Wittgenblogging: Proposition 4 and the Cartesian Circle
November 11, 2010

Meditationes de prima philosophia - Renatus Ca...
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Peter highlights one of the more intriguing findings of the Tractatus Logico-Philosophicus’ fourth proposition, regarding the slipperiness of trying to describe or prove logic itself. Logic is the underlying framework of the universe; you can’t construct a proof to demonstrate the validity of logic, or precisely describe logic itself, because doing so would require stepping outside of logic. That’s not something we’re capable of. Peter has a good analogy:

Sort of how I can’t really tell you what it’s like to be alive, because both you and I would have to be dead first to actually comprehend the contrast.

I first encountered the problem of how to demonstrate that logic or reason were useful tools for understanding the universe in Descartes’ Meditations. Early on in the Meditations, Descartes decides that if he can’t be certain of the validity of his perception, then reason is all he has to rely on. But then he starts asking himself why he has any reason to think that reason itself is reliable, and the result is the painfully contorted piece of reasoning we call the Cartesian Circle.

It goes like this:

  1. Whatever I clearly and distinctly perceive (meaning, essentially, can hold in my mind and understand wholly from a mental picture) is true.
  2. I know that my clear and distinct perceptions are accurate because they are given to me by God, and God is not a deceiver.
  3. I know God exists because I can clearly and distinctly perceive Him. I just imagine a perfect, infinite being, and understand that it is more perfect for something to exist than to not exist.

I don’t think I need to spell out the problems here. And it shouldn’t be hard to see why I prefer Wittgenstein’s far more elegant answer to the question: “How do we know reason itself is valid?”

Wittgenblogging: Proposition 3.5
November 2, 2010

Peter’s all caught up on the Wittgenblogging, and pretty close to outstripping me. I’ll admit I haven’t started on the fourth proposition yet; the third sort of took the air out of my tires, and besides that I’ve got a list of philosophy texts I want to read that’s thiiiiis big. But I will get to it soon; this week, hopefully.

Anyway, Peter raised some issues with my last post on the subject that I think I should address.

For example:

First, I would hesitate use “mental pictures,” as the litmus test for the logicality of a statement. There are plenty of statements that I can not picture, but that are almost certainly true. Examples of these include, “People with synesthesia can taste music,” “Bees can see ultraviolet light,” “When in a state of dreamless sleep, you experience nothingness,” and “The universe is infinite.” I can also picture things that, while I guess they don’t contradict logic, are physically impossible*. For example, I can imagine ashes burning.

Peter may be right here, but I think he’s actually being a little over-literal when it comes to the idea of “mental pictures.” While you might not be able to take a literal snapshot of how a synesthesiac (that’s a word, right?) perceive music, you can certainly imagine what it would be like to experience a certain coppery taste when one hears a high C-sharp. I think that when Wittgenstein talks about mental pictures, he just means imagined sets of data that it is within our capability to perceive.

As for the ashes burning thing, I think Peter’s right there. “The ashes are burning” is a phrase that obeys a certain logical form, and you can imagine how one might perceive it. As a result it has some truth value (likely negative). 

Peter also writes:

Second, Wittgenstein directly says, “It is as impossible to represent in language anything that ‘contradicts logic’.” Language is inherently logical. A statement may be meaningless, but it can never be illogical. Therefore, when somebody says “We are all one, because spirit is everything,” they are speaking a logical statement. I think that Ned is confusing the colloquial idea of “logic” with the philosophy of language idea of “logic.”

Right. The “spirit is everything” example clearly obeys the form of a logical statement. When I suggested that it doesn’t express anything, I meant that I have no idea how one would form a mental picture corresponding to that sentence. I think the spiritualist would tend to agree, arguing that these things are beyond our perception — but I think the Tractatus Logic-Philosophicus goes a pretty long way towards establishing that if there’s no faculty we can use to perceive something (even with artificial enhancements to our perception), then it’s unlikely that we can legitimately call it a part of the world.

Wittgenblogging: The First Proposition
October 6, 2010

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:



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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