Wittgenblogging: The First Proposition

Ludwig Wittgenstein 2
Image by Christiaan Tonnis via Flickr

Just started last night on Ludwig Wittgenstein’s Tractatus Logico-Philosophicus, which, as I mentioned before, Peter and I will be working through together in its entirety. So why should you non-philosophy majors care? Because Tractatus is one of the classics of the philosophy of language, seeking to, in the words of Wittgenstein (pictured), “Tractatus is intended to define the outer parameters of human inquiry, and expose why seemingly intractable philosophical problems are based on simple misunderstandings in “the logic of our language.”

He does this by building seven propositions on top of one another. In this post, we’ll look at the first one, which is, in its entirety:

1. The world is all that is the case.

1.1 The world is the totality of facts, not of things.

1.11 The world is determined by the facts, and by their being all the facts.

1.12 For the totality of facts determines what is the case, and also whatever is not the case.

1.13 The facts in logical space are the world.

1.2 The world divides into facts.

1.21 Each item can be the case or not the case while everything else remains the same.

Seems relatively straightforward so far. The only assertion in this proposition that didn’t seem immediately obvious to me was 1.1—that the world is the totality of facts, not things. After a little work, though, I decided that Wittgenstein was correct.

I worked it out using the language of first-order logic (philosophy majors, it’s been almost a year since I’ve had to work in FOL, and it was my worst subject in the department, so feel free to check my work here). Basically, I conceived of a universe that is a 2 x 2 two-dimensional grid, on which there exist two three-dimensional objects: A and B. Both A and B are cubes of the same size. It looks a bit like this:

x         x

A         B

Where the x’s mean unoccupied squares on the grid.

So if we’re to think of this world as the totality of things, then you have basically described all there is to say about this world just by saying “A and B” (or, if you prefer, A ^ B). But that’s clearly not true. You can also say:

Cube(A)

Cube(B)

Adjoins(A, B)

SameRow(A, B)

LeftOf(A, B)

RightOf(B, A)

SameSize(A, B)

SameShape(A, B)

Only now have we exhausted all the facts about this world. Or maybe we haven’t—maybe we’ve just exhausted my limited FOL vocabulary. But even then, you get the point, which is that there are apparently a finite number of factual claims we can make about this world. Put all these claims together, and you have a complete picture of the world—far more complete than if you just listed the objets within it.

One more thing: 1.21 might seem incorrect based on the list of facts I’ve provided, but that’s only because there’s some overlap between a lot of these facts—many of them are different ways of expressing the same propositions, so of course making one of them not the case would render its cousin also not the case. If we were to make a list of facts that don’t overlap, then 1.21 is certainly correct.

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