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Justin Woods

Wittgenstein's Dilemma


Either language can be defined or it can be investigated empirically. If language is defined then this will be mere tautology. If language is investigated empirically then this will lead to a substantial yet contingent truth.

The cure for this dilemma for Wittgenstein in his Tractatus Logico-Philosophicus was to submit the doctrine that the structure of language cannot be said but only shown.

This doctrine is vague and misconceived. In this essay, I will show that it is vague and misconceived and, consequently, why it does not cure his dilemma.

Wittgenstein stated in the preface of his book that he had solved the problems of philosophy. That these problems had been formulated by the misuse of the logic of our language by philosophers. What philosophers had been saying could simply not be said. Their philosophy was beyond the scope of what could be said and was therefore nonsense.

By plotting the limits of language, Wittgenstein expected to be able to deal with the problems of philosophy finally.

Outside the limits of what can be said lies nonsense, so any theory of language must occur within these limits.

Wittgenstein thought that the nature of language could tell us what can and cannot be done with it. He believed this because he deduced that language had its own limits fixed within its structure.

So, in his theory of language, he revealed the structure of language to entail these limits of language which were also necessary truths. However, this meant that they would also be empty tautologies!

Wittgenstein believed that language disguises thought and therefore the nature of propositions would reveal the nature of the language that represents it. So, Wittgenstein based his theory of language on the nature of propositions.

Within the nature of propositions, Wittgenstein found a satisfactory account of logical necessity. This lead to the fact that the limits of language were logically necessary.

In this essay, I shall give an account of Wittgenstein's theory of propositions and show that his elementary propositions are in fact divisible. I will outline his 'picture theory' and show that the consequential 'doctrine of showing' is vague and misconceived. I shall submit my own theory of the tautology as a possible cure for the above dilemma. Numbers appearing after quotes refer to the numbered passages in the Tractatus.

To begin, then, some detail of Wittgenstein's theory of propositions is needed in order to see how the important 'atomic' propositions idea came about.


Arguably, the main 'stars' of the Tractatus are the 'objects' and the 'atomic facts'.

They are presented at the beginning of the book. The somewhat, startlingly brief, if not inadequate, explanation of them has been the source of much discussion hitherto.

David Pears, in his book Wittgenstein, notes, "The text of the Tractatus is formidably difficult...Certainly the way in is not through the opening sentences." (London, 1971)

In A Study in Wittgenstein's Tractatus (Bristol, 1961), Alexander Maslow states that "...Wittgenstein is not at all clear as to what he means by objects and atomic facts."

Wittgenstein thought that the structure of language could be discovered by an investigation from within language. Thus, he was lead to begin his investigation from the inside out. The real content of our thoughts can be discovered by analysing language, which expresses our thoughts through symbolism, into its basic components- 'elementary propositions'.

He proposed that there must be such things as the elementary proposition, which is that which represents the simplest things in the world.

Further, those elements, or 'objects', in the world that are indivisible must be represented in language by names which would constitute an elementary or 'atomic' proposition. Such objects appear as names in the proposition only.

In the proposition the name represents the object. (3.22)

This logically entails the ability to form complex propositions, which would represent a group of objects by naming, in the world. Therefore, an analysis of any proposition would reveal further propositions, in the case of propositions reflecting multiple objects, or no proposition, in the case where the proposition was itself atomic.

It is obvious that in the analysis of propositions we must come to elementary propositions, which consist of names in immediate combination.

The question arises here, how the propositional connexion comes to be. (4.221)

Language must be broken down into its ultimate components- elementary or 'atomic' propositions.

The analysis is complete at this point by the fact that these elementary propositions cannot be broken down any further, or into other propositions. These propositions are meant to represent the simplest objects of existence.

He gives no examples of elementary propositions; he probably thinks that he does not need to. He is not concerned with the epistemology, only the logical structure of language.

Elementary, or 'atomic', propositions are simply the class of factual propositions which are logically independent of each other. This means that the truth-value of one proposition is never implied by the truth-value of another, making them wholly independent and indivisible. No atomic proposition can be formed out of another.

Atomic facts are independent of one another. From the existence or non-existence of an atomic fact we cannot infer the existence or non-existence of another. (2.061-2.062)

So, Wittgenstein had to prove that all factual propositions can be reduced by logical deduction to elementary propositions. The proof comes from the very nature of the proposition's being logically necessary.

The logical necessity of propositions can be appreciated when we recognize that the very fact that logic exists presupposes the necessary truth that reality consists of simple objects.

This is necessarily so because the very existence of logic depends upon the possibility of combining factual propositions.

This presupposes the construction of factual propositions which in turn presupposes the possibility of elementary propositions and then to the objects of reality.

Logic uncovers the structure of factual discourse, which is the sum of elementary propositions and the simple objects they represent. Therefore, the structure of reality is revealed.

The dilemma begins with the question "How does logic, whose propositions are empty tautologies, reveal anything about the nature of reality?"

Here Wittgenstein states that the very fact itself that tautologies occur at all 'points' to something about reality's structure, its logical form, which can only be shown and not spoken of.

Wittgenstein had plotted the limits of language by showing the structure of language to involve necessary truths between reality and the propositions representing it.

He was able to deduce from factual propositions to elementary, which represent the simple objects of reality. Therefore, the limits of factual discourse are fixed in advance of experience and are objective.

The essential nature of language indicates that reality is reflected by it. Yet this is a tautology that has something to say about the nature of reality and is therefore substantial.

This point will be treated later to philosophical attention in my chapter 'Substantial Necessary Truths'.

Now, however, we shall outline Wittgenstein's 'doctrine of showing' by investigating the 'Picture Theory' of the Tractatus. This will show how Wittgenstein was able to keep his theory of language while holding that its propositions were substantial necessary truths.


Wittgenstein uses the analogy of the 'picture' as the 'model for reality'; now commonly referred to as 'The Picture Theory of Language'.

The picture theory is probably the best place to start in the Tractatus for a study of the doctrine of showing. So, I shall begin with a brief outline of the picture theory and the consequent formulation of the doctrine of showing.

His theory starts:

We make ourselves pictures of facts. (2.1)

Basically, the picture stands for the fact. The fact is that proposition which says something about the world, but is not that which it talks about- just as the various characters in a painting of a family represent the 'real' members of that family.

It follows, therefore, that the picture is a link to reality. Each of the elements of a picture represents each object of the fact.

To the objects correspond in the picture the elements of the picture. The elements of the picture stand, in the picture, for the objects. (2.13)

The sticky point then follows that there is a thing that links the picture to the fact. This thing, which both have in common, Wittgenstein calls its "form of representation" (2.17)

This form of representation also belongs to the picture and is therefore, inexpressible- hence the doctrine of showing.

The picture, however, cannot represent its form of representation; it shows it forth ...the picture cannot place itself outside of its form of representation.

What every picture, of whatever form, must have in common with reality in order to be able to represent it at all- rightly or falsely- is the logical form, that is, the form of reality. (2.172-2.18)

Wittgenstein's theory of language would not allow him to use language in order to explain its structure, or logical form. This could not be spoken of at all; it could only be pointed to, or shown.

The structure of that which we express by is itself inexpressible.

The doctrine of showing is also revealed to us later in the Tractatus thus:

Propositions can represent the whole reality, but they cannot represent what they must have in common with reality in order to be able to be represent it- the logical form.

To be able to represent the logical form, we should have to be able to put ourselves with the propositions outside logic, that is outside the world.

Propositions cannot represent the logical form: this mirrors itself in the propositions.

That which mirrors itself in language, language cannot represent.

That which expresses itself in language, we cannot express by language.

The propositions show the logical form of reality. They exhibit it. (4.12-4.121)


Now that the doctrine of showing has been outlined, we can move on to its critique.

Wittgenstein believed that the truths of logic are empty tautologies.

This poses a big problem for his critique of language since his goal is to establish that the limits of language are logically necessary. So language being our key to understanding reality is based on empty tautologies.

In the Tractatus, Wittgenstein tells us that the limits of language are necessary truths deduced from the essence of language; which avoids the deference to them being established empirically, in which case they would not be necessarily but only contingently true, thus undermining the ability to plot the limits of language with as much certainty.

Further, necessary truths are logically so, and are therefore empty tautologies. This was no good to Wittgenstein who wanted substantial necessary truths about reality but did not believe that these were possible.

So to keep his theory of language substantial and necessarily true Wittgenstein employed the above doctrine of showing or pointing to reality instead of speaking about it.

The doctrine is misconceived for which reasons I will impart on soon. But first I will criticise the details of this doctrine.

Wittgenstein's doctrine of showing hinges on the following conviction:

Propositions can represent the whole reality, but they cannot represent what they must have in common with reality in order to be able to be represent it — the logical form.

In order for this to be true by correspondence, propositions must first be capable of representing reality, but not that which enables such a representation. That which enables representation is inexpressible.

However, this would establish, correspondingly, that the meaning of 'representation' could not be understood. For, by understanding the meaning or idea of 'representation' logically implies expression of that which language and reality have in common.

That which language represents and language itself have 'representation' in common. To understand 'representation' is to know the logical structure of language.

The only way to agree with the above proposition is not to be able to express 'representation' which is in fact expressible.

Having shown that the 'doctrine of showing' is wholly misconceived, I shall now consider the possibility of substantial necessary truths as they appear in the Tractatus.

My own theory of tautologies will be put as a solution to Wittgenstein's dilemma of having a language theory based on substantial necessary truths.


Here I shall submit my own attempt at curing Wittgenstein of his dilemma by my redefined theory of the tautology as a source for contingent, and therefore substantial, truth.

Firstly, it is most important, prior to my proposal, to note Wittgenstein's view of tautologies and contradictions as they are found in the Tractatus.

Perhaps the most definitive summary of his opinions is found from the following excerpt:

The proposition shows what it says, the tautology and the contradiction that they say nothing. The tautology has no truth-conditions, for it is unconditionally true; and the contradiction is on no condition true. Tautology and contradiction are without sense. (4.461)

Wittgenstein was correct in saying that necessary truths are logical propositions and therefore tautologies. He was wrong in saying that tautologies tell us nothing about the world, or nothing outside of what we already know from that which is contained within the tautology.

Wittgenstein's cure for his dilemma was to avoid self-contradiction by asserting the doctrine that the newly found nature of propositions revealing the necessary truths of language was able only to show us something of reality.

This turning point in his whole theory forced Wittgenstein, through a will to consistency, to adapt his theory to the new doctrine. As a result his theory lead him to its conclusions and consequences found thereafter.

What Wittgenstein did not do was to redefine his theory of tautologies. He could have cured his dilemma by paying more attention to the scope and limits of the tautology. Instead, I shall do this myself with the following theory.

I propose that the tautology does indeed say something new to us of the world, of reality. Tautologies are not empty; they do not lack substance, they contribute to it.

Because a tautology is that which is arrived at through a combination of premises, which are contained within its sense, does not mean that new knowledge is not acquired.

The reason is that that which is contained within any proposition is a different sense to that which is meant by those who use it.

In other words, when I express a proposition I may in fact know, or be proposing, only a 'portion' of the content or scope of that proposition or the objects which are contained within it, which may in turn entail further objects.

The rest of the propositional 'pie', its logical extension, is discovered by logical analysis. Since I do not have the complete knowledge of that which is the extension of the proposition or its elements (objects), this analysis will reveal to me new knowledge.

I shall elaborate on this important point with the following assumptions, forming the logical conclusion:

  1. It is not possible to know the entirety (possible infinity) of all given propositions' extensions, including that of tautologies; all those propositions which are logically entailed by a given proposition.
  2. An analysis of any given tautological proposition would reveal, sooner or later, unknown propositions and elements, previously hidden within their implicated propositions. For instance, "My black cat is a cat" contains the implied propositions "I have a cat", and "some cats are black". This is how we acquire knowledge about the world through analysis of a tautologies extension- its logically entailed propositions.
  3. Unknown propositions and elements afford previously unknown, or new, knowledge of the world.

Conclusion: New knowledge of the world is afforded by an analysis of the extension of any given tautology and its elements, the extension being considered as possibly infinite.

Now, the obvious problem with this idea is that of the atomic fact, or indivisible proposition. If Wittgenstein was right then such propositions would have no extension at all. This would, in turn, foil my theory of substantial tautologies thoroughly.

Aside from this is the consideration that not all propositions need have an extension at all.

My counter-argument is that Wittgenstein is wrong; the atomic fact of the Tractatus is not 'atomic' at all — it is not simple, and it is not indivisible.

I propose that even if Wittgenstein could give an example of an atomic fact, it could be further divided: I must, therefore, be contending that the possibility of indivisible propositions is logically invalid.

Any proposition, or fact, about the world can be divided into another fact about the world. Since no fact can be atomic, my theory of tautologies stands unassailable.

It is demanded of me, therefore, to put down, in adequate detail, my argument against the possibility of atomic facts and elementary propositions.


It seems that the vagueness of Wittgenstein's exposition of atomic facts, and the objects of reality entailed by them, is his undoing.

The lack of detail makes the whole idea subject to philosophical attack from several different perspectives. I shall submit one such attack, which is sufficient to invalidate this thesis.

In the Tractatus Wittgenstein introduces simply that 'atomic facts' are:

An atomic fact is a combination of objects (entities, things) (2.01)

That they are at all is logically determined:

In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing...If a thing can occur in atomic facts, this possibility must already lie in them. (2.012)

The very fact that logic exists, according to the Tractatus, presupposes the possibility of complex propositions of the world which are added and subtracted to form logical conclusions, analysed to reveal the source or extension of propositions, contradicted, negated and tautologised.

Accepting this, Wittgenstein proposes that analysis of complex facts will reveal other facts, and that a complete analysis would reveal an atomic fact — wholly indivisible. This idea, however, is not secured with the logical rigour that the theory of complex facts are.

After reading the description of atomic facts, that Wittgenstein gives us, we are left with only analytical reason to believe in their possibility.

It is possible then, to put forward another analytical argument such as 'the atomic fact is nothing more than a complex fact wrongly conceived to have the concept of indivisibility attributed to it.' I assume this position.

There is no valid argument put forward in the Tractatus that states why or how certain facts are not themselves formed out of other facts.

Instead, the only possible proposal of such a proposition is merely stated, unqualified:

Objects I can only name. (3.221)

And a little later on:

The name cannot be analysed further by any definition. It is a primitive sign.

These are arguments by definition, and can be assailed with their negation.

To continue, it is put to us that those propositions which contain symbols that represent the objects of the world, cannot be further analysed themselves making the analysis complete and showing the proposition itself to be elementary. So, the obvious argument against this is that any object can be both named and defined.

This because objects are not simple: no object is simple. Wittgenstein gives us no example of an object and no argument that would prevent us from stating that objects are not simple. There is no reason, outside definition, to believe that simple objects subsist, yet there is every reason to believe that analysis of the objects of the world can be possibly, infinitely analysable by enumerating all those propositions entailed by any object, by observation of it with its fellow objects.

We could consider elementary propositions, which are formed out of simple objects, to be observations of the world- expressions of direct perception- by noting that, in the Tractatus, names that represent objects are primitive signs that refer to elucidations:

The references of primitive signs can be made clear by elucidations. Elucidations are propositions containing the primitive signs. Thus they can only be understood, if one is acquainted with the references of these signs. (3.263)

If this is true, then it is also correspondingly true that an object could be analysed by further observation, or acquaintance, of that object as the object is observed in relation and context with the other objects that it must be thinkable with.

Since Wittgenstein has already told us that the object is unthinkable without the context of other objects- these being known to us by what appears to be a direct acquaintance- then analysis of the propositions that would result from such observations are possibly infinite, although just one proposition is enough to secure the object's divisibility.

Simple objects, therefore, do not combine to form atomic facts; they combine to form any fact.

Complex propositions are not completely analysed to reveal those propositions entailed by them which may not be analysed any further. Complex propositions are analysed into propositions that may be analysed infinitely. This is because not only is it conceivable to think of a continuous analysis by logical entailment of any proposition, but there is no provision in the Tractatus that would not allow this to happen.

It is not clear what Wittgenstein means when he discusses them, but if by 'objects' he means that which Bertrand Russell referred to as 'sense-data' then at what point is the analysis complete of 'grass' or 'green' in the proposition 'the grass is green'?

Surely, grass can be analysed into its various components (such as chlorophyll and water), which in turn consist in molecules- yet these could no longer be called 'sense-data' because they could not be 'sensed'. Therefore, knowing that grass is not a completely simple object we should have to admit, for the sake of Wittgenstein's argument, that it is.

Such an atomic fact as 'the grass is green' entails in its extension the fact that "'greenness' is a Platonic form"; "greenness may be attributed to a sense datum — 'grass', the one being an objective concept, the other empirically subjective, both occurring together as a meaningful statement of possible fact."

Thus, it is shown that a seemingly 'atomic' fact may be analysed into a complex fact, whereby we must commit the idea of 'atomic facts' to the Humean flames.

Now, to continue on with our quest to place a new theory of tautologies in Wittgenstein's theory of language, we must discover whether it is possible for this new knowledge that tautology's reveal to be in itself a proposition about the world or reality.

This requires analysis of the tautology into its logical scope or extension. I propose that the propositions discovered through this analysis may reveal substantial propositions.


Take for instance, 'All wise men are wise'. This is a tautology because it is a proposition that asserts one thing as being attributed to another and that which is attributed is contained within that which asserts that it is thus. So within the definition of the tautology itself some facts about reality and the nature of language may be revealed to us already. These can be exposed by the following analysis.

Firstly, tautologies are propositions expressed by symbolism, in this case words. Now the above statement made about tautologies is peculiar because it is not necessarily true itself.

That tautologies are propositions expressed by symbols is a result of the use and application of them in language rather than the result of an analysis of those things attributed to tautologies.

If a proposition expresses something, a proposition expresses 'All wise men are wise' and is not identical with it but relates to it, then the fact that it expresses is not itself tautological. The relation of expression between the proposition and that which it expresses cannot itself be the subject of a proposition and therefore cannot be said to be tautological itself. Yet, this can be true of all tautologies. In particular we may consider the following example.

For an example that would also show my idea at work think of the old stock example of 'the morning star' and 'the evening star'.

To what do these stars refer? Do they refer to two different stars, or the same star? Is the statement 'the morning star is the evening star' the same statement as 'the evening star is the evening star'? This would be a tautology, the analysis of which would arrive at the preceding propositions that are entailed by it.

Or, is the statement referring to Venus and its description — which is not Venus but about Venus. Such are the fruits of tautological analysis.

So the nature of the tautology is that its own logical components suffer from an inability to themselves put into propositions that which would necessitate its capacity to reveal nothing of reality or the world. Therefore, this being a proposition about the world revealed from analysis of the tautology we can now say that tautologies are indeed substantial.


I have given my interpretation of the Tractatus. I have presented a dilemma that it contains and explained how it came about. I have attempted to cure the dilemma by exposing and criticising Wittgenstein's doctrine of showing, as it is found within his 'picture theory of language', and re-defining his theory of the tautology.

I have shown the logical problems with Wittgenstein's theory of propositions, and exposed the divisibility of his atomic facts. I have also put forward the argument that his 'objects' are either names and descriptions or just descriptions- either way, they are not logically independent.

There is now no such dilemma of establishing a theory of language that will reveal a theory of reality but be based upon necessary truths lacking substance.

Analysis of the nature of the tautology has revealed an important and substantial fact about reality and has thereby conquered what had hitherto run the risk of being purely logical.