“An artistic rather than a scientific achievement”: Frege and the Poeticality of Wittgenstein’s Tractatus

In this article I explore some implications of the correspondence that went on between Ludwig Wittgenstein (1889–1951) and the logician and mathematician Gottlob Frege (1848–1925). Part of this exchange was focused on the envisaged publication of Wittgenstein’s Tractatus Logico-Philosophicus, and on the philosophical or literary character of that work. The problem discussed concerned the question of whether the Tractatus should be seen not as a scientific but as an artistic achievement. My first goal is to present what, given Frege’s writings, his phrase “an artistic rather than a scientific achievement” could be understood to mean in terms of the Tractatus itself. Secondly, I seek to determine the extent to which traces of Frege’s understanding of such terms as “mock thoughts,” “fiction,” “elucidation,” “paintings” and “colouring” are to be found in the language of the Tractatus. This should then make it possible to show how Wittgenstein’s work, viewed from a Fregean perspective, can be seen as furnishing a logic and semantics not only for the languages of logic and natural science, but also for something that is “an artistic rather than a scientific achievement”, while also indicating that the content of the Tractatus as a whole could not have been captured independently of the unified form Wittgenstein himself gave it.

interpretations and is by no means readily translatable into English. There is no exact English term corresponding to the German verb "dichten," which means to create poetry. Perhaps the most accurate translation is: "Philosophy should be written only as one would write poetry" (Schalkwyk 2004: 56;cf. Perloff 2018: 10-25). 1 When it comes to writing philosophy as one would poetry, as this relates to contexts specifically pertaining to Wittgenstein's Tractatus Logico-Philosophicus, I propose that we take note of the correspondence that went on, mostly between Wittgenstein and the logician and mathematician Gottlob Frege (1848-1925, and that was focused on the envisaged publication of that work. Taking those letters as its basis, the present article will pursue two principal goals: firstly, to present what, given Frege's writings, the phrase "an artistic rather than a scientific achievement" could be understood to mean in terms of the Tractatus, and secondly, to determine the extent to which traces of Frege's understanding of such terms as "mock thoughts," "fiction," "elucidation," "paintings" and "colouring" are to be found in the language of Tractatus. This should then make it possible to show how Wittgenstein's work, viewed from a Fregean perspective, can be seen as furnishing a logic and semantics not only for the languages of logic and natural science, but also for something that is "an artistic rather than a scientific achievement." 1 The correspondence between Wittgenstein and Frege concerning the Tractatus behind how it is said." And had the former instead been the case, then "the greatest clarity [Deutlichkeit] would indeed have been the greatest beauty." Frege tries to come to terms with the idea that the reader should derive satisfaction from the work's form rather than its content, making the Tractatus an artistic rather than a scientific achievement in respect of its ultimate goals. Anticipating what I have to say later in this article, I wish to claim right away that poetry is, after all, manifested in a poetic form that is essential, and that such a form cannot be abstractive. A paraphrase of a poem is no substitute for the poem itself, and neither can its poetic force be unfolded or developed independently of the actual poem.
Wittgenstein, on Frege's earlier construal of his intentions, had just wanted to communicate some new content in a new way. In this regard, it is worth considering the initial sentence of the Preface to the Tractatus, where Wittgenstein writes that the whole book is both a literary and a logical work: The book deals with the problems of philosophy and shows, as I believe, that the method of formulating these problems rests on the misunderstanding of the logic of our language. Its whole meaning could be summed up somewhat as follows: What can be said at all can be said clearly; and whereof one cannot speak thereof one must be silent. (Wittgenstein 1922: 23) What this passage tells us is that the book deals with the "problems of philosophy," albeit philosophy "written only as one would write poetry," where this in and of itself entails that it also addresses what we might call "the problems of life." Such an interpretation made it possible for Wittgenstein to adopt a quite different slant on issues of communication and interpretability in the context of his work on the Tractatus, such that it made sense for him to write that: This book will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in itor similar thoughts. (Wittgenstein 1922: 23) The task of the philosopher (and of the poet) is to make clear to himself, and also to others, what Wittgenstein notes later when he writes that "The object of philosophy is the logical clarification of thoughts" (Wittgenstein 1922: 4.112). Yet the logical or scientific point of such an undertaking then seems unclear to Frege. To grasp the type of expression at work in the Tractatus, we must view it not in strictly logical terms, but rather, at the level of expression, in broadly dialectical ones (cf. Ostrow 2002). That is to say, we must keep in mind the tension between how Wittgenstein might have been seeking to communicate de facto via form itself, and in a mode of communication that counted (for him) as logico-philosophical, so that it would stand in place of an artistic one.
Frege's response was more insightful than he himself could have realized. He suggested to Wittgenstein that he split the book up into as many sections as the number of philosophical problems he was seeking to address, where the result of this would be that it would be more feasible for the Tractatus to be published in a literary periodical.
If publication in a journal were to be considered, it would be necessary to permit a division of the Tractatus. … Now could not one of these thoughts, in which the solution of a philosophical problem is contained, be taken as the object of a treatise, and thus the whole be divided into so many parts, to be handled as philosophical problems? (Letter dated 30 th September, 1919;Frege 2003: 27-28) The inseparability of the various parts of the Tractatus from one anothere.g. the accounts of demonstrative showing (Wittgenstein 1922(Wittgenstein : 4.1212) and reflexive showing (4.461), or of pictures (2.173-2.174) and the visual field (5. 633-5.6331)lies at the core of its dialectic understanding. Wittgenstein acknowledged the literary nature of the Tractatus himself in a letter to von Ficker, who was considering publishing it in Der Brenner, the literary journal of which he was himself the editor: "The work is strictly philosophical and at the same time literary, but there is no gassing in it" (McGuinness 1988: 288).
Wittgenstein was unwilling to accept Frege's suggestion. To divide the Tractatus up in that sort of way would, in his opinion, be to "mutilate it from beginning to end and, in a word, make another work out of it" (Monk 1991: 176). This is exactly the reaction we would expect to encounter from a poet to whom it had been suggested that they split up their poem and publish a few lines at a time, in a piecemeal fashion. Here, the indivisibility of the form corresponds to an indivisible unit of philosophical significance, just as the indivisible form through which a poem is expressed is essential to the nature of such a work as a whole. There is, then, some evidence to support the belief that Wittgenstein came to think of the Tractatus as a work that ought to be viewed as being both poetic and philosophical, and this in respect of not only its construction, but also its underlying purpose.
At this point, it is worth mentioning that on 6th October, 1919, Wittgenstein in turn wrote to Russell, saying that: I am in correspondence with Frege. He understands not one word of my work and I am already completely worn out with nothing but explanations (Frege 2003: 18).
While in the Preface to the Tractatus, he writes: I will only mention that to the great works of Frege and the writings of my friend Bertrand Russell I owe in large measure the stimulation of my thoughts (Wittgenstein 1922: 23).
On the one hand, needless to say, Russell likewise failed to properly understand Wittgenstein's thoughts. In his correspondence with Lady Ottoline Morell, he writes: "I feel sure it is really a great book, though I do not feel sure it is right..." (letter dated 20th December, 1919;Wittgenstein 1974: 82). Though quicker to grasp the ontology and logic of the Tractatus, he repudiated both Wittgenstein's important distinction between "saying" and "showing," which he considered a useless mystification ("a curious kind of mysticism"), and the treatise's key point: namely, that of drawing attention to "the ethical" as that which cannot be said but only showni.e. made manifest. On the other hand, though, taken as a whole, Russell's otherwise straightforward commentary on the Tractatus proved beneficial in respect of helping to bring about its publication as a unified whole, without any "dividing up." Russell also ensured that the Tractatus would be translated into English.

Frege on fiction and poetry
One of Frege's most fundamental realizations takes the form of his assertion that the concept of truth is simple and undefinable: i.e. that the notion of truth has to be the central notion in his logic and semantics. Truth is a primordial phenomenon, and our notion of it cannot be dissolved into logically more simple parts and reductively defined as such. The following may be regarded as conveying his anti-psychologistic stance: Logic has a closer affinity with ethics [than with psychology]. The property 'good' has a significance for the latter analogous to that which the property 'truth' has for the former (Frege 1979a: 4).
Frege and Wittgenstein underlined the distinction between logic, ethics and aesthetics on the one hand, and empirical sciences such as physics and, in particular, psychology, on the other. Frege was specifically concerned with logic and, in his opinion, truth was the genuine subject-matter of the latter. As he puts it: Just as 'beautiful' points the way for aesthetics and 'good' for ethics, so does the word 'true' for logic. All sciences have truth as their goal; but logic is also concerned with it in a quite different way: logic has much the same relation to truth as physics has to weight or heat. To discover truths is the task of all sciences; it falls to logic to discern the laws of truth (Frege 1997a: 325).
That is why we have to proceed from truth, and use it as guide when making further logico-semantic distinctions. Yet even so, how are we supposed to know that a phenomenon has to do with truth at all? In this regard, we can only remark that truth is articulated in a speech act of asserting, in uttering a sentence with assertoric force (behauptende Kraft), which is what tells us whether, in expressing a thought (i.e. some sentential content), 3 an assertion is made or not (cf. Polimenov 2018: 130). We first comprehend a Fregean thought, and afterwards acknowledge the truth (or falsity) of this thought in an act of judgment. The judgment itself is revealed in an assertion. Whoever is competent in the practice of making assertions knows what it means to make a truth-apt sentence. It is therefore hardly unexpected that the topic of fictionali.e. poeticdiscourse surfaces in Frege's works precisely together with the notion of truth.
Frege points to the distinction between the strict sciences (strengen Wissenschaften) and the humanities (Geisteswissenschaften). According to him, the latter are less scientific and closer to fiction (Dichtung) than the former. When he has in mind or speaks about fiction, he usually uses the German word Dichtung (or dichterische Sprache). Apart from fiction, this word Dichtung can likewise mean "poetry" or "poem" (and, in parallel, its derivatives can also mean "the language of poetry," "poetic use," "poet," etc.; cf . Polimenov 2018: 122). When the role of particular linguistic units is to serve aesthetic enjoyment (aesthetischen Genuss) by imparting a euphonious character to speech (through tone, rhythm and intonational melody), or by eliciting feelings and imaginary images (Vorstellungen) in the memory and the intellect of the listener or reader, "Dichtung" tends to be translated into English as "poetry" (see above: "Philosophy should be written only as one would write poetry").
Here, we shall try to address Frege's own relation to both poetical language and fictional discourse. To do so, we must appeal to his understanding of figurative speech (the use of metaphors, parables and other figures of speech), taking into consideration how this appears in poetical and fictional speech or language on the one hand, and in non-fictional discourse on the other. This reflects the fact that Frege also applied metaphors in the language of science. In particular, he used these in his critique of the psychologistic understanding of logic and mathematics: I understand by 'laws of logic' not psychological laws of takings-to-be-true, but laws of truth. ... If being true is thus independent of being acknowledged by somebody or other, then the laws of truth are not psychological laws; they are boundary stones set in an eternal foundation, which our thought can overflow, but never displace (Frege 1964: 13).
Frege uses the metaphors and language of "Dichtung" (e.g. "boundary stones set in an eternal foundation") on different levels and in various thematic contexts (in the above case, in a logico-psychological context).
Firstly, we encounter these in the context of his underlining of the contrast between fictional (dichterisch) discoursewhich is, so to say, "truth-free"and the language of the sciences, whose goal is "to discover truth": ... in fiction words only have a sense, but in science and wherever we are concerned about truth, we are not prepared to rest content with the sense, we also attach a meaning to proper names and concept-words... (Frege 1979b: 118) The sense of an expression, according to Frege, helps to determine the thought expressed by a sentence, while its reference determines the latter's truth or falsity. In other words, "reference," usually translated as "Bedeutung," was Frege's term for that characteristic of a linguistic expression which is its contribution to determining the truth or falsity of the sentences in which it appears.
We should also note that practically anything Frege writes about "fictional discourse" is, in a sense, a negation. For example, we may take the following, which we shall hereafter refer to as "quotation (A)": (A) In myth and fiction thoughts occur that are neither true nor false. Logic has nothing to do with these (Frege 1979c: 198). This could be paraphrased as "Proper names have to have a reference." Nevertheless, there is some ambiguity in Frege's writing here. In the case of nearly every sentence where Frege discusses empty singular terms, (such as express "mock thoughts" or "sham thoughts" (Scheingedanke, Gedanke, dem Scheine nach), these not being thoughts at all), the idea of myth or fiction, sometimes even poetry, is close at hand: Instead of speaking of 'fiction,' we could speak of 'mock thoughts.' Thus if the sense of an assertoric sentence is not true, it is either false or fictitious, and it will generally be the latter if it contains a mock proper name. Assertions in fiction are not to be taken seriously: they are only mock assertions. Even the thoughts are not to be taken seriously as in the sciences: they are only mock thoughts (Frege 1979d: 130).
"Scheingedanken," like paintings (Bilder) or images (Vorstellungen), only aim to furnish us with appearance (Schein), and do not aim to convey truth. Utterances of sentences that contain non-referring expressionsi.e. "mock thoughts" or "sham thoughts"-are, for Frege, treated on a par with utterances that lack assertoric force. Both types of utterance, according to Frege, are instances of fiction (Dichtung), and do not count as acts of assertion (cf. Frege 1984a: 362).
Secondly, Frege (i) discusses poetry, stage art and fiction more universally, and (ii) frequently provides us with examples pertaining to his own preferred hero -Odysseus. In line with (i), he writes: In hearing an epic poem, for instance, apart from the euphony of the language we are interested only in the sense of the sentences and the images and feelings thereby aroused. The question of truth would cause us to abandon aesthetic delight for an attitude of scientific investigation (Frege 1997c: 157).
He suggested that it would be preferable to have a special expression for signs that are meant to have a sense but no reference (Bedeutung). They could, according to him, be called "images" (Bilder).
At the same time, where (ii) is concerned, Frege statesas we already know that thoughts are indeed to be found in poetry. If a sentence involving the name "Odysseus" is used in fictional discourse, the name is taken as empty, i.e. meaningless, but if the name appears in a sentence from factual discourse (e.g. discourse about fiction), it should be provided with some meaning or other. Yet could it ever be the case that a sentence as a whole has only a sense, and no meaning? Frege's sentence "Odysseus was set ashore at Ithaca while sound asleep" (Frege 1984b: 162) obviously has a sense (cf. Zouhar 2010). But since it is doubtful whether the name "Odysseus" occurring therein has a reference (to a really existing person), it is also doubtful whether the whole sentence does. Could we say that the thought remains the same, no matter whether "Odysseus" has a reference or not?
Sentences featuring empty terms involve the meanings that are conventionally chosen for them. Frege admits there are various expressions in language (used seriously) whose senses are not modes of presentation of anything. This is also the case for the language of mathematics (Frege 1984b: 169). Such expressions will be meaningless, and if they are to be used to say something true or false, they must first be provided with some meanings.
Quotation (A) above simply purports to tell us why fictional discourse is not a case of logical discourse. We may surmise that "myth and fiction" are most likely meant to refer to a specific type of context, either spoken or written, rather than just some wellknown mythological or fictional stories. The semantic content of a phrase presented in fictional discourse cannot be separated out onto two levels, as in factual discourse: the level of Fregean meanings is ruled out from the semantic schema, leaving simply that of senses (Sinn). Typically, in such cases, assertoric sentences express thoughts without being either true or false. Hence, in fictional discourse, all offering up of judgements will be excluded: since we cannot identify thoughts as true, we are unable to make assertionsi.e. to express our judgements.
Insofar as poetry states things, it generally exhibits the form of assertions, and so might appear to merit being regarded as putting forward truth-apt claims. However, to say that any such assertions can be understood, as one might well do if, say, the complete poem were amenable to being pinned down as or replaced by some abstract moral, is not an option. The speech acts that occur in poems do admittedly have the form of assertions, but they lack assertoric force (cf. Frege 1990a: 347).
Thirdly, Frege uses metaphors, and the language of "Dichtung," to make clear the varying extents of the difficulties involved in translating poetry from one language to another, and to show that the poetic elements almost always make a "perfect translation" (vollkommene Übersetzung) impossible. This is because languages differ most strongly in respect of precisely those elements that poetic works are most heavily involved with (cf. Frege 1990a: 347). As regards Frege's understanding of fictional discourse, similar difficulties will occur in various translation-related contexts: as we move from one common language to another, from one scientific discipline to another, or from poetry or literature written in one language to poetry or literature in another.
Fourthly, there are our encounters with those words or means of expression through which the "colouring" (Färbung) of thought, as it is commonly known, is conveyed. These correspond to those parts of a sentence whose meanings do not influence the truth-apt essence of the sentence's content (the thought). Colourings do not represent the senses of thought contents. 4 Rather, they are intelligible as additional psychological elements that possess some other psychological associationbe it systematic or contextualwith senses. Burge, for instance, states that "Frege often assimilated colourings to images or feelings, not thought contents" (Burge 2013: 575).
Frege only writes about colouring on a few occasions, but he does take it to be a universal property: every word has it, and such phenomena as word order and intonational patterns may also add to the colouring of a phrase or sentence. In this regard, it may be worthwhile to reflect upon his own examples, as given below: (1) Alfred has still not arrived.
(3) Alfred has not arrived. (Neale 1999: 36;cf. Frege 1990a: 348) According to Neale's interpretation of Frege, someone who expresses (1) or (2) "actually says" that Alfred has not arrived "and at the same time hintsbut only hints that Alfred's arrival is expected." The hints provided by "still" or "yet," as used in (1) and (2), make no difference to the reference involved: if Alfred is not expected, (1) and (2) are still true, so long as Alfred has not actually arrived. Moreover, "still" and "yet" make no difference to sense: (1)-(3) all express the same thought. Indeed, Frege's view may well be that although "still" and "yet" have colouring, they have no sense: 'although' ... has no sense and does not change the sense of the clause [to which it is attached -JB] but only illuminates it in a peculiar fashion. (Frege 1980: 73) 5 As with "although," so also for Frege with "but" and "yet." Such colourings are not objective, yet each hearer or reader must still construe them on the basis of hints provided by the poet or speaker. (Put simply, without any relationship to our human imagination, all kinds of art would be impossible.) Of course, how far such construals will be in line with the purposes of the poet is quite another question. The colourings and elucidations do, however, give sense to poetics, and to human persuasiveness (cf. von Kutschera 1989: 72). (We shall come back to this issue in the final part of this article.) As a consequence, Frege also tries to remove from the scientific use of language any connotative or metaphorical elements of language such as might add "colouring and shading" to the sense of our thoughts. Colouring and shading count as belonging to the Fregean domain of mental "ideas," but where these are concerned, one person's is not another's. Colouring differs from sense only in respect of (a) its degree of specificity and (b) its context-sensitivity. In contrast to sense and reference, ideas are, for this reason, not objective but rather subjective, "and must be evoked by each hearer or reader according to the hints of the poet or the speaker" (Frege 1980: 61;cf. Gabriel 2018: 15-16).

Frege on elucidation
Frege uses two terms: Beleuchtung (illuminating, shining light on) and Erläuterung. For example, in his introduction to the "Begriffsschrift" (Jena, den 18. December 1878) he writes that he intends to embark upon "Die weitere Verfolgung des angedeuteten Weges, Beleuchtung der Begriffe der Zahl, der Grösse, usw." (Frege 2014: XIV)meaning "The further pursuit of the path indicated, the elucidation of the concepts of number, magnitude, etc." (transl. -JB; cf. Frege 1997d: 52). 6 Both terms (Beleuchtung, Erläuterung) tend for the most part to be translated as "elucidation." At this point, it is of interest to consider once more a certain feature of Frege's writings: namely, his tendency to include a brief mention of poetry in many of his discussions of what language expresses. In fact, Frege does suggest that there is something other than thoughtsother than what is subject to laws or can be true or falseexpressed by language. The difference between the use of the term "nag" (Gaul) or "steed" (Ross) is one of his examples.
What are called the humanities are closer to poetry and are therefore less scientific than the exact sciences ... for exact science is directed toward truth and truth alone... Where the main thing is to approach by way of intimation what cannot be conceptually grasped, these constituents are fully justified. ... It makes no difference to the thought whether I use the word 'horse' or 'steed' or 'nag' or 'prad.' The assertoric force does not cover the ways in which these words differ. What is called mood, atmosphere, illumination in a poem, what is portrayed by intonation and rhythm, does not belong to the thought. (Frege 1997a: 331) The terms in question ("horse," "steed," etc.) have, according to Frege, the same sense but different colourings. What is expressed by poems and poetryjust like in elucidation ("Erläuterung")is incompletely expressed and cannot be made unambiguous. The outcomethough Frege was unlikely to have been fully aware of this himselfis that taken in this sense, his writings may have the same status as a special kind of poetry. All the same, he may not have been completely unaware of this implication.
Given his view of his own philosophical writings as serving the systematic sciences of arithmetic and logic, it is tempting to think that he was indeed not inclined to regard his work as belonging to the humanities. But actually it is not clear that this supposition is warranted. It rather looks like this: that Frege was constantly aware of the dissimilarity between his discursive writing on the one hand, and the proofs in his logical notation or in arguments oriented towards "scientific achievement" on the other.
Instead of focusing just on Frege's substantial contribution to the formal sciences, we might consider his remarksin the introduction to "The Foundations of Arithmetic" or "On Concept and Object"to the effect that any accurate analysis of the concepts number and object are bound to turn out to be rather philosophical. Let us pay attention to an example offered by Frege himself, and in particular the intentionally paradoxical-sounding sentence "The concept 'horse' is not a concept." 7 Frege was speaking about different aspects of language and its connections to non-linguistic objects or things. The first three words in this odd sentence ("the concept 'horse'") function as a saturated expression, and thus must designate an object. Hence, given that "the concept 'horse'" designates an object, it follows that the concept horse cannot be a concept (cf. de Rouilhan 2015: 120-121). These features led him to the aforementioned paradoxical-sounding conclusion that "the concept 'horse' is not a concept." To keep matters brief and avoid any complex digressions not actually decisive for our investigations here, we may just say that the crucial assumption that brought Frege to assert this was his conviction that phrases beginning with the definite article ("the") denote objects, not concepts.
What we take Frege to have been saying, then, is that within his formal language concepts cannot be referred to by using namesthey themselves can only be used. And at this point we realize that there is no possibility of translating into a fully logical language what he was trying to impart through this paradoxical sentence. His method for addressing difficulties of this sort is to bring into play elucidations, in the sense of sentences and expressions that serve a pragmatic and propaedeutic function but have no place within the systematic frameworks of scientific inquiry. Indeed, in relation to the wider debate, his use of elucidationssuch as cannot be expressed in logical language is often invested with an exemplary status. In "On Concept and Object," he discusses what is involved in pursuing a clarification of the logical distinction between "object" and "concept"namely, the supposed inadequacy of everyday language when it comes to allowing him to convey what he would like to say about how concepts and objects differ. He writes: I have got hold of a distinction of the highest importance. I admit that there is a quite peculiar obstacle in the way of an understanding with my reader.  (Frege 1990c: 177) In relation to this quotation, I shall make two remarks.
Firstly, when Frege hopes for a reader prepared, as he puts it, "to meet me half-way," this reminds one of the point in Wittgenstein's Preface to the Tractatusalready quoted earlierwhere its author states: This book will perhaps only be understood by those who have themselves already thought the thoughts which are expressed in itor similar thoughts. (Wittgenstein 1922: 23) Two things, at least, are clear in this respect: that, as subsequent sentences of this introduction make clear, we are dealing here with a book of quite uncommon ambition, and that Wittgenstein's aim is to draw our attention to something we are all fully equipped to see for ourselves.
My second remark would be that Frege's approach, when it comes to seeking to overcome the above-mentioned "peculiar obstacle," is not substantially different from the one commonly attributed, rightly or wrongly, to the Tractatusnamely, in respect of its "ladder strategy" (see below). If we cannot say what we wish to say (e.g. that concepts, for their part, are not objects), then at least we can indicate it and count on a concession of sorts from the kind of reader or the hearer "who would be ready to meet … half-way," and to whom, through elucidation, we will at least be able in the Wittgensteinian sense to show it. This may be accomplished by momentarily distracting language from its usual function (e.g. as a means of expressing Fregean sense), to the point where it comes to be used instead as a means for suggesting or showing what, rigorously construed, amounts to inexpressible non-sense (cf. de Rouilhan 2015: 122). When this unusual mode of employment for language has achieved its anticipated results, when it has enabled us to see what needed to be seen, we will be able to return to our more typical way of operating with language and remain there. Surely, one really does not want to begrudge Frege his "pinch of salt" at this juncture. After all, everyday language itself is very open-handed when it comes to the issue of minimizing the number of predicates in play, and the semantics of ordinary language use has to embrace more than just the comprehensive findings of scientific and logical theorizing, in that it must also describe and explain the language through which we have arrived at this theorizing itself, as well as what we are supposed to do with any theories we design or build.
In the context of his mathematico-logicist program, Frege assigns to elucidation a qualified but essential role. On the one hand, he excludes elucidation from any sort of logical system, on account of its being imprecise. On the other, he claims that it stands prior to the construction of a system in terms that render it indispensable. Now Frege was, of course, committed to his program for the reduction of mathematics to a logical system. In order to finalize this program, he permitted himself to introduce terms into the system in two ways: via definition and via elucidation. Definition could capture what is logically complex, but not what is logically simple. Only elucidation could reach to something primitive (and so indefinable)in this case, for Frege, such terms as "function" or "object," together with something about how linguistic terms operate in the realm of poetry. Elucidation alone was such as to make it possible that "that which is said therein steps back behind how it is said" (see Frege's letter to Wittgenstein of 16th September, 1919 in Dreben andFloyd 2011: 41).

The Tractatus and its pseudo-propositions (Scheinsätze)
Frege describes a proper name lacking reference as a "mock proper name," and views the assertions (generally Sätze) that involve such mock proper names as conveying "mock thought." His proposal is that we are merely seemingly able to grasp the senses of such assertions. This would seem to indicate that (what we take to be) the constituents of such an assertion only make an apparent contribution to establishing its sense.
Such a thought then paves the way for a Tractarian interpretation of Frege's statements about "mock thought," side by side with what the Tractatus itself has to say about pseudo-propositions (Scheinsätze). The latter are propositions which have no sense (i.e. they are senseless), but which furnish the illusion that one is able to grasp their sense. An example of a pseudo-proposition could be "There are objects," while an example of a proposition with sense could be "There are streets." Only the latter conveys a fact.
Wittgenstein argues for a reciprocal relationship between propositional sense and sub-propositional reference. On the one hand, he holds that a proposition only has sense if its expressions have reference: A possible sign must also be able to signify. Everything which is possible in logic is also permitted. ("Socrates is identical" means nothing because there is no property which is called "identical." The proposition is senseless because we have not made some arbitrary determination, not because the symbol is in itself unpermissible.) In a certain sense we cannot make mistakes in logic. (Wittgenstein 1922: 5.473; cf. 6.53) On the other, he takes it that a sub-propositional expression only has reference in the context of a sinnvoller Satz: "Only the proposition has sense; only in the context of a proposition has a name meaning." (Wittgenstein 1922: 3.3). For a Tractarian example of what a "pseudo-proposition" or "apparent proposition" looks like, we have the following: And we see that apparent propositions (Scheinsätze) like: "a = a", "a = b . b = c.⊃ a = c", "(x).x = x", "(∃x).x = a", etc. cannot be written in a correct logical notation at all. (Wittgenstein 1922: 5.534) Sentences in logical notation that are not definitions, but that contain the equals sign, are pseudo-propositions. They are typically formulated for the purpose of speaking about logical primitives (formal concepts), such as "object" and "sentence." Adopting such an analysis of identity statements, we arrive at a point where all problems connected with such pseudo-propositions disappear (cf. Wittgenstein 1922: 5.535).
At the same time, such methodological pseudo-propositions will still be needed to delineate the sayable from the non-sayable. Our seeing the world from the appropriate and correct logical point of view involves our knowing the difference between what it is "to say" and "to show" something and, what results from this, our being able to distinguish between nonsensical propositions (Wittgenstein 1922: 6.54), propositions with sense (natural sciences), and senseless propositions (tautologies, 4.461). Wittgenstein does not actually elucidate any particular propositions, but just by making clear all these differences he can be seen to be putting in place the procedures required for every kind of proposition to be elucidated. The mathematical propositions are pseudo-propositions; like the tautologies, they say nothing: "Mathematical propositions express no thoughts" (Wittgenstein 1922: 6.21). "The tautology has no truth-conditions, for it is unconditionally true, and the contradiction is on no condition true" (4.461). They are no pictures of reality. Tautology and contradiction are without sense.
In regard to the analytical points pursued here in relation to the Tractarian context for understanding pseudo-propositions and philosophy as poetry, it is surely worth noting Wittgenstein's assertion that "[m]ost propositions and questions, that have been written about philosophical matters, are not false, but senseless" (Wittgenstein 1922: 4.003). By way of contrast, he did not claim, for example, that poetry, or "artistic achievement," is composed of nothing but nonsensical propositions. The sentences in most poems would certainly be seen as unambiguously belonging to that category, were they to be treated as propositions. The point is that poems (poetry), unlike philosophical treatises, are not in general held to be composed of "propositions" asserting some truth or other about the world. Moreover, for Wittgenstein: We feel that even if all possible scientific questions be answered, the problems of life have still not been touched at all. Of course there is then no question left, and just this is the answer. (Wittgenstein 1922: 6.52) If all questions can be answered in sentences that have sense, then it cannot be intelligible to say that poetry or artistic achievements are nonsensical. Wittgenstein's remarks thus serve to remind us of the important distinction between scientific matters (or questions) and poetic ones.
Wittgenstein acknowledged his own use of Fregean elucidation in the Tractatus (6.54), and grasped its consequences, concluding the book with his well-known remark about pushing away the ladder that has brought us to a point where, if we now truly understand Wittgenstein's aims in the text of that work, we recognize the propositions we have just read to be nonsense.
My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used themas stepsto climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He must transcend these propositions, and then he will see the world aright. (Wittgenstein 1961: 6.54;cf. Conant 2000;Perloff 1996: 47-48, 134) Articulating Frege's own conception of elucidation in Tractarian terms, we may say that what cannot be said can still be shown to those who have not seen it yet by putting up the ladder of nonsense for them to climb. Once we have seen what needs to be seen, we shall have to throw away the ladder, and we shall, in the end, see the world aright. What Wittgenstein supposedly also recognized was that this same warning would hold good not only for any discourse about the structure of the Tractatus, but also, and similarly, for any discussion about how and for what reason the theory presented there had been constructed, and for any claims about how the theory ultimately advocated there was to be applied in the light of the warning about throwing away the ladder itself (cf. Ludlow 2019: 18-19).
Independently of this, Wittgenstein's uses of the term "elucidation" have proved perplexing for manyin part because it is not clear what he himself meant by the expression, and in part because his three Tractarian cases seem inconsistent. Apart from the passage already quoted, the term "elucidation" occurs in the following two paragraphs in the Tractatus: The meanings of primitive signs can be explained by means of elucidations. Elucidations are propositions that contain the primitive signs. So they can only be understood if the meanings of those signs are already known. (Wittgenstein 1961: 3.263) Philosophy aims at the logical clarification of thoughts. Philosophy is not a body of doctrine but an activity. A philosophical work consists essentially of elucidations. Philosophy does not result in 'philosophical propositions', but rather in the clarification of propositions. Without philosophy thoughts are, as it were, cloudy and indistinct: its task is to make them clear and to give them sharp boundaries. (Wittgenstein 1961: 4.112) Names are primitive signs: i.e. they cannot be defined. They form the end-points that connect the world of a picture of the world to a situation. They exemplify the moment when language comes into direct contact with reality, and thus the point where a speaker may well be at a loss for words and wish to just gesticulate at the object. To say that philosophy "consists essentially of elucidations" means that philosophy is not primarily a theory but an activity.
The puzzling relationship between elucidations and primitive signs is brought out in the formulation in 3.263, which states that elucidations are propositions that contain primitive signs, which are explained by means of elucidations. On the one hand, it is puzzling how the speaker and hearer could ever achieve a shared referential understanding, given that the meanings of primitive signs are only shown in propositions, with no unambiguous explanation. It is possible that Wittgenstein is just seeking to point here to some fact of shared understanding of the kind that psychologists or sociologists might be expected to concern themselves with, and that there is nothing for philosophers to attend to here.
On the other hand, though, in 4.112 we learn that elucidations are what is of primary importance for philosophy insofar as it "aims at the logical clarification of thoughts". And in addition, in the already-mentioned 6.54, Wittgenstein comments on the status of his own philosophical propositions by talking about elucidations that are nonsensical, but by means of which he aims to help us "to see the world aright." How, then, might we arrive at a more or less homogeneous picture of Wittgenstein's uses of Tractarian "elucidation"?
One possible answer could go as follows: for Frege and Wittgenstein, elucidation is performed in language of the most everyday sort, for which truly precise meanings never get to be specified. As a consequence, elucidation is notstrictly speakingapplicable to science. To be sure, when establishing a scientific discipline, a scientist does need to have a basis for communicating with other scientists, and even if elucidation is not sufficiently accurate, it is nevertheless required for precisely that pragmatic reason. Yet the fact remains that where any such system is concerned, elucidation only comes into play at the beginningand given its indeterminacy, it should not be taken to belong to the system itself. (Fregean elucidations, inasmuch as they involve "relying upon a reader who would be ready to meet … half-way" (Frege 1997e: 192), also imply a willingness to make certain suppositions about others.) In the Tractatus, meanwhile, Wittgenstein takes over the notion of "elucidation" from Frege, but he does so in a critical way, opposing to Frege's example the categorical notions and elements of our logical apparatus, construed as inherently undefinable: Wherever the word "object" ("thing", "entity", etc.) is rightly used, it is expressed in logical symbolism by the variable name. … Wherever it is used otherwise, i.e. as a proper concept word, there arise senseless pseudo-propositions (Wittgenstein 1922(Wittgenstein : 4.1272; see also 5.4) Wittgenstein (1922) claims that only names are primitive signs: "The simple signs employed in propositions are called names. The name means the object. The object is its meaning" (3.202 and 3.203). "The name cannot be analysed further by any definition. It is a primitive sign" (3.26). Yet even so, both philosophers do still share the idea that elucidation differs from definition and serves to explain the meanings of primitive signs.
While Frege and Wittgenstein converge on the idea that elucidations are not implemented within the sciences, the roles they are prepared to allow it to have are different (cf. Maruyama 2009;Rozema 2002). Frege's elucidations acquire their rationale as a propaedeutic to this or that science, but the fact that they cannot be accurate means they are ultimately reliant on someone else's guesswork. Wittgenstein's, meanwhile, can only be called upon when the logic of thought is itself not unmistakably clear, or has been misunderstood. Elucidations are deployed only temporarily, and are to be "thrown away" once the logic has been properly understood, for the simple reason that they themselves are nonsensical pseudo-propositions, only guiding us towards seeing the world arighti.e. from a logically appropriate point of view. They exercise their "elucidatory" effect upon the reader "in advance," so to speak: upon the reader, that is, who is brought to understand that Wittgenstein himself regarded them as nonsensical. They are by no means Fregean elucidations, in the sense of investigations of how scientific propositions decompose into their elements.
According to Wittgenstein (1922), "[t]he limits of my language mean the limits of my world" (5.6). In adhering to the thesis that the only truthful conveyors of meaning are elementary, logically independent, fact-stating propositions, the Tractatus is, by virtue its own form and content, an advance attempt to transgress these very limits. That is because its propositions are elucidations and tautologies that say nothing. The elucidations are, like all authentic philosophical utterances, deeply nonsensical attempts to say the unsayableor, as Frege put it, to say something in such a way that "that which is said therein steps back behind how it is said." Thus, Wittgenstein's entire Tractatusincluding both its form and its contentis, as he recognizes, a "throwing away" of the ladder that consists of the nonsensical sentences the philosopher will give up once he or she has used them to "see the world aright" (Wittgenstein 1961: 6.54).

Conclusion
In the remarks posthumously published as Zettel, Wittgenstein writes: Do not forget that a poem, even though it is composed in the language of information, is not used in the language-game of giving information. (Wittgenstein 1967: § 160) This could well be paraphrased in the following terms: the Tractatus, even though apparently composed in the language of logic and philosophy, is not merely an example of the language-game of logic. Through its form and its language it elucidatesi.e. showswhat is inexpressible. This, in turn, suggests that when similarities between philosophy and poetry or literature (Dichtung) are highlighted, what we are dealing with is an approach corresponding to a highly disparate conception of philosophy itself. In particular, in any such context two beliefs will have to be relinquished: firstly, that the content of a philosophical text can be separated from its initial form and still be communicated without significant loss of meaning via other texts (e.g. interpretations, periphrasis, or summaries of its main theses), and secondly that philosophical activity should consistas with the hard sciencesin experiments and theory-construction. Thus, though Wittgenstein neither explicitly regarded the Tractatus as a poetical work nor deliberately wrote it as such, it becomes apparent that it is a kind of poem, in the sense that the form fits the content. Both of them, however, do accurately picture a certain form of life, and the unqualified outcome of this logico-poetical construction is a certain quite appropriate directing of our attention away from the form of life it pictures. This, then, is what we propose with regard to the Tractatus: that it is best and most beneficially read as "an artistic rather than a scientific achievement." I have tried to show that this is how Wittgenstein himself, in the light of his Frege correspondence, came to think it should be readsomething which, in turn, may help us to understand why it is that in the first instance he allowed, and then later continued to permit, the Tractatus's publication.
So what does it mean to consider the Tractatus an "artistic achievement," in the sense of a work-cum-poem picturing the form of life implicit in the investigations of such philosophers as Frege or Russell? Well, in the Tractatus, Wittgenstein takes some of the key claims of Frege's logic and philosophy (pertaining to definition, fiction, Dichtung and elucidation)such as that all words refer to objects, and that all meaningful propositions represent a feasible configuring (ordering) of these objectsand draws out the full implications of adopting them in a principled way. Moreover, in the closing paragraphs of the Tractatus, he demonstrates the practical implications of living a life in accordance with these ideas, concluding that "Whereof one cannot speak, thereof one must be silent" (Wittgenstein 1922: 7). The double-edged assertion this remark presents us with carries an appropriate force, for it is both descriptive and figurative (pictorial). It describes Wittgenstein's own thought when he realizes that, because of his Fregean-Russellian philosophical obligations, he, as a philosopher, has nothing logical-cum-ethical-cum-aesthetic to say in regard to the truth, the goodness, or the beauty of life. And it is itself a picture of the sine qua non that a good, true, beautiful and fortunate life -"Die Welt des Glücklichen ist eine andere als die des Unglücklichen" (6.43)be lived and not just theorized or verbalized (i.e. that there comes a point where we have only to "throw away the ladder … and [we] will [in the end] see the world aright" (Wittgenstein 1961: 6.54). This is why, when Wittgenstein draws a picture, some of the "propositions" (elucidations, tautologies) in it are not genuine propositions, but just look like propositions.
The overall findings emerging from the foregoing discussion are summed up in the points below.
Firstly, Frege's understanding of fiction entails that the thoughts uttered by sentences in fiction are "truth-free." Because such sentences, in such a context, are so, the expressions embedded within them can only be non-referring (meaningless). Moreover, given that the latter is so, sentences in fictional discourse are about nothing whatsoever. To be fictitious is inconsistent with being either true or false, in that a Fregean thought can neither give up its truth and become a fictitious thought (Scheingedanke), nor acquire truth and become a factual one. For this reason, we should not expect that a thought that is either true or false in one kind of context could become fictitious in another. (The Odysseus example shows what happens when the context changes). This is an uncontroversial consequence of Frege's standard claims. However, as I have presented the matter (also in relation to the case of Odysseus), Frege himself was also willing to entertain a contrary opinion, and because of this we encounter a certain tension in his views about fiction. Even so, to suggest that Frege actually held different views would be to completely lose sight of any sort of proper assessment of his analyses of fiction. We are just forced to conclude that he did not furnish us with an unambiguous theory of fictional discourse. The apparently inconsistencies in his views originate from the absence of a comprehensively gapless semantic theory of fictional discourse, not from any inherent deficiency of such a theory.
Secondly, seen from his own point of view of Dichtung, of elucidations, Frege was justified in his view that the Tractatus was mainly an "artistic rather than a scientific achievement." Nevertheless, for all of that, he was wrong to believe that the whole content of the Tractatus could be captured independently of the unified form that Wittgenstein (1961) himself gave it -"anyone who understands me eventually recognizes them [i.e. all of the sentences -JB] as nonsensical" (6.54). It could not be divided up, for publication, into, say, ontological, logical, ethical, aesthetic and mystical parts. The Tractatuslike a poemhas an indivisible form through which it is expressed, and this form is essential to the nature of the whole work. From this perspective, we cannot say that its content is insignificant, because it isin its various partsactually something known by us, but rather, just that it is conceptually impossible for the work to have that content without that form. The Tractatus is neither classical poetry nor a straightforward piece of work in logic. Wittgenstein speaks about this question both in his Preface and in his letter to von Ficker, and the view developed here is that, as an "artistic… achievement" rather than some other sort, it is located between, and transgresses the limits of, both logic and poetry. An excellent poem and a good philosophical treatise both show, in their integral wholeness, what they likewise point to in their content: that the form of such a work and its content cannot be just "divided into so many parts." Thirdly, the Tractatus is not a purely "artistic… achievement," but rather also, at least from a certain limited point of view, an aesthetic, logical andwhat should be notedethical one. Pondering the Tractatus in such terms, we can understand Frege's words when he writes that "Logic has a closer affinity with ethics [than with psychology]" (Frege 1979a: 4). Moreover, Wittgenstein himself held that for an achievement to possess real credibility, it must simultaneously do justice to the philosophical facts (whether logical or otherwise) and enable the reader to recognize himself or herself within it.
Fourthly, taken as a whole, the Tractatus is neither senseless nor nonsensical (4.4611)so long, that is, as it is informing us about what language must be like if it is not to mislead us; yet its particular statements can equally be regarded as senseless (4.461) or nonsensical (4.4611), in that taken by themselves, and outside of the Tractarian framework, they have no sense. A similar type of judgement has to be made about great poetry (Dichtung), which is almost impossible to define, but nevertheless integrated to a precise degree in respect of how its elements fit together. Great poetry, one might say, "investigates" a larger realm than the Tractatus. For one thing, it pushes us in the direction of close encounters with the stuff of the world (objects, state of affairs, colours, etc...)where this, however, is never quite pinned down directly by the poet. For another, poetry strives toward the inexpressiblewhich, nevertheless, the poet can never arrive at an ultimate conception of. Characteristically, the stuff of the world is shown in the Tractatus in its different parts, but its limits only at the end -"The limits of my language mean the limits of my world" (Wittgenstein 1922: 5.6). Of none of these can one speak, though somebody may show them.
A fifth point is this: to say that "A philosophical work consists essentially of elucidations" (Wittgenstein 1922: 4.112) is to imply that it is made up of propositions that use, or adopt, signs in ways that are correct and appropriate. Wittgenstein anticipated his later conception of "use" in connection with words, even though, at the time of the Tractatus, he believed in the overriding significance of the picture theory of language and focused on the importance of the structure in language itself. In using an elucidation, we correctly apply a sign (Wittgenstein 1961: 3.263). Because we are doing so correctly, it must be the case that we understand the meanings of the language's primitive signs, and somebody who sees that we are doing so properly must likewise understand them in the right way (3.263). The Tractatus, as we have seen, can be understood by someone who speaks the language anyway: i.e. by someone who thinks like Wittgenstein, who has had the thoughts Wittgenstein has had. Hence, when it comes to using language to disclose the form of either the world or thought, philosophy is not granted any particular or privileged competence.
The sixth point to be made here is that to do its work, philosophy must use pseudopropositions and tautologies. By the last of these, Wittgenstein (1922: 4.462) means a kind of statement that cannot be false in that it cannot stand in a relation of not being consistent with the facts ("... it stands in no presenting relation to reality"). Examples of a literary use of tautology as a form of elucidation might be the statement "if I perish, I perish" (The Book of Esther, 4:17), or Heidegger's more philosophical "language is language" (Heidegger 1968: 153) or "speech speaks" (Lawlor 2003: 161)these being tautological, yet still propositional. Elucidations cannot define or explain a sign: rather, they only instruct us by example, almost like a kind of ostensive definition that specifies the meaning of an expression by indicating examples of things to which the expression applies.
Tautologies exhibit the same properties as propositions, even to the point of being internally structured just like completely meaningful propositions: "objective," "real," they say somethingand, in particular, the situation they describe is indeed the case. Even so, their internal arrangement does not say anything (they are propositions that lack sensethat are senseless; see Tractatus 4.461). And yet they do show something: namely, the logical form of language (6.1), and with this the properties of the world. Moreover, if we are tempted to think that this comparison is misplaced, we should consider what Wittgenstein wrote in his Notebooks (Wittgenstein 1969: 40) on 7th February, 1915, which was that "Musical themes are in a certain sense propositions," or later (on 4th March, 1915) when he observed that "A tune is a kind of tautology, it is complete in itself, it satisfies itself," or in the Tractatus itself, where he states that "A proposition is not a blend of words. -(Just like a theme in music is not a blend of notes.)" (Wittgenstein 1961: 3.141). Wittgenstein treats the arts, and music in particular, in terms of rules (e.g. the rules of harmony, or those dictating how elements of a melody may relate to one another). Naturally, the wholeness of a poem, a piece of music, or a literary novel, does not in exact terms constitute a tautology. Hence we should instead just say that what these furnish us with is analogous to propositions that are nonsensical: i.e. (unsinnig) propositions that say nothing but, as was already mentioned, show something whose significance is itself as indispensable as what tautologies in the strict sense do actually show, and thatwe should not forgetpotentially have an elucidatory role to play, in the context of either language learning, or poetry, or philosophical activity itselfwhich last would imply, for the Tractatus as philosophy, being closer to an "artistic rather than a scientific achievement." Finally, it may be said that elucidations stand in a class all of their own: as not quite poetry, aphorisms, or logical formulae, they resist categorization. Yet much like poems and aphorisms, Wittgenstein's elucidations employ signs in some quite distinctive ways. They instruct us by example, which is to say by showing rather than saying (cf. Tractatus 1961: 3.263): as mentioned above, in 4.112, Wittgenstein argues that a philosophical work essentially consists of elucidations, while in 6.54 he stresses that his propositions aim to elucidate and ultimately guide us to a position from which we can see the world aright. In this way, philosophy is conceived not as one of Frege's "strict sciences," but instead as consisting in propositions and utterances that resemble those of the "humanities" inasmuch as the latter approximate to artistic achievements. Philosophy, thus understood, is therefore not an arrangement of theoretical claims, but an elucidatory activity: one that itself results not in philosophical theses or propositions, but rather in the clarification of propositions (cf. 4.111-4.112).
To what extent, then, does Wittgenstein's Tractatus corresponds to Frege's understanding of fiction? This question turns out to be essential to any proper grasp of the options made available by, and possible usefulness of, Wittgenstein's theory of language and, more precisely, his theory of meaning. Certainly, we cannot avoid it if we want to accurately comprehend how the Tractatus is meant to work as a characterization of linguistic meaning. The conveying of thoughts in poetry or in works of literary fiction is probably a no less meaningful use of language than the putting forward of propositions in a scientific exposition. Thus, we might well conclude that the Tractatus, to be seen as offering a generally valid analysis of linguistic meaning, would have to provide both a logic for science and a closely related description of fiction, treating both in the same underlying terms. And it seems fair to say that what our own analysis of its propositions has shown here is that it does contain, at the very least, the foundations for such a logic and such a description.
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