Simple Objects, Complex Questions
Summary: The essay examines Wittgenstein’s doctrine that there must be simple objects that form the substance of the world. Focusing on the 1914-1916 notebooks it seeks to determine the emergence of this doctrine and the reasons for its ultimate destruction.
Is a point in the visual field a simple object? What is the significance of this puzzling question at the outset of Wittgenstein’s 1914 notebook? To appreciate its meaning and weight we must remind ourselves that the start of that notebook on August 8, 1914 marks a decisive moment in Wittgenstein’s life. After spending much time in England and Norway on his logical and philosophical problems Wittgenstein returned to Austria as the clouds of the First World War were rolling in. With Britain’s entry into the conflict, on August 4, Wittgenstein’s personal and philosophical links with Russell and Moore that had been so important to him over the preceding years were broken. By August 8, he had volunteered to serve in the Austro-Hungarian army and was getting ready to fight in the war – entirely uncertain over his chances for survival. Yet he was also determined to sort out, once and for all, the problems that had preoccupied him in the previous three years. It was a make or break moment. The beginning of the 1914 notebook thus recapitulates some of Wittgenstein’s most important philosophical insights and some of his most pressing questions. In the light of all this one is forced to ask what significance he saw in his specific concern with points in the visual field.
My attention was drawn to this question when I recently re-read Hide Ishiguro’s essay “Use and Reference of Names.” Its discussion of names and simple objects in the Tractatus has been of enormous importance for our understanding of Wittgenstein’s early philosophy. It has impressed on me, in particular, Wittgenstein’s conviction that the notion of an object is a purely formal one, that the “Names” of the Tractatus are mere “dummy names” and that “to ask what kind of familiar entities correspond to the objects of the Tractatus seems to lead us nowhere.” Now, re-reading Ishiguro’s essay I still find myself in agreement with many of her conclusions though at odds with some of her arguments. What has struck me in particular is her complete lack of attention to Wittgenstein’s query whether points in the visual field might count as simple objects. This is no accidental omission. Ishiguro’s entire line of argumentation is based on what she calls “the Tractatus theory of Names” with its focus on “the problem of the identity of names and the problem of the use of Names in propositions.” From this perspective questions about visual space will, indeed, seem out of place. But why then do they matter to Wittgenstein?
When he first raises the issue Wittgenstein notes, indeed: “Up to now I have always regarded such questions as the real philosophical ones.” (p. 3)  Months later he adds that “as examples of the simple I always think of points of the visual field (just as parts of the visual field always come before my mind as typical composite objects).” (p. 45) Does this mean that he considered such points to be exemplary cases of simple objects? And even that only such things could be regarded as simple objects? Was he, perhaps, in agreement with the Russell of The Philosophy of Logical Atomism who thought that “the ultimate constituents of the world” were sense data? Items like the points in our visual field with which we have direct acquaintance. A number of Wittgenstein’s interpreters have, in fact, taken that line. That reading of Wittgenstein’s early thought is, however, sharply at odds with Ishiguro’s formalistic conception of simple objects which rejects outright any suggestion that they might be either spatio-temporal objects or sense data. This may explain why she shies away from considering Wittgenstein remarks on visual points. I certainly agree with Ishiguro’s conclusion that a sense data conception of Wittgenstein’s simple objects is untenable. But that Wittgenstein’s remarks on visual points can be misinterpreted should not keep us from paying attention to them. For that they are too prominent in Wittgenstein’s thinking in the pre-Tractatus period and too prominent also in the place they occupy on the first pages of the 1914 notebook. Our task should be, instead, to determine the function of those remarks, if they are not meant to endorse a sense data view of simple objects.
The notebooks certainly give us few reasons to consider Wittgenstein a sense data theorist. That he tends to think of points in the visual field as examples of simple objects does surely not mean that he really takes them to be simple objects. His reflections on the topic are, in fact, shot through with all sorts of doubts. He is certainly far from assuming that such points are objects of acquaintance. Thus, he wonders whether we see all its points, when we see a space. (p. 48) And, indeed, whether we see any such points at all. “Who knows whether I see infinitely many points?” (p. 65) And he wonders even whether there are any such points: “Are there parts in our visual field that have no extension?” (p. 51; translation modified) These concerns force upon him an even more radical question which he had asked right at the start of his 1914 notebook: “What evidence could settle a question of this sort at all?” And already at this point he concludes that there seems to be no such evidence. On the contrary: “It looks as if I could say definitively that these questions could never be settled at all.” (p. 3)
In the same period in June of 1915 in which he is writing extensively on the topic of points in the visual field, Wittgenstein is, moreover, also asking himself whether his simples could not be material points. He considers the possibility that “every spatial object consists of infinitely many points,” i.e., presumably, infinitely many material points. (p. 62) And he concludes that “the division of the body into material points, as we have it in physics, is nothing more than analysis into simple components.” (p. 67) Surely, he cannot be thinking of both visual points and material points as simple objects. That he should be reflecting on the possibility of material points as simple objects throws, moreover, a new light on what he has been saying about visual points. In contrast to the latter the material ones are quite obviously only theoretical constructs. No one would take them to be possible items of acquaintance. The concept of a material point belongs, in fact, to classical, Newtonian mechanics. For Newton, physical events are law-governed motions of material points in space. And these points are conceived as bodies of finite mass whose geometrical dimensions, locality and ‘inner’ qualities can be neglected for the purpose of studying their motions. In a notebook remark incorporated into the Tractatus Wittgenstein writes: “Newtonian mechanics brings the description of the world into a unitary form … This form is arbitrary … In this way too it tells us nothing about the world that it can be described by means of Newtonian mechanics.” (p. 35) Material points belong to this machinery; and they are simple objects only within the framework of Newton’s theory.
The devastating implications of all this for Wittgenstein’s official “mirror” account of meaning have generally gone unnoticed. According to the official account a sentence must be an exact mirror of the state of affairs it is about. “What the picture must have in common with reality in order to represent it after its manner – rightly or falsely – is its form of representation,” we read in the Tractatus. (TLP, 2.17) A sentence and the state of affairs it is about must have the same logical form. But this does obviously not hold for the propositions of Newtonian mechanics. Their form is said to be arbitrary. Why then should this not also be true of all other kinds of proposition? Wittgenstein asks that question, unfortunately, only around 1930. Both in the notebooks and the Tractatus he holds firmly on to the mirror conception of meaning, insisting that “a proposition can express its sense only by being its logical depiction.” (p. 6, translation modified) The remarks on Newtonian mechanics throw, however, an unexpected light on what he has been saying about visual points. Is it not possible that they, too, are only theoretical constructs, postulated by some theory of the nature of space and that their simplicity is also only a merely relative one, relative, that is, in this case to the language of visual imagery. How else are we to understand the insertion of the word “theoretical” in the remark that “it is certain – moreover – that I do not see all the parts of my theoretical visual field?” (p. 65) The word suggests that the conception of the visual field as composed of infinitely many points is a merely theoretical postulate and the assumption of simple visual point a claim that is relative to that theory. That would, of course, also mean that they cannot count as contenders for the simple objects that Wittgenstein is looking for.
Whatever he may be thinking about visual and material points, he has certainly not given up on the idea of absolutely simple objects. On the contrary, he remains convinced of the need to distinguish between what we take to be simple and what is really so. “It always looks as if there were complex objects functioning as simples, and then also really simple ones…” (p. 69)
If Wittgenstein is not seriously entertaining the idea that visual points might be the simple objects he is looking for, then what is the point of raising the question? Going back to his remarks on visual points at the beginning of the 1914 notebook we see that this question is for him not a free-standing issue but connected to other, similar “such questions,” other “questions of this sort,” as he puts it. He is considering the matter of visual points, he says, only because it appears to be “simpler and more fundamental” than those others. At stake is, in fact, the entire relation of language to the world and with it the status of logic itself. Wittgenstein wants to know what the structure of our sentences reveals about the structure of the world. He wants to “explain the relation of sentences to reality,” as he had said in notes he had dictated to G. E. Moore in spring of 1914. In those notes he had also committed himself for the first time to the mirror conception of meaning according to which the relation of language to reality is as follows: “Its simples have meaning = are names of simples.” (p. 112) Simple, unanalyzable names must then be names of simple objects. And more generally, all the simple, unanalyzable features of our sentences must reflect features of reality. The question whether there are simple objects is thus on a par with the question, for instance, whether there are facts “of the subject-predicate form.” Or of a relational form. The question: Are there simple objects? Is connected to: “Does the subject-form exist? Does the relational form exist?” (p. 2) Of course, “we have signs that behave like signs of the subject-predicate form, but does that mean that there really must be facts of this form?” We would say perhaps that we have subject-predicate sentences but are uncertain about whether there are subject-predicate facts to which they correspond. And hence, again, by parallel: we have simple signs in our language but does that mean that there must be simple objects corresponding to them?
The problem is – as Wittgenstein has learned from Russell – that the apparent form of a sentence need not be its real, logical form. What may look like being of the subject-predicate form may, on analysis, turn out to be something quite different and what looks like a simple name may, on analysis, disappear. Wittgenstein is, in fact, certain that “in all the sentences that occur to me there occur names which, however, must disappear on further analysis.” (p. 61) Only a complete logical analysis can reveal the real form of a sentence and whether what looks like a name really is one. That gets him to wonder: “Does such a complete analysis exist?” (p. 2) Later on he will puzzle over how one would recognize a complete analysis as such, if we had one. But already at the start of his notebook he is agitated by an even more disturbing problem. Even if we had a completely analyzed sentence (and recognized it as such) and it turned out to be of the subject-predicate form how would that guarantee that there is a fact of the subject-predicate form in the world? And similarly, presumably, if we had a completely analyzed sentence and in it occurred a simple name why would that show that there corresponds to it a simple object in the world? Wittgenstein notes that Russell would consider all this self-evident and comments on that happy certainty with a single, sardonic “Ha!” (p. 3) It is clear then that the question whether the points in a visual field are simple objects is not Wittgenstein’s ultimate concern in the initial pages of the 1914 notebook. What agitates him is, rather, the question what reasons we have for accepting the mirror conception of meaning and whether we can rely on its assumed self-evidence. In contrast to Russell he fears that such reliance “is and always was wholly deceptive.” (p. 4) If Russell were right, logic as a whole would depend on something else, something experiential, and thus on something entirely untrustworthy.
Wittgenstein sought to avoid this kind of reliance by asserting that “logic must take care of itself.” (p. 2) This declaration of what might be called a radical logicism forms the entrance gate to the entire philosophical discussion of Wittgenstein’s war time notebooks. He will return to it again and again in the course of his notebooks and it will subsequently become a decisive proposition in the Tractatus. But how can logic take care of itself? How does that circumvent the need for an appeal to self-evidence? Wittgenstein goes on to say that Russell’s self-evidence “can only be dispensed with in logic if language itself prevents any logical mistake.” (p. 4) He can therefore also say that “language takes care of itself.” (p. 43) And he explains this by adding: “It must be unnecessary for me to trouble myself with language.” (Ibid; revised translation!) But how can logic take care of itself by language doing so? Wittgenstein admits in the Tractatus that in ordinary language the same word is often used in more than one way and that different kinds of words are used, as if they were of the same sort. “Thus there easily arise the most fundamental confusions (of which the whole of philosophy is full).” (TLP, 3.324) But he is convinced that there is a way out: “In order to avoid these errors we must employ a symbolism which excludes them.” (TLP, 3.325) We need, in other words, a symbolism that “obeys the rules of logical grammar – of logical syntax.” Frege’s and Russell’s symbolism, he holds, is approximately such a language. But their symbolism is still only an approximation as long as we do not yet have simple names for simple objects, as long as our sentences are not completely analyzed.
How did Wittgenstein come to his preoccupation with simple objects? Its ultimate source may well have been Leibniz’s “Monadology” and, specifically, the very first section of that text where Leibniz writes: “The monad of which we shall speak here is nothing but a simple substance, which enters into compounds. By ‘simple’ is meant ‘without parts.’ And there must be simple substances, since there are compounds; for a compound is nothing but a collection or aggregate of simple things.” While there is no direct evidence of a substantive link between Wittgenstein and Leibniz – Wittgenstein spoke of him only once, as far as I know, in a glancing acknowledgment of his originality – there is a striking affinity of the passage just quoted with one of Wittgenstein’s notebook entries: “It seems that the idea of the SIMPLE is already found contained in that of the complex and in the idea of analysis, and in such a way that we come to this idea quite apart from any examples of simple objects, or of sentences which mention them, and we realize the existence of the simple object – a priori – as a logical necessity.” (p.60) Like Leibniz’s monads constitute moreover the substance and, as Wittgenstein’s puts it in the Tractatus, “the fixed form of the world.” (TLP, 2.023) This is not to deny important differences. Wittgenstein’s simples are, of course, not soul substances capable of perceiving and willing. They have, indeed, no intrinsic positive qualities. “Roughly speaking: objects are colorless.” (TLP, 2.0232) And: “Two objects of the same logical form are – apart from their external properties – only differentiated from one another in that they are different.” (TLP, 2.0233) But this should not make us ignore the deep affinities between Leibniz and the early Wittgenstein. There are certainly intriguing parallels between the overall structure of Leibniz’s treatise and the Tractatus. Both texts are composed as a sequence of numbered sentences; both lay out a picture of the world without little or no argument; both advance a pictorial conception of meaning; and both advance from a description of the structure of the world to reflections on ethics.
Wittgenstein may have known of Leibniz and his remark on compounds and simples from Russell’s book which quotes the initial section of the “Monadology”. Russell himself would later acknowledge the importance of that remark for his own thoughts on the matter when he wrote in his essay “Logical Atomism”: “I confess it seems obvious to me (as it did to Leibniz) that what is complex must be composed of simples …” Like Leibniz he went on to identify those simples with the substance of the world: “It is also obvious that the logical uses of the old notion of substance … can only be applied, if at all, to simples.” By substance, he added, finally, he meant once again in agreement with Leibniz and the old Aristotelian conception something whose name “never occurs in a proposition except as the subject or as one of the terms of a relation.” (Ibid.) This allowed him to say with Leibniz that the simples may have certain positive intrinsic qualities, that they are, in other words, not “colorless” as the objects of the Tractatus.
Wittgenstein was certainly also familiar with Russell’s discussion of complexes and simples in the Theory of Knowledge manuscript of 1913 that he had demolished to effectively that Russell abandoned the project. In this work, Russell had advanced a method of analysis with which he hoped to understand both the nature of experience and of propositions. This dual aspect of Russell’s project may well in part explain Wittgenstein’s concern with both matters of experience and of logic and language in his notebooks. Russell had understood analysis in both cases as “the discovery of the constituents and the manner of combination of a given complex.” And he had added that such an analysis “is complete when we become acquainted with all the constituents and with their manner of combination, and know that there are no more constituents and that that is their manner of combination.” (RTK, p. 119) And he had defined “a term as simple when it has no constituents. (RTK, p. 120) A complete analysis required, on his account, “knowledge of all the constituents of whatever order.” (RTK, p. 120) He had for that reason expressed doubts about the possibility that a complex might consist of infinitely many constituents: “It may be argued that, owing to the infinite divisibility of space and time, any sense-datum which has spatial or temporal extension must consist of an infinite number of parts. If so, these parts are necessarily imperceptible, since they must be too small for our senses. It will follow, that every sense-datum which has spatial or temporal extension must be a complex of an infinite number of constituents with which we are not acquainted. Such an argument, however, involves an unduly naïve transference of infinite divisibility from physical space and time to the spaces and times of the senses. In regard to time, we have already seen how physical time can be logically constructed without assuming that a continuous duration actually consists of temporal parts. And in regard to space, it would seem that a similar construction is possible. There seems no reason to assume that say, a uniform patch of colour occupying a small visual area must be complex; it is quite possible that the infinite divisibility of physical space results from a logical construction out of data which are not infinitely divisible.” (RTK, pp. 121-122)
It appears that Russell had entertained none of Wittgenstein’s doubts about the possibility of complete analyses, about our capacity to recognize them as such, about what was indicated by an analysis coming to an end, and about whether we could ever come to know the ultimate, simple constituents. Wittgenstein’s notebook entries also make clear that he was far from granting Russell’s argument against the possibility of infinitely many constituents of a complex. And Wittgenstein also was not inclined to accept for certain that we could ever have knowledge of the ultimate constituents of our complexes.
Wittgenstein’s own engagement with the theory of complexes and simples emerged in four stages. In his first philosophical piece of writing, a set of notes put together for Russell in 1913, he mentions the issue only in passing when he critiques Russell’s “complexes” for having “the useful property of being compounded” combined with “the agreeable property that they could be treated like ‘simples’.” (p. 100) The quotation marks in the text and the subjunctive form of the sentence suggest little identification with Russell’s distinction. The topics that had occupied Russell in the Theory of Knowledge manuscript are, in fact, of little concern for Wittgenstein at this moment. He has no comment on Russell’s method of analysis; and he is certainly not interested in his analysis of experience. Instead, he talks about logic and language, about definitions and “indefinables.” These indefinables are linguistic expressions, constituent elements of sentences, not component elements of facts. “Indefinables are of two sorts: names and forms.” (p. 96) They are furthermore not only expressions standing for objects, i.e., names, but also “forms” such as the expression “( (p. 97) There are, finally, also “logical indefinables” such as “not” and “or.” (p. 99) It is also evident that he did not conceive of names as mere “dummy names” and of things or objects as mere formal, colorless markers of the world’s multiplicity. He writes that “this error is presumably to be explained by the fact that, by employment of variables instead of the generality sign, it comes to seem as if logic dealt with things which have been deprived of all properties except thing-hood … We forget the indefinables of symbols only occur under the generality sign.” (p. 107) That raises the question, if Ishiguro is right in her interpretation of the Tractatus, at what point Wittgenstein came to its formalistic conception of objects. Was it when he came to see that one might describe the world completely with generalized propositions and thus without names referring to actual, concrete objects? That idea was certainly present to him early on in his 1914 notebook when he wrote: “Yes, the world could be completely described by completely general propositions, and hence without using any sort of other denoting signs.” (p. 14) Or was it only a year later when he came around to the idea that the existence of simple objects was a logical necessity and that we could not actually identify any simple objects? Or was it finally only in the Tractatus when he came to speak of objects as colorless and as having no external properties when considered on their own? It appears that his formal conception of names and objects matured only over a period of four years.
The second stage in Wittgenstein’s thinking on the topic is to be found in notes he dictated to Moore in Norway in the spring of 1914. In them the idea that there are simple objects is firmly linked to the picture conception of meaning according to which “a language which can express everything mirrors certain properties of the world by these properties which it must have.” (p. 108) And this leads Wittgenstein to conclude that there is such a language:”Its simples have meaning = are names of simples.” (p. 112) He gets, however, no further than this point and makes no attempt to determine what might count as a simple name and what the named simples would be. Reflection on these topics is left to his war time notebooks and these constitute therefore the third stage in Wittgenstein’s thinking about simples. The Tractatus, finally, represents a concluding fourth stage in that story. With it the deconstruction of the doctrine of simple objects begins. The steps to this final act are thus: a theory of definition, a conception of the process of analysis, and a specific view of sentence meaning.
In his notebooks Wittgenstein speaks of “simple names” as well as of “simple objects” and this is potentially confusing since the simplicity of a name is a linguistic (syntactic and semantic) property whereas that of an object a metaphysical property. The dual use of the word is justified, of course, in Wittgenstein’s eyes by the mirror conception of meaning. In looking at the notebooks we must also pay attention to the fact that Wittgenstein speaks exclusively of the components of sentences, including names, as definable or indefinable whereas he calls both verbal expressions (sentence and their components) and what they correspond to in the world “analysierbar” (or also, indiscriminately, “zerlegbar”). Thus we read of sentence as further analyzable (zerlegbar) but also of parts of objects that “cannot be further analyzed (die nicht mehr zerlegbar sind).” (p. 10 and 62) It seems, moreover, that Wittgenstein is using the words “definable” and “analyzable” as equivalent when it comes to verbal expressions but as not equivalent when we bring in objects. “The object x is analyzable” is, in other words, not necessarily equivalent to “The expression standing for object x is definable.” And that a verbal expression is indefinable does not guarantee that it stands for something unanalyzable and hence simple in the world – and this for two interconnected reasons.
First of all: That A can be defined by means of B and C does therefore not show that A must be a more complex term than B and C and that the latter are simpler. We might, for instance, define Berlin as the capital of Germany but that does not mean that Germany is a component of Berlin and even less that Germany is simpler than Berlin. The same point is brought out in a different way when we consider the possibility of alternative definitions for a given term. We can, for instance, define material implication, for instance, through negation and conjunction but also through negation and disjunction. Wittgenstein writes in 1913 that “alternative indefinability shows that the indefinables have not been reached.” (p. 98) I assume that he means to say that alternative definability shows that the indefinables have not been reached. He seems to be taking it for granted that when we have an ultimate set of indefinable then the various alternative definitions of a complex will collapse into one or be logically equivalent. Thus, consider a sentential logic in which the Sheffer stroke is the single indefinable logical operation. With it we can define negation, conjunction, and disjunction and then define material implication either by means of negation and conjunction or by negation and disjunction. But we will also then be able to show that those alternative definitions of material implication are logically equivalent. The problem is only that this does not settle whether the complex notion of material implication contains conjunction or disjunction as a simpler component.
A second difficult is revealed by the fact that terms may be interdefinable. We can define material implication by means of negation and conjunction but conjunction also by means of negation and material implication. Or, to take a non-logical example: we can define being bald as having no hair but we can also define having hair as not being bald. Which of the two notions is the simpler, the more analyzed one? Which definition we will end up with, will depend on which terms we have introduced as basic, indefinable terms in our language. Definability is, for that reason, a language-relative notion. What is indefinable in one language may be definable in another one. That a name is simple in the sense of being indefinable will thus tell us nothing about the kind of object it stands for. The theory of definition can provide us only with a language relative notion of simplicity. Wittgenstein is not unaware of the fact that it might turn out that we have only such a relative notion. He writes in this sense: “The simple thing for us IS: the simplest thing we are acquainted with. – The simplest thing which our analysis can attain – it need appear only as a prototype as a variable in our sentences – that is the simplest thing that we mean and look for.” (p. 47) The remark does, admittedly, not speak of definability but explains relative simplicity in terms of acquaintance and analysis and I will have to come back to this aspect of the remark. But we can surely apply the remark also to the question of definability and say that we need to recognize the possibility of a relative simplicity (relative, that is to a language) if we try understand simplicity in terms of definability.
This suggests the possibility of a positive answer to Wittgenstein’s question: “Can we manage without simple objects in LOGIC?” (p. 46) He is, indeed, forced to admit that “sentences are possible which contain no simple signs … And these are really sentences making sense.” (p. 46 ) It appears, indeed, that simple names may be able to stand “for the most various forms.” (p. 59) Everything, so it seems, can be named. “I can correlate a name with all that I see, with this landscape, with the dance of motes in the air, with all this; indeed, what should we call a name if not this?” (p. 53) It would seem even “as if in a certain sense all names were genuine.” (p. 61) We must contemplate therefore also the possibility of simple names of complex, objects (pp. 52, 64, and 69)
But even so Wittgenstein still wants to hold on to the idea that there are genuinely simple objects and that these will be named by genuinely simple names in a sufficiently analytic language. He concludes that “in all the propositions that occur to me there occur names which, however, must disappear on further analysis.” (p. 61) He considers it obvious that components of such sentences “can be analyzed by means of a definition, and must be, if we want to approximate to the real structure of the sentence.” (p. 46) That this is so, follows, however, not from the definability of those components in the language we have available but from the thought that definitions should be tracking a process of analysis and that the results of that process of analysis can be made explicit in a formal definition in another more fully analytic language.
“Our difficulty now lies in the fact that to all appearances analyzability, or its opposite, is not reflected in language. That is to say: We can not, as it seems, gather from language alone whether for example there are real subject-predicate facts or not.” (p. 10) That leaves us with the question from where we are to gather the conclusion that there are real subject-predicate facts or that there are simple objects and what they are. It is at this point, I think, that Wittgenstein feels the need to look at such issues as the analysis of our visual field into visual points and that of spatial objects into material points. His hope is that these will provide us with a notion of analysis that can assure us that analysis will eventually lead to simple objects. His attention to these two model cases generates a number of important conclusions.
The first of these is that we have a notion of complexity which is independent of that of absolute simplicity. “Even though we have no acquaintance with simple objects we do know complex objects by acquaintance, we know by acquaintance that they are complex.” (p. 50) That appears at first sight to be an uncomplicated claim. But it is far from this for Wittgenstein who is committed to the idea that “complex objects do not exist.” (p. 63) Wittgenstein considers himself, instead, committed to “treating names of complexes as propositions” and thus to an “assimilation of complex things and facts.” Still, he is certain that both propositions and facts must be articulated and thus complex and that this can be known directly, without having an analysis of either propositions or facts into their ultimate, simple components.
Our acquaintance with “complex objects” provides us, secondly, with an idea of their analysis into simpler parts and thus with a relative notion of simplicity. “When we see that our visual field is complex we also see that it consists of simpler parts.” (p. 65) And this gives us, in turn, the idea of a “process of analysis” that leads us in stages to increasingly simpler components. “We single out part of our visual field, for example, and we see that it is always complex, that any part of it is still complex but is already simpler, and so on —.” (p.50)
But where will such a process end? It may possibly end up with an infinity of simple components. Here the model of the visual field and its analysis and that of spatial objects and their analysis generates an additional problem. For we imagine in these cases that the analysis would end but end in an infinite number of (visual or material) points. But an “infinitely complex situation seems to be a chimera.” (p. 50) In a passage from which I have already quoted, Wittgenstein writes: “Let us assume that every spatial object consists of infinitely many points, then it is clear that I cannot mention all these by name when I speak of that object. Here then would be a case in which I cannot arrive at the complete analysis in the old sense at all; and perhaps just this is the usual case.” (p. 62) Against the possibility that any statement about a complex object would have to be analyzed into an infinitely complex sentence stands Wittgenstein’s conviction that “the meaning of our sentences is not infinitely complicated.” (p. 46) He seeks to resolve the problem by suggesting that when we have a sentence about a complex “then infinitely many sentences of different content follow LOGICALLY from that first one.” (p. 64) The complexity of the sentence about the complex thing would thus show itself not in its syntactic structure, which would presumably be finite, but in its logical implications or, more broadly speaking in “its syntactical application.” (ibid.) But that would, of course, mean that Wittgenstein has abandoned the idea that structure of the world is mirrored in the structure of our language. A step he is not ready to take at this point.
Finally, the two model cases of analysis of the visual and of extended bodies make evident that we do not, in fact, have analyses that lead from complexes to simples. And since Wittgenstein cannot present us with a single case of an actually completed analysis, he is forced to argue that it “seems certain that we do not infer the existence of simple objects from the existence of particular objects, but rather know them … as the final outcome of analysis, by means of the process that leads to them.” (p. 50; translation modified) There remains the question why we should assume that the process of analysis has such a terminal point. Could it not go on indefinitely? “Is it, a priori, clear that in analyzing we must arrive at simple components – is this, e.g., contained in the concept of analysis -, or is analysis ad infinitum possible?” (p. 62)
The only reason for accepting the claim that there must be such simple objects is that otherwise certain compelling philosophical truths cannot hold. And on this point Wittgenstein is emphatic. Again and again “it keeps forcing itself upon us that there is some simple indivisible, an element of being, in brief a thing.” (p. 62) And immediately following this he writes that “we feel that the WORLD must consist of elements…. The world must be what it is, it must be definite … It looks as if to deny things were as much as to say that the world can, as it were, be indefinite in some such sense as that in which our knowledge is uncertain and indefinite. The world has a fixed structure.” (p. 62) But why should such feelings be reliable? What forces us to say that the world must have a fixed structure? If we had a completely analytic language in which we can depict the world completely and exactly and if we could be sure that the structure of such a language would mirror the structure of reality, we would, indeed, have grounds for speaking about simple objects.
But we do not actually possess such a language, only an approximation to one and no certainty that the process of approximation will ever come to an end. If we had such a language then it would show by itself what the structure of our reality is like. Our language would then take care of itself. Meanwhile, however, we can only repeat over and over again that the structure of such a language must mirror reality. And the problem si that “we can only foresee what we ourselves construct. But then where is the concept of a simple object still to be found?” (p. 71) Wittgenstein keeps hammering away at this point, but the more often he repeats it, it becomes clearer and clearer that he is falling back on that on that self-evidence he had rejected. And with respect to this he had already made the decisive judgment that “all theories that say: ‘This is how it must be, otherwise we could not philosophize’ or otherwise we surely could not live’, etc. etc. must of course disappear.” (p. 44) In consequence: “It keeps looking as if the question ‘Are there simple things?’ made sense. And surely this question must be nonsense.” (p. 45)
We can see then that Wittgenstein’s notebooks contained already everything necessary for the destruction of the theory of simple objects and of the whole edifice to which it belongs. In her essay, Ishiguro writes in a somewhat different tone that the concept of a simple object “was a logical requisite for the Tractatus theory, and followed from the combination of a basically correct theory about names, of a mistaken assimilation of complex things and facts, and of a wrong and unnecessary claim about the independence of elementary propositions” which Wittgenstein abandoned “in later years.” I have sought to lay out a number of other reasons for Wittgenstein’s attachment to simple objects. In my account the doctrine of the logical independence of elementary propositions plays no particular part. In contrast to Ishiguro who does not speculate on what motivated Wittgenstein to abandon the doctrine of simple objects, my story maintains that those reasons were already built into that doctrine itself. Because of this, reverberations of critical doubts can already be felt in the notebooks themselves and spread from there into the text of the Tractatus. How else are we to explain the peculiar arrangement of the Tractatus which proceeds from the dogmatic assertion of the doctrine of simple objects and its accompanying metaphysics to the conclusion that those assertions are strictly meaningless.
There is, no doubt, a strong intuitive appeal to Leibniz’s idea that complexity implies simplicity, that we are justified in postulating simples (as a logical necessity) because we know of complex things. But, instead, of taking the intuitive appeal of this kind of reason to be decisive, we should follow the later Wittgenstein and ask ourselves first of all from where that intuition draws its strength. We discover then that it has its source in three observations. The first is that we can always imagine smaller and smaller parts of our visual field; the second is that we can always break extended physical objects down into smaller bits; and the third is that we can always analyze our sentences into constituent terms. But none of these three observations is sufficient to establish the existence of absolute simples. The first two observations give us only the comparative notion of more or less complex, more or less simple or, alternatively speaking, that of simplicity relative to our theory and language. And the third gets us to absolute simples only by introducing the further assumption that a completely analyzed sentence must be a mirror image of what it talks about and that to the absolutely and logically simple constituents of such a sentence there must correspond absolutely and logical simple objects in the world. But this assumption fails on two counts. The first is that the notion of complete analysis is obscure and that we have no ways of identifying or recognizing an analysis as such, and the second is that the idea of language as a mirror of reality is a metaphor that cannot be cashed in. To be more precise, it is an idea that is grounded in the conviction that logic and language must take care of itself which, in turn, is only a metaphor, though one deeply engraved in the history of our thought. And here we want to say with the later Wittgenstein: “A metaphor that has been integrated into the forms of our language creates a false glitter; this alarms us: “But it isn’t this way!” – we say. “But it must be like this! … A picture held us captive.” (The picture, that is, of the sentence as a picture of a state of affairs.) “And we could not get out, for it lodged in our language – which seemed to recall it to us relentlessly.” (PI, 112 and 115)
I hope to have shown that Wittgenstein’s doctrine of simple objects was built on a wide range of considerations and was not just rooted in a “wrong and unnecessary claim about the independence of elementary propositions,” as Ishiguro has it. Looking at her essay now, I am not even sure how she meant to argue for that view. She is right, of course, in observing that Wittgenstein came to abandon the doctrine of simple objects at the same time at which he gave up on the claim of the logical independence of elementary propositions. But that was a moment when much else was also undergoing change in Wittgenstein’s thinking. I have argued, of course, that the failure of the doctrine of simple objects was built into that doctrine from its inception and that its deconstruction is already apparent in the final passages of the Tractatus. The official demise came, however, only around 1930 when the entire edifice of the Tractatus was coming undone for Wittgenstein. Of the greatest importance in that process was Wittgenstein’s new insight that “if we had to name anything which is the life of the sign, we should have to say that it was its use.” Seeking to emphasize the unity of Wittgenstein’s thought, Ishiguro has insisted that “the main difference between the Tractatus and the Philosophical Investigations is not the presence or absence of the ‘use’ concept but that the Tractatus conception of ‘use’ is much less comprehensive than in the Investigations.” That seems to me, however, an inadequate characterization of the changes that Wittgenstein’s thinking about language underwent after 1930. Ishiguro is, of course, right in emphasizing that Wittgenstein subscribed to the Fregean principle that words have meaning only in the context of a sentence both in the Tractatus and in the Philosophical Investigations. She is certainly right in saying that without his adherence to that principle, his formalistic conception of objects would, have been impossible. But for all that, Wittgenstein conception of use in his later philosophy is not just more comprehensive, it is substantially different and at odds with its conception in the Tractatus. In Wittgenstein’s early thinking language is a means of representation; in his later thought it is, above all, a means of communication. Language has for him now a social foundation and a social function. This implies that two speakers must be able to identify the object they are talking about when using a name. When the builders in Wittgenstein’s language game 2 in the Philosophical Investigations, for instance, use the words “block,” “pillar,” and “slab” they are not talking about postulated simple objects, the colorless, fixed substance of the world, but about ordinary things right in front of them that they can see, point to, and carry. The idea that, unbeknownst to its users, language could be referring to absolute simples has no place in this line of thinking.
 Ishiguro, “Use and Reference of Names,” in Studies in the Philosophy of Wittgenstein, ed. by Peter Winch, pp. 45 and 47.
 Ishiguro, loc. cit., p. 50.
 All plain page references are to Notebooks 1914-1916. I have found it necessary to change the translation at some points and these changes are marked at the appropriate places. Throughout, I have replaced Anscombe’s translation of Wittgenstein’s “Satz” as “proposition” by “sentence.”
 Bertrand Russell, “The Philosophy of Logical Atomism,” in Logic and Knowledge, p. 274.
 “TLP” refers here and elsewhere to Wittgenstein, Tractatus Logico-Philosophicus and references will be to the numbered sections of that text.
 G.W. F. Leibniz, “Monadology,” Selections, p. .
 Ludwig Wittgenstein, Culture and Value, p. 58.
 B. Russell, The Philosophy of Leibniz, p. 100.
 B. Russell, “Logical Atomism,” in Logic and Knowledge, p. 337.
 This and other page references marked RTK are to Bertrand Russell, Theory of Knowledge : the 1913 Manuscript.
 Ishiguro, loc. cit., pp. 40 and 50.
 Ishiguro, loc. cit., p. 50
 Ludwig Wittgenstein, Philosophical Investigations. References to this text will be identified as PI and are to the numbered sections of the text.
Ludwig Wittgenstein, The Blue and Brown Books, p. 4
 Ishiguro, loc. cit., p. 21.
Hide Ishiguro, “Use and Reference of Names,” in Studies in the Philosophy of Wittgenstein, edited by Peter Winch, Routledge & Kegan Paul, London 1969.
- W. F. Leibniz, “Monadology”, in Selections, edited by Philp P. Wiener, Scribner, New York 1951.
- Russell, A Critical Exposition of the Philosophy of Leibniz, Cambridge University Press, Cambridge 1900. Republished as The Philosophy of Leibniz, Macmillan, New York 1937.
Bertrand Russell, Theory of Knowledge : the 1913 Manuscript, edited by Elizabeth Ramsden Eames in collaboration with Kenneth Blackwell, Routledge, London and New York 1992
Bertrand Russell, “The Philosophy of Logical Atomism,” in Logic and Knowledge, edited by Robert C. Marsh, George Allen & Unwin, London 1956,
Ludwig Wittgenstein, Notebooks 1914-1916, edited by G. H. von Wright and G. E. M. Anscombe, translated by G. E. M. Anscombe, second edition, University of Chicago Press, Chicago 1979.
Ludwig Wittgenstein, Tractatus Logico-Philosophicus, translated by C. K. Ogden, Routledge & Kegan Paul, London, eight impression 1960.
Ludwig Wittgenstein, The Blue and Brown Books, Harper and Row, New York 1960.
Ludwig Wittgenstein, Philosophical Investigations, translated by G. E. M. Anscombe, third edition, Macmillan Company, New York 1969.
Ludwig Wittgenstein, Culture and Value, edited by G. H. von Wright, translated by Peter Winch, University of Chicago Press, Chicago 1980