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TRACTATUS PRINCIPIO

A PHILOSOPHICAL TREATISE

The Logic of Words

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A Treatise on Wittgenstein and the Speech Act

English-language edition

DOI: 10.5281/zenodo.24119877

Contents

At the Point of Contact

1Let us place a hand against a windowpane. At first, there seems to be little in this small act that requires explanation. Here is a hand, there is a pane of glass, and a contact occurs between them. We feel the cold of the glass, the resistance of its surface, and perhaps the edge where the pane meets its frame.

2Yet on closer inspection, we have already made a surprising number of decisions. We speak of a hand, a pane, and a contact as though we had three ready-made determinations before us that merely needed to be brought into relation. But contact itself enables us to examine this apparent self-evidence. What do we perceive when a finger moves across the glass? Where does the pressure change? At what point does the smooth surface end? And what makes the hand experienceable as touching, the pane as touched?

3The answers do not simply lie upon the glass as mutually independent properties. They become determinable within the relations we follow in touching it. The edge emerges where a particular distinction can be drawn. A different question can make a different relation visible at the very same place.

4This is where the Tractatus Principio begins: not with the pane that has already been named, nor with an observer confronting a finished world, but with the difference through which anything can appear as something determinate in the first place. The simple stroke | denotes distinction itself. In the notation A|B, its two poles become legible. And |(|) indicates that the distinction itself can once again be distinguished.

5We should not imagine these three notations as three moments in a story of origins. They do not describe a temporal sequence in which a stroke appears first, two objects later, and an observer finally. They keep apart different orders of the same act, orders that remain operative within one another. The observer’s position, too, belongs to this connection. In our contact with the pane, we experience not only a boundary of the glass but also the relation in which the touching and the touched become distinguishable for us (Volume I, Ch. V; Volume II, Ch. XVIII; Volume IV, Chs. I and XIII).

6For a windowpane, this may initially seem a considerable amount of theoretical effort. But the question it brings to light reaches further: what, exactly, has already been presupposed when we say that something is the case?

How Something Holds

1Let us run a finger along the same edge a second time. The pressure may change, the movement of the finger is different, and yet the boundary between glass and frame can be determined again. This is not the repetition of a perfectly identical moment. What persists is an order that remains legible under further distinction.

2Here lies the concrete meaning of stability within the Principio. A determination does not prove itself by having to exist as a finished thing outside every further relation. It proves itself insofar as its relevant order is preserved as distinction continues. Two observers may feel the edge in different ways, compare their perceptions, and establish which relation they can jointly take up again. Their agreement, too, must therefore be tested by whether further determination remains possible (Volume IV, Chs. III and XIII).

3The windowpane offers a second observation. If we initially ask only whether the window is closed, the distinction between closed and not closed is enough. For this question, we have already found a useful order. But what exactly does not closed mean?

4Within it, we can distinguish a tilted window, one left ajar, or one opened wide. In the case of a tilted window, we can ask in turn about the width of the gap or the manner in which the sash is held. Each new determination proceeds from a relation already distinguished and, at the same time, opens up further possibilities for distinguishing it.

5Volume I of the Tractatus Principio calls the initially open opposite side of a determination non-A. From the distinction between A and non-A, it does not yet follow that non-A must already be a pole B determined in itself. Such a B only takes shape in a further distinction (Volume I, Chs. I–II).

6This is more than a linguistic subtlety. Whoever treats the still-open side of a boundary as an already fully determined object has quietly disposed of a question that has not yet been answered. They now supposedly know what lies on the other side, although all they have distinguished so far is that it is not the same side.

McDowell and the Conceptually Given

1This difficulty touches on another philosophical dispute: the question of how perception can become a reason for a judgment at all.

2In Mind and World, John McDowell examines the relation between experience and conceptual thought. An external stimulus may cause a judgment. But a cause is not yet a justification. The fact that something elicits a response in us does not, by itself, explain why we should be entitled to make a determinate claim about it. McDowell therefore opposes the so-called Myth of the Given: the idea that a merely nonconceptual impression could already perform the justificatory role that belongs to a judgment.

3His answer is not simply to declare our perception worthless. Rather, in his view, conceptual capacities are already operative in experience itself. They belong to a human being’s acquired second nature. Experience can thus have conceptual content that matters for a judgment (McDowell, Lectures I and IV).

4But what happens when we place our hand against the glass once more?

5Someone who already knows what a windowpane is can direct their attention specifically to its edge. The learned concept helps guide the inquiry. Yet whether a transition can actually be felt at that point, how the resistance changes, and what relation thereby becomes determinable only appear in the act of touching. The concept does not perform this distinction for us.

6Volume II of the Principio describes perception as self-measurement at a boundary. Within it, the touching and the touched become legible as poles of the same relation (Volume II, Ch. XVIII). The question thus concerns a presupposition that lies prior to the attribution of conceptual content. Prior expressly does not mean an earlier second in time. What is meant is the explanatory priority of the distinction through which a perception can be determined as a perception of cold, pressure, or an edge at all.

7This is precisely where the Principio’s objection begins. McDowell asks how an experience already possessed of conceptual content can justify a judgment. The Principio asks what makes that content itself determinable.

8In McDowell, the Given returns as something conceptually determined. This does not simply refute his argument. But from the perspective of the Principio, the question of the distinction from which that determinacy arises remains open. We have received an explanation of justificatory content, but not yet an explanation of its original determinability.

What We Do with Words

1“The window is tilted open.”

2A simple sentence. Its words follow one another, and yet they refer to a connection that we can equally draw, point to, or feel by touch. In a sketch, the position of the window sash relative to the frame can be represented by lines and angles. The spoken sentence, by contrast, carries out its description in a temporal sequence of words.

3Both representations can refer to the same position. But how do we recognize which position is meant? A drawing from the front may almost conceal the gap, whereas in a side view the gap becomes the decisive feature. Only when we compare the representations does it become clear which distinction they must bear in common.

4Volume III describes language as the temporal projection of difference. What is mutually determined within a relation appears in speech as a succession of words. This succession can express the connection, but it is not identical with it. Different linguistic and pictorial readings can be made of the same relation (Volume III, Ch. XI).

5A familiar example shows just how much the meaning of a sentence depends on how it is read:

6“I always lie.”

7At first, the matter seems unambiguous. If “lying” is understood as saying what is false and the word “always” includes the present utterance, the sentence cannot be true. If it were true, it would itself have to be a lie as a present utterance.

8But the examination does not end there. If the sentence is false, at least one of the utterances covered by “always” must be true. If only the present utterance is eligible, we encounter the contradiction again: that very utterance would then have to be true. If, on the other hand, an earlier true statement is included, “I always lie” can simply be false without the same paradoxical self-reference arising.

9The sequence of words has not changed. What has changed is the determination of what “always” refers to.

10Here we can observe a linguistic reading making itself the object of a further distinction. We examine not only a claim but also ask which statements we have included within its scope. In this connection, Volume III describes consciousness as a double relation: one relation describes the world, while another observes that description (Volume III, Chs. VII and XI; Volume IV, Ch. XIII).

11It by no means follows that logical inferences are arbitrary. Within a particular reading, they may be necessary. But establishing the reading under which such an inference holds is itself a distinction. It does not disappear simply because we subsequently calculate with its results.

How Order Becomes a Supposed Ground

1We now reach the central subject of this polemic: Ludwig Wittgenstein’s Tractatus Logico-Philosophicus.

2Wittgenstein begins with what is the case. The world is determined by existing states of affairs; simple objects constitute its fixed substance. A meaningful proposition can depict a possible state of affairs because proposition and reality share a logical form. It is precisely this form that makes representation possible, even when what is represented does not actually obtain (1–2.01, 2.02–2.0272, 2.18–2.225, 4.01).

3This is a demanding explanation. Its fixed basis is intended to make it intelligible how a proposition can have a determinate sense without thereby already being true. It would therefore be too simple merely to accuse Wittgenstein of having asserted things that cannot be seen. Logical form performs a particular task within his account.

4The dispute concerns the direction of explanation.

5Take our statement about the tilted window. We can compare it with a sketch and, finally, with the position of the actual sash. To do so, we must determine which relation supports the comparison: for example, the angle of the sash relative to the frame. Once this distinction is sufficiently stable, we understand what is being claimed by “tilted open.” We can even understand the sentence when the window is, in fact, closed.

6From the Principio’s perspective, the explanatory work here lies in the determinability of a relation and our ability to take it up again. Wittgenstein makes shared form a precondition for the possibility of representation. The objection is that this precondition already lays claim to the very determinacy whose emergence we must first investigate.

7What shows itself as a stable order in the act of distinguishing and comparing appears in retrospect as a framework that was supposedly already in place before any such act. This is reification by the back door.

8The shift begins with the very question of which objects make up the world. Whoever asks it has, in principle, already posited as units those things of which the world is supposed to consist. Any further inquiry can then determine how they are connected or which states of affairs arise from them. What falls out of view, however, is how anything acquires the status of a determinate unit in the first place.

9Our windowpane is an almost inconspicuous example of this. First we distinguish it from the frame. Next we can regard it as part of a window sash, whose position is in turn determined in relation to the frame. The unit sufficient for one question is part of a different connection for the next. Whoever begins with finished units passes over the distinction from which their respective determinability emerges.

10The same difference becomes apparent in the case of number. Wittgenstein develops number as the exponent of an operation, whose continuation is determined by the form of a series. The Principio first asks how, in the self-reference of distinction, a step becomes legible as this particular step at all (Wittgenstein 5.251–5.2522, 6.02–6.021; Volume I, Chs. V–VIII).

11This does not abolish mathematics, any more than it abolishes the meaningful description of a window. Only its explanatory point of departure is shifted. Stable form remains useful. But that does not mean it must be the origin of the relation in which it receives its determinacy.

Who Performs the Promise?

1The question of this determinability becomes especially clear when we move from individual statements to linguistic actions.

2What does it mean to promise someone something? We might answer: it means to undertake an obligation. But what does it mean to undertake an obligation? To make a commitment on which another person is entitled to rely. And what do we call a commitment, or justified reliance on another person’s words?

3With each explanation, we arrive at further expressions whose meaning can in turn be explained. Language has, in this sense, a recursive structure. We can explain one word by means of others, but this does not remove the connection within which the explanation becomes intelligible. On the contrary, even the word “meaning” calls for a determination of its use.

4Consider a sentence:

5“I promise you that I will come tomorrow.”

6Two actors stand on a stage and speak these words during a rehearsal. The sentence belongs to the characters they portray. But the same actors can use it in the same room as a personal promise. In both cases, we hear the same sequence of words. What differs is the relation in which it stands to the situation and to the participants.

7Anyone listening must be able to recognize whether a character is speaking or someone is personally assuming an obligation. This determines who may actually count on whose arrival the following day. The words alone do not carry this distinction as a hidden property within themselves.

8Volume III treats language as the temporal projection of difference. In speaking, a relation is carried over into the sequence of words; in listening, that sequence is read in terms of a particular relation. The observer can then also examine their own reading. Had the rehearsal been interrupted? Was the actor still speaking in character? Was a personal promise made? Each of these questions distinguishes the connection anew (Volume III, Chs. VII and X–XI; Volume IV, Ch. XIII).

9The later Wittgenstein brings speaking itself into proximity with an activity and a form of life (Philosophical Investigations, § 23). J. L. Austin examines the conditions under which an utterance is performed as a linguistic action and distinguishes its use on stage from its ordinary use. John Searle likewise asks about the conditions under which an obligation is undertaken by an utterance; these include the recognizability of the speaker’s intention (Austin, Lectures II and IX; Searle, Ch. 3, §§ 3.1 and 3.3).

10These approaches take the performance of speaking seriously. The Principio’s objection therefore does not simply rest on the claim that no one has ever taken account of the situation of an utterance. It goes one step further: the rule by which we distinguish a rehearsal from a binding promise must itself be understood and applied within the respective situation. Its expressions are, in turn, the possible objects of another distinction.

11A rule does not bring the recursion of language to an end. It participates in it.

12Whether words count as a binding promise is determined within the relation in which the observer understands them. Whoever attributes the performance solely to the uttering of the words turns such a relation into a property of the sequence of words. And thus we face the same confusion that we encountered at the windowpane: the stabilized result appears as its own ground.

Kripke and the Shared Rule

1How far this difficulty extends is shown by Saul Kripke’s reading of the later Wittgenstein.

2Imagine someone who has so far used the word “plus” only with numbers below 57. All their previous calculations are compatible with ordinary addition. Yet the same answers would also be compatible with a different rule, one that proceeds like addition in all these previous cases but always yields 5 outside that range. Kripke calls this divergent rule quus.

3The difference becomes visible in the problem “68 + 57.” According to addition, the result is 125; according to quus, it is 5. What, in the previous applications or in what the person formerly meant by “plus,” determines which continuation is correct? This is precisely where Kripke’s skeptical challenge begins (Wittgenstein on Rules and Private Language, Ch. 2).

4In the skeptical solution developed by Kripke, shared practice takes on significance. A linguistic community has conditions under which it attributes rule-following to someone; it can examine, confirm, or correct applications. Kripke expressly does not claim that the correct result of addition is simply fixed by the opinion of a majority (Ch. 3).

5From the Principio’s perspective, however, the next question suggests itself: what is that commonality to which we appeal when we speak of the same rule?

6Let us consider the theater rehearsal once more. Two listeners agree that they have heard a promise. One means the promise made by a stage character; the other, a personal obligation undertaken by the actor. Their answers agree as long as we ask only about the word “promise.” Only when we want to know who may count on whose arrival tomorrow does it become apparent that the two have continued different relations.

7Their agreement was therefore not nothing. It simply did not extend as far as the identical wording initially suggested.

8In this connection, Volume IV describes the compatibility of observer relations. Different perspectives need not be identical in order to be related to one another within a common order. What matters is whether their distinctions can be linked in such a way that a shared continuation becomes possible (Volume IV, Chs. III and XIII).

9A linguistic community can correct applications and stabilize rules. But when it examines whether someone has followed the same rule, it already presupposes a distinguishable commonality. The community can examine a continuation. What it examines as the same rule is first determined in its shared distinguishing.

10This does not deprive shared practice of its importance. It makes visible the question that an appeal to such practice has still not answered: what makes its shared order determinable as a shared order?

A Boundary at Which Thought Can Continue

1From Wittgenstein’s conception of logical form there finally follows the distinction between what can be said and what can merely be shown. A proposition can represent reality; according to the Tractatus Logico-Philosophicus, the shared form that makes this representation possible cannot itself be stated in the same way. It shows itself in representation (4.12–4.1212). Wittgenstein also rules out a proposition saying something about itself (3.332).

2The Tractatus Principio approaches this from another direction. The order of a representation can itself become the object of a distinction for the observer. When, in the case of “I always lie,” we ask whether the present utterance belongs to what is being spoken about, we are already investigating a condition of its own reading. We consider not only the result being asserted but the relation under which the assertion becomes a determinate statement in the first place.

3The same applies to the boundary between sense and nonsense. As a weather report, “It is raining or it is not raining” tells us nothing about whether we need an umbrella. But as an expression within an investigation of logical form, the very same sentence can take on a particular role. Wittgenstein himself acknowledges the significance of tautology in logical symbolism (4.46–4.462). The Principio asks which distinction in each case supplies the standard by which we judge such an utterance.

4The limits of language thereby also take on a different meaning. Wittgenstein connects the limits of his world with the limits of his language and thus with what can be meaningfully represented (5.6–5.62). What interests the Principio is how a new determination can emerge in language.

5Someone who previously distinguished only between an open and a closed window can now learn to ask whether it is tilted open. The new designation makes a further distinction possible. Wittgenstein can regard the possibility of such a determination as already contained in logical space. The Principio directs attention to the act through which it becomes legible for an observer. What has not yet been said need not thereby mark the unchanging limit of everything that can be said.

6Wittgenstein’s first Tractatus ends with what cannot be spoken of, and with silence (6.522–7). At that same boundary, the Principio continues to ask: what exactly has been determined here? And which side of the distinction has remained open?

7If we know only that the window is not closed, we have obtained an answer to a particular question. Whether it is tilted, left ajar, or wide open remains undecided. We need not turn the window into a philosophical mystery. But neither may we pretend that the first answer has already said everything that can be distinguished about it.

8This is the central confrontation of this polemic. Wittgenstein seeks the conditions of meaningful representation and assigns logical form a foundational place. The Tractatus Principio asks about the act in which even such a form, its objects, and its boundaries can appear as determinate in the first place. It does not reject the sense of a proposition, the reliability of a rule, or the persistence of a perceived shape. It asks whether we are confusing their persistence with their origin.

9The pane is still there. We can touch it, feel its edge, and speak about whether the window is tilted open. But after following the path of our distinctions, something about this apparently simple observation has become less self-evident: becoming accustomed to the use of a determination does not, by itself, tell us what makes that determination possible.

10Before what is the case stands the act of distinguishing, through which anything can be determined as being the case at all.

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