Any foundationalism has to posit basic items to which the rest of its discursive universe is to be reduced. Those items are then said to be the starting points for transparent theoretical constructions that capture the structural nature of this domain. Logic, as conceived by the early Wittgenstein, is supposed to give a once-and-for-all account of the regularities underlying any possible state of affairs. It can - and must - furthermore be brought to an end as a matter of principle and independently of empirical investigations. I shall call this Wittgenstein's ``master thesis'':
Wenn sich die Logik ohne die Beantwortung gewisser Fragen abschließen läßt, dann muß sie ohne sie abgeschlossen werden. ( Notebooks 4.9.1914)
It follows that logic has to take care of itself (cf. Tractatus 5.473). But what about those ultimate building blocks from which, by applying logical procedures, a correct description of the world is to be constructed? We do not simply stumble upon atomic constituents of the universe. One of the guiding ideas of the early Wittgenstein is that we should be able to reach such constituents as the outcome of an appropriate process of analysis.
This much is obvious from the Tractatus, but, taking a closer look at Wittgenstein's Notebooks it is not at all obvious how his reductionism is to be understood. Wittgenstein spends a considerable amount of time discussing a peculiar difficulty. How is one to know that an analytical process has reached its end? It can hardly be obvious at the time the investigation starts. But there is nothing about the process itself that can determine at what stage it can or should be stopped. We seem to need some outside intuition enabling us to determine that we have successfully arrived at our destination. But then again: if we depend on such assurances we do not seem to take analysis seriously enough. We could just state those intuitions and spare ourselves the trouble of pretending to discover our projected presuppositions by empirical means. These worries might strike you as overly sophistical and they have certainly been absent from most discussions of the Tractatus. This is, however, a serious omission. His Notebooks show Wittgenstein to be very much aware of that kind of difficulty. They do, in fact, contain a theory of analysis that is much more sophisticated than most logical positivists would have been prepared to accept.
Consider a sentence like ``This chair is brown'' or take any ordinary watch. Such expressions or things are, on the face of it, composite entities.
Jedenfalls gibt es also einen Prozeß der Analyse. Und kann nun nicht gefragt werden, ob dieser Prozeß einmal zu einem Ende kommt? Und wenn ja: Was wird das Ende sein??'' ( Notebooks 9.5.1915)
It has been suggested that Wittgenstein's basic givens were to be sense data, but no conjecture concerning his opinions at that time can be oblivious to the following problem. What sense data are to be picked out as the elementary ones? Knowing the right kind of elementary entities does not help in deciding which entities are in fact the required outcome of the process of analysis. What exactly are the basic components of a watch? Wittgenstein offers no help in dealing with such particular questions. His strategy is, rather, to turn the problem upside down. If we want logical closure, we cannot trouble ourselves with this kind of empirical uncertainties. There has to be another way to explain the workings of analysis.
The crucial observation is the following one:
Muß aber nicht die Logik eines scheinbaren Subjekt-Prädikat-Satzes dieselbe sein wie die Logik eines wirklichen? Wenn eine Definition überhaupt möglich ist, die dem Satz Subjekt-Prädikat Form gibt? ( Notebooks 7.9.1914)
Assume that the sentence ``This chair is brown'' is to be decomposed
into its elementary constituents. In this case at least the following
is known in advance of any empirical scrutiny: eventually we are going
to end up with a couple of expressions whose logical form is going to
be based on elementary predication. If this were not the case we would
be at a loss in recoginzing the required link to the analysandum. How
could one imagine ascription of properties to be analysed
into, e.g. concatenation of terms? If elementary logic might happen to
have a structure hitherto unknown to us, Wittgenstein's master thesis
would have to be rejected. His argument is a reductio ad absurdum:
since it is unacceptable to let experience determine logic, the
possible forms of sentences have to be given in
advance. `` Jeder einfache Satz läßt sich auf die Form
bringen.'' ( Notebooks 16.4.1916) And what about
everyday sentences?
Es ist ganz klar, daß ich tatsächlich dieser Uhr, wie sie hier vor mir liegt und geht, einen Namen zuordnen kann und daß dieser Name außerhalb jedes Satzes Bedeutung haben wird in demselben Sinne des Wortes, wie ich es überhaupt jemals gemeint habe. Und ich empfinde, daß jener Name in einem Satz allen Anforderungen an den `Namen des einfachen Gegenstandes' entsprechen wird.'' ( Notebooks 15.6.1915)
Apparent names and real names fit into the same logical pattern. Analysis can only lead us from somewhat inarticulate to more determinate instances of ``things'', ``properties'' and ``relations''. It seems to run a circle.
To put it bluntly: analyzing a watch one presupposes that the ultimate components this analysis arrives at will be components of a watch. There is all the difference in the world between analysis and disintegration. The analytical process must not be thought of as a linear exploration, starting from a complex given and coming to a natural end when its simple ingredients are discovered. An analysis has to include two structural characteristics: a method to take something apart and some criterion determining when to stop. To analyze an item implies an overarching committment to search for the basic constituents of this item. Or, putting it the other way round, basic constituents are presupposed by the notion of an item's analysis.
Es scheint, daß die Idee des EINFACHEN in der des Komplexen und in der Idee der Analyse breits enthalten liegt, so zwar, daß wir ganz abgesehend von irgendwelchen Beispielen einfacher Gegenstände oder von Sätzen, in welchen von solchen die Rede ist, zu dieser Idee kommen und die Existenz der einfachen Gegenstände als eine logische Notwendigkeit - a priori - einsehen ( Notebooks 14.6.1915)
According to this insight logical investigations are essentially independent from ontological specifications of the universe. They may just posit simples.
Wenn wir auch die einfachen Gegenstände nicht aus der Anschauung kennen; die komplexen Gegenstände kennen wir aus der Anschauung; wir wissen aus der Anschauung, daß sie komplex sind. - Und daß sie zuletzt aus einfachen Dingen bestehen müssen? ( Notebooks 24.5.1915)
Wittgenstein puts a question mark behind his last sentence. It seems an
audacious move to derive the existence of simple things from
reflection on the concept of analysis. But there hardly is an
alternative, given Wittgenstein's master thesis: ``Es kommt uns ja nur
darauf an, die Logik abzuschließen '' ( Notebooks
7.9.1914). Seen against this background Tractarian ontological
neutrality makes good sense. This book's ``reductionism'' is a
by-product of Wittgenstein's idiosyncratic urge to complete his
``Logic'' once and for all. We have, however, looked behind this
surface and are left with an unresolved problem. Wittgenstein's talk
about elementary propositions and states of affairs lacks any
acknowledgement of the analytical procedures he did worry
about in the Notebooks. There is, consequently, no obvious
Tractarian treatment of how ontological reduction is to be
achieved. A second line of thought from the Notebooks is
required to get the whole picture.
Wittgenstein is puzzled by universal quantification.
SCHEINT dem Inhalt des Satzes näher zu stehen als der Form. ( Notebooks 20.1.1915)
A sentence containing general claims is considered to be true if all the things it talks about actually conform to its assertion. The Fregean tradition offers quantification as a logical tools to clarify this intuition. Now, logic has to be cut off from empirical concerns according to the early Wittgenstein. It cannot be grounded in worldly circumstances. But this makes it very difficult to understand how general claims work within language. Their analysis apparently needs some semantical account, yet, for well-known reasons, formal semantics is unavailable to Wittgenstein. His treatment of quantification puts him squarely against logical orthodoxy, a fact that has frequently been ignored. To cut a long story short: Since Wittgenstein rejects talk about how language relates to the world as ultimately meaningless he cannot accept anything like a theory of reference or satisfaction and has to renounce the apparatus of quantification. He is quite clear about this: ``Ich trenne den Begriff Alle von der Wahrheitsfunktion.'' ( Tractatus 5.521) The Tractatus does not include the predicate calculus. This is a fascinating issue in itself, but how does it relate to our topic?
The short answer is this: The question of analytical decomposition is linked to Wittgenstein's treatment of generality via his picture theory. Reductionism meets holism as Wittgenstein designs an intricate construction to join elementary propositions to his non-standard account of generality. This answer has, of course, to be spelt out, which will produce the Wittgensteinian solution I promised at the end of the first section. So, where does the picture theory fit in? We may start by observing that it's intuitive appeal rests entirely on ignoring the distinction between elementary and complex propositions. A score and a record of a musical performance ( Tractatus 4.0141) or puppets representing the result of a car crash ( Notebooks 29.9.1914) are certainly composites. Puppets are complex objects just like the chairs and watches that served as examples in Wittgenstein's reflections on analysis. Yet, the Tractarian picture theory is - on the face of it - untroubled by doubts about the basic legitimate constituents of pictures (and the reality they picture). We saw that logical analysis of a sentence like ``The book is on the table'' does not distinguish between apparent and genuine subjects and predicates. (Cf. Notebooks 20.6.1915) Wittgenstein does not seem to distinguish between elementary and complex depiction either.
But this cannot work and the reason is precisely sentences containing general claims. Suppose we had gotten hold of a specimen of an elementary proposition and that we could identify the fact it was picturing. This would give us some ultimately simple items, call them alphas. Now, how would a pictorial element designating some alpha feature in generalised sentences? How could we get from one-at-a-time elementary propositions to claims covering the universe of discourse in its entirety? This, obviously, is a crucial juncture, confronting reductionism and a general view of the world. The answer, in the present context, is that it cannot be done within picture theory as it is commonly understood. If an alpha's name is linked to an alpha in the course of elementary depiction that's all there is to this expression. We have no clue on how to designate any general feature its designatum might possess. Given a universe including cars as basic things, to single out a car could not by itself include knowledge of its type or manufacturer. In picturing a fact comprising alphas we miss all the information on alpha's possible roles in different pictures. Elementary propositions cannot provide this kind of knowledge.
So, whereas Wittgenstein could remain fairly neutral on ontological matters, the setup regarding generality does not allow him to employ the same strategy towards his picture theory. He has to provide a conceptual tool explicitly embracing low-level and high-level points of view. This is the purpose of Wittgenstein's introduction of proto-pictures.
Unser Einfaches IST: das Einfachste, was wir kennen. - Das Einfachste zu dem unsere Analyse vordringen kann - es braucht nur als Urbild, als Variable in unseren Sätzen zu erscheinen - dies ist das Einfache, welches wir meinen und suchen. ( Notebooks 11.5.1915)
This brilliant touch allows Wittgenstein to resolve the tensions within his accounts of analysis and generality with one single stroke. A proto-picture is the common feature shared by all pictorial uses of one single sentential component. The proto-picture of an alpha is what all propositions containing its name have in common. I will not bother you with a discussion of the formal apparatus necessary to handle the syntax of proto-pictures.9 Suffice it to say that Wittgenstein introduces the notion of a ``sentence variable'' i.e. a variable whose values are precisely the sentences containing a particular expression. You may think of a ``sentence variable'' as an indicator of one common feature characteristic of all the sentences in its range of values. This feature is, in turn, a general description of the circumstances appropriate for a given expression. The world shows itself by means of proto-pictures.
Der Gegenstand, von dem die allgemeinen Sätze handeln, ist recht eigentlich die Welt; die in ihnen durch eine logische Beschreibung eintritt. ( Notebooks 29.10.1914)
The general structure of the world is mirrored by a pattern of variables serving as dummies for sets of actual sentences and Wittgenstein's ``logical description'' is tantamount to elaborating - for each thing - what can only be shown, namely what contexts it essentially belongs to. Its nature, if you like.
Can this construction really solve the problem of ultimate simples? ``Sentence variables'' seem empty constructs unless one actually provides their values and Wittgenstein does not even begin to try. How can we get a hold on proto-pictures, if we don't know the composition of elementary propositions? This an entirely intelligible objection which, nevertheless, misses Wittgenstein's crucial point. Remember his master thesis, i.e. the requirement to complete logic independently from empirical investigations. Basically, he does not care about what the simplest building blocks will turn out to be. But he does offer an attractive procedure to deal with whatever is going to be taken as simple within the overall picture of how such elements hang together to determine the world as a whole. His proto-pictures are a device to capture the world's logical form, regardless of its actual content. Since Wittgenstein has denied himself the opportunity to mark the general structure of the Tractarian universe by either quantification or semantical ascent he has to employ this kind of syntactical infra-structure to carry the information more commonly conveyed by explicitly quantified statements. No matter where analysis is going to lead us to, we know in advance how to handle the dependence between its eventual results and all the contexts relevant to (re-)construct a valid description of the world from those results.