Wittgenstein's Tractatus, part 2a

Too many irons in the fire right now. So, while a massive post on Barthian epistemology (possibly broken up into a series if it keeps going on like this) and a post doing better justice to Jenson are in the works, let's get on with the next installment of Wittgenstein's far-more-interesting-to-translate-than-it-ever-was-to-read Tractatus Logico-Philosophicus, in which we consider what "what is the case" means.

What it means seems to have everything to do with Sache, and its offspring by copulation with other words. A fun little root, one that means "thing" without such material connotations as Ding, and so has more to do with events, situations, issues, "things" in the manner of conceptual entities. (Brother Ludwig is, after all, doing philosophy.) And, of course, we've already had one such offspring, Tatsachen, "what is actual," which takes after its mother. We're about to get several more.

Now, in part 1 of our series, Wittgenstein helped us to determine what the nature of the world was, and that "what is the case" is not simply the collection of all actual things, but also the logical extent of their possibilities. In other words, "the world" is not merely a synchronic set of things, but the diachronic series of sets of things by extension. And a "thing" is not merely its present existence, but also the logical scope of its possibilities. While that was implied, it's about to get explained.

Translation Notes

In section 2, Wittgenstein begins to add complexity to his description of these possibilities of things. Translating words is always tricky in philosophy, but one of the things I like about Wittgenstein is his attentiveness to the conventional meanings of words, and to clarity of speech. To do this, he plays with a number of the bastard offspring of Sache, but particularly Sachverhalt. Translation is important, here. Ogden calls these Sachverhalten "atomic facts," and apparently Wittgenstein didn't mind that turn of phrase. However, as far as I understand him, I think what brother Ludwig was getting at is more molecular than "atomic," and I'm concerned that the word "fact" has since developed problems of its own. On the other hand, Pears and McGuinness call them "states of affairs," which has its own resonance. It keeps to the sense of Sache, but pushes the sense of composition. For better or worse, I will instead be referring to these as "situations." What Wittgenstein refers to here are "situations" of actual objects relative to one another, Sachen in Verhältnisse miteinander. They are also "situations" rather than permanent states, being possibilities that are actualized in the course of time. This translation is complicated a bit by the parallel use of Sachlage, which is also "situation," but if there is a necessary technical distinction to be made between these terms, it is too subtle for me. (Corrections and clarifications are always appreciated!)

Further, in the course of this piece of text, we're going to find the important terms bestehen and Bestand. In keeping with the language of metaphysics, and the connections worth making to the classical traditions, I will translate these routinely as "subsist" and "substance." While Wittgenstein will also use the word Substanz later, the proper German terms emphasize that a "substance" is what underlies other realities, what substantiates them. Substance is not, in this way, the same as "material"; he's using this term to make a play for the most basic layer of composite reality.

Wittgenstein's text continues through a very long section 2, of which this is only the first bit. In this post I will be covering the material of 2.0.1., and stopping before we get to 2.0.2. While there will eventually be a 2.1., brother Ludwig has chosen to begin this section with several more basic points of clarification to the opening point 2.[0.], so we'll work through the first of these, going in chunks as it makes sense.

Text and Analysis
Was der Fall ist, die Tatsache, ist das Bestehen von Sachverhalten.
What is the case, what is actual, is what constitutes situations.

Der Sachverhalt ist eine Verbindung von Gegenständen. (Sachen, Dingen.)
The situation is a conjunction of objects, be they conceptual matters or material things.
Es ist dem Ding wesentlich, der Bestandteil eines Sachverhaltes sein zu können.
It is essential to a thing that it can be a substantial part of a situation.
So here we have this basic set that everything that follows here is going to attempt to clarify. What is actual, as was shown in part 1, makes up what is the case. What is actual, which goes beyond mere material things (1.1.), is what makes up the existence of situations. It is that in which situations subsist. I take this to be a direct connection between Tatsachen and Gegenständen, in that actual things, whether material or conceptual, are the substantial objects that are composed into situations.

And, as Wittgenstein clarifies, this is part of the nature of actual things, that they are parts of compositions. Rather like Lego bricks, as opposed to wooden blocks. It is in the nature of a Lego brick to be combined with others into something larger. The thing itself is not self-subsistent; what can you do with just one Lego brick? Those bumps on the top, and the spaces to grab similar bumps on the bottom, become vestigial. Ein Lego ist kein Lego. It is built to interconnect, to be the substance of other more complex things. But a wooden block can be conceived of as a monad, as self-subsistent. It may associate with other wooden blocks, or many other things, but sie werden miteinander nicht verbinden, and that interconnection is the key.

Onward! Now a section of clarification parallel to that last single point, designed in turn to clarify the one above it:
In der Logik ist nichts zufällig: Wenn das Ding im Sachverhalt vorkommen kann, so muss die Möglichkeit des Sachverhaltes im Ding bereits präjudiziert sein.
In logic, nothing is accidental; if a thing can occur within a situation, the possibility of the situation must therefore be already predetermined in the thing.
Es erschiene gleichsam als Zufall, wenn dem Ding, das allein für sich bestehen könnte, nachträglich eine Sachlage passen würde.
It would, so to speak, seem like an accident, if for something that could be totally self-subsistent, a situation were subsequently to match up to it.

Wenn die Dinge in Sachverhalten vorkommen können, so muss dies schon in ihnen liegen.
If things can occur in situations, this possibility must already be latent in them.

(Etwas Logisches kann nicht nur-möglich sein. Die Logik handelt von jeder Möglichkeit und alle Möglichkeiten sind ihre Tatsachen.)
(No logical entity can be merely possible. Logic deals with every possibility, and all possibilities are its actualities.)

Wie wir uns räumliche Gegenstände überhaupt nicht außerhalb des Raumes, zeitliche nicht außerhalb der Zeit denken können, so können wir uns keinen Gegenstand außerhalb der Möglichkeit seiner Verbindung mit anderen denken.
As we cannot possibly conceive of a spatial object apart from space, or a temporal object apart from time, so we can conceive of no object without the possibility of its being conjoined with others.

Wenn ich mir den Gegenstand im Verbande des Sachverhalts denken kann, so kann ich ihn nicht außerhalb der Möglichkeit dieses Verbandes denken.
If I can conceive of an object in situational conjunctions (contexts), I can therefore not conceive of it apart from the possibility of these conjunctions.
Das Ding ist selbständig, insofern es in allen möglichen Sachlagen vorkommen kann, aber diese Form der Selbständigkeit ist eine Form des Zusammenhangs mit dem Sachverhalt, eine Form der Unselbständigkeit. (Es ist unmöglich, dass Worte in zwei verschiedenen Weisen auftreten, allein und im Satz.)
A thing is self-subsistent to the extent that it can occur in all possible situations, but this form of self-subsistence is a form of interconnection with the situation, a form of non-self-subsistence. (It is impossible for words to behave in two different ways, one when alone and another in sentences.)
Wenn ich den Gegenstand kenne, so kenne ich auch sämtliche Möglichkeiten seines Vorkommens in Sachverhalten. (Jede solche Möglichkeit muss in der Natur des Gegenstandes liegen.) Es kann nicht nachträglich eine neue Möglichkeit gefunden werden.
If I know an object, I therefore also know the complete set of possibilities of its occurrences in situations. (Every such possibility must be latent in the nature of the object.) No new possibility can be subsequently discovered.
Um einen Gegenstand zu kennen, muss ich zwar nicht seine externen—aber ich muss alle seine internen Eigenschaften kennen.
To know about an object, I do not really need to know its external characteristics, but instead, all of its internal characteristics.
Sind alle Gegenstände gegeben, so sind damit auch alle möglichen Sachverhalte gegeben.
Along with the givenness of all objects comes the givenness of all possible situations.
The enumeration of all things involves the potential enumeration of their permutations.

Now, it's not automatically clear to me that he's right in depth, but he's got a point there. The idea that things have their possible combinations latent in them is not generally an accepted fact. It's simpler to speak of the open-endedness of the ability to interconnect, and so to deny the self-subsistence of basic elements. Wittgenstein's image goes better if you think of it as the postulate that keys do not simply happen to match up to locks, as though they developed wholly independently of one another; or that round holes and round pegs are the way they are intentionally, rather than coincidentally, so that it is of the nature of these things that they go together.

And yet what he says here does not genuinely demand this level of precise integration of thing to thing. Back to the Legos: it is of the nature of things that they interconnect. This is what I meant when I suggested that Ogden's "atomic facts" are actually molecular. It is the actual, substantial object that is atomic. And its valences, as it were, are the logical scope of its possibilities. The only "self-subsistence" such a basic object can have is the total opposite of genuine self-subsistence: situational ubiquity. A word cannot mean one thing by itself, and another in combination; it means what it means in situations, and has no abstract meaning. Only if the word means the same thing in all possible contexts is that the self-subsistent meaning of the word!

So the logical scope of basic objects, by their very nature, is a kind of possibility space of their interconnections. To keep to the atom–molecule point, think of the periodic table of elements. This is a catalog of the internal characteristics of every basic object. The chemist will, of course, not say that you can derive all possible combinations from this catalog of attributes, because it isn't really that kind of thing. For one, it is not strictly true for every instance, even though it is true on the whole. For another, it also doesn't contain all of the information that would be necessary for such a project of enumerating every possible molecule in the world. New combinations can easily be discovered that the periodic table does not imply. But, at the very least, it's a workable analogue. We know nothing about an atom in isolation, by comparison with what we know of it from its combination possibilities. And the same point applies as Wittgenstein uses it of words in sentences. Lexicography is not about finding what the word means in and of itself, but about finding out its actual valence in use. Hypothetically, if we had that, for every object, we would then be able to derive the total set of all possible situations of actuality.

Which leads on to the next clarification: things, even if they have no possibilities for combination with other things, are at least understood to be missing that. It's not a bonus that some things connect, but a deficiency that some do not. The "noble" gases, for example, are noteworthy because they do not (by and large) interact with other atoms or molecules. So:
Jedes Ding ist, gleichsam, in einem Raume möglicher Sachverhalte. Diesen Raum kann ich mir leer denken, nicht aber das Ding ohne den Raum.
Every thing exists, so to speak, in a space of possible situations. While I can conceive of this space being empty, I cannot conceive of the thing without the space.
Der räumliche Gegenstand muss im unendlichen Raume liegen. (Der Raumpunkt ist eine Argumentstelle.)
The spatial object must lie in an infinite space. (The geometric point, here, is the locus of an argument.)

Der Fleck im Gesichtsfeld muss zwar nicht rot sein, aber eine Farbe muss er haben: er hat sozusagen den Farbenraum um sich. Der Ton muss eine Höhe haben, der Gegenstand des Tastsinnes eine Härte, usw.
The spot in the visual field need not really be red, but it must have a color; it has, as it were, a color-space around it. Likewise a tone must have some pitch, a tangible object some hardness, and so forth.
Objects exist in contexts in which they make sense. The identity of the object in terms of its characteristics depends on there being a logical scope of those characteristics into which the object fits.

So far, what is the nature of a thing? The basic object of the universe is: a substantial part of larger combinations, which combines with other things on the basis of its internal characteristics, and can be described as belonging to certain contexts, along with other similar things, according to those characteristics.

And now a recap, by way of final clarification:
Die Gegenstände enthalten die Möglichkeit aller Sachlagen.
Objects contain the possibility of all situations.
Die Möglichkeit seines Vorkommens in Sachverhalten, ist die Form des Gegenstandes.
The possibility of its occurrence in situations is the form of the object.
In other words, while situation may be an externality, all situation originates with the objects themselves. Situations are not a tertium quid over and above the objects so situated. (Interesting possibilities for classic Western Trinitarian thought there…)

Having said so much in the middle, I'm going to leave off here, and if there are comments, we can play with this more below. Thanks for sticking with me!


  1. Are taxonomic categories, these "possibility spaces" based on internal characteristics, a kind of situatedness with other objects?


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