Revisiting the Tractatus

 We can all agree that Wittgenstein invented logical positivism in the Tractatus. What's striking though, upon revisiting that work, is that—in the very act of creating that philosophical position, he also refuted it and transcended it. Quite a lot to accomplish in one roughly sixty-page work!

I'm fairly certain I picked up the Tractatus at least once in college or grad school. I must have even made it past Wittgenstein's stirring preface—only to sink down in the mire of his logical symbolism a few pages later. These days, though—years later—I am more comfortable with the fact that there are certain things that I just will never learn in my lifespan: formal logic probably being one of them. And so, I simply breezed through these sections without delay or despair, so that I could pick what meat off the bones I could from the book's more qualitative sections. 

And here, I'm quite certain I got much more out of the second, finished reading than I did out of the first, aborted one. Indeed, I found so much more in the Tractatus this time around that I'm almost embarrassed. Here, after all, is pretty much everything I've ever thought and unthought about logical positivism over the last decade. If I had read it all here more closely the first time around, I might have saved myself some time. 

But then again, I probably wouldn't have understood it on that first read, even if I'd made it all the way though, because I hadn't yet independently reached the same conclusions. For, as Wittgenstein says, "This book will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in it[.]" (Ogden trans. throughout). 

I've explained on this blog before the history of my relationship with logical positivism: how, when I first discovered it, it seemed to me a complete and final statement of the limits of philosophy. Reading Ayer or Carnap, I thought: wait a minute, this is irrefutable; it discloses all that philosophy can ever achieve—which (and this is the point) is not much. 

Philosophy, as Wittgenstein says, can show the limits of thought. It can show students their error when they seek to transgress those limits. But it can't get past those limits itself; because nothing can. To think what cannot be thought is a contradiction in terms. To formulate ideas about the noumena, the thing-in-itself, that which lies beyond our brain's capacity to conceive, whatever you want to call it, is impossible by definition. 

And so, most philosophical problems are only apparent problems. They are pseudo-problems, stemming from an abuse of language—from language that aims to speak about that which cannot be thought. "What happens after death?" the metaphysician asks. The question is attempting to ask about an existence that exceeds the boundaries of existence, and so, it is self-contradictory. As such, we are not permitted to ask it. On such subjects, philosophy should simply shut up, according to Wittgenstein—for "whereof we cannot speak, thereof we must be silent."

"What is the nature of the reality that lies behind my ability to perceive and sense the world around me?" the metaphysician asks again. And, once again, the question is illegitimate. It is nonsense. For we cannot know what lies beyond our capacity to know. To put the point more strongly, nothing lies beyond our capacity to know, so far as we are concerned; because anything that did lie beyond our capacity to know would be something about which we cannot think, or speak, much less formulate an hypothesis. And so, all metaphysical speculation is baseless and empty. 

Such, at least, are the doctrines of logical positivism as a generation of philosophers extracted them from Wittgenstein's work. And such is the doctrine that persuaded me, at least for a time.

I also found it to be tremendously liberating, spending my time as I was then among the incredibly muddled thinking on display in divinity school. I would read these vaunted works of theology that were assigned in class, and I would think—this just seems to be making unfalsifiable assertions about things that cannot be defined. It doesn't appear to mean anything at all, much less to be intended to persuade anyone of its truth. But surely a whole discipline of thought cannot be founded on sheer nonsense, can it?

The logical positivists reassured me: yes, it can. Good, that settles that then! I need waste no more time on it. "Consign it then to the flames," as Hume would say, "for it can contain nothing but sophistry and illusion."

But no sooner had I adopted the logical positivist viewpoint than something started to trouble me about it. Namely, as I've explained before, I kept running up against areas of thought and experience of which we seemed forced to choose between two binary options. My logical positivist procedure would seem to tell me: exclude the one of the two options that is nonsensical or self-contradictory, and whatever remains must be true. Yet, in all too many of these cases, both options seemed to be equally nonsensical. Both seemed equally to attempt to think something that cannot be thought. Yet one had to pick one!

To give an example: 1) spacetime must either be continuous, or made up of discrete packets. We have to choose between them, because we cannot very well do without the concepts of space and time in navigating our reality. Yet, both conceptions of spacetime seem equally self-contradictory. If spacetime is continuous, after all, then you are left with all the difficulties of Zeno's paradox. That is, if space is infinitely divisible, then how is motion through it possible, since even the smallest movement must cross over an infinite number of points in space?

 If it is discrete, on the other hand, you are left with the Pythagorean problem of incommensurability. That is, if space is made up of tiny squares, then these tiny squares must be infinitely divisible in turn, because—as the ancient Greek mathematicians demonstrated to their own dismay and consternation—the diagonal of a square can never be measured in terms of whole units of the length of the sides, but rather by an infinitely-extending irrational number of such units. Therefore, if we say that space is made up of tiny squares, then we would be forced back again to a belief in a continuum, since there is no discrete unit that could measure both the sides of those tiny squares and their diagonal—and yet, it was precisely to avoid the logical paradoxes of the continuum that we were trying to introduce the hypothesis of discrete spacetime in the first place!

So, no matter which way we turn, we are still forced to accept as a working hypothesis something that is inherently paradoxical and self-contradictory. As Hume put it, after offering a similar demonstration of the problem of the continuum and of incommensurability in his Enquiry Concerning Human Understanding, humankind suffers under a "whimsical condition," in which we "must act and reason and believe," and yet we "are not able, by [the] most diligent enquiry, to satisfy [ourselves] concerning the foundation of these operations, or to remove the objections, which may be raised against them." Not even in so simple a matter as the diagonal of a square!

We seem, therefore, to be incapable of avoiding nonsense, much as we might wish to do so. Logical positivism cannot be the final word, then, because—even if it sounds right to reject all nonsense and confine philosophy to the limits of the sensical and the thinkable—even the most basic concepts by which we navigate our perceived experience, such as space and time, immediately turn out to be riddled with unthinkable and nonsensical implications. 

Or again, take the problem of death. Here, I reached yet another situation in which one seemed to be forced either way to confront something inconceivable. Therefore, the logical positivist approach once again failed. As I summarized the problem in another post last May: 

"Applying the Carnapian method, I knew that personal immortality was nonsense, because eternity was unthinkable. But then I hit the snag: personal nonexistence seemed to be no less inconceivable, from within the conceptual apparatus of the existing creature in question. 

Thus, we seemed to hit an inconceivability either way we turned. Push to the outer limits in either direction—eternal existence, or eternal non-existence—and one seemed to reach something the human mind frankly could not grasp. Thus, the whole topic of death was nonsense! Yet, one had to make a choice between the two nonsenses. One would either exist or one wouldn't, and so the very structure of our thought—which we were supposed to regard as defining the limits of sense—was actually pushing us to embrace nonsense after all."

And here is where we see, in revisiting the Tractatus, that Wittgenstein actually foresaw such difficulties long before his epigoni did. He therefore transcended the very logical positivist method that his followers would extract from his work. He was, that is to say, already ahead of them—and ahead of the very method most often attributed to him—while others were still trying to understand, formulate, and apply that method systematically. 

Specifically, Wittgenstein acknowledges the problem of death. He tells us: you can't conceive of death, the end of the self and of one's own consciousness, any more than you can see the outer boundary of one's field of vision. One cannot see the boundary of the field of vision because, in order to see it, one would have to see past it—to see the other side of it—in which case it would not actually be a boundary. And so, our field of vision is to us a totality, a "whole." 

And so it is with life—we cannot conceive of an "end" of life, because life is the entirety of our reality. To see the "end" of life would be to see the other side of it; but in that case, it wouldn't really be the end. So we must see life as a totality, with nothing capable of existing outside it. Thus, as Wittgenstein puts it, "Our life is endless in the way that our visual field is without limit."

So far, we are on safe ground with the logical positivists. We can simply say: okay, then, death is a nonsensical concept. We cannot think it. Therefore, we can reject it. 

Yet, rejecting it soon brings other inconceivabilities in its wake. If life is endless, does that mean we each have an infinite temporary duration? Yet this soon involves us in still further difficulties, for all the reasons said above. As Wittgenstein asks rhetorically, "Is a riddle solved by the fact that I survive for ever? Is this eternal life not as enigmatic as our present one?"

Surely, then, the conceptual "endlessness" of life does not mean that it actually is "endless," any more than the "totality" of the field of vision means that the individual human eye can literally see everything at a time. Just as we are forced to conclude that the world extends beyond our field of vision, and therefore that our field of vision must have a limit—even though that field of vision is, for us, unlimited—so it is with life. Life contains the entirety of our world. Yet our world has a limit, which means that there is a world that extends beyond it. The world therefore, is—in Wittgenstein's self-consciously paradoxical formulation—"a limited whole." It is a bounded totality. 

We therefore must be able to think about the world outside the limits of our world, or of life beyond our life, or of a life that continues after our personal existence has ended. Yet, this would seem to mean doing exactly what Wittgenstein's method had previously forbade. The Tractatus then seems to be inviting us to think what cannot be thought, to "speak" of that very thing—the noumena, the world beyond our capacity to conceive—of which we are simultaneously bid to "be silent." But how can one achieve such a self-contradictory task? 

This is where Wittgenstein introduces his concept of the "mystical," which his logical positivist followers politely disregarded, seeing as it pushes in the opposite direction of everything he had said up to that point. 

Wittgenstein suggests that the world can indeed be contemplated from outside our own consciousness. Our conciseness can, as it were, get outside of itself and look down at itself, in order to see its limits. We can simultaneously know that our world is a totality, a "whole," beyond which we cannot see, yet that it also has limits, and therefore, that there is a larger totality outside this totality (and perhaps a still larger totality beyond that one as well, which can be used to delimit it in turn—a possibility that Russell, in his introduction, seems to entertain under the heading of a possibly infinite "hierarchy of languages"). 

We cannot "speak" of this larger world, this world-beyond-our-world, that is implied in the concept of our world—our lives—as a "limited whole." Nor can we "think" of it. But it can be shown, according to Wittgenstein. And this, he says, is what we are really doing, when we have a feeling of the "mystical." 

When we regard our life as a limited whole, while occupying a conceptual position somehow outside of our own life and our own consciousness, we are regarding the world (and here Wittgenstein implicitly references Spinoza) "sub specie aeterni." We cannot describe what we see, when we regard the world from this vantage point. We cannot think it either, at least not by language. But we can—Wittgenstein implies—somehow apprehend it nonetheless. We can, somehow, experience it. "There is indeed the inexpressible," as Wittgenstein says. "This shows itself; it is the mystical." 

But what does it mean to apprehend or experience the inexpressible, if it is not in some sense to think it? What does it mean to assert that the inexpressible exists, if it is not in some sense to speak it? What else is Wittgenstein doing, in all of this work, but speaking of that which he has instructed us to be silent? 

And so, in the very act of formulating logical positivism, Wittgenstein seems to have gone beyond it. It would take philosophers a generation to catch up to even the method that he had disclosed; and longer still to realize he had refuted and discarded it, in the very process of disclosing it.