Wittgenstein and the Simple Object

Norman Malcolm

Wittgenstein’s famous Tractatus Logico-Philosophicus is written in a style that is austere and sometimes aphoristic. ‘The world is everything that is the case.’ ‘A picture presents a possible situation in logical space.’ ‘A logical picture of facts is a thought.’ ‘We cannot think of anything illogical, for to do so we should have to think illogically.’ ‘The limits of my language mean the limits of my world.’ ‘Whereof one cannot speak, thereof one must be silent.’

The Tractatus tells us nothing of the uncertainties and struggles that Wittgenstein went through. Fortunately, much of this is revealed in those notebooks of his that escaped destruction. Notebooks 1914–1916 makes clear what Wittgenstein felt to be the central problem of Tractatus: ‘My whole task consists in explaining the nature of a proposition.’ The solution he arrived at was that a proposition (a sentence) is a picture of a possible situation in the world. The notebook entries show that this idea did not come easily. He pursued it through a thicket of perplexities:

That shadow which the picture as it were casts upon the world: How am I to get an exact grasp of it? Here is a deep mystery. It is the mystery of negation: This is not how things are, and yet we can say how things are not.

Sometimes he was close to despair: ‘I cannot bring out in what way a proposition is a picture of a situation. I am almost ready to give up all my exertions.’

A basic contention of Tractatus is that the world has to be composed of simple objects. The actual world and any imagined world must have something in common: namely, the same form. ‘Objects are just what constitute this fixed form.’ ‘Objects contain the possibility of all situations.’ ‘Objects are simple.’ Notoriously, Tractatus provides no example of a simple object, and one might think that this was not a worry for Wittgenstein. The notebooks show that this was not so. ‘Our difficulty was that we kept on speaking of simple objects and were unable to mention a single one.’ ‘What is my fundamental thought when I talk about simple objects? Do not “complex objects” in the end satisfy just the demands which I apparently make on the simple ones?’ Wittgenstein wrestles with the question of whether such items as points in his visual field, or even his watch, or a book lying before him, could be regarded as simple objects. To the end he was unable to fix on a satisfactory example of a simple object. But this did not prevent him from believing their existence was necessary. In the notebooks he says: ‘It seems that the idea of the SIMPLE is already 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 propositions which mention them, and we realise the existence of the simple object – a priori – as a logical necessity.’

Tractatus holds that a proposition could not have a definite sense unless it were analysable into elements, simple signs, each of which means a simple element of reality. ‘In a proposition there must be exactly as many distinguishable parts as in the situation that it presents.’ But does every proposition have a definite sense? Is not ordinary language, as it is actually spoken, full of vague sentences? The notebooks disclose, more explicitly than does the Tractatus, how Wittgenstein dealt with this difficulty. In the notebooks he asks: ‘Is it or is it not possible to talk of a proposition’s having a more or less sharp sense?’ This is followed by: ‘It seems clear that what we MEAN must always be “sharp”.’ Two pages later: ‘I only want to justify the vagueness of ordinary sentences, for it can be justified. It is clear that I know what I mean by the vague proposition.’ The idea here is that the frequent vagueness of ordinary speech is only a superficial appearance, for what the speaker means has a sharp sense!

The notebooks suggest another reason for attributing a definite sense to every proposition, a reason that is also not spelled out in Tractatus:

And it keeps on forcing itself upon us that there is some simple indivisible, an element of being, in brief a thing. It does not go against our feeling, that we cannot analyse PROPOSITIONS so far as to mention the elements by name; no, we feel that the WORLD must consist of elements. And it appears as if that were identical with the proposition that the world must be what it is, it must be definite. Or in other words, what vacillates is our decisions, not the world. It looks as if to deny things [simple objects] 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.

Wittgenstein’s thought seems to have been that real situations in the world cannot be indefinite, and that therefore the propositions with which we portray real or possible situations must themselves have a definite sense. If the definiteness of the world requires simple elements, so must the corresponding definiteness of language require that our sentences be finally analysable into simple signs that match the simple elements of reality. The Tractatus says: ‘A proposition has one and only one complete analysis.’ In its completed analysis a proposition would be displayed as a combination of ‘elementary propositions’, consisting merely of a linking together of simple signs, called ‘names’, each name standing for a simple object.

Most of Tractatus was written while Wittgenstein was serving with the Austrian Army in the First World War and was completed in 1918. For ten years thereafter Wittgenstein did not engage in new philosophical work. In his informative preface to Wittgenstein and the Vienna Circle, Brian McGuinness quotes from a letter that Wittgenstein wrote to John Maynard Keynes in 1924: ‘You ask in your letter whether you could do anything to make it possible for me to return to scientific work. The answer is, No: there’s nothing that can be done in that line, because I myself no longer have any strong inner drive towards that sort of activity. Everything that I really had to say, I have said, and so the spring has run dry.’

But in 1929 Wittgenstein suddenly returned to Cambridge and plunged again into philosophy. In the beginning, he was re-examining some of the ideas of the Tractatus. This book had excited the philosophers of the Vienna Circle. During Wittgenstein’s visits to Vienna, Moritz Schlick and Friedrich Waismann met him for frequent discussions from December 1929 to July 1932. Waismann kept notes of those discussions. This record, splendidly edited by McGuinness, was published in the original German in 1967 and is now presented in English translation.

One of the first things Wittgenstein began to rethink was the conception of ‘elementary propositions’ of Tractatus. It was held there that elementary propositions are logically independent of one another, and that a single elementary proposition can be ‘laid against reality like a ruler’. Wittgenstein now sees that both positions are wrong. Propositions that, for example, describe the length of a thing are not independent of one another and cannot be separately compared with reality. Propositions about length belong to a system: ‘The statements describing for me the length of an object form a system, a system of propositions. Now it is such an entire system of propositions that is compared with reality, not a single proposition.’ The same holds for propositions about the colour of a thing:

If I say, for example, that this or that point in the visual field is blue, then I know not merely that, but also that this point is not green, nor red, nor yellow, etc. I have laid the entire colour-scale against it at one go. This is also the reason why a point cannot have different colours at the same time. For when I lay a system of propositions against reality, this means that in each case there is only one state of affairs that can exist, not several – just as in the spatial case.

An important thesis of Tractatus is that logical necessity is the only necessity there is, and that logical necessity is always tautological. A proposition, q, can be inferred from a proposition, p, only if the sense of q is contained in the sense of p. Speaking to Schlick and Waismann about Tractatus, Wittgenstein says:

I thought that all inference was based on tautological form. At that time I had not yet seen that an inference can also have the form: This man is 2 m tall, therefore he is not 3 m tall. This is connected with the fact that I believed that elementary propositions must be independent of one another, that you could not infer the non-existence of one state of affairs from the existence of another. But if my present conception of a system of propositions is correct, it will actually be the rule that from the existence of one state of affairs the non-existence of all the other states of affairs described by this system of propositions can be inferred.

I think that this new focus on different ‘systems’ helped to prepare the way for the conception of diverse ‘language-games’ that is central to Wittgenstein’s later thought.

A prominent topic of the discussions recorded by Waismann is the concern of mathematicians about the possibility of there being a concealed contradiction in a calculus, such as an arithmetic or a geometry. Wittgenstein is caustic about this worry:

People have the notion that a contradiction that nobody has seen might be hidden in the axioms from the very beginning, like tuberculosis. You do not have the faintest idea, and then some day or other you are dead. Similarly people think that some day or other the hidden contradiction might break out and then disaster would be upon us… What must appear striking in this to an ordinary person is that mathematicians are always afraid of only one thing, which is a kind of nightmare to them, of a contradiction. They are not the least bit afraid e.g. of the possibility that a proposition might turn out to be a tautology, although a contradiction is no worse than a tautology. In logic a contradiction has exactly the same significance as a tautology, and I could study logic just as well by means of contradictions. A contradiction and a tautology do not say anything, do they?, they only provide a method for demonstrating the logical connections between statements.

In the great Philosophical Investigations and the other writings of Wittgenstein’s later philosophy, there is an intensive study of so-called ‘psychological’ concepts, such as understanding, meaning, intention, thinking. The Waismann notes indicate the direction in which, as early as 1931, Wittgenstein was moving:

I again and again concern myself with the question, What does it mean to understand a proposition? This is connected with the general question of what it is that people call intention, to mean, meaning. Nowadays the ordinary view is, isn’t it, that understanding is a psychological process that accompanies a proposition – i.e. a spoken or written proposition? What structure, then, does this process have? The same, perhaps, as a proposition? Or is this process something amorphous, as when I read a proposition while I have a toothache?

I now believe that understanding is not a particular psychological process at all that is there in addition, and supplementary to the perception of a propositional picture. It is true that various processes are going on inside me when I hear or read a proposition. An image emerges, say, there are associations and so forth. But all these processes are not what I am interested in here. I understand a proposition by applying it. Understanding is thus not a particular process: it is operating with a proposition.

One should be grateful to Blackwell for publishing the English translation of Waismann’s notes, and also the new edition of Tractatus notebooks, as well as numerous volumes of Wittgenstein’s writings. But Gerd Brand’s The Central Texts of Wittgenstein is a horse of another colour.

Brand’s aim is to articulate the ‘inner unity’ of Wittgenstein’s philosophy by assembling themes from Wittgenstein’s ‘total work’, using copious quotations and paraphrases, plus the guidance of Brand’s own interpretations. But Brand has no apparent awareness of how much Wittgenstein’s thought changed from Tractatus, through Philosophical Remarks, Philosophical Grammar, Blue and Brown Books, to Investigations, Zettel and On Certainty. What is frequently ‘assembled’ from the whole range of Wittgenstein’s writings, both early and late, is a hodgepodge of quotations and paraphrases that display no ‘inner unity’ but instead present quite different or even sharply conflicting ideas.

Brand’s interpretative remarks sometimes appear to be contrived to dissuade anyone from reading Wittgenstein. In a chapter on ‘Temporality’ we find this heady stuff:

Time is, therefore, that in which sameness is given to me, namely, in difference. Sameness is generally only in difference. Only in recognition is identity shown. Recognition is, therefore, what is primary and identity is what is secondary.

Perhaps one is meant to read this standing on one’s head. In a chapter mysteriously entitled ‘The Doubling of Reality’ there is the following:

Between the world and the I there is effected a constant doubling which appears to start from things and leads even further in various stages. Finally one arrives at a doubling which appears to be accomplished by the I.

Those hopelessly obscure remarks are supposed to derive from, among other things, Wittgenstein’s criticism in Investigations of the proposition, ‘A thing is identical with itself,’ of which Wittgenstein says: ‘There is no finer example of a useless proposition.’ Brand says: ‘In the apparent uselessness of the proposition about the identity of a thing with itself is shown its original doubling.’ The ‘original doubling’ of what? May Wittgenstein be saved from such clarification!

Too often Brand reads Wittgenstein exactly backwards. For example, Brand says: ‘One cannot speak without thinking and one cannot think without speaking. If I think, I am speaking internally.’ He cites paragraphs from Investigations and Zettel, where Wittgenstein says nothing of the sort. In a chapter entitled ‘Givenness’, Brand declares: ‘What is immediately given is beyond language.’ And that is supposed to be exposition of Wittgenstein! In the same chapter Brand takes up Wittgenstein’s attempt to throw light on the concept of ‘being guided’ by studying the use of the word ‘reading’, where Wittgenstein is referring to the reading of a book or a newspaper. But that is too humdrum for Brand, who announces, pompously: ‘First of all, we can say, in general, and quite universally, that we read reality, we read the world.’ In a chapter entitled ‘Understanding’ one comes upon the following claptrap: ‘Understanding is oriented towards totality and is thereby something total.’ ‘Understanding moves in the direction of an immediate ultimate.’ Brand’s book produces the grim realisation that the depth and brilliance of Wittgenstein’s thinking can bring out the worst in philosophers.