Como citar: KUUSELA, O. Wittgenstein’s Tractatus without paradox: propositions as pictures. Revista de Filosofia Aurora, Curitiba, v. 34, n. 63, p. 85-104, out./dez. 2022

Metaphysical and resolute readings of the Tractatus

The Tractatus rejects the possibility of propositions about logic, or about exceptionless non-empirical necessities and possibilities more generally. On the traditional metaphysical interpretations, this is justified by, or a consequence of, Wittgenstein’s account of propositions as true/false pictures or representations of contingent state of affairs. As Peter Hacker, a main representative of this approach explains, Wittgenstein’s distinction between what can be said and what can only be shown by language ‘[…] provides the rationale for the conception of philosophy propounded in the Tractatus, in particular for the view that there are no philosophical propositions, that philosophy does not aim at achieving new knowledge, that philosophy is not a kind of science’ (Hacker 1986, 19). But in order for the saying-showing distinction to provide the rationale for Wittgenstein’s conception of philosophy and logic, i.e. to motivate or constitute a reason, ground or justification for it, the distinction must be established independently of this conception of philosophy. As is characteristic metaphysical interpretations, this is what Hacker maintains, explaining that the showing-saying distinction is ‘[…] held vindicated by a variety of strands interwoven in the argument of the book, namely the bipolarity of the proposition, the picture theory of meaning, the distinctions between a name and a variable, a material property and a formal property, a genuine concept and a formal concept’ (Hacker 1986, 19). Thus, on this interpretation, Wittgenstein’s account of language constitutes the basis of his account of logic.

As is well-known, interpretations that regard Wittgenstein’s conception of philosophy and logic as grounded on his account of language, the so-called picture theory of language, give rise to a paradox. Because this account of language constitutes itself a claim about logical necessity, it too is nonsense, according to the Tractatus. But if it’s nonsense, it can’t constitute a reason, ground, justification or an argument for Wittgenstein’s conception of philosophy and logic, because nonsense can’t provide a reason, ground or an argument for anything, or justify philosophical views. There’s more than one way to formulate the paradox, but it’s simple to state: if the Tractatus contains an argument, thesis or doctrine, it can’t be nonsense; if it’s nonsense, it can’t contain an argument, thesis or doctrine.

That Wittgenstein’s book contains a paradox seems often taken for granted. According to Hacker, the paradox is the reason why the book fails: ‘That the book is inconsistent, that its position cannot be upheld, is undeniable—as its author later realized. It is, as he remarked, like a clock that does not work’ (Hacker 2001, 104, note 9). Pace Hacker, however, it’s highly implausible that Wittgenstein would have been unaware of such an obvious inconsistency that can hardly be described as hidden (cf. Goldfarb 1997, 64). Indeed, the obviousness and seriousness of this problem makes it difficult to understand Wittgenstein’s comparison between his book and a clock that doesn’t tell the right time, rather than a bag of junk professing to be a clock, as the comparison says more fully stated (Anscombe 1971, 78; cf. Hacker 2001, 108). Here it’s also important that, although Wittgenstein later criticizes the Tractatus in a number of ways, he never mentions the problem of paradox in his Nachlass or lectures. Thus, there seems to be no direct textual evidence for the claim that Wittgenstein thought the book failed because of its paradox.

Neither is there anything in the Tractatus itself that indicates, independently of interpretational claims, that it contains a paradox. In particular, Wittgenstein’s statement that the book is nonsense doesn’t by itself generate a paradox (TLP 6.54). The paradox only arises if the book is read as containing a doctrine/thesis/theory or an argument from which its nonsensicality ‘follows’. It’s thus the attribution of nonsensical theses/doctrines/theory or an argument to the Tractatus that gives rise to the paradox. But then it’s crucial to remember that philosophical doctrines/theses/theories are explicitly rejected in the Tractatus, with Wittgenstein promoting a conception of philosophy as a logical clarification instead. Notably, he perceives no inconsistency between rejecting philosophical theses and endorsing a conception of philosophy as logical clarification. ‘The purpose of philosophy is the logical clarification of thoughts. // Philosophy is not a theory/doctrine [Lehre] but an activity. // The result of philosophy is not a philosophical propositions, but propositions becoming clear’ (TLP 4.112). Hence, interpretations that regard the book as containing a paradox are problematic on several grounds.

More recently, an interpretational approach has been developed that aspires to avoid the problems arising with the attribution of unsayable views to Wittgenstein, and which thus has the potential to avoid the alleged paradox. This is the resolute reading championed by Cora Diamond and James Conant. Although this reading is often described as therapeutic, Conant and Diamond themselves don’t characterize it in this way, and for reasons to be explained, the resolute reading in general ought not to be identified with therapeutic readings. (Therapeutic readings constitute a particular sub-class of resolute readings.) Regardless of such differences, however, central to all variants of the resolute reading is the rejection of ineffable truths or theses, or substantial nonsense in Conant’s terminology: ‘the aim of Tractarian elucidation is to reveal (through the employment of mere nonsense) that what appears to be substantial nonsense is mere nonsense’, with substantial nonsense serving the ‘conferral of insight into inexpressible features of reality’, as exemplified by Hacker’s view that nonsense can express ineffable truths (Conant 2002, 421).

Besides the rejection of ineffable truths, a second key commitment of resolute readings is that Wittgenstein’s aim in the Tractatus is only to clarify something his readers already know by virtue of being thinkers and language users. Here it’s important that, in order to be able to think and use language in the first place, thinkers and language users must already possess knowledge of logic, albeit with most thinkers/speakers this knowledge is implicit, and as implied by the saying-showing distinction, Wittgenstein’s conceives of this knowledge of logic as non-propositional.^[2] (Any reader of the book can be safely assumed to be a language user.) Wittgenstein’s readers therefore needn’t, and indeed can’t, be informed about logic, in contrast to how they could be informed about scientific discoveries. (One can’t be informed about what one already knows.) Neither is it possible or necessary for logicians to prescribe what can be said, because what it makes sense to say depends on thought and language, not on their prescriptions. Accordingly, as Wittgenstein remarks, ‘Everything that is possible in logic is also permitted’ (TLP 5.473). Or as he puts the point in the Notebooks, ‘Logic takes care of itself; all we have to do is to look and see how it does it’ (NB, 11; cf. TLP 5.471ff.). Rather than informing thinkers/speakers about the principles of logic, and prescribing on this basis how they must think/speak, the task of logic is to clarify and remind thinkers/speakers what they already know.^[3] Conant explains the second commitment of resolute readings as follows:

The Tractatus seeks to bring its reader to the point where he can recognize sentences within the body of the work as nonsensical, not by means of a theory that legislates certain sentences out of the realm of sense, but rather by bringing more clearly into view for the reader the life with language he already leads—by harnessing the capacities for distinguishing sense from nonsense […] implicit in the everyday practical mastery of language that the reader already possesses (Conant 2002, 423-424).^[4]

This interpretation therefore doesn’t regard the book’s nonsensicality as a consequence of an argument or thesis/doctrine that somehow leaves the reader in an illuminated state about what can be said after it has been recognized as nonsense (cf. TLP 6.54). This suggests a way to avoid the paradox, but an explanation is required for how this can be done without throwing away the insights about logic that the book appears to articulate. As I have argued elsewhere, the therapeutic reading fails in this respect, insofar as it maintains that the Tractatus only aims to bring the reader to realize the nonsensicality of philosophical theorizing (Hutchinson and Read 2010; see Kuusela 2019a). Thus, I agree with Hacker that the resolute readings risk throwing out away the baby of logic with the bathwater of nonsense (Hacker 2001, 124). This risk is then realized in the case of the therapeutic reading, insofar as it takes the sole goal of the Tractatus to be to demonstrate the nonsensicality of philosophical theorizing by bringing the reader to recognize the nonsensicality of Wittgenstein’s book. It’s difficult to see how on this reading it’s possible to retain any of the points that the book seems to make about logic and philosophy thereof, because insofar as the book only aims to show its nonsensicality, it seems to lack the resources to express any specific positive insights about logic. In this regard the therapeutic interpretation shares a crucial assumption with the metaphysical reading. Whilst the metaphysical reading assumes that in order for the Tractatus to contain any insights about logic it must put forward theses, the therapeutic reading correspondingly maintains that, insofar as the book puts forward no theses, it can’t contain any insights about logic. Both interpretations thus share the assumption that the only way to express positive philosophical/logical insights is a philosophical/logical thesis. This, however, begs the question against Wittgenstein’s attempt to abandon theses.

But a solution to the problem of paradox isn’t automatically available to Conant and Diamond either, insofar as its condition of adequacy is retaining Wittgenstein’s insights about logic. Conant’s and Diamond’s reading faces here a difficulty about how to account for the possibility of the Tractatus articulating general logical insights, such as there being a general propositional form shared by every possible proposition (TLP 4.5, 5.47ff.). This problem arises because of their emphasis on the piecemeal character of logical clarification.^[5] As Diamond explains, ‘There is no once-and-for-all demonstration in the Tractatus that sentences of such-and-such sorts are nonsensical: the task of clarifying propositions is a one-by-one task. Only the activity of philosophical clarification, or of attempting philosophical clarification, can reveal whether, in a particular case, there is or isn’t something that we mean’ (Diamond 2019, 95-96). At the same time, however, Conant and Diamond acknowledge that the Tractatus’ view of philosophy as logical analysis involves a commitment to a general account of language, even though only ‘unwittingly’ (Diamond 1991, 19; Conant and Diamond 2004, 60). With this I agree.^[6] Although logical analysis is a piecemeal activity, by maintaining that all sensible propositions can be analysed into truth-functions of elementary propositions that consist of logically simple names, Wittgenstein commits himself to a general account of language, i.e. that all sensible language use conforms to this model of analysis (TLP 5.55-5.557). The commitment to a general account of language thus enters Wittgenstein early philosophy covertly, through his conception of philosophy as logical analysis.

Wittgenstein is therefore ultimately committed to a thesis about language on Conant’s and Diamond’s resolute reading too. However, on this interpretation Wittgenstein’s mistake emerges as significantly subtler than on the metaphysical reading. Rather than simply putting forward nonsensical theses, as if he didn’t realize or care about their nonsensicality and the consequent paradox, Wittgenstein can now be understood as relapsing to philosophical theses, despite having a strategy to overcome logical or philosophical theses/doctrines/theories qua true/false propositions about essential necessities. I outline Wittgenstein’s strategy in section 2. By contrast, Conant and Diamond leave unexplained how it’s possible for Wittgenstein to articulate any general logical insights. By filling in this lacuna I take myself to be further developing the resolute reading, characterized through the preceding two key commitments.^[7]

A resolute dissolution of the paradox

Having discussed the dissolution of the paradox elsewhere, I will only outline it instead of providing a full exegetical justification.^[8]The core idea can be stated simply. Rather than an attempt to articulate unentertainable thoughts, a nonsensical argument or theses, the purpose of the sentences of the Tractatus is to introduce the formal concepts and principles constitutive of a logical language that Wittgenstein proposes as a general framework for logical analysis. Rather than expressed in terms of any theses/propositions, Wittgenstein’s insights about logic are encoded into the structure of this language which constitutes the proper expression for relevant exceptionless logical necessities. Consequently, there’s no need to attribute any theses regarding ineffable truths to the Tractatus, and no need to think that Wittgenstein somehow manages to communicate ineffable truths by means of nonsensical theses/propositions. Likewise it’s now easy to explain how the book’s readers can hold on to the Tractatus’ insights about logic after they have thrown away its sentences as nonsense.

What the readers are expected to hold on to is the logical language introduced in the book, or more abstractly the formal concepts and principles constitutive of such a language as opposed to any specific system of signs (see end of section 3), that is expressive of what Wittgenstein calls ‘the correct logical conception’. Having grasped how this language works, the readers can throw away the sentences used to introduce it, and proceed to practice philosophy as the activity of logical analysis, with Wittgenstein’s logical language supplying a methodological framework for such analyses. Thus they can stick to the strictly correct method of philosophy in the sense of 6.53, whereby one refrains from making any substantial assertions and proceeds purely formally (see Kuusela 2019b, chapter 3). Here it’s noteworthy that Wittgenstein’s introductory sentences can’t be expressed in this language, and insofar as it gives expression to the correct logical conception, they are nonsense. Contrary to the metaphysical reading, however, the criterion of correctness for the correct logical conception isn’t the correspondence of Wittgenstein’s nonsensical logical theses with any ineffable truths or necessities. Rather, the criterion of correctness for an account of logic is the absence of anomalies in the logical symbolism and its applications, such as arise with ‘Frege’s and Russell’s concept-script’ which ‘fails to exclude all mistakes’ (TLP 3.325). As Wittgenstein explains: ‘[…] we are in possession of the correct logical conception, once everything adds up in our symbolism [Zeichensprache]’ (TLP 4.1213). Such a language in which ‘everything adds up’ then ‘obeys the rules of logical grammar—of logical syntax’ in that the uses of its signs display perspicuously their modes of signification, thus revealing how symbols symbolize (TLP 3.325, cf. 3.323).

As a nod to the metaphysical interpretation, one might say that through his introduction of a logically correct language in which ‘everything adds up’, Wittgenstein aims to express a fundamental truth about logic. As he comments: ‘All propositions of our colloquial language are actually, just as they are, logically completely in order. That most simple thing which we ought to give here is not a simile of truth but the complete truth itself’ (TLP 5.5563). Crucially, however, this isn’t a truth expressible by means of theses/propositions, nonsensical or otherwise. Rather, clarifying this truth is matter of giving clear expression to the logic of language that colloquial language disguises by devising a symbolism that reflects logic perspicuously.

This helps to explain Wittgenstein’s conception that the proper way to articulate or express logical generality and necessity is to encode it into the structure of a logical language. For example, the point that every proposition possesses the general propositional form is made perspicuous in the envisaged language through the feature that it’s impossible to formulate any proposition in it without it being evident that it possesses the general propositional form. In this language every possible proposition is a substitution instance of the variable of the general propositional form which Wittgenstein characterizes by saying that every possible sense can be expressed by a proposition satisfying the description by means of this variable, and that very such a propositions expresses a sense, provided its names have meaning (TLP 4.5). Insofar as this symbolism is expressive of the correct logical conception, it has then been made clear, through the exclusion of other ways to express propositions, that every possible proposition does indeed have the general form. The same goes for the expression of any other logical generalities and necessities that Wittgenstein aims to clarify, for example, that propositions are functions of names, that names are referring expressions, that Frege’s and Russell’s logical constants don’t refer to anything, and so on. The proper way to express and clarify these points is to devise a symbolism that reflects them in its structure.

As Wittgenstein also explains: ‘The expression of a formal property is a feature of certain symbols. […] // The expression of the formal concept is therefore a propositional variable in which only this characteristic feature is constant’ (TLP 4.126). In exactly this way it’s a feature of propositional symbols in Wittgenstein’s language that they are all instances of the variable of the general propositional form, this being their characteristic constant feature. After abstracting away all particular features of propositions, this general form remains. By contrast, any attempt to express this logical generality/necessity by means of propositions misfires, exemplifying ‘the confusion, very widespread among philosophers, between internal relations and proper (external) relations’ (TLP 4.122). For example, no informative statement can be made about every proposition possessing the general propositional form because, assuming Wittgenstein is correct, anyone who knows what a proposition is already tacitly knows they have this form which is implicit in propositions of the colloquial language.^[9]Neither does it make sense to prescribe that in order for a symbol to count as a proposition it must have this form. For, if a symbol doesn’t have this form, it’s not a proposition, and thus it’s pointless to require propositions to conform to this form. The notion of a general propositional form therefore doesn’t constitute a general criterion of sense comparable to the logical positivists’ employment of the principle of verifiability as such a criterion. Rather than a stick to beat up metaphysicians into conformity with logic, the general propositional form is merely a formal description of the form of possible propositions that provides us with a rule for the construction of any possible proposition (see Kuusela 2019b, chapter 2). Whether a particular string of signs counts as a proposition is decided case by case, as Diamond emphasizes.

As regards the Tractatus’ programme for philosophy as logical analysis, whilst analysis always proceeds piecemeal, the preceding explains, consistently with the two commitments of the resolute reading, how Wittgenstein’s programme can get off the ground. It explains how it’s possible for him to introduce a general framework for logical analysis without having to justify it in terms of nonsensical theses/propositions or a nonsensical argument about the nature of language. Although this framework for analysis does indeed involve a general account of language as a truth-functional calculus, its proper expression is, as explained, the symbolism introduced in the Tractatus, not nonsensical theses. The latter view is indeed inconsistent, but given the possibility of a more charitable interpretation, it ought not to be attributed to Wittgenstein, pace Hacker.

As for the justification of Wittgenstein’s analytic framework, i.e. the possibility of bringing the reader to comprehend his logical conception and to recognize its correctness, this is explained in terms of the second key commitment of resolute readings. What Wittgenstein assumes is that his readers will recognize as correct, on the basis of the logical capacity they already possess, the logical conception embodied in the symbolism. The readers are thus expected to recognize the symbolism as mirroring the principles of logic they already know as language users. As regards making this logical conception comprehensible to the readers at all, on the proposed interpretation there’s no need for Wittgenstein to make any informative statements about logic by communicating propositional content. Nor does he need to convince his readers about anything by means of arguments that would have to make sense. Instead, he merely needs to introduce the formal concepts and principles constitutive of his symbolism and, as Carnap also recognized later, it’s perfectly possible to do this by means of sentences that have the appearance of material substantial propositions, but whose purpose is the introduction of formal notions (see Kuusela 2019b, chapter 3). An example of such a sentence is ‘A name refers to an object; the object is its meaning’ (cf. TLP 3.2ff.) which employs formal concepts as if they were proper concepts. Although this makes it appear like a thesis about the nature of names, the sentence can be readily understood as indicating the logical role of names in Wittgenstein’s symbolism: in this system all names are referring expressions, the object of reference being their meaning. Similarly, sentences like ‘A proposition consists of names’ (cf. TLP 4.22), can be employed to indicate the relationship between the formal concepts of a proposition and a name in Wittgenstein’s symbolism. Whilst both exemplary sentences are nonsense read as theses/propositions, they can be readily construed as non-substantial stipulative statements whose purpose is to indicate the logical role of relevant notions in Wittgenstein’s symbolism. Here it’s important that, given the symbolism’s justification in terms of whether ‘everything adds up’ in it with regard to language users’ knowledge of logic, there’s no problem with it being introduced by means of mere stipulations.

On the proposed interpretation, the justification of Wittgenstein’s symbolism and the logical conception it expresses therefore consists in the readers’ recognition of it as giving a perspicuous expression to logic they already know as thinkers/speakers. However, the recognition of the correctness of Wittgenstein’s logical conception at a general level, which the reader is hoped to have achieved when they are finished with the book, is provisional in an important sense. Ultimately, the test for the correctness of Wittgenstein’s logical conception is that logical analyses in terms of his symbolism can successfully clarify logic without giving rise to anomalies so that ‘everything adds up’. As Wittgenstein later recognized, this isn’t the case. As ‘Some Remarks on Logical Form’ explains, the logical relations between colour terms can’t be clarified in terms of Tractarian truth-functional analyses. Hence, rather than failing because of its paradox, the Tractatus failed because its method of analysis couldn’t deliver the analyses it was meant to deliver. This failure is connected with a number of confusions about the notions of logic, as discussed in the Philosophical Investigations (see Kuusela 2019b, chapter 4). However, in the absence of problems such as the colour-exclusion problem,^[10] Wittgenstein’s later clarifications of his early errors and his revision of his philosophy of logic would lack motivation.

Having thus outlined an interpretation that can avoid the alleged Tractarian paradox whilst retaining Wittgenstein’s logical insights, let me turn to how the so-called picture theory can be interpreted consistently with the resolute reading.

Wittgenstein’s account of propositions as pictures

I hope that the preceding sections have managed to make this clear: it’s wrong to think that the only way to express logical necessity and general logical insights is logical/philosophical theses. Correspondingly, by attributing general logical insights to Wittgenstein one isn’t automatically attributing theses to him. Let me now explain how the so-called picture theory can be interpreted consistently with outlined strategy for overcoming philosophical theses qua propositions about essential necessities.

Wittgenstein’s account of propositions as pictures can be understood as a further clarification of the formal concept of proposition elucidated by means of the notion of the general propositional form whose proper expression is his symbolism. Likewise the proper expression for Wittgenstein’s account of propositions as pictures is a symbolism that obeys the principles articulated as part of the ‘picture-theory’. His account of propositions thus further clarifies the logical principles governing names and propositions, and more abstractly what it’s to speak/think about reality truly/falsely. As the latter formulation indicates, Wittgenstein’s account of propositions can be understood as a contribution to the Fregean-Russellian project of clarifying the logical principles that govern thinking that aims at truth. Although explaining the principles of logical inference is an important part of this, this leaves unexplained the logical relations within propositions, and how propositions manage to represent truly/falsely in the first place. As Wittgenstein knew, Russell’s attempts to articulate a theory of judgment had ended in anomalies, with Russell unable to explain the possibility of false judgments and the unity of propositions, i.e. how the terms constituting propositions hang together. Dissolving these problems by introducing an account of propositions and a symbolism in the context of which they no longer arise can therefore readily be seen as part of Wittgenstein’s attempt to spell out the correct logical conception. Accordingly he speaks about the issue of how language represents as a matter of ‘the logic of picturing’ (TLP 4.015).

More specifically, the early Wittgenstein maintains that what makes it possible for an expression to express a particular meaning or sense is whatever is common to all expression that are capable of expressing this meaning/sense. This is what is essential to them.

A proposition possesses essential and accidental features.

Accidental are the features which are due to a particular way of producing the propositional sign. Essential are those which alone enable the proposition to express its sense.

The essential in a proposition is therefore that which is common to all propositions which can express the same sense.

And in the same way in general the essential in a symbol is that which all symbols which can fulfil the same purpose have in common (TLP 3.34-3.341).

Wittgenstein’s account of propositions as pictures clarifies, exactly in this sense, what is common to all expressions capable of representing truly/falsely, i.e. expressing propositional content. As he also remarks, ‘A proposition states something only in so far as it is a picture’ (TLP 4.03). Thus, by clarifying what is common to all propositions, i.e. their pictorial character, Wittgenstein aims to clarify what makes it possible for them to represent truly/falsely, i.e. what thinking about reality truly/falsely logically presupposes. With regard to this task, it’s then important that there are essential features of propositions that the notion of the general propositional form presupposes rather than clarifies. Among such features is that a proposition must be capable of expressing a new sense. ‘It is essential to propositions that they can communicate a new sense to us’ (TLP 4.027). Two further features, connected with the first one, are the requirement that a proposition must be logically articulated, and that, in order for a proposition to be able to represent a state of affairs, it must have the same logical multiplicity as the state of affairs represented. As he says, ‘A proposition is a picture of a state of affairs, only insofar as it is logically articulated’ (TLP 4.032). ‘In a proposition there must be exactly as many things distinguishable as there are in the state of affairs it represents’ (TLP 4.04). Among other things, the clarification of these features of propositions then makes perspicuous the logical difference between names and propositions which Frege’s and Russell’s accounts of logic and logical languages obscure, consequently failing to ‘add up’. Accordingly, the criterion of success for Wittgenstein’s account of propositions as pictures is the same as for reaching the correct logical conception generally: the absence of anomalies in a symbolism based on these principles.

More specifically, the Tractatus’ account of propositions as pictures can be outlined as follows. By a proposition Wittgenstein understands a ‘propositional sign in its projective relation to the world’, whereby a ‘sign perceptible to senses’ that ‘consists in the fact that its elements, the words, are combined in it in a definite way’ is employed ‘as a projection of the possible state of affairs’ (TLP 3.11, 3.12, 3.14). A propositional sign in this sense constitutes a fact (TLP 3.14), a ‘combination of objects (entities, things)’ (TLP 2.01), although Wittgenstein, of course, doesn’t identify propositions with any particular tokens of propositional signs. A proposition is something more abstract. It’s that which a class of visible or audible signs ordered in space or time and employed as a projection of a state of affairs expresses. As for Wittgenstein’s notion of projection, a proposition is an orderly combination of names that represents a state of affairs, an orderly combination objects, through the arrangement of names in the proposition. Here the capacity of the proposition to represent a state of affairs is based on 1) the fact that the names in the proposition refer to the objects that make up the represented state of affairs, and 2) that the combination of names in the proposition corresponds to the combination of objects in the state of affairs which is made possible by the names and objects sharing a logical form. (By logical form Wittgenstein means the possibilities of combination of objects with other objects or names with other names; TLP 2.01-2.0124.) A proposition therefore represents a state of affairs, so to speak, by (re)creating it in the proposition through names going proxy for the objects that constitute the state of affairs. A proposition is, in this sense, a model of a state of affairs with the configuration of names corresponding to the configuration of the objects (TLP 2.12-2.15, 3.21-3.22, 3.201, 4.01, 4.031-4.0311, 4.2, 4.22, 4.24).

The preceding explains Wittgenstein’s point about logical multiplicity and the requirement that a proposition is logically articulate. In order for a proposition to be able to represent a state of affairs accurately, it must be capable of representing any features that might be regarded as essential for representing the states of affairs. In order for a proposition to be able to do this, there must be as much distinguishable in it as in the state of affairs represented, and the proposition must also be structured. A mere collection of names can’t represent a state of affairs (TLP 3.142). Likewise, as Wittgenstein explains, to accurately express generality one needs to be able to clearly indicate which parts of the proposition the quantifiers apply to (TLP 4.04-4.4011).

Further, according to Wittgenstein, ‘To understand a proposition means to know what is the case, if it is true. […] One understands it, if one understands its constituent parts’ (TLP 4.024). A proposition says that such and such is the case, with this state of affairs constituting its sense. Understanding the sense of a proposition thus means understanding how things are if it’s true. Given that a Tractarian proposition only presents a possibility, i.e. a state of affairs, a possible fact, however, Wittgenstein is able to avoid the problem that plagued Russell’s theories of judgment that already by constructing a proposition one, as it were, brings about what it represents (TLP 4.031). Whilst Russell was consequently unable to explain the possibility of false propositions, this problem doesn’t arise for the Tractatus. It’s dissolved through Wittgenstein’s account of propositions as pictures.

Relatedly, Wittgenstein’s conception that a proposition pictures a state of affairs through the arrangement of names enables him to explain the possibility of a proposition expressing a new sense. Although we need to already understand the meanings of names or have them explained to us in order to understand them, this isn’t the same with propositions with which ‘we can make ourselves understood’ (TLP 4.026; cf. 4.03). Based on our understanding of the logical forms of names we can construct new propositions and be understood by those who know the meanings of the names. Hence, the possibility of a proposition expressing a new sense can be explained on the basis of the mentioned two characteristics of Wittgenstein’s account of propositions as pictures, the referring function of names, and that a proposition must have a determinate logical form (TLP 4.026-4.032, 4.06). The requirement that names have a determinate logical form also dissolves Russell’s problem about how names are combined into a judgeable propositional unity. Because there’s no such thing as an isolated name without a specific logical form for Wittgenstein, i.e. names can only occur in the context of propositions combined in definite ways, there’s no need to try to find any additional ‘cement’ that connects names, such as Russell tried to identify (TLP 3.3, 3.311, 4.22, 4.23). The problem is thus dissolved, rather than answered in Russell’s terms.

Provided this outline of Wittgenstein’s account of propositions as pictures, let me turn to how it informs his conception a correct logical language. In Wittgenstein’s symbolism a logically simple proposition is written as a function of names. ‘The elementary proposition I write as function of the names, in the form “fx”, “ϕ(x, y)”, etc.’ (TLP 4.24). As this indicates, elementary propositions aren’t merely a speculative theoretical postulate. They are really meant to be expressible in Wittgenstein’s symbolism as the terminus of logical analysis. Accordingly, his account of how elementary propositions represent is meant to inform the design of a correct logical language. Indeed, the latter seems clearly the point of the following sequence of remarks, concerned with how propositional signs express their sense, and what, consequently, is the right way to express them in a logical symbolism:

Only facts can express a sense, a class of names cannot.

That the propositional sign is a fact is concealed by the ordinary form of expression, written or printed.

For in the printed proposition, for example, the sign of a proposition does not appear essentially different from a word. (Thus it was possible for Frege to call the proposition a compounded name.)

The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs.

The mutual spatial position of these things then expresses the sense of the proposition.

We must not say, “The complex sign ‘aRb’ says ‘a stands in relation R to b’”; but we must say, “That ‘a’ stands in a certain relation to ‘b’ says that aRb”.

States of affairs can be described but not named (TLP 3.142-3.144).

These remarks can naturally and plausibly be taken to be concerned with the principles for the design of a correct logical language that makes perspicuous how symbols symbolize. In particular, Wittgenstein’s focus here is the logical difference between names and propositions, i.e. that it’s essential for propositions to have an articulate logical structure, and that their having such a structure is what enables them to represent. This, I maintain, is the point of 3.1342, according to which ‘aRb’ represents by ‘a’ standing in a certain relation ‘R’ to ‘b’, instead of its function being misleadingly conceived on the model of a complex sign ‘aRb’ naming the complex object of aRb, and symbolizing in this way.^[11]

Indeed, the same point is made also later in Wittgenstein’s elucidations on the remark that ‘The proposition is a picture of reality’ (TLP 4.01), where he returns to the issue that a propositional sign might not seem like a picture. Here he ventures to claim: ‘It is obvious that we perceive a proposition of the form “aRb” as a picture. Here the sign is obviously a likeness of the signified’ (TLP 4.012). Perhaps we can, in a certain sense, grant this point to Wittgenstein. Regardless of how exactly we should symbolize a standing in relation R to b by using marks ordered in space or time, in some way or another this needs to convey the fact that a stands in relation R to b. To do this we must be able to distinguish a, b, and R, and then represent the fact that they stand in specific relations, like ‘aRb’ does by ordering the names in question from left to right. Whilst there’s a number of possible conventional arrangements to represent this fact, such as writing horizontally from right to left or vertically up or down, the logical structure of this fact must nevertheless be conveyed in some way. In a logically correct language it’s then crucial not to let this be obscured by misconstruing the representation of the fact as a complex name. This, I take it, is one key point of the account of propositions as pictures. This is also important for my argument, because it reveals how the account of propositions as pictures bears on the task of designing a logically correct language. As this indicates, the ultimate expression for Wittgenstein’s account of propositions is a logical symbolism constructed according to its principles. By contrast, conceived as a theory expressed by means of nonsensical theses, the account of propositions as pictures collapses into nonsense.

In conclusion, the point about different possible vs. misleading ways of representing the fact aRb enables me to explain the sense in which I take the Tractatus to be concerned with a correct logical symbolism. As implied by the possibility that we might express the relation aRb by writing horizontally and vertically into different directions, on the Tractatus’ account it’s ultimately whatever the different logically correct ways of representing aRb have in common that enables them to symbolize. Correspondingly, the interpretational claim that Wittgenstein is concerned with the principles governing a correct logical language isn’t to be understood as the claim that he is identifying the correct symbolism with any particular system of signs. Rather, the conception I wish to attribute to the early Wittgenstein is that in logic and philosophy we need some such symbolism that correctly reflects the principles of logic, and that it’s by means of some such symbolism that the correct logical conception is expressed.^[12]

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Notes

Notas de autor