6
The End of an Affair

Charles Travis

A third realm must be acknowledged. What belongs to it accords with Vorstellungen in that it cannot be perceived by the senses, but with things in that it needs no bearer to the contents of whose consciousness it belongs.¹

Introduction

In 1911, on Frege’s advice, Wittgenstein went to Cambridge to study philosophy with Russell. Perhaps he was ill-advised. For though, it seems, he did his best to depart from Russell, still, this was within a common framework. Which took as given what most fundamentally distinguished Russell from Frege. To the detriment, and ultimate demise, of Wittgenstein’s early work (as he himself saw in 1929).

What separated Frege and Russell so fundamentally can be put in few words. Where Frege spoke of Sinn, thus thoughts (Gedanken), Russell spoke of propositions (sometimes ‘objective sentences’). Russell failed to grasp such Fregean notions. He thus failed to understand, or grasp the point of, Frege’s two most important distinctions for understanding the phenomena of thought expression, and of being true (this last most central to Frege). Those distinctions are: between the logical and the psychological (being true and holding (forth as) true; between the particular and the general. Tractarian Wittgenstein followed Russell, if not entirely in vocabulary, at least in insensitivity, or indifference, to those distinctions, most particularly the second. Compared to such agreement, what remained contentious between the two pales into insignificance.

But these few words themselves call for explanation. Again in brief, the Tractatus falls foul of Frege’s anti-reductionist point, in “Der Gedanke”, against theories of truth; a point turning essentially on a categorial distinction between what is innocent of generality, and that for which generality is its life. For all of which, Frege and the Tractatus agree on this much: truth first comes into question with representing something as being something (henceforth “representing-as”). It is this (even if not in all cases) which is liable to be representing things as they are, or as they are not—as Aristotle pointed out, just what being true (or false) consists in. But Frege and the Tractatus have very different ideas as to how this core idea unfolds. The Tractatus unfolds it in terms of a certain presumed relation holding between representer and represented, depiction and depicted. What Frege shows, in effect, is that there could be no such relation: No relation of the needed sort could cross the categorial gulf between the two relata, which come together in representing-as.

1. 1902–1904

Russell did not understand Frege’s logical-psychological distinction. Such is one complication in their debate between 1902 and 1904 on (presently) crucial notions. Such will be our starting point.

The topic of the logical, for Frege, is the pure business of being true (or false); of ways the world may be made to matter to whether there is truth, to whether, that is, things are or not as represented. Frege makes the central item for logic’s purpose what he calls a thought (Gedanke). A thought is what makes truth turn in some given determinate way—the thought’s proprietary way—on how things are. It represents things as being some given way for things to be. Its truth is thereby made hostage to how things are. It represents in a particular aspect of that verb, roughly: For a thought to represent things as it does is for such to be what one would do in expressing it. One might usefully think of a thought as the representing of things as thus and so; as something to be done (rather than any particular doing of this). A thought thus identifies a particular achievement, one to be attained in thought-expression; in authorship.

A thought is purely that by which, as Frege puts it, “truth can come into question at all”; one of the two elements which make for truth or falsehood. Two thoughts can thus differ only by a feature which distinguishes two different ways for truth to be hostage to the world (i.e. the represented): for a representation to be hostage to how what it represents as something in fact is. So it is only by such features that a thought is identified as the thought it is. A thought, thus, cannot be an object of sensory awareness. Thoughts are invisible. So, too, a thought must be separated out from anything which has merely to do with achieving its expression, such as visible or audible forms of words thus used, or accompanying demonstrations.

Such are logic’s needs. By which we arrive at Frege’s notion Sinn. A thought is the fundamental case of a Sinn. It identifies, and is identified by, a way to represent things as being. It captures something an act of representing may be understood to do. Other Sinne are carved out of whole thoughts. They are partial doings of what that whole thought does. A whole thought represents things as being a certain way. It is true or false outright. So the question which things it so represents lapses. It makes truth outright turn on how things (mass noun) are. A proper thought element makes truth turn in part on how things are, e.g., on how some object is, or on what things fall under some given concept. A proper predicative element represents things as being some given way. For it, though, unlike the thought, the question which things is very much à propos. An answer mentions objects. The (Logikgemäss) notion object is thus introduced. There is nothing even faintly psychological about any of this, contrary to what Russell seemed to think.

If a thought element is carved out of a whole thought, so, too, in a different way, is a concept. But concepts are not thought-elements in present sense. As I will use the term here (Frege’s use is unsteady), for any way for things to be there is a concept which is the concept of things so being. It is intrinsically so: to be that concept is eo ipso to be of being that way. If an object is what a concept is a concept of, I will say that the object falls under the concept. One might also have said: If for something to be as that object is would be for it to be what that concept is a concept of being, then that object’s being as it is falls under the concept. But to avoid confusion I will say instead: then the object’s being as it is is a case of, or instances the concept. A concept generates answers to questions whether something falls under it; equally whether something instances it. Following Frege we can suppose that it is identified as the concept it is by the answers it thus generates. So a concept does not engage in representing-as. It is representationally inert. Sid may fall under the concept to be a wheezer. But it is all one to the concept whether he does or not. Such is part of what suits a concept to the logical role it is to play; a role distinguished by the above from naming. For present purpose, though, this is an aside. A concept is thus not a thought-element, any more than an object is. (Objects do not make truth turn on themselves.) But it may be put into service, inter alia, by a predicative thought-element: that element may make truth turn on what falls under that concept.

A thought’s work, making truth turn in some determinate way on how things are, may be broken up into subtasks. To do so is to decompose the thought into proper elements. For an element to be the element it is is for it to perform the subtask that it does. The tasks of proper elements are ones which could be performed only in the context of a whole thought. An artist who paints the nose on his subject’s face and then goes out for a six pack and a chilidog has at least painted a nose, even if fate decrees that he shall never return to paint more. A thought-element which makes truth turn on how Sid is would do nothing at all but for the other elements in the decomposition to which it belongs. There is no such thing as making truth turn on how Sid is, never mind turn how. Such might be seen as Frege’s context principle. The elements of a decomposition jointly do precisely what the whole thought does. Such it is for there to be a decomposition. It follows that a given thought may be—Frege tells us always is—decomposable in any of many ways, none with a claim to ‘objective priority’.

What sort of thing is as a whole thought represents things if that thought is true or false outright? If an object, then the same object for every thought, since otherwise the question ‘Which one?’ would not lapse, as it does. Anyway, objects combine with concepts (or what they are of) to form things to be so or not outright. If the thought is that Sid wheezes, Sid is the one thus represented as a wheezer. But what is it represented as such that Sid is a wheezer? Truth or falsehood do not await an answer to this question. There are different vocabularies for handling this issue. I will speak here of things as what plays the role, where such is to be read as things in general, and as rejecting questions which ones. ‘Things’ should be thought of as a mass out of which objects (inter alia) may be carved, not as itself an object.

The most crucial thing about a thought for our present purpose is its generality. This shows up with the fact that there might still have been that thought, that way to think things were things not just as they are. Thus that things may be represented as they are not. There would still be such a thing as things being such that Sid wheezes even if he did not. He might still have been a wheezer even were he, let alone things, other than he is/they are. For there to be such a thing as wheezing, the existence of chilidogs is optional. Nor is such just stipulation. It is part of what fits concepts to their role: to stand far enough apart from that which, in fact falls under them for there to be some truths which are contingent. (A concept must not be a name of what so falls.)

If an object does fall under a concept, it need not have done, nor, for that matter, have been, for that concept to exist. On the other hand, if it does so fall it must be intrinsic to the concept that this object, in being as it need not have been, so counts. Such belongs to the idea that truth is the joint work of precisely two, distinct partners: how things were represented as being; how things are. Nothing else could make a difference. It must thus be intrinsic to a thought’s proprietary way of generalizing over cases that it captures just what it in fact does; that it be true given how things are if it is true at all. Mutatis mutandis for a concept. So a concept’s (or a thought’s) proprietary way of generalizing—of generating answers to questions whether this is/would be how things were represented/what falls/fell under the concept—must be such as to generate precisely the answers there are to those questions history provides to be posed. Grasp of the thought, or concept, would be a capacity to recognize what answers are thus generated; how to answer such questions to the right proprietary standard. Thus, we see how thoughts and concepts belong to thought, not history.

2. Russell

With this background we turn to Russell. ‘Proposition’ is a standard philosophical waffle word. It comes squarely down on neither side of that distinction between a sentence (or Satz, or Aussage) and a thought (thinkable) which Frege highlights. (‘Satz’, too, on the evidence is fit for waffling.) Writing in German, Russell sometimes uses ‘Satz’, sometimes ‘Proposition’. But in 1902–04 his waffle appears of a different order. He writes,

One does not assert the thought, which is a private psychological matter. One asserts the object of the thought, and this is, in my view, a certain complex (one could say an objective sentence (Satz)) in which Mont Blanc itself is a constituent. If one does not allow this, one thus gets the conclusion that we actually know nothing about Mt. Blanc itself. Accordingly, for me the Bedeutung of a sentence is not the true, but rather a certain complex which, in given cases) is true.2

Both conceiving/envisioning[/imagining?] [‘vorstellen’] and judging always have an object. What I call a ‘proposition’ can be the object of a judgement, and can equally well be the object of a representation. There are thus two ways in which one can think of an object in the case where this object is a complex: one can picture it, or one can judge it; but the object is the same in both cases (for example, if one says, ‘the cold wind’ and if one says, ‘the wind is cold’.) So for me the judgement stroke signifies a different manner of being directed at the object. Complexes are true or false: if one judges, he means to be treating a true complex; though naturally he may be mistaken. But truth is not an ingredient of being true as green is an ingredient of a tree.³

In this we already see the germ of the collapse of the Tractatus. Though there is a bit here of vocabularies passing each other in the dark, and a bit of plain misunderstanding of Frege’s point. Part of what is missed is Frege’s logical-psychological distinction. For, as we have seen, there is nothing a bit psychological about a Sinn or a Gedanke. Such things are tied to proprietary ways of generalizing over the historical, whereas human psychology, or that of other beings, belongs to history, to what there simply is to represent as being one thing or another. Another perspective: If A and B are thoughts, then for A and B to be one is, for Frege, for any proof of A to be eo ipso a proof of B. What is proof of what is neither for psychology to decide nor for it to discover.

As for Mt. Blanc being a thought element, the misunderstanding here is still more fundamental. A thought-element, at least for Frege, is a partial doing of what a thought does (whole thoughts coming first in logical and ontological priority). A whole thought makes truth turn in some given determinate way on how things are. (The two-party enterprise again.) As it may be, it makes truth turn on how high Mt. Blanc is (whether more than 4000m). Making truth turn (somehow) on how Mt. Blanc is may be, in the context of the whole, doing part of what that thought does. We may thus speak of an element which so does. But Mt. Blanc makes truth turn neither on itself nor, for that matter, on anything else. It is something on which truth can turn, not something which makes truth depend on the world in any such way. Thus it is that Mt. Blanc cannot be a thought-element on Frege’s scheme of things. And, like the scheme or not, there must be some ingredient in the business of being true which does what a Fregean thought-element does; which plays party of the first part in that two-party enterprise.

If thoughts were both private (the only thing, it seems, Russell can understand by ‘psychological’) and that by which truth can come into question at all, then, indeed, we would be cut off from the world in thought, and we should never know (or so much as think) anything about Mt. Blanc. But perhaps there is another reason he thinks Frege is cutting us off from our environment. In “Der Gedanke”, Frege speaks of three realms. The first is a realm of private objects of consciousness. In this realm, truth makes no appearance at all. Nor does perception. We do not see or hear the denizens of this realm, Frege assures us, we have them.4 In the second realm, we find denizens of an environment, objects of perceptual awareness, about which (non-accidentally) there may be truths, with all the objectivity which forms part of that notion. In the third realm, we find thoughts, concepts, thought-elements. These, like occupants of the first realm, are not possible objects of sensory awareness. Like occupants of the second, however, they are objective. There are matters of fact, e.g. as to how a given concept generalizes. Russell seems simply blind to the possibility of such a third realm. If not the first, he is also certainly not the last otherwise first-rate philosopher with such a blindspot. To which one can only say: Without such a realm, there are no thoughts (in the non-psychological sense); thus, correlatively, there is no truth.

What of Russell’s ‘objective complexes’? The problems with these will be spelled out in detail later. For the moment, a complex is a structuring of a particular set of elements, in terms of given relations. From his examples (that cold wind, Mt. Blanc reaching upwards as it does, a certain green tree), these would seem to be denizens of an environment: the sort of thing which can pierce through one’s fleece into his chest as he pushes north; the sort of thing planes must avoid by remaining at a certain height, and so on. In what sorts of relations do these things stand towards one another? For example, temporal ones: The wind preceded the avalanche. Or spatial ones: The mountain is to the port side of our flight path. Such elements, so structured, do not add up to anything either true or false. What is true may, metaphorically, touch one’s heart, but not, literally, pierce one’s chest. But we need not dictate what Russell’s elements must be. Anyway, a complex which was true or false would first of al be one which posed, or presented, a particular question of truth. Its elements would be, or what made, particular contributions to that question (or its posing). Such elements would not be the sorts of things which could pierce chests or rise to immense, or even minute, heights. But to see this one must grasp, as Russell did not, the point of Sinn; see why making truth turn on itself is not something Mt. Blanc might do.

3. Relating Realms

The realm of Vorstellungen (what is proprietary to a particular consciousness) does not concern us here. Russell seems to picture the relation between Frege’s second and third realms as though that third one is so independent of the second (of an environment) that if thinkables belonged there we would be cut off from anything to think about. But it is not like that. As Frege insists, a concept cannot have ‘an independent existence’. Several ideas coincide under this rubric. Here is one:

What I see as essential to a concept is that the question whether something falls under it has a sense … A concept is unsaturated in that it requires something which might fall under it; thus it cannot exist on its own.5

A concept is identified by its proprietary way of generalizing, of answering, across an indefinitely extendible range of cases, questions whether something falls under it. But this generalizing cannot stop anywhere short of capturing or rejecting these particular cases, anywhere short of objects actually falling under it or failing to. A concept maintains its decorous distance across a sort of buffer zone from that which does fall under it. Its logical role (notably its role in making for contingency in truth) requires this. Nonetheless, what there is to fall under it must, in fact, do so or not. The concept, in being of what it is, must decide this where there is such to be decided. If a concept named what fell under it, perhaps polysemously, then if Sid were pear-shaped he would be necessarily so; if he were not, then again this would be necessarily so. Truth would be analytic through and through. Thus the buffer just described. But for the concept of being pear-shaped to generalize as it does, for it to answer questions who falls under it in its own proprietary way is, inter alia, for the way Sid is to be a case of someone being pear-shaped. Thinking Sid to be so shaped does not cut one off from the circumstance of his so being. Quite the contrary.

Mutatis mutandis for thoughts. A thought element (on some decomposition) may make the whole thought’s truth turn per se on how Sid is (in this thought he is the one who must be pear-shaped). But for Sid there would have been no such element in any thought. By contrast, a thought-element may make truth turn on who is pear-shaped. Were Sid not shaped as he is, there would not be this to make for truth or falsehood. If, otherwise shaped, he were not pear-shaped, that way for things to be would not have had the instances it does. It would, for all that, still be the way it is. Inter alia, there would still be thought-elements making truth turn on which things are it. Such distance between a concept and what falls under it, or between the way things are represented and what is so represented, does not distance the truth of a thought from things being as they are represented.

Being pear-shaped is what it is no thanks to Sid, or his being as he is. For all of which, among the questions to which the concept of so being generates an answer is the question of whether Sid being shaped as he is is being pear-shaped. Russell (of this period) seems to think as though if a thought needed a thought-element to make its truth turn on how Sid is, then the thought itself would not really be about Sid, so that to subscribe to its truth would not really be to subscribe to a view about him. But such merely misunderstands the role Sinn is meant to perform.

Frege also stresses a still more fundamental point. Holding true, and holding forth as true, cannot be (or merely be) predicating anything of anything—truth, included. For the result of doing that is just something which one can hold/hold forth as true, or, equally well, as untrue. Rather, to hold a representation true—to take it to represent things as they are—is to subscribe to its truth; to be prepared to treat it, hence what it represents as it does, accordingly. To hold something forth as true is to underwrite subscribing to its truth, thus so treating things. It is to offer authority as to what one purports to be authoritative. Frege writes,

[The word] ‘wahr’ really only makes a failed attempt to identify logic, in that what it [logic] is really about does not lie at all in the word ‘true’, but rather in the assertive force with which a sentence is uttered … That which most clearly contains indication of the essence of logic is the assertive force with which a thought is expressed.6

For a thought to be true is for what it represents as being such-and-such to instance (be a case of) things being the way it represents them. Assertive force is offering authority for, underwriting, so treating what it so represents, namely, things being as they are. A thought represents the way things are as a certain way. Two thoughts are distinguished from each other only by what way they represent what they do. But it is not as if the truth of a thought concerns only that identifying feature and not both those sides of the representing-as relation. On the contrary, there is an intrinsic connection between truth and the thing to do; how a thinker’s goals are, or may be pursuable. To subscribe to the truth of a thought is to subscribe to acting accordingly, or if not that, to recognizing so acting as the thing to do, as how the world is treatable. There is a thought, Frege tells us, just where it has applications; where its truth matters in determinate ways to questions what to do.7 If thinkables, Sinne of a certain central kind, are what are true or false, this by no means cuts us off from knowledge of the world we live in. On the contrary, it precisely is such knowledge. Frege’s third realm is exactly what he says it is and no more. What inhabits it belongs to thought, not to an environment. But its existence is not independent of our environment.

4. Russell’s View

What is true, Russell tells us, is a complex of a certain kind. A complex consists of given elements structured (in the complex) in some given way. E.g., a certain wind and cold (a rather unpleasant physical phenomenon). Russell is less clear as to the sort of structuring he has in mind. In any case, a complex (of his sort) is to be one to which a thinker can stand in either of two ways. He may present it to himself (e.g. imagine or remember it). Or, it may be what he thinks in thinking that such-and-such. In this last guise, it may be true or false. Curiously, mention of it in the one role would take a very different grammatical form than mention of it in the other would. How could this be?

Compare the case of sentences and thoughts. A sentence, say, “Sid is pear-shaped”, used to express a thought, might be thought of as presenting that thought as decomposed in a given way—in the example, say, into an element which makes truth turn in part on how Sid is, and another making truth turn in part on who is pear-shaped. On Frege’s view, another sentence—say, “The concept being pear-shaped is satisfied by Sid”, might be thought of as presenting that same thought; but then, of course, decomposed in a different way. The difference: Decomposing a thought in different ways yields different elements, standing towards one another in different relations. For Frege, to repeat, whole thoughts come first. They are there to be carved up in any of many ways. A thought is not a given complex. It does not have a unique structuring. Which allows Frege to recognize such a relation between sentences (or what he calls ‘Aussagen’) and thoughts. For Russell, though, that which can be mentioned in those different grammatical forms is a complex. It must thus be supposed to be identified, inter alia, by its proprietary structure. This analogy between Russell and Frege thus breaks down.

In 1879, Frege tried out the idea of a language with only one predicate. So a sentence for expressing something true or false (a ‘judgeable content’) might look like this: “Lager/lager’s containing yeast”, or “Odysseus/Odysseus’ having sailed”, or “Sid/Sid’s being rotund”. The predicate might then be something like ‘obtains’, or ‘is so’, or ‘is a fact’. He proposed this for Begriffsschrift. Thus, where ‘A’ stood in for a judgeable content, the horizontal stroke, ‘— A’, was to be read: ‘the circumstance of A (or A’s) being so. Adding a vertical stroke (‘|— A’) would then turn this into the form of an assertion: that A (that A is so/a fact).8 So here we have a complex which is not itself either true or false, but which is, so to speak, but one step away. It calls only for a predicate. Could such a complex be what Russell had in mind?

Prescinding from the fact that thoughts (coming first) are multiply decomposable, the occurrence of the same content-indicating letter, ‘A’, might be taken to indicate that the same complex of elements occurs twice, in the structure with the horizontal stroke only, and again in that with the vertical stroke added. The same elements, perhaps. But not the same structuring of them. But this is not the point to push hardest here. That point can start from the observation that if the proposed single predicate (‘is so/is a fact/obtains’) genuinely predicates some way for something to be, then that way-to-be is of a very peculiar sort. (Perhaps in something like the way in which being true is a peculiar way for something to be, if one at all.) For though a way for things to be (equally concept thereof, equally what predicates some such of something) is, in general, identified as the way it is by its proprietary way of generalizing (of yielding answers to questions whether such-and-such is a case of so being), the proposed single predicate here can have no such proprietary way of generalizing. Rather, when combined with, say, Sid’s being rotund, it acquires the generality of that way for things to be (for them to be such that Sid is rotund), when combined with, “Lager’s containing yeast”, it acquires the generality of that way for things to be, when combined with “there being no largest prime”, it acquires the generality of that way for things to be, similarly for “every prime being divisible by 2”, and so on. What it does, in effect, is to unleash a generality already present in, e.g., (the circumstance of) Sid being rotund; that is, put just that generality to predicative work; work in the project of representing things as being some given way for them to be outright. So, second, such generality is already present in what follows the horizontal stroke (in Sid’s being rotund). What the one predicate ‘predicates’ of is not some historical state of affairs, say, Sid’s rotundity from the time his romance with lager began up to the present (something to be experienced palpably). It is rather a sort of thing liable to occur (be so) or not. It is thus, unlike that cold nortada, not something one may recall (with yet a shiver). Unlike Mt. Blanc, it is not located in an environment. Exactly not. It belongs to thought in just the same way that Frege’s Gedanken do. Russell gets to say whether this is what he had in mind. But it is embracing, rather than rejecting, Frege’s notion Sinn.

5. Two Distinctions

Representing-as is the prerogative of thinkers, or, secondarily, of their means of achieving it (their words), or of that abstraction from their so engaging, something there is for them to do (‘der Gedanke’). It is marked by its contrast with factive meaning: if Sid’s unsteady gait is due, not to imbibing, but to an inner ear problem, then it cannot mean falsely that he is in his cups. It does not mean he is in his cups at all. It is in opening up that first possibility that representing-as brings truth, or questions of it, onto the scene. Frege made two fundamental contributions to clarity as to what thus comes into view. They are his distinction between the psychological and the logical, and a distinction between the particular and the general (one with which he was not always surefooted himself). Russell, in’02–’04, was insensitive to both.

Truth is a cooperative enterprise between precisely two parties. The work of party of the first part is to fix what truth (or a certain truth) depends on; when there would be (the relevant) truth. The work of party of the second is, in being as it is, to make good on the demand thus imposed—or, again, to fail to. Party of the first part must, inter alia, assure that party of the second will, in fact, settle that question of truth it thus poses. It cannot be settled only relative to some third party. Such is the objectivity of truth. In representing-as, party of the first part is the representing-as, or what does it. So where there is truth, party of the first part is that truth. Party of the second is what is so represented—where there is truth outright, whatever is a case of the relevant way for things to be outright. As discussed already, party of the first part is always distinguished by its proprietary generality. To be a party of the first part is to have and deploy generality: As Frege put it, “something reaching beyond the particular case, whereby this is presented to consciousness as falling under some given generality”.9 Party of the second (in re truth outright) is always devoid of such generality. It just is a particular case. If to be as Sid is is to be rotund, nothing in that decides what another case of rotundity might be. If this is all there is to say as to what it is to be rotund, then as for Pia, sylph-like as she remains, such might or might not be rotundity if there could be any such thing as her being or not at all. And so it is with particular cases in general, always in re truth outright, so, too, for truth of anything environmental.

It follows that what is true or false cannot be a particular case; cannot thus be a complex of elements all of which are innocent of generality (of the sort just scouted), or any structuring of elements which does not arrive at deployment of such generality. If Russell’s complexes are meant to contrast as he thinks they do with Frege’s Sinne, then he falls afoul of this fact. The generality of a way for things to be is as fundamental to representing-as, and thus to truth, as is that objectivity crystallized in the idea of an essentially two-party enterprise. It is just by this generality that the predicative distinguishes itself from the designative, making truth turn on how some given object (or collection) is. It is just this distinction which allows for contingency in truth.

A concept, a way for things to be, a thought: one cannot watch these “reaching over and beyond the particular case”, generalizing so as to capture or reject further cases. Such things are necessarily not objects of sensory awareness. Features of which to enjoy such awareness are not ones by which one way of generalizing is distinguished from another. By contrast, one can watch Sid getting them in him, one can witness Mt. Blanc rising into the sky (from where he stands). Being Mt. Blanc has a generality under which that particular mountain and it alone falls, which it alone instances. Nothing falls under the mountain in that sense. It alone can be Mt. Blanc. But not even it can Mt. Blanc.

Russell insists that one does not assert a thought (Gedanke), but rather the object of the thought “das Objekt des Gedankens”, a complex formed of, e.g., Mt. Blanc and its stature, or that cold wind and attendant mean molecular motion (or lack thereof). But truth is a phenomenon arising with representing-as. There is none of that to be found in such complexes. There is no way things are according to that cold wind; nor in that mountain in towering as it does. So Russell’s complexes are just the wrong sort of thing to be either true or false. To begin (but not end) with, they lack the requisite generality. Sid, of course, plays some role in the thought that he is in his cups. He is that object (in his case, that obstacle to free passage) on which, in that thought, truth is made to turn. But it is not so made by him. He is not a partial doing of that which the whole thought does, namely, to bring truth into question in a particular way. Nor is he what so does. To repeat, a person cannot make truth turn on himself. (Nor can this be done at all except within some decomposition of a whole thought.)

Russell simply misses the difference between particular and general, or the point of that distinction. As he misses the difference between (a) Gedanke (count) and Denken (mass), and the two readings of this last: on one an historical phenomenon, the Denken that is done, or in currency among given thinkers; on another a body of thought there is to be thought. Accordingly, he misses the possibility for Frege’s Sinn (among which Gedanken) to lie on the logical side of the logical-psychological distinction, to be in no sense psychological. He thus arrives at, perhaps is driven to, complexes which are ineligible for truth. His story collapses at that point.

The particular does not generalize. Its home is firmly in the represented. It cannot do double duty on both sides of the representing-as relation. It cannot, thus, form complexes which are either true or false. Russell rejects Frege’s third realm. But what one loses with that is truth überhaupt. Objectivity may seem (as it seems to have seemed to Russell) to require locating objects of thought in the historical, or the environmental. But, so doing, the very idea of objectivity vanishes. The Tractatus may not follow Russell in all above details. But it follows him in erasing, or ignoring, the distinction between particular and general. Therein lies its downfall, as we shall see.

At first it may seem that Russell’s concern is just to place such things as Mt. Blanc within truth-bearers themselves. But it is perhaps better seen as placing truth-bearers themselves within the realm to which Mt. Blanc belongs; having them be, or consist of, solely such things (portending, perhaps, Quine). As though if there is really to be such a thing as thought, then thought itself must be situated in the world just as Mt. Blanc is. As indeed it is if we read thought as our thinking, rather than as the thinking there is to do (i.e. what there is to think). Well, there may be plenty of objective complexes in the world, one of which, perhaps, is to be found there at all only if Mt. Blanc is more than 4000 meters high. But if I were now to try to speak on that topic, why should anything I say be taken to speak of any of these? Rather than rendering thought real, the move Russell tries to make simply abolishes it altogether.

6. Correspondence Theories

The Tractatus, I will argue, founders on the means it allows itself for unfolding the notion to be true. We can see this by working through Frege’s critique, in “Der Gedanke”, of correspondence theories. But for this we first need to consider what a correspondence theory might be. Such a theory is not simply the remark that a true thought (or statement) is one which corresponds with the facts. Not, at least, if all this means is that a representation represents things other than itself as being something or other, so that its truth depends on how those further things are. And not, again, if all it means is that if it is true that P then it is a fact/so that P. Here I will suppose that a correspondence theory aims at satisfying two demands. First, it aims to answer the question what being true is; and to do so in a non-question-begging way. Second, it aims to define a relation between representations and what they represent as being such-and-such (that representation’s represented, or, to use a Tractarian term, Abgebildete), in terms of which one can define when any given representation would be true: either for a representation to be true would be for it to stand in that relation to an Abgibildete, or it would be for the Abgebildete it anyway so relates to to have some further property it might or might not have. (The Tractatus’ story is essentially of this second sort.)

There are thus two forms for a correspondence theory to take. For an account of the first form we might start from the truism that it is true that P just in case it is a fact that P. Now, to generate answers to questions when a representation would be true, when it would have that feature, we must start with a domain of representations. If what we aim to explicate is the phenomenon, or feature, of being true as such, we should, with Frege, put whole thoughts first. Such will be the representations in question, which identify particular questions as to being true. As to the domain of items to which these are to relate, we might develop the truism by nominalizing. We might suppose that wherever it is a fact that P, there is a corresponding fact, namely, the fact that P. This would not be a representation, but might rather be conceived as some circumstance, or state of affairs obtaining in, or some feature of, the way things are, something for one to steer a course through, which, we might suppose, would be there to be encountered only if things were now such as to make for a case of its being so that P. So we now have a domain of thoughts and a domain of facts. What we would like to complete the account is a function which would map each item in that first domain onto one of two things. For any thought that P, the function should map that thought onto the fact that P if there is such a fact. If not, then the function should map that thought onto some designated item, say, Russell’s left big toe. Then the theory can tell us that a thought is true just in case the designated function maps that thought onto a fact, false just in case it maps that thought onto Russell’s left big toe.

The rub here is evident. Letting all the above as to what a fact would be pass, there is no problem saying what fact would thus correspond to a given thought, were there such a fact. But to fix when a thought would be true it remains to say when there would be such a fact. For which thoughts there are such facts depends, rather heavily, in general, on how the world is. (Grasping the thought that Sid is in his cups as the thought it is does not yet enlighten one as to whether it is true.) The end of time would be a bit too soon to demand a theory which actually took account of how all such dependencies panned out. So what we still need is an adequate explication of just how a thought, never mind which, depends on things being as it represents them (for its being a fact/so that things are thus). We need, that is, an adequate general explication of what the dependency in question is. But to say this is to say that what is so far unexplained is simply everything as to what being true is.

With which we return to the second option. On this option, there are two domains, the first made up of thoughts, the second made up of ‘complexes’ of some sort, which are to count as Abgebildete, each for some thought or other. The idea would be that, for each thought, there is some proprietary such complex which is that which it in particular represents as thus and so. So we now want a function which maps each thought onto its proprietary Abgebildete. For example, suppose we thought that a thought (Gedanke) has a unique (fundamental) decomposition, and that these could be specified in some systematic way. The thought that Sid is in his cups, for example, might be per se to be decomposed into an element which made it about Sid, and another which made it about one being in his cups. Then we might suppose we could identify things to be found in what any whole thought represents-as the way it does, which form an Abgebildete peculiar to the thought in question. Such might look like a Russellian complex of the Russellian sort exemplified by ‘the cold wind’— say, Sid and the worldly presence of a person being in his cups (whatever that is), and those two items relating to each other as they in fact do.

Such sketches an idea for a way of associating each thought with some worldly complex which is peculiar to it. On this sketch of an idea, for each thought there would be such a complex, independent of whether the thought was true or false. So we would not have to wait until the end of time, not nearly that long, to be able to say what the value of the relevant function from domain to range would be. The thought that Sid is in his cups maps onto the same Abgebildete in this sense whether he is in his cups or not. So far, let us suppose, so good. (Though in fact an immense amount must be assumed to get us this far.) Now, of course, the same rub. If both true and false thoughts map onto proprietary Abgebildete of this sort, then everything remains to be said as to when a thought which so did would be true: when an ordered pair of thought and Abgebildete so relates that that first element in the pair is true. What remains undone is to specify what property an Abgebildete would have when it was the second member of such a pair. And this must be done in a non-question-begging way, as per the first demand above on what would count as a correspondence theory. So, for example, one could not say that the relevant property, for the value of the relevant function for the argument, the thought that Sid is in his cups must have the property of being as represented in that thought. Such is a property any Abgebildete would have if the thought which abgebildet it is true. But to say this is not to say in non-circular terms what it would be for something to be true.

For either of these two forms of correspondence theory there is, of course, another fundamental, but so far unmentioned problem at the very start. To identify a function from thoughts to something—whether to a domain of facts plus a designated object, or to some domain of Abgebildete, we must make intelligible, or presuppose to be intelligible, what the relevant domain of the function is to be. What, notably, are its inhabitants? When would we have a given one in hand? What would it be to be a given one? The obvious problem: a thought is identified entirely and exclusively, by its way of making truth turn on how things are; its proprietary way of bringing truth into question. But if the account is to be non-circular, its aim to answer the question what being true is without presupposing that notion itself, then the notion of being true is not yet available to it. Inter alia, it cannot be presupposed in identifying the domain of the relevant function.

We might, then, try departing from Frege, letting arguments for the function we seek be, not thoughts, but items such as sentences, identifiable as the items they are by visible or audible forms, or by other features had or not independently of how they represent something as being. Then, indeed, e.g., “The sentence ‘Sid is in his cups’ is true just in case Sid is not sober” is informative, if true, in a way that a parallel remark about the thought that Sid is in his cups would not be. But then, as Frege remarked, “One cannot forbid anyone from adopting any arbitrary producible event or object as a sign for whatever he likes”.10 Suppose what was wanted was a function which mapped sentences such as this into, say, abgebildete. Specifying the right function now simply becomes still more problematic. Not only must we say, without circularity, what property an abgebildete should have for true to be the value for what represents things as a given way as argument, but also what property a sentence should have to have as its value an abgebildete with such a property.

A last remark. Suppose a would-be correspondence theory proceeded piece-wise, for the thought that Sid is in his cups, saying what its being true would be, for the thought that Pia just nutmegged Max, what it would be for it to be true, for the thought that sea water is saline what it would be for it to be true, and so on. Well, as they say, there’s one borne every minute. Another human, or anteater, a new blade of grass, and so on. With each such thing comes a mass of thoughts there need not have been but in fact are. Frege’s birth, we may suppose, is a highly contingent matter (that unusually cold February, etc.). But for it there would be no thoughts of Frege that he was thus and so, nothing to think about him at all. So take any piece-wise theory and wait for tomorrow. There will then be countless unforeseeable cases of items being true or false, and no account of what it would be for them to be this.

There is, thus, a fundamental problem with the idea of a correspondence theory of truth. For any given version of the theory, there may well be a way of pushing that problem under the rug (by moving to another form of theory). But, it seems, such merely makes the problem push up from under in a different place. Such sketches the form a correspondence theory might take, and at least gestures at a fundamental problem it would then face. With which, we are now prepared to look at Frege.

7. Defining Truth

Early on in “Der Gedanke”, Frege presents a case which concludes, oddly, thus: “From this it is probable that the content of the word ‘true’ is entirely singular and undefinable”.11 To understand an argument, or train of thought, one must first look for its beginning and then for where it aims to end. Frege’s case starts from a question:

Is a picture, as mere visible, touchable thing, really true, and a stone, a leaf not true?¹²

To which he answers,

Clearly one would not call a picture true if an intention did not attach to it. The picture is to be taken to represent something.¹³

His case expands on this last remark. As for termini, there are two: one immediate, the other, more general, later on. The immediate conclusion:

What emerges from this as the only thing by which truth can come into question at all is the Sinn of a sentence.¹⁴

The only thing as opposed to what? There are two answers to that. First, the case is inter alia against Vorstellungen as truth-bearers. These, in Frege’s sense, would be objects of (e.g., sensory) experience and, if truth-bearers, of thought; would require a bearer and brook no two—would belong exclusively to a given consciousness. Inter alia, were they truth-bearers, their objects would cross a certain categorial line separating off the sensible from the thinkable. Already reason to object. Aside from that, though, good riddance to them, and bracket them here.

A second more general concern is evident in the above immediate conclusion. One might think words as such were the fundamental truth-bearers (that by which ‘truth comes into question at all’). Or one might, as in Frege’s initial question, think pictures, as, e.g., the products of a Sunday painter, could, on their own, raise questions of truth. Or, more generally, something or other with a visual, or audible form; still more generally, something identifiable as the item it is independent of when it would be true. Frege’s main aim in the ensuing discussion is to help that idea out of the world. That by which truth can come into question at all is, he insists, a thought (Gedanke), as per above. Such, in one form, is the main point to be established. (A thought is a kind of Sinn in Frege’s technical sense; since whole thoughts come first, the fundamental kind. Thoughts, as we have seen, have a non-linguistic nature.) Such fits Frege’s longer-term conclusion, that a ‘third realm’ must be recognized. (See above.)

Frege’s answer to his initial question is: A picture can only be true if an intention (‘Absicht’) attaches to it. Perhaps ‘Absicht’ is not quite le mot juste. What matters is that a picture, to be in the business of being true, must first represent things as some given way. For that it cannot just be, e.g, a pattern of paints on canvas. Insofar as it has such a Gestalte, said Gestalte must be to be taken, understood, in some given way. It must bear an understanding as to how it is depicting; thereby how it is that things are being depicted as. What it does in being so understood is not reducible to how the picture is anyway (e.g., what paint in what places), independent of the understanding it is thus to be given. Exactly not: just so that there is room for an understanding (or bearing one). The canvas cannot be to be understood to have paint on it, as if there might be some other way of perceiving it correctly. It just is painted (modulo, perhaps, what is to count as being painted). How it depicts is another matter; one which contrasts with this.

I will divide Frege’s case in fourths. The first quarter runs:

Accordingly one might suspect that truth consists in a correspondence of a depiction with what it depicts. A correspondence is a relation. The use of the word ‘true’, which is not a relation word, and contains no reference to some further thing with which something is supposed to correspond, speaks against this.15

The thought that Sid is in his cups is decomposable into, inter alia, a predicative element which predicates being in one’s cups of someone. If we ask whether that element thus predicates truly, we may fairly be asked in return, ‘ Predicates of what?’. For such representing may be true of one object, false of another. By contrast, where there is truth outright, there is, eo ipso, no question ‘true of what?’. In that sense, truth outright is indeed not a relation between a representation/depiction and an object. If we insist that a relation relates objects, then indeed correspondence of the sort truth might consist in is not a relation. On the other hand, the truth of a thought depends on how things are. For there to be truth is thus for something, how things are, to oblige. Such just is a sense in which to be true is to correspond with the facts—though not thus with an object. Whether the word ‘relation’ fits here can remain moot. Frege is thus not off to a good start.

On, then, to the second quarter:

If I do not know that a picture is meant to represent Cologne Cathedral, I do not know with what I must compare it in order to decide its truth.16

Some lines on a napkin, or color patches on a canvas, might or might not depict Cologne Cathedral. They might be just doodling or paint spills. Or they might depict a cathedral, though no one in particular. There would thus be no question of truth. (If your picture of a cathedral looks more like a car park, such is not how a cathedral looks. Still, falsehood is not quite yet in the cards.) There is thus a distinction between properties a picture would have no matter how it was to be understood (so no matter how it represented things), and properties it has only understood as it is to be. No properties of the first sort can decide whether the picture is true, much less how it would be. There are indefinitely many manners of depicting something. Think of a recreation of ‘Las Meninas’ by Lichtenstein, or Braque. One source of need for an understanding; one source of things for understanding to accomplish.

There is a converse point. Suppose a particular picture, or drawing, represented Cologne Cathedral as with four flying buttresses on its river side. What follows as to how the picture looked? Nothing. Frege’s point again: anyone can use any means to represent anything. A representation need not resemble what it represents. Thus it is that a sentence can represent—if, that is, it bears a suitable understanding. A point impressed on Wittgenstein by the Tractatus’ collapse: a sentence is “a picture which hasn’t the slightest similarity with what it represents”.¹⁷

Frege’s crucial move comes in the third quarter, partly disguised by his treating two issues at once:

[A] correspondence can only be complete if the corresponding things coincide, thus are not different things at all. One can test the genuineness of a banknote by trying to make it coincide stereoscopically with a real one. But the attempt to make a gold piece coincide stereoscopically with a twenty mark note would be ridiculous. To make a Vorstellung coincide with a thing would only be possible if that thing were also a Vorstellung. And then if the first corresponded completely to the second, they would collapse into one.18

The point about Vorstellungen is crucial to a case for the publicity of thoughts. But such is not our present business. Prescinding from it, what is left? There is this idea: complete correspondence is identity. Thus, where a Bild represented-as (thus might be true), the correspondence between it and its Abgebildete (depicted), no matter how we conceived the latter, could not be complete. (Of course not: It is intrinsic to a way to represent things that, if this is a way they are, things need not be just as they are for such to be so. (The intrinsic generality of thought.))

How, then, would a Bild and its Abgebildete correspond if the Bild were true? Here there is a useful comparison with the case of stereoscopic coincidence, e.g., that between a putative 20-mark note and a certain one—a coincidence there could not be between a bank note and a gold piece. Where the comparison is intelligible, there is something it would be for there to be complete stereoscopic coincidence. Such coincidence would not be identity (or stereoscopes would lose their point. To grasp what it would be, one thus needs to understand what the relevant notion of stereoscopic identity is to be. There is something such identity is to be understood to be. On such understanding, two banknotes are to be counted as identical (the same) if, while distinct, they share relevant properties. If one is torn or stained, such does not count. There are certain visible features by which a banknote (of relevant sort) ought to be identifiable as genuine. Those features, whatever they are exactly, must be shared by the exemplary exemplar (the real thing) and the merely putative instance. What is fixed here, with the help of stereoscopy, is a particular proprietary sense of (being) the same.

Here we see the burden a correspondence theory of truth must bear. If truth is correspondence, such must be so on the right proprietary understanding of corresponding. In effect, the theory must fix a particular understanding of the same on which a picture and its depicted are the same just in case that depiction is true. For which it must first, of course, fix what a ‘depicted’ is to be: not just that on which truth outright always turns, but rather such that, for each depiction (each true or false way to represent things) there is its proprietary depicted. The problem now is to see in what relevant ways a truth-bearer and what it depicts as such-and-such could be alike. For the note in Frege’s pocket and the one fresh from the mint to match stereoscopically— on the relevant understanding of matching—is for them to share certain specifiable visible patterns (e.g., lines per centimeter in a certain region). By what sorts of properties of a Bild and its Abgebildete could the two match, or fit each other? And what sort of such match would there be just in case there were truth?

This last question is so far neutral as to what properties a truth-bearer might have. So far, a truth-bearer might be sentence-like, or portrait like, admitting of such things as visual features. Or it might be thought-like. A dilemma; on either branch of which a correspondence theory is doomed. A correspondence theory must relate representer to represented. It must do so in such a way that there is truth just where the right relation holds between these two. Suppose (first horn) that we conceive the representer, the depiction/Bild, on the model of a sunday-painter Bild. In the Bild, then the depiction of a cathedral—let it be the Stephandom—has two spire-shapes and six flying-buttress shapes suitable placed around a cathedral roof shape, and so on. And there is the Stephansdom, with its two spires and six flying buttresses. There is certainly some kind of correspondence here. But now Frege’s point: A shape on a canvas can only represent if it is to be understood/taken in a certain sufficiently determinate way. And its converse: And then how it represents things as being depends on how it is thus to be understood: Any shape can be used to represent anything. So the correspondence we have so far identified cannot be one which would hold just where there was truth (where things were as represented).

The relation we are looking for cannot thus be found in topology or geometry, or so on. No common structure found there can yield the theory we seek. What other structure, then, might a representation have? Well, a representation is structured, or anyway structurable, in a certain way (or certain ways). So perhaps the sort of structure we are after is to be found there. In brief, what we are looking for is the sort of structure which might structure a thought. Reasonably enough since, as Frege points out, a thought is just that by which truth can come into question at all. But the problem with this plan is that the sorts of structures to which a thought is liable are those in terms of features which a thought has, more specifically, by which one thought may be distinguished from another. But since a thought is just that by which truth can come into question, such features are only definable in terms of truth. If they were not, they would not be ones such that two thoughts which differed, one in having, one not, some such feature would thereby differ in how things would be if they were true.

The point here can be filled in as follows. A thought just is a determinate way to make truth turn on how things are. Or, if you like, just that which makes truth turn in this way. To structure a thought is to decompose it into elements, each of which is a partial doing of what the whole thought does—in the singular case, say, some singly designative element and some proper predicative one. But what it would be for a given such element to be the one it is is to be defined—is only definable—in terms of the notion to be true. To be a given such element is to do just that part of what the whole thought does that that element does; to make truth turn in just that part on how things are.

Trivially, a thought is true just in case things are as per that thought. Frege’s case against ‘defining’ truth does not exclude such truisms. But then such truisms do not pretend to be an account of what being true is, or anyway a non-circular one. They do not meet the first of those two demands a correspondence theory aspires to satisfy. Drop this demand and it is easy to say when a thought would be true. But the problem for the sort of theory, or ‘definition’ of truth against which Frege’s case is directed is that to be able to say this of any given thought one would first need to identify it, pleonastically, by identifying when it would be true.

There is a crucial moral to this story which it is now time to state. The representation of things as some given way—a representer, where this is conceived as just that by which things are represented as they are (that is, a Gedanke)—does not, and cannot, share any (identifying) features with that which it depicts as being such-and-such. Or at least not in the case of truth outright, and not in any case where the depicted objects are environmental. So truth cannot consist in the sharing of any such features. Notably, a thought and what it represents as being such-and-such are not structurable in terms of any one set of features, or features of any one sort. So a representer and what it represents as such-and-such, a Bild and its Abgebildete, are not eligible to share a structure. So truth cannot consist in any such sharing. Sid stands before the Stephansdom, chilidog in hand. Here is a scene structurable in the way such scenes are. Sid is 20 meters from the main entrance, at an angle of 67°, and so on. The thought that Sid stands before the Stephansdom is structurable, for example, into a two-place predicate predicating standing before of a pair <A, B>, and an element making truth turn on how the pair <Sid, the Stephansdom> is, for example, two very different kettles of fish.

In the fourth quarter, Frege generalizes the point from correspondence theories of truth to, as he puts it, any attempt to define it. Any definition, he thinks, will founder on an inevitable, and vicious regress:

Could one not maintain that there is truth just where there is correspondence in a certain respect? But in which? What would we then need to do to decide whether something was true? We would need to investigate whether it was true that—say, a Vorstellung and something actual—corresponded in the indicated respect. And with this we would again face a question of the same sort, and the game could begin anew. Any attempt to define truth as correspondence thus comes to grief. But any other attempt to define truth would also thus fail. For in a definition one would indicate a certain identifying mark. And when it came to applying this to a particular case, it would then always come to the question whether it we truth that this mark was encountered. Thus one would go around in circles.19

In this generalizing of the result, we also find a new form of argument to make the case. This argument turns on a certain principle. Frege states the idea in a number of places, for example,

One can certainly say, ‘the thought that 5 is a prime number is true’. But if one looks closer, he notes that really nothing more is said thereby than in the simple sentence’5 is a prime number’.²⁰

[T]he word ‘true’ has a sense which contributes nothing to the sense of whole senses in which it occurs as a predicate.²¹

This last states the idea in general. It can be put as follows: truth is an identity under predication. (The thought that P and the thought that it is true that P are one.) Call this principle IUP. Suppose now that being true were equivalent to, or the very same thing as, being F, for some way, F, for a thought to be. Then being F would also need to be an identity under predication. Suppose that being true were analyzable non-circularly as being F. Then what it would be for something to be F is independent of what it would be for something to be true. Where there is, and where there would be, a case of something being F is fixed, definable, without appeal to the notion of being true. Then, the point is, being F cannot be an identity under predication. For establishing that, say, the thought that Sid is in is cups is F would now be a different matter from establishing whether Sid is in his cups, whereas by IUP establishing that the thought that Sid is in his cups is true is not a different matter than establishing whether Sid is in his cups, since there is just one thing to be established. So if we insisted that being true is being F (that being F is just what being true is), we would violate IUP.

It is crucial here that being F must be such that an account of being true on which being true was being F would, if correct, satisfy the analytical ambitions of a correspondence theory as per the previous section: for being F to be what being true is would be for the notion being true to reduce to something which does not itself presuppose this; to a way there would anyway be for an item to be whether or not there was such a phenomenon as representing-as. For suppose we do not insist on this. Now consider the idea that a thought is true just in case it is such that things are as it represents them. What, now, of the property a thing has just when things are as it represents them? There is no reason not to regard this as an identity under predication. It has as good a claim to this as does to be true. But then taking this to be what being true is does not land one in a regress, since IUP applies here as above.

The case here does, of course, rest on IUP (a sort of idea of finite descent). I think both that, when properly formulated, it is correct, and that Frege makes good and proper use of that idea (in insisting that the word ‘true’ only gestures at what really belongs to assertive force, and thus cannot correspond to a thought-element).22 But, as just shown, a proper formulation does not rule out what Frege promises at the outset in “Der Gedanke” in the remark, “the meaning of the word ‘true’ is unfolded in the laws of truth”.²³ It is hardly the case that there are no laws of truth. However, a further exploration of IUP and its credentials is not part of present business. So I rest with the autobiographical.

8. The Tractatus

I turn now to the Tractatus account of representing-as. This begins with an account of what there is to represent as something:

• (1) The world is everything that is the case.
• (1.1) The world is the totality of facts, not of things.
• (1.11) The world is determined by the facts, and by the fact that these are all the facts.²⁴

Facts rather than objects are put in lead position here. Such could be seen as a material mode correlate of Frege’s insistence that whole thoughts come first (or immediately after being true itself). Which could be the beginning of a good point. But it is not.

The next step is to explicate representing-as. This begins as follows:

• (2.1) We make for ourselves pictures of facts….
• (2.12) A picture is a model of reality (Wirklichkeit).
• (2.13) The elements of the picture correspond in it to [given] objects.
• (2.131) The elements of the picture stand in for (‘vertreten’) these objects.²⁵

A picture depicts Wirklichkeit as being some given way. Such a picture is made up of (given) elements structured in a given way. It is uniquely decomposable. The picture depicts these elements as structured in a given way. It is a picture of them as so structured. Part of its depicting as it does is fixing a relation, in fact a function, between these elements and discernible elements in what it depicts. It maps each of its elements into some distinguishable element of the depicted. The picture is a model of what it depicts. In the model, its elements stand in for the elements of the depicted they map into. Let us call the function the picture thus determines a V-function (‘V’ for Vertretung). For it to be the picture it is, I will suppose, is (inter alia) for it to determine the V-function it does.

The idea of a Vertretung-function gives us means for associating with a given picture, as its depicted, not just Wirklichkeit—though every picture (of present sort) does depict Wirklichkeit—but something specific to that Bild. This could be the range of its V-function—some set of objects— related to each other (structured, organised) as they are in fact (a condition of, and in, the world). The idea of a proprietary depicted—for each depiction, its unique Abgebildete—promises a possible way of counting Abgebildete. Suppose a depiction depicts Porto’s Sé. What are the elements of the Sé? What objects make it up? There is, as noted previously, no answer to this question. It is ill-formed. For the notion object does not itself give us any way of counting same. But suppose a depiction fixes a given V-function. For a given function, a given range. So we can take it as intrinsic to its depicting (to its being the depiction it is) that what it depicts is essentially composed of the items in that range. That item (as opposed to the Sé) could not be carved up differently. Different sets of elements, on this way of thinking, would eo ipso identify different (if any) depicteds (Abgebildete). Such makes an Abgebildete in our present sense nothing like what is depicted by the Sunday painter, e.g, the Sé.

With this conception of an Abgebildete comes an obvious way for a depiction to be correct or incorrect: the depiction depicts the elements in its depicted as structured, related to each other, in such-and-such way. They may or may not so be. The picture is correct (true) just where they are, incorrect (false) just where they are not. Which brings us to the Tractatus’ own account of true and false, or correct and incorrect, representing:

• (2.14) The picture consists in the elements being related to each other in a determinate manner and way.
  …
• (2.15) That the elements of the picture relate to each other in a given way presents it as so that things so relate to each other …
  …
• (2.21) The picture agrees with reality or not.; it is correct or incorrect, true or false.
  …
• (2.221) Its sense is what the picture represents.
• (2.222) Its truth, or falsity, consists in the agreement or disagreement of its sense with reality.
• (2.223) In order to recognize whether the picture is true or false, we must compare it with reality.26

The sense of a picture would then consist in the picture’s depicting the image of its elements under its V-function as relating to one another as its elements themselves relate in the picture to each other. Agreement with reality would then consist in that image (the depicted) so relating to one another. If a picture’s sense is what it represents (how it represents things), there remains the question what a picture does represent on this account. Is it to be compared with a sentence, say, which may represent, speak of, (there being) pheasant on a (contextually definite) lawn? Or a thought which is of, say, there now being pheasant on Pia’s lawn? This last, one might hope, if such pictures are to be true or false. Whether it could do either of these things remains to be seen.

As the Tractatus acknowledges, on this account of truth and falsehood, a depiction can be so much as true or false only if there is something (suitable) in common to it and its proprietary Abgebildete. The Tractatus puts this thus:

• (2.16) In order to be a picture, a fact must have something in common with what is depicted.
• (2.161) There must be something identical in both the picture and the depicted in order for the one to be able to depict the other at all.²⁷

What, then, must be in common to a depiction and what it depicts (as thus)? The Tractatus answer:

• (2.17) What a picture must have in common with reality in order, in its own manner, to be able to depict either truly or falsely, is its form of depicting.
• (2.18) What every picture, of whatever form, must have in common with reality, in order to be able to depict it at all—truly or falsely—is the logical form, that is, the form of reality.
• (2.181) Where the form of depiction is logical form, the picture is called a logical picture.
• (2.182) Every picture is also a logical one. (By contrast, not every picture is spatial.) …
• (2.2) A picture has its logical form in common with the depicted.²⁸

So reality (the depicted) has a form (one intrinsic to it). And this is logical form. So it is a form of what engages in the business of being true: a representation. Such a form would cross categories. It would be present in thought, in depicting, and also in what thought is true or false of, Wirklichkeit. A false picture, of course, would have a form which its depicted lacked. But this would still be a form of a genre available both to representers (thoughts) and represented. If there are such forms, there may indeed be something in common to depiction and depicted, representer and represented. If, but only if. But we have seen already, in the collapse of correspondence theories, why there cannot be such.

Young Wittgenstein has now set himself up to be gored by the horns of a bull we have already engaged. As things stand, he still gets to choose his horn. For he has left it unclear which he has in mind: Whether his depictions (representers) are to be conceived on the model of a painting of the Sé, or on the model of a thought. Perhaps he intentionally omitted distinguishing these two categorically different things. But such is at best a way to make things seem alright. The damage is the same either way.

Suppose we think of representers, Gedanke- like, as distinguished from one another solely by features which make for different ways for truth to turn on how things are. Then they are structurable solely by relations defined in terms of being true, as a Gedanke is structurable in terms of elements each in that same business which is its. A representer so conceived is not the sort of thing which might, e.g., come before one’s eyes. Nor is it some structuring of things which might. The point generalizes from the visible to any items identifiable as the ones they are independent of how they make truth depend on what they do. Relations of which such things are relata are not ones in which thought-elements might stand, hence not ones in terms of which a representer as now conceived might be structured.

Conversely, what comes before the eyes is not the sort of thing which can stand in those relations out of which a Gedanke-like representer might be structured. What come before the eyes are bits of history, things being as they are. One might generalize over and beyond them. But they do not. Sid, Mt. Blanc, are not ways for truth to turn on things; nor what does so. Particular cases are silent on what another case of any way they are might be. The point starts with what any thought represents as something: things (as a whole) being as they are. This surely does not represent anything as anything. Its business is simply to be as it is. A fortiori it is innocent of any feature which might identify a given thinkable, or given truth, as the one it is. So, too, for what there is to carve out of it, notably objects—items which may combine with partial ways to represent it being to form a way for it to be or not outright. Sid and Mt. Blanc are some simple examples. What a representer represents as such-and-such cannot, in such representing, stand in those relations in terms of which such representing is structurable.

Pia drinks Billecart-Salmon (that magical potion concocted since 1818 in Mareuil-sur-Ay). There are thus relations she bears to that potion in relating to it as she does, among which some Sid bears to a different potion (lager) in relating to it as he does. Sid’s relating to lager as he does is part of his way of relating to Billecart-Salmon, a way thus quite different from Pia’s. A thought (thinkable) might represent Pia, Sid, Billecart, lager, as standing in such relations to one another. They might structure what it thus depicts. But they do not sructure the representing as such.

Now the other horn. Suppose we conceive a representer as itself identifiable by features independent of what identifies the representing accomplished as the representing that it is. It might, for example, be a sentence, with its syntactic identity. Or a visible image, with its geometric structure. Such a representer does have features shareable by what it depicts as such-and-such. Sub-images in such an image and values of the relevant V-function may, e.g., share spatial structure. But now Frege’s point. You can use any arbitrarily occurring object or event to represent anything. So samenesses definable in terms of shared features of the just-mentioned sort settle nothing in themselves as to whether there is truth (nor as to how (if at all) things were represented as being). To settle this, the sentence, or image, must be assigned just those features which would identify some representer of our first kind: a Gedanke, something thinkable. Nothing so far tells us what those features must identify. Whatever it is, we are thus back on the first horn, saddled with what cannot share a structure with what it depicts.

At 2.18, Wittgenstein speaks of what any picture and its depicted must have in common as “the logical form, that is, the form of reality.” But there is no such thing as ‘the conceptual structure of reality’—a structuring of generalities under which reality might fall or not. Logical form cannot be the structure of reality because reality has no such form. It does not generalise beyond a particular case (itself, perhaps?) to reach something general under which to present this. Conversely, reality, anyway an environment, might be structured in some objectively fundamental way for some given purposes, e.g., those of physics. It may not permit certain would-be ways of generalizing across or beyond it. Such is for physics to say. But just as the fact of Sid loving lager cannot of itself fix what another case of someone loving lager might be, so things being as they are cannot decide how one must generalize beyond things so being to other ways things might have been.

Thus, the Tractatus picture of representing-as collapses. Not that this is quite the way Wittgenstein saw its collapse in 1929. The trouble struck him when he approached what the Tractatus left as an outstanding problem: what an atomic proposition might be. The immediate symptom emerged in the realization that this ‘problem’ had no solution. The trouble lay in what made this appear to be a problem at all. The mistaken assumption: that there is such a thing as a class of propositions, ‘the atomic ones’29; an assumption at work here:

3.25 There is one and only one complete analysis of a proposition (Satz).³⁰

Such an idea could not have arisen had young Wittgenstein followed Frege:

I do not believe that for each judgeable content there is just one way in which it can be decomposed, or that one of the possible ways may always claim an objective priority.³¹

For Frege whole thoughts (thinkables) come first; other notions involved in representing-as are to be defined in terms of these; in terms, that is, of truth outright. To be a proper predicative thought-element, e.g., is to play a particular role in a decomposition of such a whole; thus to do what could only be done at all in the context of that whole. From the thought that Pia has a red dress on, one may carve a part which makes truth turn on who has a red dress on. But there is no such thing as making truth turn on this, fertig. There is so far nothing for truth to do. But decompose a thought in some one such way, and one is immediately struck with the possibility of others. Such is what Wittgenstein came to realize in the wake of 1929 (by, say, 1931). It is what he is on about in the Investigations discussion of logical atomism, e.g., around §§47–48, in stressing that the notion simple, like the notion same, needs filling out to have an application. Simplicity an sich, like sameness an sich, is not a feature for anything to have or lack. With which 3.25 is consigned to the dustbin. But this merely points at issues to be treated elsewhere.

The deeper root cause of the fall of the Tractatus is inattention to the second of Frege’s two fundamental distinctions: that between the particular and the general—a neglect inherited from Russell. For if it is the general—the depiction, and not the depicted—which is to be analyzed, as per 3.25 or otherwise, it is fairly obvious that there can be no one right way of carving up a proprietary way of generalizing over particular cases into parts. Suppose we carve up for things to be such that Sid is pear-shaped into a part, for things to be such that relevant things are pear-shaped; for things to be such that Sid is relevant ways. Each of these parts, like the whole, denizens of Frege’s third realm, their homes representing-as, has its own proprietary generality. There are those particular cases which are ones of an item being pear-shaped, and those which are ones of an item being Sid, or of Sid being some way or other. The generality of our initial whole is the resultant (as it were vector sum) of those of these parts. But if so, it is also, inevitably, the resultant of the generalities of indefinitely many sets of different parts. Thus simplicity an sich classifies with sameness an sich (a point stressed in recent times by Noam Chomsky among others). Thus the collapse, not just of that wild goose chase on which the Tractatus sent Wittgenstein in 1929, but the whole Tractarian picture of representing-as. The Tractatus thus came to grief for much the same reason as correspondence theories of truth come to grief.

9. Thenceforth

In the years 1929–1931, Wittgenstein wrestled with the failure of his early efforts—while also following assiduously developments in foundations of mathematics, with a special interest in Hilbert. By 1931, a changed view had emerged. What happened? Here, in briefest and sketchiest form, is an answer. In pursuit of that latter interest, Wittgenstein returned to reading Frege (at least Grundgestze vol. 2, specifically Frege’s attacks on ‘formalist arithmetic’, chez Thomae and Heine). One thing which emerged from this, I believe, is the Investigations idea of a language game. Another theme, though, for expansion elsewhere. Russell and early Wittgenstein leaped with insouciance across that categorial gulf Frege stressed, between the particular and the general, in particular, between the second and third of Frege’s three realms. In these years of, inter alia, renewed interest in Frege, Wittgenstein took the lesson not to do so. He came to see the importance of this distinction.

But, as Wittgenstein saw, it is easy to mystify Frege’s third realm and that distinction it represents. It is easy, e.g., to make it seem puzzling (as it appears to have seemed to Russell) that a way for things to be—what belongs in the third realm—can reach all the way to what belongs in the second, things being as they in fact are. That independence of truth from what we think true which Frege stresses can also be read as assigning such things as thoughts, or concepts, mystical powers to reach all the way to particular cases not yet, and perhaps never, part of history. How business is conducted in the third realm can come to seem even more distanced from how we think of things than it in fact is. Things are not helped here by Frege’s own occasional blind spots, notably what shows up in the idea (pretty clearly insisted on in Grundgestze vol. 2) that Begriffsschrift is a language—an idea Frege felt pushed to by his own (mis)perception as to how his dispute with Kant about arithmetic would have to play out.

So Wittgenstein’s turn towards Frege came with a rather heavily underlined asterisk or two. Frege, but with an improved view of the place of the logical in the psychological, and of the relation of logic to thought, and to language; thus, too, an improved view of logic’s province and its inexorability and universality such as that may be. Frege at least showed us where there are questions of the logical’s place in the psychological, and something as to how these should be framed. So one could see later Wittgenstein as, in large part, just a purer version of Frege.

The point which put paid to the Tractatus begins in Frege as targeting correspondence theories of truth, but becomes, in his hands, deeply, and generally, anti-reductionist. It puts paid to any idea of reducing the business of being true, thus equally that of reducing representing as— representational or conceptual content—to anything else. It applies equally to would-be reductions of any of this to what might be perceived, more generally, to anything environmental, as to reductions to something psychological, in Frege’s phrase, what “belongs to the contents of someone’s consciousness” (or which might be proprietary to any one). The idea that being true, so the conceptual, does not reduce to the environmental has proven, for many philosophers, the hardest to swallow. But that point can also be put this way: Naturalism is not the price of objectivity. Such is just what one recognizes in recognizing Frege’s ‘third realm’. That such must be recognized is what is shown by his argument against the ‘definability’ of truth (that is, against any account of truth on which being true fails to be an identity under predication).

All this, though, is but the briefest of sketches, likely too brief to be of any use. It may also seem dogmatic, and to many, eccentric. As I stand here I can no other. What I want to stress most, though, is that later, Wittgenstein was concerned with the same philosophical problems as the Tractatus was, as philosophers have long been, and as many of us are today. These problems concern the relation of thought, or representation, to what there is to be thought about; to the world. He was, throughout, a philosopher, not a post-philosopher, or some other alternative to philosophy. Or so I mean to suggest.

Notes

1 Gottlob Frege, “Der Gedanke”, Beiträge zur Philosophie des deutschen Idealismus, v. 1, n. 2, 1918, 69.

2 Bertrand Russell, “Letter to Frege, 12.12.1904”, Gottlob Freges Briefwechsel mit D. Hilbert, E Husserl, B. Russel, sowie ausgwählte Einzelbriefe Freges, eds. G. Gabriel, F. Kambartel, and C. Thiel (Hamburg: Felix Meiner, 1980), 99.

3 Russell, “Letter to Frege, 24.5.1903”, Gottlob Frege’s Briefwechsel, 91.

4 Vide Frege, “Der Gedanke”, 69.

5 Gottlob Frege, “1882 letter to Anton Marty”, Gottlob Frege’s Briefwechsel, 118.

6 Gottlob Frege, “Meine Grundlegenden Logischen Einsichten”, Nachgelassene Schriften, 2nd ed., eds. H. Hermes, F. Kambartel, and F. Kaulbach (Hamburg: Feliz Meiner, 1983), 271.

7 Vide Gottlob Frege, Grundgesetze der Arithmetik (Jena: Verlag Hermann Pohle Band I/II. 1893/1903), §91.

8 In fact, in the context of Begriffsschrift it would mark something being asserted—add assertive force. Vide Gottlob Frege, Begriffsschrift, eine der arithmetischen nachgebildete, Formelsprache des reinen Denkens (Halle a. S.: Louis Nebert, 1879), 2.

9 Frege, “1876/1882: ‘17 Kernsätze zur Logik’”, Nachgelassene Schriften, 189–190.

10 Gottlob Frege, “Über Sinn und Bedeutung”, Zeitschrift für Philosophie und philosophische Kritik, NF 100, 1892, 26.

11 Frege, “Der Gedanke”, 60.

12 Ibid., 59.

13 Ibid.

14 Ibid., 60.

15 Ibid., 59.

16 Ibid., 59–60.

17 Ludwig Wittgenstein, The Blue and Brown Books (Oxford: Blackwell, 1958), 37.

18 Frege, “Der Gedanke”, Beiträge zur Philosophie des deutschen Idealismus, 59.

19 Ibid., 60.

20 Frege, “Über Sinn und Bedeutung”, 34.

21 Frege, “Meine Grundlegenden Logischen Einsichten”, 272.

22 Vide ibid., 272.

23 Frege, “Der Gedanke”, Beiträge zur Philosophie des deutschen Idealismus, 59.

24 Ludwig Wittgenstein, Tractatus Logico-Philosophicus, trans. D. F. Pears and B. F. McGuiness (London: Routledge and Kegan Paul, 1922), 5.

25 TLP, 9–10.

26 Ibid., 10–12.

27 Ibid., 10.

28 Ibid., 11–12.

29 Vide Ibid., §2.061–3, 9.

30 Ibid., 18–19.

31 Frege, 1882 letter to Anton Marty, 118.

References

Frege, Gottlob, Begriffsschrift, eine der arithmetischen nachgebildete, Formelsprache des reinen Denkens, Halle a. S.: Louis Nebert, 1879.

———, “Ueber Sinn und Bedeutung”, Zeitschrift für Philosophie und philosophische Kritik, NF v. 100, 1892, 25–50.

———, Grundgesetze der Arithmetik, Jena: Verlag Hermann Pohle, Band I/II, 1893/1903.

———, “Der Gedanke”, Beiträge zur Philosophie des deutschen Idealismus, v. 1, n. 2, 1918, 58–77.

———, “1882: letter to Anton Marty”, Gottlob Frege’s Briefwechsel mit D. Hilbert, E Husserl, B. Russel, sowie ausgwählte Einzelbrefe Freges, G. Gabriel, F. Kambartel, and C. Thiel, eds., Hamburg: Felix Meiner, 1980, pp. 117–119.

———, “1876/1882: ‘17 Kernsätze zur Logik’”, Nachgelassene Schriften, 2nd ed., H. Hermes, F. Kambartel, and F. Kaulbach, eds., Hamburg: Feliz Meiner, 1983, 189–190.

———, “1915: ‘Meine grundlegenden logischen Einsichten’”, Nachgelassene Schriften, 271–272.

Russell, Bertrand, “1903: Letter to Frege, 24.5.1903”, Gottlob Freges Briefwechsel mit D. Hilbert, E Husserl, B. Russel, sowie ausgwählte Einzelbrefe Freges, G. Gabriel, F. Kambartel, and C. Thiel, eds., Hamburg: Felix Meiner, 1980, 87–90.

———, “1904: Letter to Frege, 12.12.1904”, Gottlob Freges Briefwechsel, 96–99.

Wittgenstein, Ludwig, Tractatus Logico-Philosophicus. Translated by D. F. Pears and B. F. McGuiness, London: Routledge & Kegan Paul, 1922/1967.

———, The Blue and Brown Books, Oxford: Blackwell, 1958.