On Philosophia Mechanica

‘World, Fact, Case’ explained.

Title illustation

To common knowledge, a joke explained is a dead joke. However, apparently it’s totally accepted and “ok” to explain a mechanical joke. As our last installment was pretty much a mechanical joke (it even has a crank!), we may thus feel free to do so. And, as we’re feeling like it, we’ll attempt to do so…

As you, the all-knowledgeable, well informed, ideal reader, being the picture of civility and erudition that you are, will have readily observed, this scaffold of sentences was nothing but the beginning of Ludwig Wittgenstein’s “tractatus logic-philosophicus” (yes, it’s all lower case in the German original.) To be precise, it’s the entire first “chapter”, comprising proposition #1 and all its direct dependencies.

It’s a reasonable beginning, starting with some reasonable facts, which are hard to argue against.

Here, provided as

  1. The revised translation by D. F. Pears and B. F. McGuinness, first published in 1964 by Routledge & Kegan Paul, revised in 1974 based on Wittgenstein’s own comments and suggestions regarding
  2. the original English translation by C. K. Ogden, assisted by F. P. Ramsey, published also by Kegan Paul in 1992 in a bilingual edition,
  3. and the German original, Wittgenstein’s own words.

The Pears/McGuinness version of the text in normal writing, the Ogden/Ramsey edition in small capitals, and the German original in italics.

There seems to be not much to write home about, even the translations are pretty much in synchronization (we’ll see later where they begin to fall apart). However, we may appreciate much of the aesthetic fascination that is emanated by the tractatus: A precise wording, which starts with indisputable facts, a monolithic text, but also, despite the apparent lack of preconditions (which is quite deceitful, as there are a ton of imports in this), an opaque one, and, thanks to the index numbers, which arrange the individual propositions by logical weight and dependency, a pretty neat one, as well.

The beginning is one of the best ones imaginable. Starting with the world makes a great beginning, and referring to it as being the case and, more precisely, being the totality of what is the case, is not only an as positive as bold statement but also newer wrong. Jokes aside, there’s already work done. By the first sentence we already know that this is both about positivist philosophy and transcendental philosophy. Written, as Kant put it, sub specie aeterni and its realm is that clear and bright space that is the reign of logic. To be sure, facts become separated from things, the mess found in the real. And, it’s a constituting quality of facts that they can be the case or not the case, so their primary value is a logical one. Which finally constitutes this world as a totality in logical space.

This is also, where the original manuscript ends on the first “chapter”. The next two sentences were added in the lost diary IIa, meaning, they are not in diary II, but they are already (just) there in diary III. In the extensive genealogy of the tractatus, consisting of the first unnumbered core structure (just sentences 1,2,3,4,5 and 6), the Ur-Tractatus, Core-Prototractatus, proto-Prototractatus, Prototractatus, and the final corrections, we’re near the final arrangement of the proto-Prototractatus: the incorporation of diary IIa into the text, done in 1917, while on a stay in Olmütz, having returned from the Brussilow offensive in Galicia. So we know when they were added into the manuscript, but we do nothing about why and how they came into being, in the first place, as the diary that would have comprised them is lost. So, they are pure text, standing on their own feet:

Proposition 1.2 apparently doesn't add much to what has been achieved already. It clarifies. (Also, we learn, composition and analysis are the same, which will become important later.) But then, there is,

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

Again, this may look like a clarifying reprise of what has been said already, but there is much more to it. First, it declares facts to be independent from each other. Moreover, it refers to a greater everything, which ‘remains the same.’ What these two sentences achieve is separating facts from structure. (We may notice that Pears/McGuinness are emphasizing this separation more than Ogden/Ramsey do in their translation.) Which is important, since this is very much a book about structure, about what it may mean to look into this abyss spanning facts and structure, and if there may be anything learned from this.

However, this last proposition is also peculiarly askew, even tangential to what has been said before. While it does do quite some work, it is not apparent, how this is done.

Wittgenstein is writing this much from a anglo-german position, where the interest in language is an interest in propositional logic. However, this is not the only perspective on this, as there is also the franco-swiss tradition, which became the core of the linguistic turn. Namely, there’s Ferdiand de Saussure, born in 1857 and reading lectures on comparative linguistics at the university of Geneva from 1891 until his death in 1911. Transcripts of these lectures (spanning 1906 to 1911) were eventually published as the Cours de linguistique générale, five years after his passing in 1916. Notably, in this tradition, the value of a sign is only determined by the totality of the structure, which is language. There are two axes to this, a horizontal one, along which we align and compose things, and a vertical one, where we substitute one ‘thing’ for another — and is only the totality of what compositions and substitutions are legitimate (meaning, understandable to others) and which are not that these ‘things’ and their compositions have meaning. The signified is famously “sliding” under signifier in this ever-changing structure.

This is really a great divide: you can choose either way, here propositional logic, there the linguistic turn, but you cannot have both.

Wittgenstein, unaware of this (we cannot blaming him for not receiving the latest news amidst the cruelties that were World War I), is here proposing a system, where we may ‘switch’ facts (concepts) on and off independently, while not affecting the structure of “everything else”, which is apparently entirely separate from this.

From the point of view of the franco-swiss tradition, we had to ask, « Oh Monsieur, celui ca, this must be one of your famous ‹puns›, n’est-ce pas ? » — As this doesn’t make sense at all.

While Wittgenstein introduces this without further precedence or substantiation, by this also beginning to squeeze the world.

So, as we have given away our little joke, already, we may risk a glance at what follows immediately after this, as well. Which is also what followed immediately after proposition 1.13 in the earlier states of the manuscript. Here, we learn about Sachverhalte and Gegenstände and how they are composed, and it’s not before proposition 2.034, several pages later, that we meet facts again, now embedding themselves into an established concept of structure. Notably, this is also where the two translations fall apart — and there is a reason for this.

There’s quite a remarkable difference between “atomic facts” and “state of affairs”. Not only are these different concepts, they also come from entirely different realms. Ogden/Ramsey (in small capitals) are trying too much to be precise, aligning the idea of “atomic facts” in hierarchy with the concept of “facts” that has been already established. However, this doesn’t end well, as in propositions 2.02 and 2.021, we learn, “Objects are simple. (…) Objects make up the substance of the world. That is why they cannot be composite.“ (Der Gegenstand ist einfach. (…) Die Gegenstände bilden die Substanz der Welt. Darum können sie nicht zusammengesetzt sein.) So, if objects (Gegenstände) are the atomic building blocks of the world (not subject to any further analysis), how are atomic facts be composed of them and still be atomic?

Pears/McGuinness are a bit better about this, suggesting “state of affairs”, a political or diplomatic term, which is nearer to the German concept, but just somewhat “ok”. However, neither attempt is really to blame, as this is utterly untranslatable. There is simply no English concept for Wittgenstein’s “Sachverhalt”.

This is, because “Sachverhalt” is a juridical term of positive law. It comes in a pair, and its counterpart is “Tatbestand” (which doesn’t make an appearance in Wittgenstein’s text.) Famously, Wittgenstein was inspired for this very section by the court proceedings of a traffic accident, namely, a model to illustrate the particulars of the scene, the position of the vehicles involved, etc. In positive law “Tatbestand” is the ideal concept of a specific deed, an act of crime. It’s what categorizes acts of crimes by their determining features and attributes. Like “Sachverhalt”, this is pretty much untranslatable (Google Translate suggests “facts”, which may be entirely confusing in this context) and is a compound of “Tat” (deed, act) and “Bestand” (totality of an inventory, that what is in existence). “Sachverhalt” is its messy brother of the real world. It comprises all that has been observed and found about a specific act, all its accidentals, that what may be established about a specific act of crime in court. The task and duty of the court is to match the ideal “Tatbestand” defined in the codex of law and the empirical “Sachverhalt” and to assign an appropriate punishment, if these are found to match. (BTW, punishing the crime and not the criminal.) We may be enticed to translate “Sachverhalt” by circumstance, but this won’t do either, as circumstances are determining, are causing a “Sachverhalt”, which is a configuration that may be observed. The important part is really that this is one part of pair, and that its twin counterpart is somehow missing. And, that this is a term born out of a duality of an ideal description and the requirements to match this with an empirical description.

This requirement introduces an important split in the anglo-german tradition with the anglo-saxon tradition of common law on the one hand and the German tradition of positive, codified law on the other hand, which relates back to the tradition of ancient Roman law (as in SPQR). A split, which has its impact on philosophy, causing an anglo-german schism in empiricism that can be traced back to Kant and Hume. (For common law, there must be some natural interest or even instinct, which turns us towards this system and by this regulates it, in codified law, this is pretty much a quality maintained in the ideal structure that is the system of law, which must be protected from any contradictions at all costs.)

What is of note here is that these objects are not the messy objects found in the real world, these are the atomic entities of descriptions. They are without attributes, as external properties are external to them. (As pointed out in 2.0232, “In a manner of speaking, objects are colourless.”) According to Wittgenstein, the substance of the world cannot determine material properties, it just determines form — and objects are, what constitute form, they have logical form. This suggests a curious duality, a duality, which has been already drawn on in the introduction of ‘facts’, their separation from “everything else” and their now established counterpart of “Sachverhalte” and their atomic components, objects.
Notably, Wittgenstein’s fact, Tatsache, is a portmanteau, which already comprises ‘objects’ (Sachen) as they are introduced as “Gegenständen (Sachen, Dingen)” and also alliterates to “Tatbestand” (as in Tat-), but are much more down-to-earth than the juridical term, translating perfectly to “facts”. This rhyme, Wittgenstein’s choice of words, already provides a ghostly image of the structure behind these concepts.

The specific position, from which Wittgenstein’s text emerges as these terms are employed, is the very split in the anglo-german tradition. This is his very high-ground, consisting of not more than a hiatus, from where he delivers his blows left (Russell) and right (Frege), from where he constructs his investigation by definitions.

The space established by ‘facts’ is the clean, logical space of codified law. Its facts adhere to inner structure, which doesn’t allow for any contradictions. While we can perfectly well grasp the meaning of the sentence about the King of France, who is bald, in ordinary language (while knowing that there is only a president of France), the same sentence, is entirely without sense as logical proposition. It simply doesn’t exist thanks to the inner structure, which makes the world. So, can we peek into this abyss? Is there anything looking back at us?

In other words, can we say anything about this structure, as in an investigation into what regulates the structure? However, there is just structure and facts, which make propositions, and these are entirely separate, as we have established in “and everything else remains the same.” There is no way around this, and, to be sure, we make short work of Russell’s theory of types: there is no essential hierarchy to propositions, therefor, there is no structure to describe this structure. Propositions can only show aspects of the structure, but they cannot say them. The structure becomes only apparent, “manifests” itself in precious moments, it may be experienced, but nothing of logical value may be expressed about it. We cannot express from the inside the form of the outside, as the entirety, the world as a whole, is not part of what is contained in and by this entirety, which is the world. While the form of this structure, which ist the world as a whole, may be experienced as “the mystical”, in terms of sensical expressions it doesn’t even exist as a riddle. It is not a question that may be asked, as there is no answer to it. And this is namely the question regarding ethics, which was eventually discarded from the final text. At a certain stage (the Bergen-Oxford transcription of the Nachlass, the ending of the book was,

In the book as published, 6.2 started the investigations into mathematics as a logical method, which finally give way to a more moderate expression of the same thought, but in reversed order:

So while making a strong case for the specific form of the tractatus, there is nothing of importance to write home about, because there is no way, we could write about it at all, home or not. Which is, sadly, also about the only thing Wittgenstein would have been interested in writing home about. We can’t demonstrate by language how to conjure something to become manifest. (This kind of instruction is left to J. K. Rowling.) A frustration, which expresses itself in the proposition just before the very last and famous one.

But I’m pretty sure, what we cannot speak about we’re still allowed to be played with… ;-)