same sign as ‘A’.)”

    If we take the proposition as logically depicting the fact, this makes sense – so long as the proposition is true, applies. Since they share form of representation the gap between proposition and fact is eliminated.

    But what if it’s false? We know what would be the case if “Travis is wearing a black hat” was true. It represents certain objects in a certain configuration, say. So if we encounter that configuration, we’re golden, and we can pick out the objects, the names refer, etc. But if it doesn’t apply, what then?

    Well, if it doesn’t apply, in what sense do the names refer? But here one wants to put one’s foot down and say, “wait, I knew that I was talking about Travis, and it was only because I knew that that I could see he wasn’t wearing a black hat.”

    I am prone to feel this sort of thing also, but last Friday’s class called that feeling into question for me. You might reply – “Look, I know Travis, he’s in the room, but he’s not wearing a black hat. So in what sense does the proposition “Travis is wearing a black hat” apply to him? He’s sitting right there, and he’s not wearing a black hat.”

    The thought here would be that you can’t possibly think that THIS Travis, the one sitting at this desk, is wearing a black hat, because he’s not, so when you say “Travis is wearing a black hat” the fact that you look at him to discover that the sentence fails to apply (and understand that when you understand the sentence) doesn’t make the name ‘Travis’ in that sentence refer to him in the way that it would if he were wearing a black hat.

    As I just finished writing to Lynette, I think we need to get the views on sense from last Friday’s class out there clearly before we can fully evaluate this sort of question. But these are good things to think about.

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