Tractatus, Application and Use

3.1 McGuinness

McGuinness argues that the Tractatus’ first two groups of theses are best read negatively: there is no ground to read them as offering the classic statement of a realist semantics. For one, the Tractatus does not mention any kind of ostensive definition that would turn tractarian names into proxies of objects given independently of language. There is no “lucky power of our minds” that makes tractarian names answerable to the configurational combinatorics of sempiternal objects (as Hacker^[22] would have it). In general, there is no metaphysics to be recognised in logic or the nature of our language on which, once discerned, logic and language happen to depend. Rather, “it will be clear on reflection that such arguments would be the sort of metaphysics that [Wittgenstein] condemns”.^[23]

With this negative aspect in place, what is Wittgenstein doing in the Tractatus? McGuinness holds “he is doing logic and basing philosophy on it”. He concludes:

[…] the whole ontology is a transferred and illegitimate use of words like ‘bestehen.’ It is a kind of ontological myth that he wants to give us to show the nature of language. As is well-known, one of the chief results of the view of language so attained is the rejection of all such myths.^[24]

For McGuinness, too, philosophy is clarification, it is “the activity of making clear the limits of language.” However, since what is to be clarified cannot be described – namely, the logic of our language – the clarification is an attempt to show rather than to state. This after all was the mistake of much previous philosophy: that it modelled itself on the scientific approach and so was forced to hold that its “necessary truths” were of a special kind. The logic of our daily language is no science, nor is it dependent on a quasi-scientific ontological structure. Logic takes care of itself. This does not mean that McGuinness does not recognise a certain “hardness” of the world. It is not up to us to decide which elementary sentences are true or false, or to ensure the world is as we wish. But in the last analysis, Wittgenstein’s logic of language does not fit any “ism”:

His position is one, as indeed he tells us, from which realism, idealism and solipsism can all be seen as one.^[25]

3.2 Rhees

There is much in McGuinness’ position with which we find ourselves at ease. Still, we think that its core – viewing ontology as a myth – is one bridge too far.^[26] McGuinness’ takes Rhees’ position as a point of departure, which is mainly developed in the first half of the 1960s.^[27] Rhees was among the first to warn that the Tractatus’ opening should not be read as providing a classic ontology. Black^[28] used ontology as a standard for the adequacy of a symbolism, but Rhees’ counters:

If we ask what Wittgenstein means by “adequate symbolism,” we shall look to the relation of sign and syntax: for it depends on that. So it is pointless to say, as Black does: we must have some view of what reality is like, before we can ask if the symbolism is adequate to describe it. […] What comes first is the truth or falsity of material propositions – in other words sense. Without this we could not even speak of possible signs. But to call this “ontology” is confusing. And to say that the discussions of logic are important because of the ontology which is built on them, is to stand the whole thing on its head. […] Logic is the basis of philosophy. And Wittgenstein did not say there or anywhere else that logic has implications.^[29]

Rhees is subtle. What is he after in this quote? Does he think, as does McGuinness, that a realistic ontology is a myth? When comparing Rhees’ view with that of McGuinness, we see important differences. Nowhere does Rhees hold that Wittgenstein’s use of words in the Tractatus is illegitimate. He rather reminds us of their humble origins – e.g. the connection between the noun “Bild” (picture) and the verb “abbilden” (to picture) (4) – and stresses the human aspect of the Tractatus, where our ability to invent logical forms (2) or to use logical operations (31–36) takes centre stage. In clarifying this aspect of language, our common language may be stretched to its limits, when philosophical confusion urges us. But that does not make its use illegitimate.

In Rhees’ own vocabulary, the term “syntax” may be an example. Even in the 1960s, it may have signalled to a reader the rules governing the generation of a set of well-formed strings. Winch held this position, and more recently Kuusela comes close.^[30] Instead, we think Rhees’ use of “syntax” is akin to Wittgenstein’s use of “logic” or “grammar:”^[31] it is concerned with all forms and rules that may be applied in the expression of sense prior to any evidence for truth or falsity. Consider, for example, how in the above Rhees connects the possibility of a sign with its sense.

It is also worth noting that Rhees, like McGuinness, takes for granted that reality has a certain “hardness.” Reality makes some sentences true and others false, independent of how we have constructed them. Still he does not presume that any realistic ontology is given in advance. What appears to be an independent, realistic ontology is part of the logic that we must use to express sense. Realism takes the shape of an applied syntax or logic in which there is an intra-logical balance between “what is out there,” independent of what we wish or do, and our ability to describe it. Thus, the adequacy of a symbolism does not lie in a perfect fit with an independently given reality: it should fit, among other things, the descriptive purposes of the logical nets we cast over reality.

We, too, think the word “logic” is used to indicate the scheme that must be adhered to when expressing sense. It encompasses elementary propositions, facts, names, objects, truth-table signs, truth-operations, and so on. On this view, tautologies and contradictions are limit cases of logic, which exhibit its structure in a pure manner. The perhaps unexpected intertwining of the ontological terms “facts” and “objects” in this list is due to the intra-logical nature of the how these notions are related, respectively, to “sentences” and “names.”

That Wittgenstein was not after an independent investigation into the structure of ontology is strongly suggested in the Notebooks 1914–1916.^[32] All phrases pertaining to ontological categories, like “function” or “thing,” are “on the Index; but how is shown what we want to express by means of them?” (8.10.14.r). The answer is, or so we think: by means of an adequate, applied logic. In the use of logic, “names,” “things,” and “projection” are logical notions that capture all that are needed to get an instantiated logic going. No “theory of types,” or syntactical rules to that effect, is to be had:

If syntactical rules for functions can be phrased at all, then the entire theory of things, properties, etc. would be superfluous. It’s also very remarkable that neither the ‘Grundgesetze’ nor the ‘Principia Mathematica’ speak of such a theory. Once more: logic should take care of itself. A possible sign must be able to signify. Anything that is possible, is also allowed. Let’s remind ourselves of the explanation of why ‘Socrates is Plato’ is nonsense. Namely because we have failed to establish an arbitrary convention, not because the sign in and of itself is illegitimate. 22.8.14.r

Wittgenstein once suggested that the time prior to finishing the Tractatus was his only truly creative period.^[33] The above passage presents his supposed realistic ontology as a logical breakthrough different from what Frege or Russell had achieved in their major works. What appears to be ontology is much rather like applied combinatorics that should make clear which ingredients go into the logical modelling that our descriptive capabilities must make use of, and this without falling prey to contradictions or having to introduce an ingenious but wanting “theory of types.” Is not the novelty of this insight sufficient reason to have it open the book that aims to indicate how applying logic can provide definitive solutions to all philosophical problems?^[34]

If this is indeed the case, and we think there are good reasons for thinking it is, then the contextualised reading of the book as a whole is mirrored in the fundamental role of application in logic, and so in ontology. But how does that affect the status of logic as such? Is logic relative, in the sense that its structure is given only in application, or is it absolute, entirely independent of application?^[35] In the next section, we will take up this question.

4.1 Stenius

Recognition of the practical nature of Wittgenstein’s view on logic goes a long way back. Rhees^[37] takes the embedding of logic in human abilities for granted. And as early as 1960, Stenius^[38] argues that substance should be understood in a relative, not in an absolute manner:

The formation of the system of atomic states of affairs is, to be sure, prior to a description of the world, and forms a framework for it, but this framework can be chosen in different ways, and every choice determines a separate system of possible worlds.^[39]

Stenius based his suggestion only on the Tractatus, which, as he hastens to acknowledge, has quite a few theses that suggest the opposite: an absolute rather than a relative totality of states of affairs, e.g. 2.022, 2.023, 2.0124, and 3.25. However, in line with Stenius’ suggestion, these theses can be understood as concerning “the world as I found it,” in which humans use their ordinary language in a determinate meaningful way, within a particular framework.

According to Stenius, substance is first and foremost a logical notion that figures prominently in the application of logic. It is what instantiates the forms that a framework of application supplies, in the context of states of affairs. Substance is at the heart of the type-token ambiguity that Ramsay made us aware of in his “Critical Notice.”^[40] Here the ambiguity extends to frameworks, of which one and only one can be instantiated at any given point. Logically, objects are content and form; in other words: they are tokens or instantiations of types. To put it somewhat misleadingly: bare being (content) can be taken as an absolute totality, but its form is unique only relative to the framework that is instantiated. Similarly, analysis is unique within a framework. It should be emphasised, however, that instantiation is always holistic.

In his argumentation for a pluralistic take on substance, Stenius makes a concise but strong appeal to 5.55 and its offspring, which also figures prominently in our elaboration below. For now, let us draw attention instead to some entries from MS101, of which a selection was published one year after Stenius’ book. At the end of MS101 in particular, Wittgenstein makes a holistic move toward “systems of co-ordinates,” which “for sure” need not be unique:

The internal relation between the sentence and its meaning – the method of signification – is the system of co-ordinates that project the state of affairs into the sign. The sentence corresponds to the basic co-ordinates. […] For a statement to be possible the logical co-ordinates must really determine a logical location! 29.10.14.r

If we allow for these methods of signification, what then is really characteristic for the relation of representation?

Can’t we say: for sure there are different systems of logical co-ordinates!

For sure there are different methods of representation, and what represents is not just the sign or the picture but also the method of representation. All representation has in common that it is either right or wrong, can be true or false.

For picture and method of representation are entirely outside of what is represented! Both together are true or false, namely the picture, in a determinate way. (Of course, this also holds for the elementary sentence!) 30.10.14.r

It is worth emphasising that it is the assumption of determinate sense which is held to be characteristic of all representation, and not a determinate structure of ontology that must be adhered to.^[41] Quite contrary to what is often assumed, we think in the Tractatus examples of such co-ordinate systems can be found, e.g. the networks discussed in 6.341-2. Stenius already made clear – using the additivity of velocity as an example – that the choice of network helps to simplify the application of logic, in this case in a scientific context. It is also beneficial to recall Wittgenstein was among the first to realise that such pragmatic variation does not hamper the tautologies and contradictions of logic “proper,” in which in the final analysis all descriptive contents typical of a framework are dissolved.

4.2 Ishiguro

This brings us to Ishiguro’s classic paper on the use and reference of names.^[42] We read it as focusing on a crucial feature of Stenius’ approach. The main thrust of Ishiguro’s paper is that reference cannot be secured prior to, or independent of, description. In defending this thesis, Ishiguro makes clear that in the Tractatus names and their reference are different from the proper names in natural language and their reference. Names and reference are logical notions. Similarly, the Tractatus notion of object is a logical one and differs from the ordinary notion. Consequently, language and its logic are not held to be answerable to, or to be dependent on, any realistic ontology. Instead, Ishiguro makes a strong case for continuity in Wittgenstein’s work, based on the notion of “naming” and that of “use” that she sees involved in it. The nub of Ishiguro’s position is a strong form of contextuality: “We settle the identity of the object referred by a name by coming to understand the sense, i.e., the truth-conditions of the proposition in which the name occurs.”^[43] Indeed, the “use” of names that the title of the paper refers to is grammatical: it concerns the part that names play “in making up propositions which have sense.”^[44] Particularly important examples of such propositions are the notorious elucidations of 3.263.^[45]

This is a good occasion to stress that the words “context” and “contextuality” are somewhat ambiguous. Ishiguro uses “context” logically: it concerns the context of a name (or an expression) as proper part of a sentence used with sense. This is the notion of Frege’s context principle and of Tractatus 3.3.^[46] But when applied logic is at stake, the term “context” has a broader, perhaps also vaguer application, which includes one’s logical abilities and aspects of the world used to express sense.

In her analysis, Ishiguro stresses an important feature of Wittgenstein’s early philosophy: do not separate what should only be distinguished, since no philosophy is able to mend such separation. For example, Wittgenstein does distinguish the sign of a sentence from its sense, yet sense cannot be had without sign. In a similar vein, sense cannot be separated from the projection of elementary sentences, of which the reference of names is an essential part: “The identity of the references of the names and the sense of the elucidations are nor logically separable.”^[47] Indeed, objects need not be perceptible or present prior to the creation of sense. They instantiate co-ordinates of a logical possibility and so should be understood intentionally. In short, “name,” “reference,” and “object” are all notions in the province of applied logic and its intensional space of logical possibilities.^[48]

It would lead too far to discuss all the ins and outs of Ishiguro’s seminal article.^[49] But there is one aspect with which we disagree and that has an important bearing on the current subject. Ishiguro holds that “unlike Frege, Wittgenstein does not think in terms of saturated and unsaturated sense, or complete and incomplete parts of thoughts.”^[50] Also, the signs of names, she claims, are “completely conventional” and “display no logical structure.”^[51] Instead we would argue that what Ishiguro says of the identification of objects hold as much of names, for logically names are objects used as names.

In the Tractatus itself there is evidence that the interaction between language and reality is more subtle than Ishiguro suggests. To begin with, here are two such indications:

A picture is a fact. 2.141

The sentence-sign is a fact. 3.14b

As the world is the totality of facts (1.1), there must be at least some part of language that is in the world. But how can this be if the most basic element of language is purely conventional and without logical structure? The Tractatus remains silent on the issue, so we must look at its sources to get a feel what insights 2.141 and 3.14b distil. MS101 is particularly helpful in this regard. On 23 September 1914, Wittgenstein writes:^[52]

It could be asked: how can a state of affairs p have a property, if in the end nothing such is the case? 23.9.14.r

To get clarity on this important topic, Wittgenstein makes an identification.

[…] this is identical with the question of how states of affairs can be correlated with each other (one that signifies and one that is signified).

This is only possible via the correlation of constituents; the correlation of name and thing named gives an example. 25.9.14.r

About a month later, Wittgenstein moves from elementary sentences to sentences in general, with a special focus on the puzzling, completely generalised sentences in which no material content appears to be present. Here he has a breakthrough:

[…] completely generalised sentences are logical constructions from states of affairs. 20.10.14.r

In 2.141 and 3.14b, Wittgenstein refines this by taking the signifier to be (a logical construction) of a fact, which concerns realised and not “just” possible states of affairs. We only make pictures to ourselves with what is really available.^[53]

The entries make clear that “material” in “material sentences” should be taken quite literally: elementary sentences are states of affairs used as sentences and, consequently, the names in such sentences are objects used as names. The model of two strictly separated realms with language modelled as reality requires is wrong. The relationship between language and reality is much more subtle than that: language and reality are intrinsically intertwined. That also makes clear why in the Tractatus names and objects are logically identical to each other: both are form and content. For objects, cf., 2.02, 2.025, for names (i.e. simple expressions), cf., 3.31. The external properties of names and objects may of course be vastly different. But logically speaking the difference is just in application: one is used to name the other.

That the use of “use” in the last paragraph is indeed justified can be seen as follows. Wittgenstein was quick to realise that identity of logical form among states of affairs may leave sense underdetermined. There should be at least two states of affairs with identical logical form – one for the sign, one for what is signified – but there may be even more. After all, we are dealing with

[…] the general concept of two complexes of which one can be the logical picture of the other, and so in a certain way is. 6.10.14.r

To keep sense determinate – which is the Fregean assumption that shapes much of the Tractatus’ logic – “use” comes to the rescue. The following entry is crucial in this regard:

In a sentence something must be identical with its meaning, but the sentence should not be identical with its meaning, so something in it should be different from its meaning. (The sentence is a formation with the logical features of what is represented and with yet other features, which will be arbitrary and different in different sign-languages.) So, there must be different formations with the same logical features; what is represented will be one of them, and it is crucial when representing to distinguish what is represented from other formations with the same logical features (for else the representation will not be univocal). This part of the representation (the naming) must happen now by means of arbitrary determinations. Accordingly, each sentence must have features with meanings that are determined arbitrarily. 22.10.14.r

Indeed, even at this early stage Wittgenstein holds that to attain determinateness the use of signs is crucial, and this in a way that extends the context names occur in to make up “propositions which have sense” that Ishiguro considers:^[54]

What if our signs where as indeterminate as the world that they mirror?

To recognise the sign in the sign one must pay attention to its use.^[55] 23.10.14.r

The point is just that the logical features of what is signified are determined completely by the logical features of the sign and the method of signification. Sign and method of signification together must be logically identical with what is signified. 26.10.14.r

Determinate sense is had by logically projecting one part of logical space isomorphically onto another. And, Wittgenstein claims, by nature humans are able to do so even without being aware of all the logical and conventional complexity this involves (4.002).

Thus, we consider Ishiguro’s focus on names used in elementary sentences as an important first step but maintain it should be followed by considerations that encompass all of logic. And here, too, an important continuity in Wittgenstein’s philosophy can be argued for. Reference of names is always within the broader scope of projecting logical complexes. Extending what has been discussed thus far, we claim that quite generally projection in applied logic is best seen as an intra-logical affair. Wittgenstein’s philosophy of logic is introduced from the Tractatus’ very first theses. The clarification of logic begins with the elementary part that indicates the kind of logical structures that are involved in description. Its initial sequence of theses clarify what common notions as “world,” “thing,” “state of affairs,” “situation,” “name,” and “sentence” contribute to logic. The book continues to clarify logical complexity, which, when properly compressed and clothed, enables humans to handle the structural intricacies involved in our daily language use. But when it comes to sense and truth, in the end it all boils down to truth patterns of elementary structures of which one half is used to logically model the other.

Thus, we strongly disagree with those who ascribe to early Wittgenstein the conception of languages and their logic having to be answerable to reality and who view the later Wittgenstein as reneging on that claim.^[56] Logic, like grammar, takes care of itself. The differences, which of course there are, are rather to be found in the numerous simplifying idealisations on which the early logic is based, which later make place for richer families of grammars that, when philosophy calls, “teach us differences.”

There is reason to believe that already at the time Wittgenstein was completing the Tractatus, he started to sense a tension between rigid logical modelling and everyday meaningful language. We think his suggestion was that we may need to approach the matter not from an absolute but rather from a contextual perspective. In the next sections, we will argue for this position. We do so by staying close to the Tractatus’ text and by identifying and systematically discussing the various statements concerning use and application that support this contextualised reading.^[57]

5.1 Setting the scene

Some observations. “Logic must not clash with its application:” this can be read as stating that whatever constraints logic imposes, it should always be able to meet them. Now, if logic would not impose any constraints, this would be trivially true, but note that Wittgenstein also states that “logic has to be in contact with its application.” That seems to indicate that logic does impose constraints. So the key question is how can we make sense of a logic that constrains but does so in a way that does not preclude any type of application? Here the transcendental nature of logic (6.13) comes to the fore: it defines a framework that has no substantial effect on anything contingent; any application is contingent, and no application is ruled out. Yet logic is “in contact” with application: for it is what defines in the most general sense what application is, it is what makes application possible. Hence Wittgenstein’s “Therefore logic and its application must not overlap:” this is indeed what follows from the transcendental nature of logic and the empirical nature of application.^[58]

What is crucial to note is what logic does. It supplies concepts and their relations, but in such a way that as far as truth-functionality is concerned nothing follows with regard to concrete instantiations of those concepts. Thus, logic supplies the concept of an elementary sentence, but it puts almost no constraints on what elementary sentences are. That is by and large determined by application. But what is that?

The Tractatus does not say much about application. The term occurs eleven times in the text. Six of these refer to the application of an operation to its argument(s) (5.2521, 5.2523, 5.32, 5.5, 6.001, and 6.126), and one is about self-application and the theory of types (6.123). These are clearly not relevant to the meaning of application that is at stake here. That leaves four other occurrences. Two of these concern the application of signs (3.262, 3.5), and the other two are explicitly about the application of logic (5.5521, 5.557). It is these four that we need to draw upon.

Let us first take a look at the two earlier passages, 3.262 and 3.5. These occur in the long discussion on the fundamental properties of linguistic signs, symbols, and meaning that begins in 3.1 and continues to 4, where Wittgenstein starts to discuss the basic logical structure of language. In this context, 3.262 claims:

What signs fail to express, their application shows. What signs slur over, their application says clearly. 3.262

The point here is that no sign is able to express what makes it meaningful or what its meaning is. What is interesting is that Wittgenstein states that it is not logic but application that comes to the rescue. Of course, the sign itself is unable to state its own logic, i.e. its fundamental properties and its relations to other signs. But it is not logic (as a formal scheme) that supplies that information, rather it is the application of the sign, i.e. how we set up and use a system of signs. Apparently, that is where the actual logic of a sign is determined, not by an ideal, non-applied logic as such.

That application determines the meaningfulness, and the actual meaning, of any form of symbolic representation is further supported by 3.5:

A propositional sign, applied and thought out, is a thought. 3.5

It is never the symbolic system as such that makes a sign meaningful, rather its meaningfulness depends on the application that we make of it. Cf., in this connection also 2.1, the statement that opens the section of the Tractatus that deals with the picture theory: “We picture facts to ourselves.” The reference to an animate subject may come as a surprise at that stage in the text; but in view of the essential role that application plays, it makes perfect sense. Further confirmation comes from other passages, such as 3.11:

We use the perceptible sign of a proposition (spoken or written, etc.) as a projection of a possible situation.

The method of projection is to think of the sense of the proposition. 3.11

Note that both logic and the human element are crucial: logic provides the mould that we use to capture reality (actual or hypothetical), and reality should allow such use. Cf., also 3.341:

So what is essential in a proposition is what all propositions that can express the same sense have in common.

And similarly, in general, what is essential in a symbol is what all symbols that can serve the same purpose have in common. 3.341

The reference to “purpose” is an implicit reference to the use that we make of signs to application. That is, besides to a criterion of identical sense, 3.341 also refers to the pragmatic criterion of identical purpose as essential for propositions, symbols, and their signs. Apparently, it is a specific use of a sign that ensures that a sign expresses one sense rather than another one.^[59]

Of course, these remarks are suggestive rather than definitive. But they do fit a pattern and we feel that they strengthen the interpretation of the later passages, viz., 5.5521 and 5.557, that we argue for. And there are other passages that do not mention “application” but rather talk about “use” that adds further evidence.

The German original has two terms that are commonly translated as “use,” viz., “Gebrauch” and “Verwendung.” The first occurs in 3.326, 4.123, 4.1272, 4.241, and 6.211, and, in the negative, in 3.328. The second occurs in 3.327, 4.013, and 6.1202. The occurrences of these terms in 4.103, 4.123, 4.1272, 4.241, 6.211, and 6.1202 are straightforward and do not relate to the issue that is under discussion here. But the passages 3.326–3.328 are interesting because they tie meaning directly to the use or the employment of a term:

In order to recognise a symbol by its sign we must observe how it is used with a sense. 3.326

The sign determines a logical form only together with its logical syntactic application. 3.327

If a sign is useless, it is meaningless. That is the point of Occam’s maxim.

(If everything behaves as if a sign had meaning, then it does have meaning.) 3.328

The symbol and sign that 3.326 refers to is the distinction between a mere orthographic or phonetic object and a meaningful expression. What 3.327 and 3.328 imply is that meaningfulness and use are intrinsically tied: there is no meaning without use, and use is decisive to determine meaning. Again, despite crucial differences, the role of logic in the Tractatus has much in common with that of grammar in Wittgenstein’s later work.^[60]

5.2 Logic and application

The passages just considered provide further support for our interpretation of how logic and application are related. Explicitly, Wittgenstein talks about that in 5.57, with which we started our discussion, and slightly earlier, in 5.5521:

And if this were not so, how could we apply logic? We might put it in this way: if there would be a logic even if there were no world, how then could there be a logic given that there is a world? 5.5521

In order to understand what the opening remark refers to we have to look at the preceding remark, 5.552:

The ‘experience’ that we need in order to understand logic is not that something or other is the state of things, but that something is: that, however, is not an experience.

Logic is prior to every experience – that something is so.

It is prior to the question ‘How?,’ not prior to the question ‘What?.’ 5.552

What Wittgenstein is saying here is that in a specific way logic is dependent on reality: not on any contingent feature of it but on their being reality to begin with. To put it bluntly: logic exists only because there is reality. So even though logic is not tied to any specific way the world is, its raison d’être is the pure existence of reality: it can be any world but there must be a world. The transcendental conditions that logic formulates cannot be not met.^[61]

The justification for the claim made in 5.552 is provided in 5.5521: the relationship between logic and the world, which is a relationship of application, necessitates that logic and reality are bound together in this specific way. For if logic could exist without reality, then its very essence would have nothing to do with reality. But it is only due to its essence that logic can be applied, so this essence has to rest on a relationship with reality. And that relationship is that of applicability; without application logic loses its point.

All this can still be read as somehow neutral with respect to the nature of the dependency between logic and reality. But 5.557 is explicit about that: it is application that determines the substance of logic, i.e. application tells us how logic is put to use. By itself, i.e. outside the context of application, logic can state only very general conditions that fall short of specifying what is needed for concrete application. So logic is not self-applying, it needs to be applied in a context, and that means that we need to set the terms.^[62]

Read in this way, 5.557 (repeated here for convenience) and 5.5571 make explicit what was implicit in the other remarks on use and application:

The application of logic decides what elementary propositions there are.

What belongs to its application, logic cannot anticipate.

It is clear that logic must not clash with its application.

But logic has to be in contact with its application.

Therefore logic and its application must not overlap. 5.557

If I cannot say a priori what elementary propositions there are, then the attempt to do so must lead to obvious nonsense. 5.5571

What is interesting to note is that Wittgenstein makes the point in terms of language, not ontology. What is at stake is what elementary sentences are, not states of affairs simpliciter. The two are logically linked, of course, as language and ontology are throughout the Tractatus. But apparently from the perspective of application the focus is on language, and ontology is certainly not sui generis.

And this makes sense. Application of logic is something we do, and we do so in the first instance through the language that we bring to bear on the phenomena that we want to analyse. To a certain extent we can decide what that language will look like, setting up the vocabulary and the grammar, and employing the resulting expressions in particular ways.

5.3 The human context

Now that we have argued for the centrality of application, we turn to context how does application support a contextual reading of logic’s transcendentality? The very wording seems an oxymoron: how can what is necessary be read in terms of what is changing and contingent?

Let us start with contextuality. Although there is limited support for this in the text of the Tractatus, we think it makes sense to think of application in the context of logic, or in the context of signs, in a concrete manner. Application is the actual application that we make of signs, be they the words and phrases of a natural language, the signs that make up formal languages of logic and mathematics, or the elements of some other symbolic system. With that actuality and concreteness come contextuality. For not every application is the same, not every language that we use serves the same purpose.

In some contexts, it makes sense to disregard certain structural features whereas in others these features are relevant and hence necessitate a different take on complexity. In fact, the wealth of formal languages that we have developed in the course of our history, each of them fine-tuned to tackle a particular set of problems or phenomena, testifies to the intrinsic contextuality of the core concepts involved. There is no fixed, a priori established set of elementary sentences. It is our application that decides what to treat as such, depending on the context in which we apply logic.

We think that the key to a proper view on the relationship between the necessity of logical transcendentality and the contingency of application is contained in Wittgenstein’s statement in 5.57: “What belongs to its application, logic cannot anticipate.” This is because the two do not operate on the same level: there can be no clash between necessity and contingency, precisely because we are dealing with necessity that is of a transcendental nature.

The transcendental nature of logic resides in the constraints, or norms, it formulates on any application: that there be names, elementary sentences, and truth-functional operations that generate complex meaningful expressions; that there be objects, states of affairs, situations; and that these be linked by the relation of picturing, i.e. by means of the relationship between names and objects and identity of logical form. That is what is necessary, and that is what can be established a priori.

On this view, what are elementary sentences, and all that follows from that, can be determined only when we have access to a concrete context of application. It is how we use the concepts that logic provides, what we deem a useful and meaningful application of them in context, that determines what are elementary sentences. And that can be established only a posteriori by looking at the concrete context of application.

5.4 Logical scheme and instantiation

How should the Tractatus be read then? On first sight, it appears that Wittgenstein develops an integrated scheme of language and ontology that can be read as a metaphysical specification of a number of concepts and the principles that connect them in an abstract, yet substantial way. However, from the current perspective, what the Tractatus has to say about language and ontology is not itself an applied instantiation but a clarification of the logical scheme that each and every concrete application must adhere to.

This is in many ways akin to how Wittgenstein describes the status of Newtonian mechanics in 6.341 ff.^[63] The opening passage of 6.341 introduces the core idea:

Newtonian mechanics […] imposes a unified form on the description of the world. Let us imagine a white surface with irregular black spots on it. We then say that whatever kind of picture these make, I can always approximate as closely as I wish to the description of it by covering the surface with a sufficiently fine square mesh, and then saying of every square whether it is black or white. In this way I shall have imposed a unified form on the description of the surface. 6.341

This passage illustrates Wittgenstein’s conception of logic’s transcendentality clearly. A set of logical concepts and principles determines logical forms, but it does not determine the content or instantiation of these logical forms. It specifies conditions of possibility of content. What concrete description we will give will depend on the level of accuracy we want to achieve. But any such description will be of the same form, which is given by the logical scheme. The same point is made in 6.342:

[…] The possibility of describing a picture like the one mentioned above with a net of a given form tells us nothing about the picture. (For that is true of all such pictures.) But what does characterise the picture is that it can be described completely by a particular net with a particular size of mesh.

Similarly the possibility of describing the world by means of Newtonian mechanics tells us nothing about the world: but what does tell us something about it is the precise way in which it is possible to describe it by these means. We are also told something about the world by the fact that it can be described more simply with one system of mechanics than with another. 6.342

That the world can be described by a particular scheme underdetermines what the world actually is like. However, it does say something about the world: it reveals some of its formal but none of its material properties.

In the case of physics, no theoretical framework can claim necessity: there is an element of arbitrariness in the form that a framework specifies:

[…] The form is optional, since I could have achieved the same result by using a net with a triangular or hexagonal mesh. Possibly the use of a triangular mesh would have made the description simpler: that is to say, it might be that we could describe the surface more accurately with a coarse triangular mesh than with a fine square mesh (or conversely), and so on. The different nets correspond to different systems for describing the world. […] 6.341

This distinguishes the case of physics from that of logic. It is generally assumed that for Wittgenstein logic, unlike physics, is absolute, i.e. does not allow for alternatives and hence lacks the kind of arbitrariness that is inherent in a framework of physics, such as Newtonian mechanics. The difference between logic and physics is also addressed in the opening remark of 6.342:

And now we can see the relative position of logic and mechanics. (The net might also consist of more than one kind of mesh: e.g., we could use both triangles and hexagons.) 6.342

The parenthetical remark characterises physics as relative, and apparently this is to be understood as the difference between logic and physics, as especially the non-elementary, truth-functional part of logic allows no such variants. This is the part of logic that “must take care of itself” (5.473). However, that logic and physics differ in this respect does not mean that the relationship between a framework and the use that we make of it, its application, should be absolute. As Wittgenstein describes in the last part of 6.341, it basically works in the same way:

[…] Mechanics determines one form of description of the world by saying that all propositions used in the description of the world must be obtained in a given way from a given set of propositions – the axioms of mechanics. It thus supplies the bricks for building the edifice of science, and it says, ‘Any building that you want to erect, whatever it may be, must somehow be constructed with these bricks, and with these alone.’

(Just as with the number-system we must be able to write down any number we wish, so with the system of mechanics we must be able to write down any proposition of physics that we wish.) 6.341

If we apply this to the case of logic and language, the thing to note is that the “bricks” are not concrete elementary sentences. What counts is their being elementary, i.e. their having a specific form and also the way in which they can be combined into truth-functional complexes. The actual bricks need to come from elsewhere, but any building needs to be constructed from bricks, i.e. it needs to use building materials in specified ways. The parenthetical remark on numbers makes the same point. This reading receives further support from the following remark:

We ought not to forget that any description of the world by means of mechanics will be of the completely general kind. For example, it will never mention particular point-masses: it will only talk about any point-masses whatsoever. 6.3432

The same can be said of the Tractatus’ logical scheme of language and ontology: examples of names and objects are never given, and it suffices to assume that there are such, and up to a certain point we are free to choose what we will regard as such. The scheme provides just enough constraints to be able to answer the question: How is meaningful language possible?

6.1 Determinate sense and logical modelling

That sense be determinate is stated clearly in 4.023:

Reality must be fixed by a sentence to either ‘yes’ or ‘no.’

To do so, it must describe reality fully.

A sentence is a description of a state of affairs. 4.023

The principle is inherited from Frege but is used here in a novel way. We read 4.023 as stating that somehow a sentence describing a state of affairs must already be logically in order: there must be a bedrock where no further refinement is possible. At this point, it becomes clear how a sentence and its use fixes reality to either “yes” or “no.”^[65]

Determinate sense is at the heart of Wittgenstein’s claim that truth-functionality captures the general form of sentences, and this is where the core of the logical scheme is located:

That there is a general sentential form is proved through the impossibility of there being sentences whose form we could not have foreseen (that is: constructed). The general form of propositions is: the facts are so and so. 4.5

The general form indicated in 4.5 is a loose way to phrase the main characteristic of truth-functionality, which is captured more precisely in 6. Wittgenstein’s contention that this rudimentary logical form suffices is based on some clever reductions that eliminate the need to consider identities, the most common quantificational forms, and even intensional contexts. Or so it seemed at the time.^[66]

Given what we have noted earlier on application and use, it is interesting to see that to arrive at general form Wittgenstein argues from the constructive nature of language, not from a realistic ontology. One does wonder how the argument goes; cf., the great variety in views on abstract constructions. What is important for now, however, is that early Wittgenstein states that the sense of a sentence can always be modelled as a truth table, which in the Tractatus is a sign that in use shows its sense. It is not a language-independent semantical object like a Fregean truth value. A truth table is based on enumerating all truth possibilities of its elementary content (sentences). Such enumerations force elementary sentences to be logically independent of each other, or else certain truth possibilities of a truth table may have to be excluded for non-truth-functional reasons. This would introduce non-truth-functional forms of necessity, contra the Tractatus’ claim truth-functional necessity is the only form of necessity (6.37).^[67] It is in this way that logic frames the overall shape of ontology.

Wittgenstein’s emphasis on a unique general form of sentences comes with logical independence at the elementary level, and so seems to hamper a straightforward application of his philosophy to sentences used in daily life. And it is not the only obstacle, for a similar logical radicalisation is found at the sub-sentential level.

6.2 Sense as a projected logical model

To clarify how sense can be determinate and prior to truth, Wittgenstein compares the sense of a sentence with a logical picture, or in the Tractatus’ alternative terminology: a logical model (2.12, 4.01). In such a model “its elements are related to one another in a determinate way” (2.141). These objects have a double role: they allow us to abstract regularities across sentences and what they describe, and they ensure logical analysis is well founded, i.e. comes to an end.

Our daily sentences often compress and conceal how, if at all, they fit the sub-sentential aspect of the logical scheme, since they are constructed for ease of use rather than for philosophical clarity. Indeed, that the overt form of our common language may deviate from its logical form is held to be a main source of philosophical confusion. To eliminate such confusion, we analyse the forms of language use that seem to mislead us, and we do this with activities and tools that help us to clarify which sense is expressed or to show why the language analysed does not have meaning.

The Tractatus’ focus is hardly on the process of analysis but more on its outcome: either we exhibit the sense of a sentence as a projected truth-table sign or we give sufficient indication that no sense is forthcoming, as projection of, or reduction to a truth-table sign fails. The process of analysis comes in different stages in which we apply definitions and notations to exhibit the sign and its projection step by step.

Whatever the nature of analysis may be, it is crucial that it hits rock-bottom. The Tractatus introduces substance to cater for this in a way that leaves sense independent of, even logically prior to truth. To determine whether a meaningful sentence is true or false, its sense should project its logical model onto what it purports to describe. Substance is non-composite and unchanging, and so ensures that the analysis of meaningful sentences comes to an end.

Objects make up the substance of the world. That is why they cannot be composite. 2.021

If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true. 2.0211

In that case we could not sketch any picture of the world (true or false). 2.0212

Logical modelling as a universal characteristic of sense comes with the claim that everything which can be described can be so modelled. Objects are at the core of our models. However, in the final analysis these objects may not be of the kind that furnish our daily surroundings. First and foremost Tractarian objects are content and form (2.025). That is, an object is an instantiation of a certain way in which it may combine with other objects to form part of the complete configuration of a state of affairs (2.01, 2.0141). These barren objects are not in space or time and have no colour or other material or sensory properties. Their forms rather seem to constitute space, time, colour, and the like (2.0232, 2.0251):

The substance of the world can only determine a form, and not any material properties. For it is only by means of sentences that material properties are represented – only by the configuration of objects that they are produced. 2.0231

Since spatial, temporal, chromatic, material, and sensory properties are interdependent – the realisation of one excludes others – one would expect the configurations inducing these aspects to be interdependent. That is, even though the elementary sentences describing the states of affairs must be logically independent, the states of affairs described need not be “ontologically” independent of each other. However, as we know, ontology exhibits the independence that logic requires.

States of affairs are independent of one another. 2.061

From the existence or non-existence of one state of affairs it is impossible to infer the existence or non-existence of another. 2.062

As we have argued earlier, e.g. in Sections 3.2 and 4.2, we take this as a clear indication that language and its ontology are intra-logically related. As became clear only later, having ontology comply with logical independence at its elementary level engenders a tension that often hampers applicability of the tractarian system in more mundane settings. Again, a radical consequence surfaces of assuming sense to be a fully determinate affair, especially when combined with an idealised notion of sense as logical model.

Q1: A hidden life of language?

Applied logic is at the heart of the Tractatus and so is its assumption of determinate sense. To what extent can such a philosophy still be called human?

This is a good point to remind ourselves that at the time the Tractatus was conceived, the apparent gap between daily use and idealised logical analysis still seemed bridgeable. Wittgenstein must have convinced himself that what appears nebulous in everyday language, somehow can always be analysed in the finest determinate detail. Such confidence grants the radical, logical abstractions of elementary sentence and state of affairs, of name and object rather the status of “regulative ideas,” which only need to be attained if deep philosophical confusion requires it.^[68] Then, as 3.1431 suggests, it is quite natural to expect that under normal circumstances, an analysis in terms of our common context suffices.

Still, if at its highest resolution language may come with enormous complexity, one does wonder how its use comes off the ground. An indication is given in 4.002:

Man possesses the ability to construct languages capable of expressing every sense, without having any idea how each word has meaning or what its meaning is – just as people speak without knowing how the individual sounds are produced.

Everyday language is a part of the human organism and is no less complicated than it.

It is not humanly possible to gather immediately from it what the logic of language is.

Language disguises thought. So much so, that from the outward form of the clothing it is impossible to infer the form of the thought beneath it, because the outward form of the clothing is not designed to reveal the form of the body, but for entirely different purposes.

The tacit conventions on which the understanding of everyday language depends are enormously complicated. 4.002

Although the use of language is presented as a human ability, much of its workings is presented as concealed and hidden. Why? Some of the observations in 4.002 hold unaltered for Wittgenstein’s later philosophy; e.g. that the tacit conventions on which the use of everyday language depends can be complicated, or that it need not be humanly possible to gather immediately from everyday language what its logic (or later: its grammar) is.^[69] It requires a perspicuous representation, which in the later work can take on a multitude of appearances, but in the early work should always confirm to one and the same logical scheme. That the complex structure of language is often hidden, is characteristic only of the early work, and seems mainly due to its unrealistic assumption of determinate sense. The sources of concealment are logical modelling and its idealised notions of object and structure, which force a gap between everyday language and the purported models of its meaning.

There is no need to give an indication of the human abilities that 4.002 intimates, for details are philosophically irrelevant. In Wittgenstein’s later work, such abilities are part of the forms of life in which language is used. What we should note, though, is that in the Tractatus they are non-material, ineffable features of language creation and use:

What signs fail to express, their application shows. What signs slur over, their application says clearly. 3.262

Q2: A merge of language and ontology?

It has often been observed that the Tractatus’ opening remarks on ontology are infused with observations on logic or language: cf., 1.13, 2.012, 2.0121, 2.0122, and 2.0201. Conversely, remarks on picturing or language are mixed with comments on ontology: cf., 2.1, 2.141, 2.16, 3.14, 3.142, and 3.1431. To us this suggests that language and ontology are intertwined and even intra-logically related. What strengthens this suggestion is that at the elementary level language and ontology must be isomorphic to each other. Cf., 4.26 and 5.53:

The specification of all true elementary sentences describes the world completely. The world is completely described by the specification of all elementary sentences plus the specification, which of them are true and which false. 4.26

Identity of object I express by identity of sign, and not by means of an equal sign. Difference of objects by difference of signs. 5.53

These remarks imply that elementary language and ontology are identical qua form and only differ in instantiation. However, 4.26 ensures that all names have a reference, and 5.53 ensures that this reference is unique. If so, the projection of elementary sentences onto the states of affairs they describe must be an isomorphism. The idea of an isomorphism, which we think originates in the requirement that sense be determinate, also tallies seamlessly with the fact that the Tractatus maintains that the essentials of names and objects as well as those of elementary sentences and states of affairs are identical.

At this point, we should wonder how these claims combine with Wittgenstein’s even stronger claim that linguistic and ontological entities are of the same category. That the Tractatus claims this is not uncontested. A reading which attributes a substantial ontology to the Tractatus often comes with a strict separation of world and language, so that the latter can be held answerable to the first. By contrast, as we have already argued for in Section 4.2, we read the Tractatus as presenting world and the signs of language logically as of one kind.

The justification for this is that sentence signs, and pictures in general, are facts, just as what they describe or model (2.141 and 3.14). These statements convey first and foremost that both language and ontology must be structured: sets of names or things lack the structure that is needed to express sense. Second, they indicate an early move away from mentalism and toward the world in which language is used. The crux here is the identification of thoughts with meaningful sentences (4). On our view, the world instantiates the logical scheme. Meaning comes from logically projecting one part of the world, taken as the elementary part of a logical model, onto another part of the world that which is so modelled.

Again, with meaning being a worldly matter does this mean ontology comes first, language second? No. Sections 6.1 and 6.2 already strongly suggest that the highly abstract nature of states of affairs and their objects, with characteristics far out of the ordinary, derives from applied logic, not vice versa. On our reading of the Tractatus, the application of logic is most basic: its logical space of possibilities is a pre-condition for language and ontology. According to the Tractatus humans can sense that something is regardless of how it is (6.44).^[70] This “experience” is at the heart of our ability to apply logic and thus to construct meaningful languages (5.552, 4.002). Strictly speaking, the direct confrontation with being is not an experience, it is part of the human ability to cast logical nets on what there is (5.511). Yet all descriptions are embedded in logic: a formal logical scheme, the use of which puts no substantial restrictions on what is or what is not the case.^[71]

Of course, in many ways language and the world it describes are different, but according to the Tractatus the differences concern their external, not their internal properties.

At first blush, the signs of elementary sentences and the states of affairs they describe appear totally different. But these differences mask an essential identity: we manage to wrap and compress logical models in signs that are convenient to use. As far as showing sense is concerned, the wrapping and compressing are inessential. When philosophical problems force use to unwrap and uncompress a sentence, we should be able to show the forms of its elementary sentences to be the same as the states of affairs they depict; they differ in “bare” bits of substance but instantiate identical forms. In case this cannot be done, the problem is resolved and leaves the insight of a completed philosophical therapy.^[72]

Q3: An open logical toolbox?

According to the Tractatus, philosophical problems incite us to analyse our language, in order to make logical structure explicit. Let us now turn to the third question posed and try to get more clarity on the nature of the tools that we have at our disposal to do this. One may be inclined to think it is “just” truth-functional logic, perhaps finite, perhaps infinitary. We think this is incorrect if “logic” is taken in the sense of modern logic, for that has inherited too much from Frege to be counted as tractarian.

Several conventions and definitions can be used that allow us to model the sense of a sentence as a truth-table sign, i.e. as a sign that is projected 1-to-1 onto the states of affairs corresponding with the elementary signs it contains.^[73] Is this all? No.

For what is the aim of analysis? Based on the fixed truth-functional character of an otherwise quite open scheme, we construct our logic so that clarity is achieved. That is, for the puzzling, unanalysed sentences, we make clear which parts are pure logic, which parts carry sense (and show how), and which parts are gibberish (and show why). We cannot get around the logical scheme, but within its boundaries, we let our tools show what has sense and what dissolves into nonsense. The Tractatus offers no independent arbiter that decides this for us.

Let us be more precise on what the Tractatus’ logical toolbox has to offer. Its tools come in five categories: sentences, names, expressions, variables, and operations.

Sentences are bipolar, complete configurations of names, or logical complexes thereof. They can be used to describe the world, which they fix to either “yes” or “no.” The bipolarity of sentences is the static core of the logical scheme, a scheme which in almost all other respects is quite open.

Names are incomplete and can only contribute to sense in the context of a sentence (3.3). They provide the content and non-truth-functional form of sentences, which via projection enables sentences to model situations in the world; i.e. realisation patterns of elementary logical structures that in the logical scheme are called “state of affairs.” Apart from stating that names are simple and implying that as simple expressions they have form and content, the Tractatus leaves their further specification open. This is deliberate. They can be Russellian relational (as the examples in the Tractatus are), but they can also be Fregean functional, or connected-graph-like or have whatever form that suits the purpose of their application.^[74]

Somehow bounded by the totality of objects, the types are for us to specify when applying and refining the logical scheme in a process of elucidation:

There cannot be a hierarchy of the forms of elementary propositions. We can foresee only what we ourselves construct. 5.556

Expressions are (possibly incomplete) configurations of names, which can be used to highlight that different sentences have a form in common. The category is as open as that of names. Which sub-configuration can be considered an expression does not seem to be fixed in advance; this, too, is to be decided in the process of clarification. Expressions help to abstract tractarian variables. Variables correspond to formal concepts; they are sequences of sentences that highlight a shared logical form.

Operators, finally, are rules that transform truth-functional signs into a truth-functional sign or transform variables into sentence signs. Wittgenstein only names the operator N, which elegantly captures the truth-functional essence of transcendentality.

All that is a toolbox. It is not an end result, but our starting point; it provides the means to our ends:

Now we understand our feeling: we have a correct logical point of view, as soon as everything in our sign-language is all right. 4.1213

Indeed, “our feeling,” “we,” “our sign-language”; the tractarian philosophical tools are as human as they can get.