1.
The world a totality of facts, facts as the existence of states of affairs; possibilities as the “facts” of logic. Gottlob Frege and Bertrand Russell were rightly puzzled when they encountered those notions on the first page of the Tractatus. What is a fact, Frege wondered. (Frege 1989, 19) What is the difference between a fact and a state of affairs, Russell asked. (Wittgenstein 1995, 125) As for a realm of possibilities, there was no place for it in their logic. And what could they make of Wittgenstein’s talk about the world and its totality? That they had difficulties with the book is not surprising given its indubitable originality and its exceptionally condensed formulations. It has taken several generations of scholars and a rich body of secondary literature to give us a better understanding of the work.
But in this course of things something has also been lost. Frege and Russell approached the Tractatus naively but they did so also in a genuinely philosophical manner. Today, the book is shrouded in a veil of commentary that is becoming thicker with every year and this makes it almost impossible for us to look at the book in its own terms. Can we still free ourselves from the secondary literature enough to read the Tractatus once more in the way it must have appeared to Frege and Russell? As an occasion for philosophical engagement and not one for practicing the hermeneutic arts.
2.
Gottlob Frege was, for all we know, the very first reader of Wittgenstein’s book. Wittgenstein’s sister had sent him the manuscript in December 1918 at the request of her brother who was at the time a prisoner of war in Italy while Russell was to receive his copy only half a year later. (von Wright 1984, 111). Was the delay due merely to the uncertainties of the mail, as Wittgenstein explained to Russell, or was he keener at this point to hear of Frege’s response to his book? He had been closer to Russell during the pre-war years, but he had never felt comfortable with Russell’s careless mixing of logical, epistemological and psychological considerations. In Frege he admired the clarity and succinctness of his formulations and his sharply concentrated focus on logic. When he started work towards his book in 1914, he had done so under the Fregean motto that logic must take care of itself – a decidedly un-Russellian formula. (Wittgenstein 1979, 2) And in the preface to the Tractatus he had distinguished accordingly between “the magnificent [grossartige] works of Frege and the writings of my friend Bertrand Russell.” (Wittgenstein 1960, 29)
But Frege’s response was to disappoint him. After months of silence, Frege wrote apologetically that “protracted business matters” had prevented him from engaging with Wittgenstein’s treatise. “I can therefore give you no considered judgment… I find it difficult to understand.” (Frege 1989, 19) He was particularly bothered by Wittgenstein’s preface. “After one has read your preface one doesn’t quite know what to do with your first sentences.” (Frege 1989, 23) He picked, in particular, on Wittgenstein’s remark that the Tractatus was not saying anything new. Surely, this was not the case. When Wittgenstein supplied him (in a letter now lost) with an account of his intentions, Frege did not find that helpful either. “What you write about the purpose of your book is bewildering to me,” he responded. (Frege 1989, 21)
When he turned his attention directly to the book, Frege could not manage to get beyond the first page. He was taken aback right at the start by the dogmatic tone of Wittgenstein’s words. “One expects to see a question, a problem posed,” he wrote, thinking possibly of the opening of his own essay “On Sense and Reference”. But the Tractatus started with bare assertions without the kind of justification “that they evidently need so urgently,” How did Wittgenstein come to his propositions about a world of facts and a space of possible states of affairs? With what problems were they connected? “I would like a question to be put at the beginning, a riddle of which one would enjoy to learn the solution.” (Frege 1989, 23-24) If he had read on, Frege might, perhaps, have discovered that the Tractatus begins, indeed, with a riddle, but one that is cast initially in the form of a simple assertion.
Instead, he remained stuck with a number of unexplained terms in the first sentences of the book. There was, above all, the question: “what is a fact?” He also wanted to know what Wittgenstein meant by the expression “being the case”? Was there a difference between “being the case” and “being a fact”? Or were the first two sentences saying the same thing? But why then the duplication? And what about “states of affairs”? How did they differ from facts? What did it mean to speak of the Bestehen of states of affairs? Was the Bestehen and Nichtbestehen an existence or nonexistence of states of affairs, as our translations now make it? Were there then nonexistent states of affairs? This touched on one of Frege’s deepest insights – the realization that existence is not a property that things may have or lack. It looked to him, as if Wittgenstein was going back on that important conclusion. Wittgenstein was borrowing his terms, moreover, from ordinary language which was surely an unreliable guide. “We need, so it seems to me, elucidations (Erlāuterungen) to make the sense more precise,” Frege complained. (Frege 1989, 19) His words suggest that he had, perhaps, read further into the Tractatus than he admitted. Had he seen TLP 3.263 “The meaning of primitive signs can be explained by elucidations” and perhaps even TLP 4.112 that “a work of philosophy consists essentially of elucidations”? So, where were the sorely needed elucidations? Wittgenstein’s response that question left Frege nonplussed: “I would hardly by myself have come to what you write to me about state of affairs, fact, or situation (Sachverhalt, Tatsache, Sachlage).” (Frege 1989, 21)
It was the notion of fact that particularly irked him. He had found no use for it in constructing his own logic. In his Begriffsschrift he had once considered the possibility that the judgment-sign he put before propositions in his formal notation might be read as saying that the proposition was a fact. (Frege 1997, 34) But he had never returned to this idea in his subsequent writings. It was only in his essay “The Thought,” written at about the same time as Wittgenstein’s Tractatus, that he returned to the issue. “Facts, facts, facts, cries the scientist, if he wants to bring home a firm foundation for science,” we read in that essay. Was Frege thinking of Wittgenstein at that moment? (Sluga 2001) His own position was clear and straightforward. “A fact is a thought that is true.”(Frege 1997, 342) The thought in question was, of course, not a psychological moment but a supposedly objective content of thinking, the sense of a sentence, as he had previously described it. The thought and its truth were thus fundamental to him. “Fact”, on the other hand, was an uncertain and at best derivative notion. A true proposition did not stand for a fact but referred to truth or the truth-value True – a basic and undefinable notion. We know that Wittgenstein did not agree much with Frege’s essay. Despite his broad admiration for Frege, he felt no attraction to either objective thoughts or truth-values. The thoughts he wrote about in the Tractatus were psychological in character, not Frege’s senses. To Russell’s question about their constituents, he responded: “It would be a matter of psychology to find out.” (Wittgenstein 1995, 125) He also considered Frege’s account of truth mistaken. The True and the False were not objects for him. (TLP, 4,431) A proposition was made true, rather, by picturing a fact. To Wittgenstein, the notion of a fact was clearly more fundamental than that of truth.
But Frege was right in being wary of the concept of fact. When is a fact a fact? Are there identity criteria for facts? How many facts are there, for instance, when the black cat is looking at me from the sofa? We might say one single fact or speak of the cat’s being black, of it looking at me, and of it sitting on the sofa as three distinct facts. But is the cat’s being black a single fact or does it, in turn, consist of its head, body, and legs being black? And so on. And how many facts are there when a train is rolling past in the course of the next three minutes? Is the entire passing of the train one fact or are there non-denumerably many momentary facts? If we can identify facts only in terms of the descriptions we give of them, it appears that they are what they are only because we speak or think of them in a particular way. Nietzsche acidic comments seems to get close to the matter: “Facts is precisely what there is not, only interpretations. We cannot establish any fact ‘in itself’; perhaps it is folly to do such a thing.” (Nietzsche 1968, 481) Only if there exist elementary facts that are what they are quite independently of how we see, describe, or interpret them and if those elementary facts have clearly specifiable identity conditions and if, moreover, what we ordinarily call facts are just composites of those elementary facts, only then can we be sure that the notion of fact has a sharply defined meaning. It requires, in other words, the resources of logical atomism with its distinction between the elementary and the composite to make sense of the notion. But Frege – and Nietzsche – did, of course, not make such assumptions and we have no reason to make them either. When we talk about facts we mean, in effect, to refer to bits of reality which may be small or large or everything in between. It’s a convenient but not very precise way to speak. Philosophically, facts have not much to go for them.
To complete this line of reasoning would, of course, require a critical dissection of logical atomism. That task lies beyond the present essay. One consideration will have to suffice. It is that we should not take for granted that analysis leads inevitably from something more complex to something simpler and that we have therefore reasons to assume that there must be absolute simples at the imagined end of the analytic process, even if we can never find that end. The ancient Greek atomists thought in that way, but contemporary physics which has led us from atoms to particles and from there to quantum fields and strings shows that the process of analysis may actually lead us to ever more complex structures. The same is true in the case of logical analysis. If we analyze “Berlin” as “the capital of Germany” and “Germany” as “the country at the center of Europe,” that does not mean that Germany is simpler than Berlin and Europe simpler than Germany. So much for a stab at a critique of logical atomism. A thorough review of it would have to include an examination of the concept of analysis as well as critical attention to the concept of simplicity – a topic Wittgenstein himself took up in Philosophical Investigations.
3.
Russell did somewhat better than Frege when he first read the Tractatus. Within three weeks of receiving the manuscript he wrote to Wittgenstein that he recognized the importance of the book but this did not mean that he fully understood or agreed with it. “I have now read your book twice carefully. – There are still points I don’t understand – some of them important ones…. But in places it is obscure through brevity.” (Wittgenstein 1995, 121) He then appended a list of queries, beginning with “What is the difference between Tatsache and Sachverhalt?” The letter left Wittgenstein convinced that Russell had not really grasped what he had sought to communicate. “Now I’m afraid you haven’t really got hold of my main contention,” he replied. Frege “wrote to me a week ago and I gather he doesn’t understand a word of it all…. it is VERY hard not to be understood by a single soul.” (Wittgenstein 1995, 124)
In contrast to Frege, Russell had no difficulties with Wittgenstein’s facts. After initially agreeing with G. E. Moore’s view that truth was a simple and indefinable property of judgments or propositions (Moore 1900, 180) he had shifted to the view that “belief is true when there is a corresponding fact.” (Russell 1959, 129) In his Theory of Knowledge he had written in 1913:
Our mental life is largely composed of beliefs, and of what we are pleased to call
“knowledge” of “facts”. When I speak of a “fact”, I mean the kind of thing that is
expressed by the phrase “that so-and-so is the case”. (Russell 1992, 9)
A fact was, he added, “the kind of object towards which we have a belief, expressed in a proposition.” He relied thus in essence on a linguistic characterization of facts. But he didn’t mean to say that facts could be identified only via propositions expressing them. He believed, rather, that there were also ‘primitive’ facts “which are known to us by an immediate insight as luminous and indubitable as that of sense.” (Russell 1992, 9) We might even in some cases speak of “perceiving a fact“ and such “perceiving the fact cannot be identified with believing the proposition.” (Russell 1992, 133) By 1918, when he delivered his “Lectures on Logical Atomism,” Russell was still more certain about the reality of facts. “The first truism to which I wish to draw your attention,” he told his audience, “is that the world contains facts, which are what they are whatever we may choose to think about them.” And he added at once that truisms of this sort “are so obvious that it is almost laughable to mention them.” (Russell 1984, 182) The world was not completely described by “particulars”, he said, there are also facts “which are the sort of things that you express by a sentence and … these just as much as particular chairs and tables, are part of the real world.” (Russell 1984, 183)
Given that facts were the sort of things that can be expressed by sentences, it seemed natural to Russell to postulate different kinds of facts corresponding to the different kinds of sentences. There were, he said, both positive and negative facts as well as general ones and among the latter, in particular, “the completely general facts of the sort that you have in logic.” (Russell 1984, 184) This was a point of contention for Wittgenstein. He had adopted Russell‘s linguistic characterization of facts. He took it, in fact, more strictly than Russell hd dne and did not assume that one could also have direct, perceptual acquaintance with facts. He was not, however, ready to go along with Russell’s proliferation of kinds of facts. In order to resist it, he thought it necessary to introduce states of affairs. What Russell had called negative facts, he said, consisted simply in “the non-existence of states of affairs.” (TLP, 2.06). He also needed to distinguish between genuine propositions expressing facts and expressions that only looked like such. In section 6 of the Tractatus he reviewed a whole series of the latter. There were no logical or mathematical facts. The assertions of natural science were not propositions depicting facts. The purported claims of metaphysics and ethics were literally meaningless. Much of the Tractatus was, indeed, designed to prune back the Russellian overgrowth of facts. On Wittgenstein’s view, elementary sentences expressed states of affairs and their combination, if true, depicted positive particular facts. There were no others
The linguistic characterization of facts on which Wittgenstein agreed with Russell, left him however, with a problem that he could not solve. He may, in fact, not even have been aware of it. It concerns the question how one is to find out that a sentence is true. Wittgenstein’s proposed answer is that we must discover a corresponding fact. “The sentence is a picture of reality, for I know the situation presented by it when I understand the sentence… The sentence shows how things stand if it is true. And it says that they do so stand.” (TLP, 4.021 and 4.023) But how do I know that sentence S is made true by fact F? It appears that I must be able to determine that S actually depicts F and that means that I must be able to find out that the proposition and the fact have the same logical structure. But how I do I know the logical structure of F? If the answer is that I do so only through the proposition that represents it, then it turns out that we have no independent means of establishing that S represents F. If, on the other hand, we have an independent means of establishing the logical structure of F, Wittgenstein’s assumption that the structures of facts can be determined only linguistically must be given up. Russell avoided this difficulty by assuming the possibility of direct acquaintance with primitive facts of the form “This is white.” But that solution left him, of course, with the problem that the linguistic characterizations of facts was insufficient and that he had no other way to characterize what a fact was.
Wittgenstein did not go along that route and stuck, instead with his linguistic characterization. He was, in other words, unwilling to contaminate logical questions with psychological and epistemological considerations as Russell was prone to do. For Russell it was clear that “what appears to be known without inference involves psychology.” Since he assumed that elementary facts could be known by acquaintance, he could thus conclude that “the epistemological order of deduction involves both logical and psychological considerations.” (Russell 1992, 50) The Wittgenstein of the Tractatus was, however, a “logicist” in the Fregean mold who dismissed psychology as merely another natural science and as such irrelevant to philosophy and who took the theory of knowledge to be no more than “the philosophy of psychology.” (TLP, 41121) Having rejected the possibility of an immediate acquaintance with facts, he was left with saying that they could be identified only linguistically through the sentences expressing them. And this meant for him also that they could only be identified logically since language and logic were for him intimately related in a way that was entirely foreign to Russell.
Russell was, however, rightly concerned over Wittgenstein’s attempt to solve his problems by introducing the notion of a state of affairs. What were they? How did they differ from facts? Wittgenstein responded to Russell’s query by arguing at first that they were “what corresponds to an Elementarsatz if it is true,” (Wittgenstein 1995, 125) That explanation ultimately motivated Ogden’s translation of the German “Sachverhalt” as atomic fact. But this was not the full story. According to the Tractatus: “What is the case, the fact, is the existence of states of affairs.” (TLP, 2) The shift from the singular to the plural suggests, indeed, that what Wittgenstein calls “facts” without qualification are complex in contrast to states of affairs which are atomic. But the remark also indicated that a fact is what is the case, whereas a state of affairs may or may not exist. What Russell found problematic was in the concept was not the idea of atomic facts but Wittgenstein’s talk of non-existent “possible states of affairs” (TLP 2.0124). He took Wittgenstein’s states of affairs to be the kin of what he and Moore had once called “propositions.” The two had assumed at the time that there were both true and false propositions and that the true ones constituted reality. Truth, on this view, was an intrinsic property of propositions that they possessed as constituents of reality. But Russell had eventually abandoned this way of talking in favor of speaking of reality as made up of facts and of truth as a correspondence of our beliefs or judgments to those facts. In his “Lectures on Logical Atomism” he wrote: “Time was when I thought there were propositions, but it does not seem to me very plausible to say that in addition to facts there are also these curiously shadowy things going about such as ‘That todays is Wednesday’ when in fact it is Tuesday. I cannot believe they go about the real world.” (Russell 1984, 223)
When Russell read the Tractatus, he must have thought that Wittgenstein was returning to a view he himself had found reasons to reject. Wittgenstein had, in fact, introduced the notion of a state of affairs to explain how a sentence like “Todays is Wednesday” can be meaningful when it is false. While a true sentence is said to stand for fact, there is no such thing in the case of a false sentence. But such a sentence still has meaning as we can see from the circumstance that its negation will be true and will be so by standing for a fact. For Wittgenstein, both the true and the false sentence express states of affairs; the difference is that true sentences express existing states of affairs and false ones states of affairs that do not exist. But was that an adequate solution to he problem of falsehood? Were states of affairs not exactly the kind of thing Russell sought to avoid?
Russell meant to solve the problem with the help of his multiple relations theory of judgment. In a judgment or belief, he argued, a subject entertains a number of separate items together in their mind. When the belief is true there will correspond to it a fact in the world; when it is false there are only the subject and the separate items in the mind. no need then to postulate some intermediate shadowy entity lik a state of affairs. Thus, when Othello falsely believes that Desdemona loves Cassio, there is only Othello’s belief which is about the separate items of Desdemona, Cassio, and love. There is not in addition the proposition that Desdemona loves Cassio. Wittgenstein’s possible states of affairs were, so it must have looked to Russell, exactly what he was seeking to avoid.
The problem was, however, that Russell never managed to give give a fully satisfactory account of his multiple relations theory. Wittgenstein found it easy to poke holes into its various versions. Would any items held together in a mind at one moment constitute a belief? Would “the desk penholders the ink” be a possible belief? Wittgenstein summarized his objection in the laconic statement: “The correct explanation of the form of the sentence ‘A judges that p’ must show that it is impossible to judge a nonsense. (Russell’s theory does not satisfy this condition.)” (TLP, 5.5422) And if Othello’s belief concerned only the separate items of Desdemona, Cassio, and love, how could there be a distinction between Othello’s belief that Desdemona loves Cassio and the belief that Cassio loves Desdemona? Russell responded by postulating that the subject would also have in their mind a propositional schema – a “logical form” – that indicated how the other items were to be combined. But this still did not explain in what order the other items of the belief were to be assigned to this schema. In the face of these difficulties, Wittgenstein concluded that one could not get around the assumption that the object of a belief, whether true or false, had to be some unified whole. Wittgenstein’s resolution of this problem was to talk of states of affairs expressed by true and false sentences alike. But what exactly were they? And where were they to be found? Not in the real world, but in logical space. But what and where was logical space, if the world is everything that is the case?
In TLP, 2.01 Wittgenstein tells us that a state of affairs is a combination of objects, entities (“Sachen”) or things. One is reminded at this point of Frege’s observation that Wittgenstein’s terms call for elucidation. They are, once again, taken from ordinary language and as such suggestive but Wittgenstein evidently uses them in a new and distinctive way. A “Gegenstand,” as the term is commonly understood, may be anything from a material thing to the topic of a conversation. And the word “Sache” has almost the same wide range of meanings. A “Ding,” on the other hand is generally a solid, material object. Wittgenstein’s use of those three terms suggests that he may not have objects in the usual sense in mind. In 1930, he told the members of the Vienna Circle: “When Frege and Russell spoke of objects, they had always before their eyes what is linguistically represented by a substantive, let us say bodies like chairs and tables.” He went on to argue that we can describe the world also in very different terms as for instance through sets of equations. This indicates, he concluded, that, “We speak of objects simply wherever we have equivalent elements of representation.” (Waismann 1967, 41-43) Did Wittgenstein have that view already when he was writing the Tractatus? IHis characterization of objects in the Tractatus is certainly sparse. He says that they are simple and “colorless” when considered by themselves, mere place holders, dummy objects indicating some kind of multiplicity. He means presumably that taken on their own they have no concrete properties, for to assign a property to them is to think of them as constituents of states of affairs. They have nonetheless formal properties that determine how their “Verbindung” in states of affairs. (TLP, 2.0121) To translate the Gernan word as “combination” is, however, misleading since that suggests an arbitrary assemblage. Wittgenstein means, in fact, something different as he makes clear from subsequently speaking of a “Konfiguration,” an appropriately configured joining of objects. (TLP, 2.0231). Later on in the Tractatus, he adds in an echo of Frege’s account of the unity of sentences: “Where there is compositeness, there is argument and function.” (TLP, 5.47) The range of possible states of things, it turns out, is determined by the various ways in which “objects” can be or cannot be joined together. These possibilities are said to be due to “the nature of the object” (TLP, 2.0123) and to its “form” (TLP, 2.0141) which is determined by its “internal properties” (TLP, 2.01231). But what is nature, what is form, what are internal properties? Objects are independent of any particular state of affairs in which they occur, but since we can think of them only in their configuration in some state of affairs or other, this independence is also a form of dependence. (TLP, 2.0122). That raises another problem. Is the occurrence (“Vorkommen”) of an object in a state of affairs a form of existence? Do we have here yet another kind of entity to which are meant to ascribe existence as a property? And what is the relation between the “Vorkommen” of an object in a state of affairs and the “Bestehen” of s state of affairs? As the substance of the world, objects must be, presumably in the world. When they occur in an existing state of affairs, will they be part of the fact which is the existence of that state of affairs? And what does it mean to say that an object occurs in a non-existing state of affairs? How can something real be a component of something merely possible?
4.
Such uncertainties do not mean that we should bypass what Wittgenstein seeks to say when he speaks of states of affairs. Our task must be rather to get behind his terms so as to discover the substantive philosophical point he is seeking and sometimes struggling to make. In speaking of the world as the totality of facts, he is using, no doubt, the questionable language of logical atomism. But when we set the atomistic imagery aside, we discover the idea of the factuality of the world which proves genuinely insightful in thinking about logic, natural science, and ethics, as Wittgenstein sets out to show in the course of the Tractatus. We need to look in the same way at his use of the language of states of affairs. It, too, belongs to the vocabulary of logical atomism. We can get beyond that, however, by noting that Wittgenstein talked initially about states of affairs in order to explain the semantics of false sentences. He had then concluded that every false sentence expresses a possible state of affairs. The outcome was that he found himself talking of a space of possibilities complementary to the world as the totality of facts. This space, he concluded, was the domain of logic. Possibilities, he wrote, are “the facts” of logic. (TLP, 2.0121)
Once we are properly alerted to this view, we will also begin to notice how often he speaks of possibility in the Tractatus. Straightforwardly assertive propositions alternate regularly throughout his text with ones cast in modal language. The first of those modal propositions comes at the end of section 1: “Something can either be the case or not be the case, and everything else remains the same.” (TLP, 1.21) And it is with yet another variation between the assertive and the modal that the Tractatus ends when Wittgenstein writes first assertively in TLP, 6.54: “My propositions are elucidatory in this way…” and then follows this up with the modal proposition “Whereof one cannot speak, thereof one must be silent.” (TLP, 7)
In this he differed profoundly from both Frege and Russell who had found no use for modal concepts in their logical theories. But he equally differed from traditional ways of thinking about logic in that he was giving priority to the notion of possibility over that of necessity. Frege had touched on the subject only once, in his Begriffsschrift, where he had declared modalities to be of merely “grammatical” interest.” To speak of a proposition as necessary or as possible, he insisted, was to indicate only one’s grounds for judging it and this did not concern its ”conceptual content.” To call a proposition necessary was to indicate only that it followed from a universal law. To call it possible meant that one did not know any laws from which its negation followed or that one could not negate the proposition in its universal form. (Frege 1997, 54-55) But all this was irrelevant to logic. Russell dispensed with topic even more quickly. In his Theory of Knowledge, we wrote: “When analysis is completed, only the actual can be relevant, for the simple reason that there is only the actual, and that the merely possible is nothing.” (Russell 1992, 27)
Though Wittgenstein departed from Frege’s and Russell’s “amodalism”, he sought at the same time to preserve some of their critical insights. Like Russell, he conceived the world as a sphere of pure factuality and thus as one that has no place for the merely possible. He rejected for that reason a picture in which we see the facts surrounded by possibilities that are already there in a shadowy fashion. There are, as we know, philosophical views which conceive the actual to be pregnant with possibilities. Aristotle’s metaphysics gets close to this and so does Leibniz’s. Even the Tractatus itself has been interpreted in this way. When Friedrich Waismann sought to capture Wittgenstein views in the 1930s he wrote of the relation of the factual to the possible: “Reality is as it were an island within possibility.” (Waismann 1967, 261) That is, however, a misleading metaphor. On Wittgenstein’s view the world is what it is. Given its pure factuality, it has no room for possibilities either in it or surrounding it.
It was in his positive view of modality that Wittgenstein got close to Frege’s thought that modal notions are grammatical in nature. Frege had considered this to be a reason for dismissing them from logic. Wittgenstein concluded, instead, that grammar and logic belonged together. The space of possibilities with which logic was concerned existed, in fact, neither in the world nor in some other imaginary domain, but in language or, properly speaking in our system of representation which might be linguistic or pictorial or given only in thought. He grounded his account of modality thus in a particular conception of the nature and function of symbolic representation. ( 1) According to it, the purpose of the symbolism is to supply us with a correct representation of reality. Wittgenstein takes no notice at this point of the communicative and performative functions that come to matter to him later on. (2) Every symbolic system will allow the construction of both correct and incorrect representations. A picture can depict both a real and an imaginary scene, a sentence can say something true and something false. (3) A correct representation is a “projection” of a bit of reality and thus isomorphic with it. We can thus derive an account of the structure or reality from the structure of its representation. (4) Incorrect representations depict possibilities. We can use the perceptible signs of the sentence, he writes, in this way “as a projection of a possible situation.” (TLP, 3.12) A sentence is in this way like a picture. And “the form of depiction is the possibility that the things relate to each other like the elements of the picture.” (TLP, 2.151). States of affairs exist only as projections of possible situations. Sentences consist of combinations of names which refer to actual objects. Their combination in a sentence may present a picture of the configuration of those objects that exist or that does not exist. What is depicted in the sentence has only a virtual reality as a picture. It exists only in the picture just as an imaginary Tower of Babel exists only virtually on the canvas painted by Breughel. Logical space is thus something quite different from the world. The totality of facts is actually there; the totality of possibilities exists only in our system of representation. States of affairs exist only virtually.
In the Tractatus Wittgenstein speaks of just one logical space that includes all possible states of affairs. But if there are different of systems of representation we may not be justified in that assumption. The Tractatus considers, however, just one language that can represent all facts and thus all possibilities. But that can be only an imagined language; it is certainly not the language of everyday life. Once we abandon the assumption of a single complete and adequate language, we have to recognize that there may be more than one way to speak. If the facts are what we can talk of in our true propositions talks and possibilities are what we can talk of in both true and false propositions, we may then have to speak not of the world but of my world and not of the space of possibilities of my space of possibilities. And if we furthermore realize that our language is not fixed once and for all but changes and expands over time, we may have to talk about the changing space of our possibilities. And if, finally, the notion of necessity is to be defined in terms of th notion of possibility, we may even have to recognize a changing space of necessities. All this far outside the horizon of the Tractatus.
If the linguistic (or, properly speaking, the representation-theoretical) account of the notion of possibility is one of Wittgenstein’s achievements in the Tractatus – and with it the characterization of states of affairs as merely virtual, the second is his assertion of the priority of the notion of possibility over that of necessity. According to the traditional and classical view of modality, necessity is fundamental and possible derivative. The two concepts are, of course, formally inter-definable. We can define “p is possible” as “it is not necessary that not-p” but also define “p is necessary” as “it is not possible that not-p”. While both ways of proceeding are formally equivalent, there is nonetheless a substantive philosophical difference between them. On the classical view, necessary truths establish the framework for what is possible. In Greek metaphysics that thought is linked to the belief that only the changeless is fully real. The unchanging is, on this view, assumed to be the ground of the changeable. A great deal of Western philosophy and theology have been built on that assumption. Wittgenstein’s assertion of th priority of the possible overturns that way of thinking. On this account, necessity has to be understood as the limit of the possible. The impossible is what is excluded from the logical space of possibilities; the necessary is what holds for everything in that space. The necessary holds whatever possibilities are realized. Necessary truths can therefore say nothing about what distinguishes the actual world form all other possibilities. They are empty tautologies. This account dethrones and demythologizes the classical idea of necessity and thus strips away the basis for much traditional metaphysics.
The assertion of the primacy of the possible over the necessary has implications that Wittgenstein did not realize – at least not in the Tractatus – for it gives us reason to rethink the entire enterprise of philosophy. From the pre-Socratics to the present day, philosophers have seen themselves as engaged in the search for necessary truths. Taking the primacy of the possible as given, we may instead want to think of philosophy as the exploration of possible points of views. Philosophy will then come to be seen as an enterprise in imagination whose products may serve a variety of purposes among them that of playing an auxiliary role in the discovery of scientific and other sorts of truths. That is, in fact, what philosophy has always been doing in contrast to what philosophers have often said about it. is often asserted. With this idea of the priority of the possible in hand, we can also set out to look at the Tractatus in a new way. Wittgenstein presents the work in a series of apodictic propositions. In his preface e writes: “The truth of the thoughts communicated here seems to me unassailable and definitive.” (Wittgenstein 1960, 29) We have no reasons to agree with this. Many of Wittgenstein’s statements are neither unassailable nor definitive. We may want to read the Tractatus, instead, not as advancing series of truths but as proposing a possible way of looking at things. I am inclined to conclude that it invites us, in fact, to look at a whole series of possibilities – some of them more plausible than others. This way of thinking may give us also another perspective on Wittgenstein’s judgment on metaphysics. He is certainly convincing in saying that metaphysics can’t be a science and that its propositions are not scientific statements, that metaphysical propositions (or what goes as such) are full of unexplained terms, terms to which we have given no precise meaning. But such is the work of the imagination. Our conception of what is possible is often confused, unclear, and not even consistent. But for all that we can’t do without it. For to act and to think is to conceive of possibilities. There is thus no reason to shun metaphysical propositions but we must always ready to overcome them and set them aside in the endeavor to see the world in the right way. A simple, positivistic rejection of all philosophical attempts to say something about the world leads nowhere; holding on to any such attempt as an affirmation of necessary truth is stultifying
5.
The Tractatus deals not with facts and states of affairs, but not with individual facts and states of affairs or even a multitude of them; its concern is, from the first page to the last, with ALL the facts and with ALL possible states of affairs, that is, with their totality (“Gesamtheit”) as they constitute the world and logical space. This concern with totality takes Wittgenstein beyond the atomism of Moore and Russell.
But that does not mean that he returns to the sort of monistic view of reality advanced by Schopenhauer and Bradley. The Wittgenstein of the Tractatus is a pluralist and he will remain one for the rest of his life. Where he talks of a plurality of facts and states of affairs in th Tractatus, he will later on speak of the many ways we use language. The world of the Tractatus is a pluralistic totality for him: he does not question that there is a multiplicity of facts, states of affairs, and objects. His holism is, in fact, highly restrictive. The world is a totality but one that falls apart (zerfāllt) into facts. (TLP, 1.2) We must certainly not think of the world as an organic, essentially interconnected whole. Complexes are for Wittgenstein nothing over and above their parts: “Every assertion about complexes can be decomposed into an assertion about their constituents and those sentences that describe the complexes completely.” (TLP, 2.0201) We commonly conceive the world as a whole in which things have their locations and events follow each other in a regular fashion in the singular frame of space-time. Wittgenstein’s world is, by contrast, a loose assembly of existent states of affairs without any relations between them. Something may be the case or not and everything else remain as it is. (TLP, 121) There are spatial objects (TLP, 2.0131) and there are temporal happenings. But space and time are not characteristics of the world as whole, they are reduced to being “forms of objects” (TLP, 2.021). Wittgenstein’s world remains thus a curiously abstract whole from whose characterization evolution, history, culture, tradition, and the human forms of life are all absent. “The Darwinian theory has no more to do wit philosophy than has any other hypothesis of natural science.” (TLP, 4.1122) And not only biological evolution, but also the evolution of the cosmos as a whole is irrelevant to Wittgenstein’s thinking about the world. And so, also, is human history. “What has history to do with me,” he writes in his notebook. “Mine is the first and only world.” (Wittgenstein 1979, 82) The Tractatus notion of world is a severely minimal one. Any arbitrary collection of individual facts, so it seems, will constitute a world as long as they are all the facts. The black cat sitting right now on the sofa, the train rolling by this moment, and Berlin being the capital of Germany will constitute an entire world, as long as those are all that is the case. Can we even coherently contemplate that possibility? The minimalist account may be sufficient as long as we think about “the world” only in abstractly logical terms, as we do, for instance, in possible worlds semantics. But for all other purposes it will no be enough. It can’t be enough if we seek to think about human life and its place in the world. Such are the questions of ethics, as Wittgenstein understands it. To contemplate those we need a richer notion of world. Common sense and everything else we know from history to cosmology suggest a different view of the world than that of a kaleidoscopic assembly of facts – as neither an undifferentiated whole nor a mere collection of discrete facts, but as an integrally connected system.
To give a complete description of the world means for Tractatus to enumerate all the individual facts in it. But how can this be enough? How do we know that we have enumerated all the facts and thus given a description of the world and not just a description of a part of it? The question what constitutes a totality, what is meant by “all” in this encompassing sense occupies Wittgenstein throughout the Tractatus. To see the world as a whole, he concludes, must be to see it from outside. The contemplation of the world “as a bounded whole,” he writes, is its contemplation “sub specie aeterni” and it is as such a “mystical” feeling. (TLP, 6.45) The notion of the world thus turns out to be a limit notion to which we cannot give a scientific meaning. On the one hand, it is clear to him that we must speak of the world, if we are to think in the right and comprehensive way about science and life. On the other, we seem to be unable to make precise sense of the required notion of the world. When we have enumerated all the individual facts that constitute the world there is nothing additional to be said. That these are all the facts is not an additional fact. In order to talk about the world, it appears we have to position ourselves outside it to see it as a whole. “To be able to represent the logical form, we should have to put ourselves with our propositions, outside logic, that is outside the world.” (TLP, 4.12) But that is clearly impossible because there is no such outside. The only thing left for us is to to enumerate the facts as we see them. That we have described the world as a whole will show itself then in that we have run out of more facts to enumerate. The unity of the world will manifest only in the limits of our language, in our running out of words.
Totality is thus an evanescent notion but it is, nonetheless, also a crucial one in the Tractatus. Wittgenstein bring it up in the first two sentences of the book. Those sentences may strike us as peculiar, just as they did strike Frege, for they appear to be both weighty and bland. Their placement at the beginning of the book and their apodictic tone surely lend them weight. But as to their content, they sound almost trivial. What, if anything, are they meant to communicate? In order to appreciate their importance, it helps to recall what Wittgenstein told his students about philosophy in the 1930s. He said:
“(1) It has to be very general. (2) Fundamental both to ordinary life & science
whatever answers it gives. (3) Therefore has to be independent of special
results of science – e.g. of latest experiments on codfish or guinea-pigs.”
(Wittgenstein 2016, 103)
The first sentences of the Tractatus clearly satisfy two of those requirements They are as general as it can be and they are certainly not propositions of empirical science. But are they fundamental to life and science? We may assume that Wittgenstein took them to be so in 1918. As we start reading the Tractatus, we will want to keep Wittgenstein’s dual focus on “life” and “science” in mind and ask heuristically how his first sentences are meant to be fundamental to both.
The world as a totality of facts proves to be a decisive theme throughout the book. Wittgenstein mentions the world a remarkable 43 times in it. When we look into his war-time notebooks we find additional numerous references to it and more of them once again in his “Lecture on Ethics” of 1929. The world is evidently a major theme in Wittgenstein early thought. The Tractatus speaks of the world, moreover, in a variety of ways. We can distinguish at least four of them. Some of the propositions speak in an objective tone about “the” world. Then there are others in which he writes in a subjective tone of “my world.” (TLP, 5.62 and 5.63). In a third context, we read of the description of the world (“Weltbeschreibung”) by science: “Mechanics determines a form of description of the world” (TLP, 6.342) And in order to appreciate that remark we must keep in mind that “Weltbeschreibung” is a technical term to whose exact meaning we need to pay attention. Finally, and fourth, there Wittgenstein writes of different ways of viewing the world. In TLP 6.371 he contrasts “the whole modern world view” (“Weltanschauung”) with that of the ancients. And at the end of the book he calls on us to overcome the propositions of the Tractatus, in order “to see the world in the right way.” (TLP, 6.54)
In addition to the world as a totality there is, as we have seen, the totality of logical space. This is a space of possibilities and specifically the space of possible states of affairs. It constitutes a totality in that “every thing is, as it were, in a space of possible states of affairs.” (TLP, 2.013) This encompassing space is the space of logic. “Logic treats of every possibility, and all possibilities are its facts.” (TLP, 2.0121) Logic does not deal with any kind of possibility. Etwas Logisches kann nicht nur möglich sein.“ (TLP, 2.0121) Literally translated: “Something logical cannot be merely possible.” We need to ask what Wittgenstein means by the peculiar expression „etwas Logisches”. Ogden makes it out to be “a logical entity.” But this is must be wrong, since the Tractatus denies that there are such. (TLP, 4.441) Pears and McGuinness translate the expression more boldly as “the province of logic.” But this is also flawed. It is not the province of logic of which Wittgenstein says that it can’t be “merely possible” It is rather what we find in it. “Das Logische” is the way objects can be configured in states of things. This possibility is essential to the objects. “If a thing can occur in states of affairs, this possibility must already lie in them,” that is, in both the objects and the states of affairs. (TLP, 2.0121) And as such this possibility is “not merely possible.” To be not merely possible means to be not contingent. It is not contingent that things occur in states of affairs and are joined together in them in particular ways. “P is possible but not merely possible” implies “It is not contingent that p is possible.” Logic is not concerned with contingent possibilities such as the possibility that Russell and Wittgenstein met in Vienna or that Vienna is the capital of Switzerland. Logic is concerned, rather, with the possibility that a state of affairs may exist or not exist. And it is also concerned with the possibility of objects occurring in states of affairs. These possibilities are not contingent, for they are essential to the nature of states of affairs and of objects.
The world and logical space, the totality of facts and the totality of possible states of affairs. In order to see why we need to speak of both, we must consider their decisive difference. In the world everything is contingent, in logic nothing is so. In order to understand this, we must consider the passage in which Wittgenstein finally elucidates the first sentences of the Tractatus.
That is belatedly in TLP 6.41 where he writes that all happening and being so is “zufållig.” (TLP, 6.41) The phrase “all happening and being-so” may be taken to refer to and explicate the meaning of “world.” All there is to the world are things being one way or other and things happening this way or that. That is what it means to say that the world is one of pure factuality and nothing else. And as such the world is entirely zufållig. Our English translations have struggled with that term and have made understanding the meaning of Wittgenstein’s words more difficult by translating it as “accidental.” But Wittgenstein does not mean to say that the world is accidental or full of accidents. He means rather that there is nothing necessary in what happens in the world or in anything being so and not otherwise. The world is entirely a domain of contingency. TLP 6.41 is intended to say that all happening and being so is contingent and since that constitutes the world, that the world itself is contingent. This thought is, in fact, already suggested in the first sentence of the Tractatus according to which the world is all that is the case. For to be the case means to be the result of the falling of dice. To be “der Fall” and to be “zufållig” are clearly the same.
We find ourselves thus faced with two complementary totalities: the totality of facts which constitutes the world and the totality of possibilities which are the “facts” – metaphorically speaking – of logic. The world is a domain of sheer factuality; logic is a domain of possibility. In the world everything is contingent. By contrast: “in logic nothing is contingent (zufällig).” (TLP, 2.012) In consequence, nothing “in logic” can be part of the world. We have to conclude that “logic is transcendental.” (TLP, 6.13)
But how can we be sure that the possibility of states of affairs to exist or not exist is not a merely contingent possibility? The answer is that we need to be able to survey the totality of states of affairs to see that all possible states of affairs have the possibility of existing. And how can we be sure that the occurrence of objects in states of affairs is not a contingent matter? In order to be sure of this, we must be able to conceive of the totality of all objects and of all possible states of affairs. We can then determine that objects never occur on their own. Wittgenstein: “If I know an object, I also know all the possibilities of its occurrence in states of affairs… If all objects are given, then thereby all possible states of things are also given. (TLP, 2.0123 and 2.0124) A new possibility cannot subsequently be found. Logic is thus concerned not just with possibility but with all possibilities, that is, with the totality of possibilities, “with every possibility.” While the world consists of the totality of facts, logic treats in this way of the totality of possibilities. It is this totality that constitutes logical space.
6.
We still need to ask why Wittgenstein concerned himself with the world and logical space in their totality. Why did he consider it essential to go beyond the strictly atomistic point of view in the direction (if tentatively) of a holistic perspective? The answer is that he thought that only in this way could he make sense of the ideas of logical necessity and natural law and advance a coherent understanding of ethics and aesthetics.
It is only by considering the whole of the logical possibilities, he thought, that one can see what is excluded from logical space and thus impossible but also what is true of all possibilities and thus necessary. And something similar holds for natural necessity expressed in our so-called laws of nature. In science we construct frameworks of concepts in which we seek to model our reality. We are looking for a description of the world according to one single plan. (TLP, 6.343) But every such framework or plan will envisage only a certain range of possibilities. Natural necessities are what all those possibilities have in common.
Ethics and aesthetics, in particular, require us to think about the world as a whole. If we conceive ethics simply as a system of rules prescribing or forbidding particular actions, this will, of course, not be obvious. But Wittgenstein’s view of ethics follows Schopenhauer in taking it to be concerned with the ultimate question of human salvation and damnation. We can see, perhaps, from a somewhat different perspective how the threat of environmental destruction forces us to consider our place in the world as a whole. In the Tractatus, Wittgenstein lays out yet another line of thought. Values cannot be conceived as contingent and thus cannot be part of an entirely contingent world. But the world is a domain of sheer, naked factuality and as such contingent. Values must then lie outside the world, if they are anything. But thiere can be no extra-worldly realm of values since the world of facts is all that is the case. We must, instead, abandon the language of value, and speak of ways of seeing the world as a whole. To attach a particular value to the worlds means to see it in a certain way. Following Schopenhauer and through him Spinoza, Wittgenstein speaks of the aesthetic and ethical view of the world as one in which we the world appears to us as a bounded whole “sub specie aeterni.” (TLP, 645) In thinking about logic, about laws of nature, about causality, or the subject, or ethics and aesthetics, and the meaning of life, we find ourselves, according to Wittgenstein, forced to consider again and again the world as a whole.
That was where he had begun in the first sentences of the Tractatus. Looking back rom the end of the Tractatus we realize how much is already suggested in them. What is also already suggested in them is the realization how impossible it is to speak about the world and its totality. Those first sentences contained thus a whole series of riddles, though that might not be immediately visible to the eye. Frege certainly never caught on to those riddles. He passed over Wittgenstein’s remark in his preface that his book sought draw a limit to thinking but had found this impossible because “in order to draw a limit to thinking we should have to be able think both sides of this limit.” (Wittgenstein 1969, 27) Wittgenstein’s first two sentences illustrated the dilemma. To think of the world as a whole was to think of a boundary beyond which there could be nothing. But to think in that way was to recognize the possibility of something beyond that boundary. To resolve the dilemma, Wittgenstein’s preface concluded, required setting limits to language and this meant that one needed to dismiss certain tempting ways of speaking as “simply nonsense,” The first sentences of the Tractatus would thus have to be dismissed and with them all the limit notions that depended on them. This was not something Frege was ready to contemplate. Russell was similarly taken aback by Wittgenstein’s paradoxes. “What causes hesitation,” he wrote in his Introduction to the Tractatus, “is the fact that, after all, Wittgenstein manages to say a good deal about what cannot be said, thus suggesting to the sceptical reader that possibly there may be some loophole through a hierarchy of languages, or by some other exit.” (Wittgenstein 1960, 22) Wittgenstein’s belated response to this was to accuse Russell of a “loss of problems” – a condition in which “everything seems quite simple…, no deep problems seem to exist anymore, the world becomes broad and flat and loses all depth.” (Wittgenstein 1967, 416) But philosophy was, as Wittgenstein said with a bow to Heidegger and Kierkegaard, something more serious – “a running against the limits of language.” (Waismann 1967,68)
Notes
