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Language, Vorstellung, and meaning as use.

1. Introduction

If meaning is use in Wittgenstein's public sense and Vorstellung looms as large as it does in the Philosophical Investigations and his other manuscripts, then the use he makes of Vorstellung is an important language-game with a special relationship to meaning. Before I address this relation in detail I want to propose a picture of language, though not quite a traditional picture language, in which Vorstellung occupies centre stage. A string of substantial, recent publications in the field of the philosophy of language may give the impression that the turn to Vorstellung has been rightly discarded as an unwarranted reduction of meaning to psychology and that the research domain of natural language has now been secured and its problems are largely resolved, or at least are resolvable in a certain way. (LePore and Smith 2006; Devitt and Hanley 2006; Davis and Gillon 2004) It is in the spirit of presenting an entirely different approach to natural language that this paper has been written. As such it is part of an attempt to reinsert Vorstellung, translated here as "mental replication and variation of perception," into the theorization of linguistic meaning. It would cause little controversy if one were to say that all features of language, from phonemes to syntax and pragmatics, serve the production and communication of meaning, even if one were to acknowledge at the same time that semantics is by far the least successful theoretical enterprise in the linguistic arena. Nor would it raise eyebrows if one were to align the bulk of existing language studies in order to demonstrate their function in such an emphasis. But it would be an entirely different matter if one were to put forward the hypothesis that all features of natural language are in the service of the imaginability of linguistic expressions. (Ruthrof 2011)

Such a claim flies in the face of the vast majority of theoretical positions on natural language, and yet I want to place this claim at the very heart of this paper. In this choice I have been encouraged by a reading of Wittgenstein which pays attention to the dominant role in the PI of such propositional attitude phrases as "Ich koennte mir leicht vorstellen ..." (I could easily imagine), "Wir koennen uns nicht denken ..." (we cannot think of), "We can imagine ...", "Suppose...." How important a role Vorstellung actually plays in the PI becomes clear by imagining what would happen if we were to eliminate the author's use of Vorstellung and all its derivates from this text. The PI would simply collapse. And without paying attention to Vorstellung we may very well be led, as Wittgenstein was himself in the Tractatus, "to think that if anyone utters as sentence and means or understand it he is operating a calculus according to definite rules." (PI [section]81) The argument in favor of my opening hypothesis is developed in six steps. I begin with a summary of the kind of ingredients and their relations that could make up a theory of meaning in which perception and Vorstellung play a prominent part as components of language. Second, the paper takes issue with the standard view of intension and extension, reserving intensions as appropriate only to formal sign systems and offering a redefinition of extension. In a third move, I address Wittgenstein's use of Vorstellung. The fourth section asks the question of how private mental images really are. I do so from the perspective of Wittgenstein's "private language" argument. In step five I propose to replace the notion of "mental image" by the more general notions of "mental schema" and degree and manner of schematization. Section six addresses the kind of "assertability conditions" that govern the language game of Vorstellung and the aboutness of language. The paper concludes with a proposal for resolving the tension between Wittgenstein's public definition of meaning as "use" and his own ubiquitous use of Vorstellung.

2. How Does Vorstellung Relate to Language?

I take it to be one of the tasks of speculative philosophy to design the kind of frames of inquiry needed in anticipation of science being able to produce a new paradigm for the description of mental acts. Such a new paradigm is evolving as we speak, even if at present we can be no more than reasonably confident about its general direction. (Just et al. 2010) Once our colleagues in neuro-semantics have advanced their research to the point where they are able to offer a persuasive picture of the relation between the semantic features of natural language and their neural basis, philosophers should be ready to assess its results in terms of what actually occurs in language, challenging, as well as interacting with, the new science. This is my second motivation for constructing the kind of projectionist pragmatics advanced here. What is meant by projectionist? While Hume's projectionism refers to the human propensity to spread our mental acts across the world, in Kant, projectionism is enlarged to cover all a priori principles required to form judgments, even to the point where perception, his absolute starting point of knowledge, is colored by the transformations that Anschauungen undergo in human cognition. In Hintikka's mildly Kantian formulation, "as far as our thinking is concerned, reality cannot be in principle wholly disentangled from our concepts." (Hintikka 1969: 109) The kind of projectionism envisaged here is compatible with such a Kantian perspective, while focusing on the mental acts required for placing a sentence in the Vorstellungswelt, such that its signifiers are activated by an appropriate combination of nonverbal signs under the auspices of sufficient semiosis. The habitual or interpretive decision of what is to be imagined in accordance with the directionality and semantic scope of the expression is in each such case a mental projection, which renders "scope" even more controversial than it already is. (Hintikka 1997)

The correction to the Wittgenstein's picture of language proposed here is intrinsically pragmatic in the sense that so-called natural language semantics is, strictly speaking, a contradiction in terms. Though many books have been written on the topic, they are all, without exception, disguised pragmatic theories. This is so because the meaning events generated from the given examples of necessity require a pragmatic act of placing the signifiers in a social context. Not even a seemingly neutral Austinian "locution" in speech act theory can be instantiated as meaningful without some sort of "illocution," even if this amounts to no more than the "illocution" of exemplification. (Austin 1962; Searle 1977) In this strict sense, only a fully formalized semantics could claim the title "semantics" without contradiction; but then, it would no longer deal with natural language, only its formal principles emptied of what makes natural language "natural." From this angle, it is obvious that the kind of projectionist theory advanced here is from the very start of its conception a "pragmatics" rather than a "semantics." If meaning is the community guided activation by speakers of strings of signifiers by nonverbal mental materials governed by concepts in terms of directionality, quality, quantity, and degree of schematization, then each meaning event is by definition a pragmatic event. More briefly, if linguistic meaning is the event of an intersemiotic embedding of signifiers in the communal Vorstellungswelt, then all meaning acts in natural language are pragmatic.

Another strong impulse motivating the arguments presented here has been dissatisfaction with standard descriptions of language conceived from the vantage point of formalized language derivatives, resulting in a shriveling of the "naturalness" of natural language. (Tarski 1956: 267) Given the political power of such descriptions, it should not come as a surprise that only a handful of linguists and philosophers of language are beginning to reinsert the long neglected and yet most central ingredients into the theorization of language: mental acts. (Jackendoff 2002; Hurford 2007) This "corporeal turn" has been as long in coming as it has been necessary. (Ruthrof 1997) Yet in spite of a number of research enterprises pointing towards "embodiment," there is to date no fully-fledged theorization able to embrace the new insights in a coherent theory of natural language. (Gallese and Lakoff 2005; Johnson and Lakoff 1999; Varela et al. 1993; Sweetser 1990) It is against this background that the present paper, as well as its forerunners, has been conceived. (Ruthrof 1997; 2000; 2009; 2010) The bare bones of a theory of natural language at the heart of which I place Vorstellung might look like this.

I preface my proposal by asking two questions. (1) What do we need for a theory of meaning? and (2) What do we need for a theory of meaning in which perception and Vorstellung, its mental replication and variations, play a central role? In answer to the first question I suggest that a theory of linguistic meaning must tell us how arbitrary linguistic signifiers or expressions are transformed such that the speakers of the language understand what the signifiers are about. This could be achieved by an intensional theory according to which meanings are the sort of "definitions" we find in dictionaries, or by an extensional theory according to which signifiers have been systematically related by a culture to classes of objects in the world, or a combination of the two, by a simple verification theory in which sentences are meaningful if they are true and meaningless if they are false, or by a truth-conditional theory in which sentences are meaningful if we can establish the conditions under which they can be judged as to whether the state of affairs they reflect is indeed the case or not. None of these options will be chosen as a promising avenue towards a satisfactory account of meaning in natural language. Some of my reasons for their rejection will emerge as the paper unfolds. In answer to the second question I propose the following redefinitions of meaning, the linguistic sign, the signified, and the concept. I also add the notion of sufficient semiosis as the communal set of constraints within which individual speech performance typically occurs.

Meaning in natural language is the activation by individual speakers under the guidance of a speech community of arbitrary, empty linguistic expressions by nonverbal, iconic, mental materials governed by concepts in terms of directionality, quality, quantity, and degree as well as manner of schematization. The linguistic sign is made up of an arbitrary signifier and a motivated signified. The motivated signified consists of iconic, mental materials regulated by the concept. The concept is a social rule which regulates the iconic, mental materials of the motivated signified in terms of directionality, quality, quantity, and degree and manner of schematization. Sufficient semiosis consists in the boundaries established and maintained by the speech community that constrains and delimits individual competence and performance in terms of imaginability (Vorstellbarkeit); ostension; phonological, syntactic, and lexical use; embedding; recursivity; predicability; entailment; compositionality; appropriate pragmatic activation of signifiers (e.g. degree and manner of schematization); and language-games (e.g. referring).

As a consequence of these definitions, Vorstellung, as redefined, is now at the centre of each and every meaning event. Depending whether our language use is habitual or interpretive, non-conscious and conscious processes will dominate the way Vorstellung functions in our linguistic performance. Given the emphasis here on the association of linguistic expressions with perceptual and quasi-perceptual realizations, a number of traditional approaches to meaning in the philosophy of language will have to be rejected. Meaning is argued here to be neither determined by definition, or intension, nor by the relation of a term to a class of things in the perceptual world, or extension, at least in the standard sense, nor by any verificationist or truth-conditional relations, but rather by whether a sentence is imaginable within the bounds of sufficient semiosis. If it is, meaning can be established; if it is not, the expression is meaningless. So far, what has been said, however, looks like no more than reckless assertion. So, on what grounds are some of these other theories, or rather bases for theories, so readily dismissed? Having dealt with the relation between truth-oriented theories and Vorstellung elsewhere, I will focus in the following section on intension and extension. (Ruthrof 2011)

3. Intension and Extension

Meaning in natural language is sometimes described in terms of intension and sometimes via extension. This pair of concepts is useful up to a point. We can regard intension as the kind of meaning that is defined by the internal relations amongst definitionally governed terms. In a relation of x = y + z, y is intensionally defined as x - z. Intension, then is a purely syntactic operation in formal sign systems. But how would this work in natural language? Applying the same criteria to ordinary language, dictionaries are prime examples of intensional relations. So someone could learn a dictionary by heart and as a result would be in a position to know a great many syntactic substitutions. Yet without at least one extensional link that person would only have a syntactic grasp of signifiers, but no signifieds. She would have a language without pragmatics. For the purpose of defining meaning in natural language, then, intensions do not look promising, even though, for speakers of a language they are handy shortcuts to not yet learned or forgotten meanings. When in doubt as to the meaning of a word, we turn to a dictionary. In this sense, dictionaries are part of the communal, regulatory side of languages; in short, they are part of sufficient semiosis. Yet, if we call the verbal substitutions of a dictionary "meaning," we have embraced an intensional conception of meaning without being aware that none of the dictionary entries could mean anything unless we had already acquired the pragmatic link between at least one entry and the "outside of language," either in its perceptual sense or as part of Vorstellung.

Instead of calling this "outside" the perceptual world of objects, in terms of the theory advanced here, we shall call it the Vorstellungwelt, the imagined world of a culture.

As the contradictions that flow from the translation of "Vorstellung" as "image" show, the two can only be sometimes used as synonyms without pragmatic damage. For example, neither the level of generality of Vorstellung nor its broad semantic scope from replication to the wildest speculative fantasies are well looked after by "imagination," which favors the imaginary and merely imaginary. The term Vorstellung is chosen here throughout for its analytical sense of "putting in front of one's mind," its sense of any particular imagined instance, as well as for its sense of generality which allows an olfactory or gustatory Vorstellung where "image" tends to introduce a misleading analogy. At the same time, the world of Vorstellung is not just the "outside of language" but also contains natural language as part of our mental equipment. Wittgenstein typically invites his readers to "think of" or "imagine" a sentence, as well as a variation of perceptual reality in Vorstellung.

No suggestion, however, is being made here that the Vorstellungswelt is some free-floating domain. Quite the contrary, the Vorstellungswelt of each culture is anchored in the perceptual world. Yet since perception is always already modified by Vorstellung, cultural worlds typically differ from one another to certain degrees. What is more important is the observation that such anchoring is not a continuum, but rather a sporadic occurrence. Compare, for example, the way Hilary Putnam thinks language is linked to the perceptual world. "It seems as if language is like a great balloon, anchored to the ground of non-linguistic fact only by a number of widely scattered and very thin (but all-important) ropes." (Putnam 1979: 4f.) We can take these remarks on board while insisting that language is part of a much larger balloon, the Vorstellungswelt which, like Putnam's language, is fundamentally grounded, though in a sporadic fashion, to the world of our senses. How does this position affect the notions of intension and extension?

I cannot address here the literature on intension, which is as impressive as it is vast. What I can do is pick out one intriguing defense of intension as the king pin of linguistic meaning presented by William Dowling. (Dowling 1999) Attempting a double rehabilitation of New Critical interpretive practice and the intensional theory of meaning advocated by Jerry Katz, Dowling insists that "determinate meaning" is as much part of the inside of language as is syntax. The New Criticism is seen as a sensitive forerunner of the kind of intensional picture of language we find in Katz. (Katz 1990; 1972) Two stanzas of John Donne's "A Valediction: Forbidding Mourning" serve Dowling as demonstration.
Dull sublunary lovers' love
(Whose soul is sense) cannot admit
Absence, because it doth remove
Those things which elemented it.

But we, by a love so much refin'd
That our selves know not what it is,
Inter-assured of the mind,
Care less, eyes, lips, and hands to miss.

Dowling makes the startling claim that the central meanings we construct in our reading of these lines are intensional determinations. But here lies a fundamental error which can be teased out by a comparison of the poet's stanzas with a sign system in which Dowling's assertion is actually demonstrable. In x = y x z the formal sense of x or its "meaning" is intensionally fully determined by its relation to the specific combination of x, y and z. As in the poem, knowledge of the sign system of which this equation is a part is essential to be able to make this observation. The crucial difference is that knowing a formal sign system and knowing a natural language are two fundamentally different capacities. In the formal, intensionally governed sign relations, it is only knowledge of the syntactic rules that is needed. In natural language, and its use in the poem, syntactic competence is also a necessary but not a sufficient condition. Here meaning can be achieved only if we are able to project a quasi-perceptual scenario of human interaction and speech to fit the words in their specific order. This we can do only if we have the double experience of human life in Vorstellung and its possible, highly schematic representations by language. Nor should we conflate these two. Although they go together in human existence, knowledge of life and language cannot be assumed as given. That interpreting the poem is not as easy for young readers is not just the result of limited experience of language but equally the consequence of a still evolving world of their Vorstellung. The tentatively anchored balloons of language and Vorstellung are still being filled. Why then do I think that Dowling's analysis is flawed? He thinks that the entire pragmatic performance required to bring these lines to life is contained in the signifiers. Yet signifiers are empty by themselves, "arbitrary" in Saussure's terminology, and so their aboutness cannot be contained in them. They are in need of extensions, or signifieds, for instance in the sense defined earlier. The question, though, is what kind of extensions we are talking about that would offer the best predicate for explaining the meaning events of natural language.

Extensions, in contrast to intensions, can be regarded as the links between a sign system and its outside, classes of things we discover in the real world, a possible world, a fiction, or our Vorstellungswelt, that is, the kinds of things that constitute the mental world of a culture. Since natural language is not self-sufficient like formal systems, it is therefore fundamentally extensional. But here the problems only begin. Philosophers are sharply divided as to what sort of extensions we are talking about when we describe language. If Putnam's language balloon is only sporadically anchored in the actual world, extension as the secure link between words and world does not go through, nor does Putnam's own preference for scientific theories. It is not just that the balloon analogy bites here as well, it is also that we can't entrust a scientific elite with the stewardship of natural language. Too much is at stake, and in particular the all-important idiomatic character of language, a feature which defies mathematization and curtails discursivity, and yet contributes crucially to Tarski's "naturalness" of natural language. (Tarski 1956: 267) What we are looking for is a connection which is all-embracing rather than 'scattered'. If the physical world, its scientific theorization, and propositions summing up referential backgrounds have to be discarded as extensional anchors, we may wish to consider our nonverbal readings of the world and their modifications in Vorstellung. Given the bias of this paper, it is to nonverbal readings, to iconic, mental materials that we turn, consisting of olfactory, tactile, thermal, aural, gravitational, visual, emotional and other readings of the world, under communal, conceptual regulation, as defined above. If we accept this picture, meaning would be extensional in the special sense of a relation between signifiers and nonverbal mental acts.

4. Wittgenstein's Vorstellungsklavier

To shield such a picture of language from the challenges of subjectivism and mental solipsism, we must address the question of how the competence of individual speakers relates to the speech community. An equally serious problem to tackle is the charge of the private nature of mental acts, an issue I will discuss below. While it is safe to reject the idea that natural language can be called a symbolic system in which everything is entirely ruled by definitions and so is objectively public like chess, we cannot but agree, as do most philosophers of language, that Wittgenstein is right in his critique of the very possibility of a private language. (Wittgenstein 1966: [section]202; 243ff.) Language cannot be private of necessity. Put simply, the reason for this is that our conception of language entails that it is governed by rules, and what is so structured is communicable in principle. We shall see shortly that this argument does not however protect Wittgenstein from being employed against the very element he wishes to ban from natural language, mental acts. But first, a few remarks on the public nature of language. Certainly, in actuality, there is no language that is not embedded, at least potentially, in a speech community and its pedagogy as a training apparatus for the speakers of the language. Such pedagogy, in the broad sense, amounts to making individual speakers competent in the task of linking linguistic expressions with appropriate mental, nonverbal scenes. This is why when we hear or read a sentence such as "The engagement between x and y is off" we are able to imagine, at least in a schematic manner and even if we don't want to, the scenario the sentence refers to. The guidance the speech community so exerts upon its members can be regarded as a complex network of constraints, which I have summed up under the term sufficient semiosis.

At the centre of the theorization of natural language as a public phenomenon is Wittgenstein's definition of meaning as "use" (PI [section]30, 43, 138), as for example in his statement that the "Gebrauchsarten (kinds of use) of 'understanding' make up its meaning." ([section]532) Given the parlous state of natural language semantics it should not be surprising that this pragmatic notion of meaning has become so very influential. In order to render meaning observable, Wittgenstein strips it of any possible mental, private component, instead focusing on the way the speakers of a language publicly engage in a variety of overlapping Sprachspiele or language-games. As such, meaning can be equated with use. "The meaning of a word is its use in the language," at least in most cases, as he qualifies. (PI [section]43) As powerful an intervention in the longstanding debate about an adequate natural language semantics and pragmatics this has been, its main drawback is that while it describes well what we see and so satisfies scientific demands for evidence, it may very well cover up features of natural language that are not so readily identified, yet likewise play a necessary role in the meaning process, a suspicion underlying the arguments developed here.

If we stay with Wittgenstein's position on meaning as "use," the tentative proposal for meaning as the community guided activation of signifiers by nonverbal mental materials does not go through. We must then either abandon such a scheme or modify the Wittgensteinian picture to let mental acts in through the backdoor, but not without redefining their character. To choose the latter course is to significantly broaden Wittgenstein's notion of "use." I will do so by employing his own strategy which he mounts against the possibility of a private language. But first, a brief look at the motivation behind his arguments in the Philosophical Investigations. In the Tractatus, which he strongly qualified in his later work, Wittgenstein had regarded propositions as Bilder for possible states of affairs. (TLP 4.01) The states of affairs so depicted are the sense of a proposition. This postulates a relation between reality and his picture which he describes both as "pictorial form" (TLP 2.151) as well as a "logical form" (TLP 2.18). Furthermore, language as the "totality of propositions" (TLP 4.001) presents pictures which can be either true of false. (TLP 2.21)

As Michael Beaney argues, in the Philosophical Investigations, Wittgenstein has performed a turn from "simples" to "samples." (Beaney 2006) In the PI, the simples that are supposed to make up language are rejected in favor of Sprachspiele out of which every natural language is composed. Propositions are no longer regarded as the definitionally ruled common denominator of language (PI [section]65) and replaced by looser forms of relations, "family resemblances" (PI [section]65) and language-games (PI [section]7, 22, 24, 47, 49, 53, 65, 77, etc.) This results in a radical complication of the relation between language and what it is about. What is retained, however, is the public nature of meaning. Just as the operations of logic and the senses of their propositions are open to inspection, so too are language-games publicly displayed, much as any other communal performance. Wittgenstein now makes two critical interventions. One, he stands the Augustinian "naming theory" of language on its head by saying that names are the result rather than a condition of language-games. (PI [section]49) In another decisive move he claims that "it is not the purpose of the words to evoke Vorstellungen. (It may, of course, be discovered that that helps to attain the actual purpose)." (PI [section]6) Here, Wittgenstein refers back to [section]2 in which he characterizes a "primitive" language in which Vorstellung appears to do important work, but only covers part of what we now call a language. As the PI unfolds, it is grammar, rules, the community of speakers, and justification that are stressed as more important ingredients. The question is whether Wittgenstein's Vorstellungsklavier merely produces occasional and incidental tones in the meaning symphony of natural language, whether such tones are a constant side effect, or whether the melodies so created are an indispensable and necessary feature of linguistic meaning. "(Uttering a word is very much like striking a key on the piano of our imagination)." (PI [section]6) If one of the first two answers proves to be correct, then the definition of meaning as use stands confirmed. However, if the last answer is more appropriate, then both meaning and use have to be redefined to include the very mental acts Wittgenstein set out to eliminate. Or, rather, we may have to agree with his elimination of Vorstellung as mental "image" as too specific a candidate for meaning, only to replace it by something else at a more general level. What we must retain, though, is Wittgenstein's insight that meaning is best described as a process rather than a property.

Any such attempt at redefining Wittgenstein's "use" faces a massive obstacle, his sustained rejection of Vorstellung as a mainstay of natural language. Another difficulty is the bugbear of the translation into English of the term Vorstellung itself, confounded by its ubiquitous use throughout the PI. "Vorstellung is not an image, but an image may correspond to it," depending on the kind of Vorstellung we are talking about, one might add. (PI [section]300) Or again later, "Vorstellung must be more like its object than an image." (PI [section]389) When Wittgenstein writes of the Vorstellungsbild, "image" will do. But more often than not the translation of Vorstellung as "image" muddies the theoretical waters, especially when it comes to gustatory, thermal, olfactory, auditory, gravitational and other non-visual sensory impressions. Perhaps the best solution is to leave the original term untranslated and allow readers to gradually get the author's intended meaning, as they get accustomed to his "use" of the term in context, and perhaps even by means of appropriate Vorstellungen. A case in point is Wittgenstein's phrase "motorische Vorstellung." Although we have equivalent quasi-visual mental representations, the emphasis is clearly on a kinetic conception.

In order to foreground public use as the assertability condition for meaning, Wittgenstein is trying to wean us from the habit of associating language with Vorstellung. This is why he speaks of Vorstellung as "foggily drawn scenes" which cannot "explain intention" and points out that "we communicate with other people without knowing if they have this experience too." (PI p. 155) In a strict sense of "knowing," Wittgenstein is of course right. What he wants to get away from is the psychological contamination of the process of meaning. "'I meant this by that word" is a statement which is differently used from one about an affection of the soul' (Affektion der Seele). (PI [section]676) However, the elimination of something as ethereal as the "affection of the soul" is not the same as getting rid of Vorstellung, of which we can have a much more robust conception. Certainly, within a speech community, we take it on trust that its members have more or less the same Vorstellungen as we do. Moreover, Wittgenstein's objection could, with much the same justification, be made to seeing hearing, smelling, feeling, or tasting. Sometimes, we ask "Can you smell what I smell?" on the assumption that the other person shares roughly the same olfactory apparatus and interpretations, which can be verbally confirmed. The same may go for the aboutness in Vorstellung of language in general.

In his task of demoting Vorstellung as an important ingredient of language, Wittgenstein speaks of "image-mongery" (Vorstellerei), which "is of no interest to us." (PI [section]390) He cautions against a primitive view of language, as well as allowing the analysis to oscillate "between natural science and grammar." (PI [section]392) He is adamant that the process involved in Vorstellung tends to be a distortion (PI [section]368) inclined to introduce absurd scenarios, such as imagining a parrot whom God has given the gift of inner speech. To this Wittgenstein objects by saying that first I have to imagine a god, then an unlikely situation. Vorstellung is thus heaped on top of Vorstellung. (PI [section]346) One could of course intervene here by pointing out that there is no difference between Vorstellung and language in terms of their fictional potential. Indeed, in both perceptual and fictional usage, language and Vorstellung appear to run parallel with one another without any final destination.

It would seem that Wittgenstein's assault on Vorstellung has to do with his reluctance to conduct the theorization of language via any form of interiorization. In the use of language, he writes, "it seems to us as if there were something coupled to these words, which otherwise would run idle ... As if, so to speak, they geared into us." (PI [section]507) It is not surprising that when Wittgenstein speaks as the engineer he was supposed to become, the externalization of the workings of language would be at the forefront of his mind. Not always however, does Vorstellung get the short shrift. Occasionally he concedes that Vorstellung can also function as mental replication. "The aspects of the triangle: it is as if a Vorstellung came into contact, and for a while remained in contact, with the visual impression." (PI p. 176) A similar emphasis can be found in Wittgenstein's observation that "Vorstellung must be more like its object than an image." (PI [section]389) But even then, we are left in no doubt as to where to find the essence of language, which "is expressed in grammar." (PI [section]371)

At times, Wittgenstein charges his interlocutor and, it would seem the reader, with the bad habit of "steering towards the idea of an inner ostensive explanation." (PI [section]380) Without being able here to address the much-rehearsed domain of "ostensive definition," I would qualify Wittgenstein's position by saying that his critique only works as long as we see a few ostensive explanations in isolation. As soon as we embed ostensive procedures in an ostensive series and other nonverbal explanations and comparisons, typical of teaching situations, the problem disappears. It is easy to guide the student towards the color, shape, or weight of an ostensively used object by reference to color scales, illustrations of forms, and the process of weighing in conjunction with verbal clues. As often in philosophy, if we cast our net too narrowly, a problem arises that does not occur in social practice. Quine's "indeterminacy of translation" is another case in point. The indeterminacy dissolves in sustained cultural interaction. The same rehabilitation can be made in favor of ostensive moves in Vorstellung. Likewise, Wittgenstein's objection to Vorstellung in [section]443 is open to question. "'Here is a red patch' and 'Here there isn't a red patch.' ... The word 'red' occurs in both; so this word cannot indicate the presence of something red." Yet both sentences require that we are able to imagine the color red. Furthermore, the negation rests on our faculty of imagining its opposite, presence. Wittgenstein recedes from this kind of explanation to the use of the term "Satz," which could be rendered either by "sentence" or "proposition." The standard translation goes with the latter. "The assertion of the negative proposition contains the proposition which is negated, but not the assertion of it." (PI [section]447) Do we not vary propositions as well as sentences according to their modalities? Of course we have been trained to do so. But do we not do so in Vorstellung, even if there would be no difference if we did it on paper? At the very least, performing a negation in Vorstellung has the advantage of the economy of speed. And perhaps speed is one of the advantages that made Vorstellung such a successful, evolutionary addition to the human make-up. Imagining a leopard behind foliage beats being taken by surprise.

There also hovers the more general question above the PI and its demotion of Vorstellung in that the discursive strategies of the PI interact in such a manner that Wittgenstein's critique cannot be taken as radically as it usually has. Not only is the text a 'perpetual dialectic' between the author, his "imaginary interlocutor," and the reader (Kripke 1982: 3), the reader must also deal throughout with a multiple and complicated imaginary scenario. We must follow the author's instructions to "imagine," "suppose," "think of" a variety of mental scenes, and construct two personae, the author and the author's less insightful alter ego, and their thoughts, quite apart from our own interpretive negotiations. In all this, Vorstellung proves an indispensable tool; so much so that we could say that for every Sprachspiel there is a corresponding Vorstellungsspiel.

Nor is everything that Wittgenstein wrote in the Tractatus wiped out in the later PI. Rather, the Tractatus is now seen as a specific and very limited language-game of logic that cannot be taken as a basis on which to describe the infinitely more complicated relations characteristic of natural language. For example, the idea that "If I know an object I also know all its possible occurrences in states of affairs' is compatible with Wittgenstein's tendency in the PI to invite the reader to 'imagine' this or that scenario as a reliable guide to understanding." (TLP 2.0123) Except that now it is an imaginative process rather than propositions that do the work. So frequently is this device employed throughout the PI that without it Wittgenstein's very philosophical style of inquiry could not get off the ground. Certainly and importantly, Vorstellungsspiele play as much a role in the book as do Sprachspiele. Phrases such as "We can imagine ...," "It is easy to imagine ...," "Think how ...," "Now imagine ...," or "Suppose ..." ask the reader to conjure up and participate in imaginary variations of possible actual scenarios, an exercise that is at the very heart of his philosophizing. He not only takes it for granted that we can entertain possible occurrences in our Vorstellung, he takes such advantage of this capacity that one may wonder whether this is merely a methodological device he found more convenient than to point to actual perceptual situations, or whether Vorstellung is perhaps more deeply implicated in language than his rejection of mental representations as components of meaning suggests. As Wittgenstein insists, "it is not the purpose of words to evoke Vorstellungen," even if the latter may prove helpful in the "practice of the use of language." (PI [section]6; 7) What is not entirely clear is whether this prohibition is as categorical as it looks or whether it is motivated by getting the reader to grasp the centrality of the public nature of meaning as Gebrauch and the concomitant nesting of individual use within the confines of a speech community. Or, perhaps the gulf between these two alternatives is not as wide as we may think. If so, we may ask how the reader typically follows Wittgenstein's instructions in the Vorstellungsspiel, a special version of "following a rule." We cannot help but play with variations of possible perceptual and quasi-perceptual scenarios such that our mental replication of the color sepia in our as well as in other people's Vorstellungsklavier appears in such a way as to make it fit into all kinds of "occurrences," including those belonging to memory. We can do this because we are in a position to "free" our initial experience and subsequent cases from their singularity. This ability is not a verbal act, but rather a precondition of being able to think in terms of classes, kinds, sets, and other subsumptions and as such must have preceded the invention of language by a very long shot. Nor is it plausible that whatever kind of "thinking" that tigers perform is restricted to specific percepts. Their finely honed hunting techniques are the result of training and experience both of which must draw on classifying non-linguistic conceptualization. Much the same must be assumed about our hominid ancestors. The moot point here is what form such pre-linguistic conceptualizations take. If they are not linguistic, nor propositional, they could be something like generalized percepts or nonverbal schematizations. Whichever the appropriate description, natural language did not have to invent all its generalizations into kinds and classes, but was more likely in a position to impose refinements on an already available procedure. In the PI, Wittgenstein is torn between foregrounding Vorstellung as a methodological device and dismissing it as a legitimate component of meaning, since "nothing is more wrong-headed than calling meaning a mental activity!" ([section]693)

Indeed, there may very well be a contradiction in the PI. On the one hand, Vorstellungen are dismissed as private and not belonging to language, on the other, they appear indispensable in the process of communication, of which language plays an essential role. As the text of PI demonstrates, there can be little doubt that Vorstellungspiele, for Wittgenstein, occupy a central place in our mental life and, just like Sprachspiele, are "part of an activity, or a Lebensform." (PI [section]23) The tight relation which I am arguing here exists between Vorstellung and language seems to be assumed by Wittgenstein in this passage. "When we forget which color this is the name of, it loses its meaning for us; that is, we are no longer able to play a particular language-game with it. And the situation then is comparable with that in which we have lost a paradigm which was an instrument of our language." (PI [section]57) Baker and Hacker's analysis shows that Wittgenstein merely uses this as a possible objection to his position, rejecting the relationship between simples of language and simples of Vorstellung. Yet even if we replace simples and samples by two parallel systems, those of language and the Vorstellungswelt, if there were no relation between the two, Wittgenstein's entire method of inviting us to project mental scenarios in order to get at the nature of language would be spurious. According to Baker and Hacker, "A speaker who assigned meaning to 'red' by reference to mental images and then forgot what color red was would be just as badly off as one who assigned meaning to 'red' by reference to a single physical sample which he later lost." (Baker and Hacker 1983: 117) But this is not a plausible representation of what could be going on here. If a speaker lost his Vorstellung of "red" in connection with the term she could be retrained by the community. If the community as a whole dropped the shared mental schematization of "red," its meaning would indeed be gone, as is the case with lots of forgotten combinations of signifiers and their activation by communal, conceptual regulation of iconicity. So, either Wittgenstein is wrong or Baker and Hacker's interpretation is. Certainly, the kind of systemic relation between Vorstellung and language that Wittgenstein urges the reader to perform cannot be empty. If it is, that is, if our Vorstellung fails us, then meaning fails. And since meaning in the PI is the use of a particular language-game, if Vorstellung fails, we are at the same time incapacitated to play the language-game. Note, however, that it was not first our ability of engaging in the language-game but rather the loss of the connection of the perception of a color and its name. To invoke Putnam's thinly anchored balloon once more, the failed connection between an imagined color in Vorstellung and its name was the source of the failure of meaning. This shift is supported by Wittgenstein in the same paragraph, where he insists that "the meaning of the word 'red' is independent of the existence of a red thing." Perceptual existence is of course different from Vorstellung; after all, the latter depends on the former. Could we imagine a color that does not exist? Some mixture that does not exist on the spectrum? So much seems certain, for each individual speaker, losing the Vorstellung of red would also destroy its meaning for that person. In terms of meaning being a community regulated process, such a speaker would be pragmatically handicapped. Now the merely incidental connection between mental act and word has been seriously compromised. The two main reasons why Wittgenstein did not pursue the significance of Vorstellung in this respect seem to me his behaviorist convictions and an unacknowledged Fregean assumption of the private nature of mental images. It is to the second of these likely motives that the next section addresses itself, with a double emphasis on the alleged privacy of mental representations and the question whether Wittgenstein has perhaps eliminated such phenomena too readily.

5. How Private Are Mental Images?

When Frege dismissed Vorstellung from Sinn, he felt he had good reasons to do so. Driven by the ideal of a pure and unambiguous Begriffsschrift, he thought it would be possible to transfer the characteristics of formal sense to natural language sense without damage to the description of language. This is why he did not deem it necessary to give any justification for his equivocation of the sense of geometric entities and the sense of such natural language terms as "morning star" and "evening star." Yet, justifications are normally a sine qua non in philosophy. Frege must have been sure that there was no problem to address. So it was just another similar step to disrobe the employment of natural language terms further by removing the component of Vorstellung. In this case, however, Frege did provide an explanation, namely that since different persons have different Vorstellungen associated with linguistic expressions, such associations distract from the purity of thought to which the components of sentences contribute. (Frege 1970) Though Wittgenstein was skeptical of the "clarity of logic" that "bedazzles" us when we look at natural language, he still seems to have been too much in the shadow of Frege's scientific enterprise to completely shake off the last remnants of this kind of mathematization. Certainly, mental images are not to be invoked as components of meaning in the picture of language that emerges from the PI. They are at best incidental. One objection one can make to Wittgenstein's critique of the picture theory is that it does only half the job. Intent on correcting the false start of the Tractatus, Wittgenstein was driven to show the shortcomings of that sort of picture theory in which propositions and the facts of the world are related in an isomorphic fashion. This is perhaps why he terminates his critique once he had shown that mental images may occur and that they may even assist us in understanding certain things, but cannot provide a basis on which to build a theory of natural language.

Wittgenstein's caution concerning Vorstellung applies not only to the specifics of mental images but also to their generalized form, even though the original text carefully distinguishes between the two, "Vorstellung" and "Bild." As a result, a conflict arises in the English translation. Comparing the German original and the English texts of the PI we find that Wittgenstein's Vorstellung and vorstellen are invariably translated as "image" and "imagine," a practice which contradicts Wittgenstein's point that "a Vorstellung is not an image, but an image may correspond to it." (PI [section]301) This means that his objection to regarding mental acts as components of linguistic meaning is actually stronger than it appears in the translation. Not only are the specifics of mental images discarded, but also the more general level of mental activity of Vorstellung of which images are a small part. So we need to ask and answer two questions, how private are mental images and how private are Vorstellungen? Perhaps both of them can be answered by applying the criteria provided by Wittgenstein himself in his critique of the notion of a "private language."

Roughly following Kripke's summary, the "private language" argument looks as follows. We can accept that our language expresses concepts which, once acquired, we are justified in applying. Yet, Wittgenstein insists, "an 'inner process' stands in need of outward criteria" (PI [section]580). We can find such outward criteria in "circumstances, observable in the behavior of an individual, which, when present, would lead others to agree with his avowals." (Kripke 1982: 100) This is why we must look at circumstances under which speakers employ a language-game in such a way that they can be said to have followed the relevant rules. Individual rule following, however, remains below the radar of determination. What is required is the way an individual speaker follows rules within community constraints. The success or failure of individual rule practices can now be ascertained as an empirical fact open to communal agreement. Whatever inner process makes natural language what it is, and whatever its performance by individual speakers, it is at the level of sufficient semiosis that it is decided whether or not someone can be regarded as a speaker the language.

In both Kripke's and this account, Wittgenstein's theory of natural language is "one of assertability conditions." (Kripke 1982: 110) The "private language" claim however also fails on the grounds that following a rule privately violates the very concept of a rule as something any person could follow. And since a language is by definition rule governed and so communicable, such a "private" language could be private only de facto, but not in principle. What then about a person who uses "private" words "to refer to what can only be known to the person speaking; to his immediate private sensations. So another person cannot understand the language"? (PI [section]243) Since here too, as Baker and Hacker show, "linguistic competence (understanding a language) is mastery of a rule-governed technique," speaking of a "private language" is a contradiction in terms. (Baker and Hacker 1983: 267) Or, in P.F. Strawson's words, "the idea of a language of any kind used only by one person was an absurdity." (Strawson 1971: 28) The proof of the pudding is neatly provided in Bill Bryson's account of "Boontling, or harpin' boont," which started as an attempt at creating a private language, but got out of hand and for forty years survived as a local dialect in Boonville, north of San Francisco. (Bryson 2008: 232f.) If language is by definition always already social, then we should be persuaded by the claim made by John Lyons that "there is an intrinsic connection between meaning and communication." (Lyons 1981: 32) But all this leaves us with a dilemma as we resume our discussion of mental images. On the one hand, mental images are said to be private; on the other, they appear to play a big part in social interaction. This dilemma could be resolved if one were able to show that mental images are likewise subject to rules, even if such rules may prove a little more obstinate to identify than those of language.

In an imaginary dialogue between P. and Q., John Wisdom has P. open the conversation by saying "When you say 'How blue the sky is' you know what you mean but I don't know and can't know what you mean and nor can anyone else." (Wisdom 1973: 27) To any ordinary English speaker this sort of statement looks nothing short of ludicrous. Of course, we roughly know what P. means in the sense of understanding what he is saying. Even a color blind person has become attuned to take on trust that whenever someone utters this sort of sentence, she understands what the words amount to pragmatically and accepts the statement on condition that the way she imagines the sky is consistent with the typical way people with normal vision say they see it. In other words, the sentence "How blue the sky is" is regarded by members of a speech community as standard verbal communication of mental images to be taken on communal trust.

Mental images, I want to say, are not as private as they are assumed to be in the literature and very much for the same reasons that Wittgenstein invokes for his position on the necessarily public nature of language. For whatever goes on when we have mental images is not private of necessity. It too is subject to constraints and typification. Consider the following cases of actual pictorial representation. When eight "mad" Buddhist monks of the Song dynasty in China in the 12th century AD united to paint, they created a wild "expressionism," Chinese style. Wild it may be, but it is immediately recognizable as a style, which means there are regularities within the seeming chaos. Not only have art specialists isolated these rules for the educated elite, the style itself has had its own pedagogic effects, training Chinese audiences over many centuries into appreciating the special quality of those paintings and the regularities of their iconicity. And once so trained, the viewers' mental images tend to move along the structural lines laid down by those monks. Cubist mental images became a fashion once Picasso had made his pictorial deviations from the norms of painting his personal style. The Picasso museum in Barcelona neatly demonstrates the painter's transition from the rules of the academy to the rules of the new paradigm. Much the same can be said of music and all other arts, repeating as they do this training of communal, mental acts by way of the constitution of ever new rules for Vorstellung. Such is the working of the sublime, as that which cannot yet be presented but must be, imposing rules in defiance of established forms. (Lyotard 1992: 15)

The most pervasive and non-sublime of all such nonverbal, mental grammars is the televisual screen on which prefabricated combinations of language and mental imagines appear as a never ending digital stream. As a result of this pedagogy, the viewer must make an effort not to reproduce the tele-visual images of blue helmeted soldiers on the verbal cue of "United Nations peacekeepers." Such is the power of the repetition of nonverbal typifications. In addition to cultural constraints on our mental images, there are biological constraints starting with the pre-given ratio of 1 million visual input cells compared to 1 billion neurons turning the incoming information into human perception. Roughly the same ratio applies to the perceptual realizations initiated by our other four senses. It is with reference to such ratios that Johnson and Lakoff, for example, speak of "neural concepts." (Johnson and Lakoff 1999: 19) What interests us here is that the intrinsic human neural activity far outstrips that of its perceptual antennas by such an immense margin. Nor is it likely that this asymmetry is restricted to a mere quantitative difference. Since we are able to vary perceptions infinitely, at least in principle, in Vorstellung, the resulting variations are likely to be different also in kind. After all, Wittgenstein's Vorstellungsklavier is able to replicate as well as dramatically distort perceptual input. None of these variations, though, as we have suggested, should be assumed to be any less structured than language. Hence the difficulty of originality in art.

The claim of the structured and therefore rule governed nature of mental images has found recent support also in the idea that "conceptual blending" is already part and parcel of the human perceptual machinery long before the arrival of language. Indeed, according to Gilles Fauconnier and Mark Turner, conceptual blending had to evolve to a high degree of complexity before natural language could arise. "Language arose as a singularity. It was a new behavior that emerged naturally once the capacity of blending had developed to the critical level of double-scope blending." (Fauconnier and Turner 2002: 181) Before this advanced stage of largely unconscious operations in the human brain was reached hominid development had already achieved the capacity of "single-scope blending," conceptual "compression" and "decompression" relative to conceptual "frames." As an example of single-scope blending the authors cite the sentence "He digested the book," where the conceptual domains of eating and reading are integrated in a way that allows us to unite all the features we tend to associate with each process. As a result, "the topologies of the inputs" reappear in the topology of the blend. In the conceptual blending of "double-scope networks" the relation between the topologies is complicated in that the "inputs clash on causality, intentionality, participant roles, temporary sequence, identity, and internal event structure" resulting in highly creative blends. As the authors demonstrate, interpreting such forms of blending reveals a complexity of interconnections which, in actual language use, remains typically hidden. (Fauconnier and Turner 2002: 131-135) What is relevant for our discussion here is the non-conscious as well as conscious background of nonverbal materials that are conceptually compressed, decompressed, blended and refined by language. Compression and decompression can be aligned with degrees of schematization, while single-scope and double-scope blending would be covered by the manner of schematization in our initial set of definitions.

The story of the long evolutionary road from simple mental blending in mammals to human simultaneous, multiple assemblages of meanings in double-blending in conjunction with language, as presented by Fauconnier and Turner, suggests that we should discard the view of mental images as lacking organization, structure, and rules. To this extent, then, mental acts are not as free or private as we have been led to believe. If we accept this correction, Wittgenstein's notion of following a rule applies also to Vorstellung. This paves the road for the claim that the combinations between words and their mental projections can be understood as fairly well established patterns which are neurally transmitted, culturally modified via pedagogy and reinforced by semiotic practice to form a pivotal part of our Vorstellungswelt. The same, cum grano salis, holds for nonverbal signification. As David Crystal notes, "the communicative value of tactile activities is usually fairly clear within a culture," that is, also in our Vorstellungswelt. (Crystal 2008: 6) This does not mean that members of a speech community have all been trained into producing such combinations in identical fashion. Nor is strict synonymy a necessary condition for communication. As Putnam notes, linguistic competence is always only a mastery of a portion of the totality of a language. This, he argues, is a consequence of the "linguistic division of labor." (Putnam 1977: 246; 228) Nor is any individual pragmatic mastery of specific meanings ever identical with that of any other speaker. And yet communication occurs, because both competence and performance are embedded in sufficient semiosis. We understand the language and our fellow language users sufficiently to guarantee successful linguistic exchange. Roughly the same observations can be made about the competence and performance in the domain of Vorstellung

and mental images. Each member of a cultural Vorstellungswelt shares, produces, and communicates with the help of mental images and other mental projections because they are similar enough; they suffice. This makes mental acts intersubjective rather than private. They have been de-privatised.

6. From Image to Schematization

It is now time to return to Wittgenstein's insistence that "a Vorstellung is not an image, but an image may correspond to it." (PI [section]301) Wittgenstein here employs the ordinary use of the term Vorstellung indicating a level of generality of which mental images may be specific instantiations. Olfactory memories, for instance, are thus subsumed under Vorstellung, though not as images. A further step on the ladder of generalizing mental acts is Kant's distinction between the schema as "monogram" and the image as its specific realization. "The image," writes Kant, "is a product of the empirical faculty of reproductive imagination; the schema of sensible concepts, such as of figures in space, is a product and, as it were, a monogram, of pure a priori imagination, through which, and in accordance with which, images themselves first become possible." (B181/A141f.) One obvious reason for needing a level more general than mental images is that much of the specifics of Vorstellung, such as gustatory, thermal or gravitational readings or realizations of our own emotions and sensations are not well characterized as images. This is where a reworking of Kant's schematism may prove a trustworthy old avenue for new thought. If Kant's "monogram" is the general schematic condition for mental images and other sensuous readings, such as olfactory realizations, the schema must however not be assumed to be "congruent" with such mental realizations. It cannot be transformed into an image at all. "The schema of a pure concept is something that cannot be brought into an image, for it is pure synthesis," serving as it does the purpose of subsuming all "Vorstellungen." (A142/B181) It is at the level reserved by Kant for the monogram as a tertium comparationis that we are able to collect and compare our nonverbal readings of the world and their extensions and variations in Vorstellung by way of a more general process of schematization.

What Kant lacked, of course, was the benefit of an evolutionary theory and so he viewed the entire human epistemic apparatus from his top-down transcendental, speculative perspective, even though, to his credit and in the face of so many idealist mis-readings of his work, he insisted throughout the Critiques on the primacy of perception. Unlike Kant, we are in a position to turn the procedure around and view perception itself as the complex result of a long trajectory at the beginning of which stands mere cellular interaction. Molecular action, then, rather than perception, is where the interaction of organisms and world takes its long drawn out beginnings. (Fitch 2008) Now mental acts can be seen as the intrinsic evolutionary result of information exchange amongst cells monitoring the success or failure of an organism's interaction with its Umwelt. In this reversed scenario, it is most likely that human intrinsic intentionality had already reached an advanced stage when natural language gradually transformed mere perceptual being into something radically new, a creature able to compress, decompress, and hierarchically order its Vorstellungswelt, as well as creatively experiment with those mental resources. This raw picture is supported also by recent observations made by Noam Chomsky concerning the "essential uniformity of natural languages" which we can explain as a result of "the fundamental structure-building block" he calls "Merge." (Chomsky 2002: 29) Rather than seeing such ordering as the consequence of linguistic syntax, as does for example Derek Bickerton, it seems much more likely that language transformed an already existing perceptual and gestural proto-syntax into the kind of refined relations we now associate with natural languages. (Bickerton 1981; 1990; 1995) Nor is it likely that the rich intrinsic world of Vorstellung was suddenly replaced by linguistic constructions. Why should they not have lived side by side to this very day? If so, the question is how perception, Vorstellung, and language relate to one another. Or, more to the point, what role do perception and Vorstellung play in language and how could we account for such a relation? Consider the distinction between so-called concrete and abstract terms.

This well-established distinction shows that both concepts must be broad, subsuming as they do very different intensive magnitudes as well as kinds of "concreteness" and "abstraction." At the same time, we note that the distinction is merely directional, leaving us in the dark as to where "concreteness" should be separated from "abstractness." That this is a theoretical problem only and not a dilemma that language users are bothered by demonstrates, for example, how wrong-headed the standard formulations of the so-called "sorites paradox" are; if, that is, they are meant as a characterization of natural language rather than an exercise in logic. Language users know when to use "fast" rather than "slow," "poor" rather than "rich" without much worrying about the absence of a logical dividing line between the meanings of the two terms. Nevertheless, we should ask what sort of "abstraction" is operative in such cases as in natural language generally. Is it "generalization" or "formalization"? Formalization understood as radical stripping of mental material content, of the reduction of reference and deixis to zero, only occurs in formal sign systems. In the sign sequence x = y + z we have full formalization, but it is not natural language. In "the right of every citizen to education" no such abstraction takes place. Rather, we are dealing here with generalization or, perhaps more precisely, with degrees of schematization. In the language introduced by Fauconnier and Turner, we could say that the materials covered in concrete terms have been "compressed," in abstract terms they are "decompressed." (Fauconnier and Turner 2002: 115-119) Yet what is it precisely that has been so compressed and de-compressed? I suggest that it is the iconic, mental material which, in the linguistic meaning event, reappears as the quasi-perceptual content regulated by the concepts of natural language. This is where we must leave Kant's monogram rule behind in order to be able to differentiate degrees of generalization on a scale from highly concrete to highly abstract schematizations, according to linguistic expressions and their pragmatic context of Vorstellung. We must be able to account for the difference between the generality of "I said baking, not deep frying" and the relative specificity of "baking a cake" and "baking a potato." (Pustejowsky 2006: 369-393) How do we do this? We have been taught to imagine the two different scenarios which endow the two different kinds of baking with two different imaginable schemata. On the other hand "baking" on its own is understood by way of a much broader schema waiting to be specified.

According to Wittgenstein, the meaning of "bake" in all three instances is their use, a behaviorist externalization and abbreviation of a complex process. For does this formulation capture meaning when it is externally unavailable? It is only because we know different kinds of baking and at the same time have been trained to use certain strings of words to describe them that we can be said to be speakers of a language. But what does such competence consist in? The ability to formulate appropriate propositions? They surely can be constructed, but not as a must rule. However, without imagining the appropriate mental scenarios "in a flash" we would not be able to see the crucial differences. If linguistic meaning is determined by the relation of language and world, in the absence of relevant perceptual situations, it is the Vorstellungswelt rather than the immediate Wahrnehmungswelt that we must rely on. This is where semantic externalization runs aground. And the vast bulk of language use relies on Vorstellung rather than perception. This is precisely why Wittgenstein, throughout the PI, employs the Vorstellungsspiel. But is it essential for meaning?

The assumption to be argued for is that Vorstellung as carrier and modifier of perception is not only incidental to language and useful in discussing language, as Wittgenstein thought, but that it is an essential ingredient, one without which language could never ascend to meaning. What does not follow is that Vorstellungen and linguistic meaning can be equated. Rather, it is the process and event of appropriate combinations of linguistic expression that constitutes meaning as use. This in no way dismantles Wittgenstein's proposal that meaning should be defined at the level of and as "use," but will require a modification of the concept of use, a task I shall attempt below. Important to note is that something like the Kantian schema and the notion of degree and manner of schematization allow us to both accept Wittgenstein's criticism of Vorstellung as a carrier of meaning and refine his analysis to grant mental acts their legitimate role in language. To do this, I suggest that we employ the same strategy by which Wittgenstein proceeds from individual rule following to following a rule under community control. I have already suggested that mental acts not be defined as private but rather as intersubjective and so governed by rules in principle. Now we need to establish the link between mental acts at the level of schematization with the speech community. It would be odd to assume that the speech community were in charge only of verbal communication and had nothing to do with our Vorstellungswelt. Quite rightly, Wittgenstein never questions that the community is always already also the guarantor of the way we imagine the world around us. Otherwise he could not, as he does without justification, invite his students and readers to make the myriad mental moves he does throughout the PI. This suggests to me that the Vorstellungswelt is as indispensable an ingredient of sufficient semiosis as are the specifics of linguistic constraints. In this respect, then, we can simply adopt Wittgenstein's own practice.

7. Assertability Conditions and the "Aboutness" of Language

Kripke's explanation why he regards Wittgenstein's theory as "one of assertability conditions" is that the speech community "can assert of any individual that he follows a rule if he passes the test for rule following applied to any member of the community." (Kripke 1982: 110) What kind of test then is the community applying in the following case? "Lying is a language-game that needs to be learned like any other," says Wittgenstein. (PI [section]249) How do we decide whether an utterance is the use of the language-game of lying, understood as a deliberate misrepresentation of what is the case? Take a sentence such as "She had promised him to be kind." This looks straightforward enough. If she had not intended to be kind but said she would be, it was a lie. But what sort of conditions would allow us to check whether the appropriate rules had been followed? Typically, perception does not provide the required "assertability conditions." (Kripke 1982: 73ff.) In the bulk of language use we must rely on mental reconstructions and approximations, that is, Vorstellung, as indeed Wittgenstein does in his dialogue with his readers. Without a mental rehearsal of the relevant situations of what it would be like for the sentence to be a straightforward statement of fact or a lie, we would not be in a position even to judge whatever evidence may be available. All this places a big question mark on the reduction of meaning to "use" in Wittgenstein's public sense. Certainly, if it worked, the externalization of meaning would permit public scrutiny of language use by way of justification. On the other hand, Vorstellung escapes the public eye. So "how can I justify that I form this Vorstellung in response to these words?" (PI [section]382) We cannot accept the description of Vorstellung as "testimony," because it is really only a description of what someone is "inclined to say." And "how does one point to a Vorstellung?" (PI [section]386) Nor do we have any criterion for judging whether two Vorstellungen could be called the same. "What is the criterion for the identity (Gleichheit) of two Vorstellungen?" (PI [section]377) After all, the word 'same' is justified only if someone else can also regard it as justified. (PI [section]378) Yet it is not only Vorstellung that is thus placed under scrutiny. In keeping with these criticisms, Wittgenstein also takes observation sentences to task. "To the private transition from what is seen to the word, I could not apply any rules" for "the institution of their use is lacking." (PI [section]380) The only way out for both Vorstellung and perception, then, is the assumption of a culturally shared mental world. That we are justified in making such an assumption is not something Wittgenstein would want to entertain. But is it not a necessary assumption given what we already know about the human brain and the massive and all-pervasive pedagogy that streamlines the contents and structures of our minds?

Without some such assumption, meaning as "use" remains stuck in its syntactic straightjacket, with no ropes to anchor the balloon. This suggests that Wittgenstein's notion of meaning as use is the public application of intensionally defined signifieds within the constraints of language-games. One may be tempted to read the PI in this way by the author's frequent alignment of natural language with examples from arithmetic, geometry, and chess. In order to get to the aboutness of language, however, we must be able to connect the syntactically ordered, empty signifiers, their intensional relations, with a domain outside of language, which cannot be done without an extensional connection. For unlike formal systems, language is not a syntactically defined, self-sustained sign practice. Understating the origins of natural language, Saussure held such a view, insisting that linguistic meanings were determined by the differential relations between signifiers, the chess game analogy of language. (Saussure 1974:120, 22, 88, 110) This move results in a vicious circularity that severs the vital connection between Wahrnehmungswelt and Vorstellungswelt on the one hand, and language on the other. Is Wittgenstein repeating the same kind of differential idealization? Is natural language then indeed a homo-semiotic and mono-semiotic sign system? (PI [section]31, 33, 197, 205, 337; p. 155) I want to employ his own example to demonstrate the problem. "Suppose I said 'a b c d' and meant: the weather is fine ... What is supposed to be the criterion for my having that experience." (PI [section]509) What Wittgenstein does not take into consideration here is the role of the speech community which sanctions the links between linguistic expressions and what they are about. Since we have grown into language as a pre-given system, we are lured into thinking that its meanings are inside the expressions. If they were, ostensive teaching would indeed be superfluous. The reason why "a b c d" do not grant us the experience of 'the weather is fine' is that the community has not sanctioned this particular combination of sound sequence and aboutness. Furthermore, the letters "a b c d" by themselves have already been customized to be employed in different circumstances. This means that meaning as use must somehow cater not only for the public display of linguistic competence in justifiable performance but also for the way the speech community has pre-arranged what counts as the appropriate aboutness of linguistic expressions. In this respect, Wittgenstein's advice "Let the use teach you the meaning" proves insufficient. (PI p.181) One way to fill the explanatory gap would be to follow Kripke's proposal to regard names as "rigid designators" by applying his move to a broad spectrum of signifiers. Putnam has already taken a step in this direction by including natural kind terms and mathematical magnitudes in a modified communal process of "baptisement." (Putnam 1979: 203ff.; 231f.) I am not sure whether this direction will lead us to a rich description of natural language.

We often use the interrogative "What are you talking about?" We ask this question when we are not sure what the preceding linguistic expressions were about. Or, what the person speaking to us was trying to point to by means of language; or what I was supposed to imagine as a result of her words. In such cases, we expect a rephrasing for clarification. Yet it is not the rephrasing itself that is the purpose of our indirect speech act. Rephrasing is only the necessary intermediary step for the actual purpose of the original statement to be understood. What is missing is the aboutness of language. But here an obstacle arises. Wittgenstein's notion of Verstehen appears reluctant to accommodate anything beyond thought in a minimal, syntactic form. He wants to hold on to a syntactic notion of Verstehen in two senses. In one sense we understand a sentences if we substitute it by one that says the same. This would be an "understanding" of the kind that operates when we consult a dictionary. In the second sense, Wittgenstein wants to emphasize the uniqueness of understanding a sentence precisely the way it is, as for instance in a poem. (PI [section]531) This, once more, seems to suggest that part of Wittgenstein's view of natural language meaning is intensional, a suspicion supported also by his skepticism in defining the purpose of language. Is it "to convey thoughts"? (PI [section]304) or that "someone else grasps the sense of my words"? (PI [section]363) By way of an answer he asks, "what thought is expressed, for example, by the sentence "It's raining"? (PI [section]501) Nor does grammar "tell us how language must be constructed in order to fulfill its purpose.... It only describes ... the use of signs." (PI [section]496) We are at a loss then to determine from these statements what precisely Wittgenstein took a thought to be. We do know that he did not think that the Fregean purity of thought was applicable to natural language, for Wittgenstein explicitly rejected the analogy with calculus in the PI. Yet the distinction he draws between Denkapparat and stomach in the following quotation suggests that thought is regarded as stripped of emotions. "As if the purpose of the sentence were to convey to one person how it is with another: only, so to speak, in his thinking and not in his stomach." (PI [section]317) Clearly, language, contrary to Frege, communicates more than thought in any narrow sense. At least in this sense, Vorstellung, in which thought plays but a part, would be compatible with Wittgenstein's description of meaning as use.

So far our focus has been on the question of "what is use?" and its relation to Vorstellung. We should also ask the question "what is use, as defined by Wittgenstein, used for"? One answer could be "to convey the specific aboutness of language." Yet language-games cannot be as specific as individual sentences; rather they act as generic frames for the pragmatics of specific linguistic expressions. "Requesting, thanking, cursing, greeting, praying" are all broad linguistic schemata within the confines of which specific sentences can be formed. (PI [section]23) "Could you please hand me that tumbler over there?" or "I wonder what his idea of 'freedom' consists in" are singular applications of language-games. Their aboutness exhibits a specificity that is absent in the raw contours of the language-game. We may have grasped the fact that a question has been asked, but we may still want to ask, "What precisely do you mean?" While the category of the language-game was understood, its aboutness was not. If this distinction were disallowed, the concept of language-game would lose its class character which sets it apart from the specific moves we are justified in making within a language-game. The use of a language-games, then, cannot provide meaning, only specific moves within a language-game can. In other words, the definition of meaning as use cannot be pegged at the level of the language-game.

Of course, no theory of language can legislate that meaning be defined as the purpose of language. Nor can we discover a definition as we might an empirical object. A definition is a choice and an imposition. Let us define x as follows. All we can do is to aim for the most promising level in our analysis at which we undertake the definition of "linguistic meaning." For Wittgenstein, this level is the public arena of "use." The objection to this choice made here is that it needs to be specified and above all that it leaves out essential ingredients that distinguish meaningful expressions in natural language from those of other sign systems, such as the role of Vorstellung. There are, however, some pointers in the PI towards the possibility of a reincorporation of mental acts in the notion of use. As Wittgenstein himself demonstrates, it is impossible to analyze natural language without recourse to Vorstellung. Indeed, in much of social life we cannot but make assumptions about processes which are not available to public scrutiny. But this does not mean that justification and assertability are therefore completely out of reach. In the longer term, we will notice whether our assumptions were justified or not, and the bulk of those assumptions typically turn out to have been justified. The same holds for natural language itself. When Wittgenstein notes that "in language, expectation and fulfillment touch one another" he has involved Vorstellung in an important way. (PI [section]445) What is the function of Vorstellung in this relation? We must assume a double system to be at work here, consisting of linguistic competence and Vorstellungswelt. At the same time, the two must be sufficiently aligned such that our Sprachspiele and our Vorstellungsspiele can be matched in acts of meaning. Both systems can be specific or highly abstract, with gradations in between. They are both characterized by degrees of schematization. Nor does it matter whether expectation and fulfillment refer to actual or fictional contexts. Expectation and fulfillment are able to make contact because linguistic competence and Vorstellung are intricately intertwined in the minds of speakers of a language. Whether expectation and fulfillment actually touch one another in language is not something we can witness, except in Vorstellung.

Another feature in Wittgenstein's PI that requires Vorstellung is the directionality of language, as in his formulation of the meaning as an act of "going up to the thing we mean." (PI [section]455) This implies a mental turning, a turning in Vorstellung. And this turning towards something is an approximation of the turning towards something already performed by someone whose words we are constructing as meaningful. "Meaning something," Wittgenstein confirms a little later, "is like going up to someone." (PI [section]457) In other words, the public use of ordered signifiers is accompanied by the Vorstellung of the "thing we mean." That this process can be "blitzartig" (in a flash) strengthens its characterization as a social routine, at least in habitual speech. (PI [section]317, 318, 319) But it is only in the interpretive attitude in problematic linguistic contexts that the full machinery of Vorstellung in the process of meaning making reveals itself. The social exercise of this faculty par excellence is the reading of poetry, where the prominence of Vorstellung would appear to be self-evident, though its workings cannot be publicly demonstrated.

An intriguing and fertile example of the use of Vorstellung by Wittgenstein can be found in his discussion of interpretive, modal variation in the viewing of a picture. "I see a picture which represents a smiling face. What do I do if I take the smile now as a kind one, now as malicious? ... Thus I might supply the picture with the Vorstellung that the smiler was smiling down on a child at play, or again on the suffering of an enemy." (PI [section]539) Applied to language, deictic variations of propositional content are a vital ingredient of the process of meaning constitution, especially when we are dealing with contexts requiring the construction of implied or cultural deixis, the imposition of deixis, as in the nonverbal semiosis imagined here by Wittgenstein. Indeed, in natural language, deictic modification typically overrides propositional content. (Ruthrof 1992: 4f.) If so, then his advice to "Let the use teach you the meaning" (PI, p.181) has now acquired a broader definitional scope. Without Vorstellung none of Wittgenstein's interpretive moves could have taken place, while at the same time, none of them are open to public scrutiny. And yet we are justified in employing modal and deictic Vorstellungsspiele because they are part and parcel of community practice or sufficient semiosis. They are 'indirectly' public.

If meaning is use and Vorstellung looms as large as it does in the PI and other manuscripts of Wittgenstein, then the use he makes of Vorstellung is not only a Vorstellungs-game but also an important language-game in itself with a special relationship to meaning. What are the "assertability conditions" of Wittgenstein's use of the Vorstellungs-game? What gives him the confidence that when he writes "Imagine a picture representing a boxer in a particular stance" that the reader will be able to apply the kind of community sanctioned rules in her Vorstellung that would guarantee Wittgenstein's pedagogic intention to be carried out? (PI [section]22, footnote)

He must assume that all his readers will be able to imagine in typical enough a fashion to produce sufficiently similar Vorstellungen. Or, to take another example, "The likeness makes a striking impression on me; then the impression fades. It only struck me for a few minutes, and then it no longer did. What happened here?" (PI: p.181) Wittgenstein must assume that in response to his sentences his readers will all more or less be able to construct mental representations sufficiently similar to share at least roughly the same Vorstellung of him performing a Gedankenexperiment. But how could this be asserted? Only on the assumption that Vorstellung, no matter at what level and in what manner of schematization, is rule governed and therefore not private. And since Vorstellung is neither objectively public nor private, our best predicate is that it is intersubjective. This allows us to distinguish the objectively public features of language, such as the signifiers in a dictionary or in a public speech, from such intersubjectively shared and so indirectly public instantiation of the connections we have been trained to perform between language and Vorstellungswelt as meanings.

8. Conclusion

Any theory of natural language that does not include, or at least allow for, an evolutionary perspective should be regarded as suspect. After all, language, like anything else to do with human biology, including culture, has an evolutionary trajectory, a trajectory along with which Vorstellung, as the sum of mental acts, has evolved into the most powerful component of the human organism. To eliminate it therefore from our dominant system of representation and communication, natural language, does not look promising. Without taking cognizance of this trajectory, even if so far such cognizance is bound to be highly speculative, we cannot but misrepresent the deep relations responsible for the "naturalness" of natural language. The "rear view mirror" approach via mathematization tends to distort and take our eye off what is still essential in natural language. Contrary to formal systems, descriptions of natural language semantics via intensions are doomed from the start. We must be able to address its extensional features, but in an appropriate way

In the PI Wittgenstein was intent on avoiding the path of mathematization which he had attempted in a radical fashion in the Tractatus. Instead, he now identifies what actually goes on when language is employed in its ordinary manner as an exercise of multiply overlapping language-games. At the same time he remained committed to the scientific and behaviorist ideal of publicly available evidence, as well as to frequent analogies between formal signification and language. In the process of his analysis, however, he found that he had to rely heavily on Vorstellung to which however, in keeping with his scientific method, he felt he could grant only an auxiliary role in relation to understanding and meaning. As a result, his definition of meaning captures only part of what is going on in the pragmatic employment of language and the tension between his definition of meaning as use and his ubiquitous use of Vorstellung remains unresolved.

By way of conclusion, I offer a tentative solution to Wittgenstein's dilemma in a number of distinct steps. (1) It is useful to distinguish sharply between habitual and interpretive language use in that the former suggests to the observer that natural language works like chess. Indeed, it does so as far as its syntactic relations are concerned, which is all that happens in the chess game. On the other hand, the search for meaning in interpretive use of language turns out to be a search for what language is about, or its extensional connection. What is at stake in defining meaning as "use" is the process between language and its aboutness. (2) The description of a community sanctioned use of language therefore needs the following set of rules: rules governing well-formed linguistic expressions; rules for a well-formed domain that can function as the goal of linguistic "aboutness;" and rules for combining the right clusters from both domains. Furthermore, even if the first set of rules has been applied in a flawed manner, meaning is more often than not secured as a result of negotiation and imaginative reconstruction. (3) What is so negotiated is not only the appropriate sentence structure. Indeed, the appropriate string of signifiers is often the result of a re-negotiated agreement in the kind of domain the sentence is about. I leave out linguistic self-referentiality as an added bonus. (4) As linguistic practice shows, and as Wittgenstein's own continuous invocation of Vorstellung in the PI demonstrates, the bulk of ordinary language use cannot do without Vorstellung. "I'll see you tomorrow then, at the clock tower at 7pm." "See you there." We do not understand the sentence because we have "assertability conditions" ready at hand. Our domain of "aboutness," though ultimately the real, perceptual world, is in the first instance and essentially our shared Vorstellungswelt. The scenario evoked has not yet occurred. A bit of mental time and space travel is unavoidable. If the sentence is reasonably well formed and if the two speakers are able to form a schematic Vorstellung of what the sentence guides them to project, and if they can reach sufficient agreement in their mutual assumptions of the relevant aboutness, then the process of linguistic meaning is likely to succeed. If it does, it will have been successful because the speakers involved have observed three types of rules: syntactic; nonverbal, mental schematic; and mental, pragmatic combinatory. (5) Wittgenstein's definition of meaning as use covers the syntactic side of language, in which I include everything that belongs to ordered strings of signifiers. The PI also covers part of the pragmatic, combinatory side of language, but only when we are dealing with language gearing visibly into our perceptual world, that is, language use that we can check in actuality. Yet even when perceptual evidence is available as referential background, Vorstellung as mental replication can still be shown to play a significant part. The bulk of language use though is not of this form. The much greater portion of language is either about Vorstellung of the actual world or about Vorstellung as perceptual modification and fantasy distortion. In short, in language as in human life in general, the Wahrnehmungswelt is not only well covered but also dwarfed by the Vorstellungswelt. Because we live in a technological world we tend to forget this vital ratio. And this is what an appropriate theorization of natural language must be able to account for. Putnam is only partly right when he quips that meanings "just ain't in the head." (Putnam 1979: 227) For without heads there wouldn't be any meanings at all. Meaning needs to be seen as an event that partakes of both public and intersubjective or indirectly public processes involving Vorstellung.

In light of these remarks I propose the following redefinition of Wittgenstein's description of meaning as "use." Linguistic meaning as use is the activation under community rules of arbitrary, empty signifiers, ordered into language-games, by nonverbal, iconic mental materials in and as Vorstellung, regulated by concepts in terms of directionality, kind, quantity, and degree as well as manner of schematization.


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