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The Tractatus

“The world is all that is the case”

José Zalabardo investigates which problem Wittgenstein is trying to solve.

For many contemporary interpreters of the Tractatus, its ultimate goal is not to answer philosophical questions or solve philosophical problems. Rather, Wittgenstein’s aim is therapeutic – to make his readers see that philosophy is not a legitimate pursuit: the problems are fictitious, the questions are meaningless, and engaging in the enterprise can produce nothing but nonsense.

This may well be the right account of Wittgenstein’s intentions. There are certainly things he says in the book that can only be understood in this light. However, it would be wrong to conclude that therefore we shouldn’t try to understand what philosophical questions and problems Wittgenstein was trying to address, and how he proposes to deal with them. If Wittgenstein’s goal is the dissolution of philosophy, his proposed method requires that his readers engage in the enterprise. The therapy of the Tractatus is supposed to work through the reader’s realization that what philosophy sanctions as the right answers and solutions is nonsense; and to achieve this realisation we first need to find these answers and solutions. The ladder has to be climbed before it’s kicked away.

The Tractatus isn’t written in the usual style of a philosophical treatise. It reads more like a piece of creative writing using philosophical discourse as a source of inspiration. Yet some features of its style that may be intrinsic to its literary value are certainly an obstacle for those of us who are trying to understand its philosophical doctrines, whether or not we expect a therapeutic outcome. For instance, many of its doctrines are hard to understand, let alone assess, because we are given no indication of which philosophical problems they’re supposed to be addressing. The opening proposition of the book is a case in point. Which philosophical question is Wittgenstein trying to answer with his assertion that “The world is all that is the case”?

This question is the topic of the present article. I am going to argue that with this opening claim about the nature of the world, Wittgenstein is seeking to address an ancient philosophical problem.

The Problem

The problem makes its first recorded appearance in Plato’s work. One of Plato’s most characteristic doctrines is his ‘Theory of Forms’. This view, in a nutshell, is that when several individual things exhibit a common feature, there is something – a form – that is present in all of them. For instance, the form of beauty is present in all beautiful things; and the presence of the form of beauty in some object is what its being beautiful consists in. If we apply this template to all cases in which individuals exhibit a common feature, the result is a way of thinking according to which the world contains two types of items: particulars (this table, that chair, St Paul’s Cathedral, you, me) and universals (beauty, redness, solidity, stubbornness, acidity). Let me refer to this theory as the Platonist ontology. (An ontology is a theory about what sort of things exist.)

On the Platonist ontology, whatever is the case results from a combination of particulars and universals: the fact that my table is red results from the combination of a particular – my table – with a universal – redness. When a particular and a universal are combined in this way, we say that the particular instantiates the universal. What the world is like is the result of which combinations of particulars and universals it contains. My table is combined with redness, but not with roundness; redness is combined with my table, but not with my chair. Other states of the world would result from different particular-universal combinations.

The Platonist ontology is not without appeal. However, when we examine the Platonist ontology in detail we soon see that it’s plagued with difficulties. In fact there are problems concerning particulars, concerning universals, and concerning the combination of the two.

Let’s consider particulars first. If we are going to think of my table as separate from the universals that it instantiates – as what remains when all the universals are taken away (that would make it a bare particular) – then it will have to have no shape, colour, texture, chemical composition, weight, or any other universalisable property… It soon becomes hard to understand what kind of entity we are postulating, let alone in what sense it can still be described as my table.

Universals are also a source of perplexity. It’s hard to see how they could be located in space and time. Yet if they exist somewhere else, we would need to postulate a separate, non-physical realm for them to inhabit, and we need to provide an account of how we gain access to this realm. Plato didn’t have a problem with this – he thought our souls dwell in the Realm of Forms before we’re born – but others have been more wary about it.

However, the problem with the Platonist ontology that I want to concentrate on concerns the combining of predicates and universals, a problem Plato was already aware of. It is posed by Parmenides in the Socratic dialogue that bears his name:

“Parmenides: When it seems to you that a number of things are large, there seems, I suppose, to be a certain single character which is the same when you look at them all; hence you think that largeness is a single thing.

Socrates: True.

Parmenides: But now take largeness itself and the other things which are large. Suppose you look at all these in the same way in your mind’s eye, will not yet another unity make its appearance – a largeness by virtue of which they all appear large?

Socrates: So it would seem.

Parmenides: If so, a second form of largeness will present itself, over and above largeness itself and the things that share in it, and again, covering all these, yet another, which will make all of them large. So each of your forms will no longer be one, but an indefinite number.”

(Parmenides, 132 a-b.)

Parmenides is arguing that the Theory of Forms produces an infinite regress. The fact that a number of things are large is putatively explained by the presence in them of a single item – the form of largeness. But the large things also have something in common with largeness itself, by which they are all large. Hence we will have to postulate another thing, call it ‘largeness no. 2’ that is present in the large things and also in largeness. But the same situation also obtains for the large things, largeness and largeness no. 2, forcing us to postulate yet another item, largeness no. 3; and so ad infinitum.

Parmenides’ reasoning here was endorsed by Aristotle, who gives it as one of his reasons for rejecting Plato’s Theory of Forms. Since Aristotle, who made use of the form of ‘man’ to pose the same argument, the argument has been known as the Third Man Argument.

Commentators have pointed out that Parmenides’ argument rests on some questionable assumptions. For example, it presupposes that a universal has to have the feature that its instances share: that largeness has to be large, etc. Plato may have been committed to this assumption, and the argument would then be effective against him. But those of us who are not inclined to accept this claim would seem to have nothing to fear from this argument.

However, as Gilbert Ryle showed in his commentary on the Parmenides, the Third Man Argument can be easily adapted to avoid the most questionable assumptions of Parmenides’ version of the argument. To understand this, we need to consider the application of the Platonist ontology to relational facts, for instance, the fact that my table is darker than my chair, or that William loves Kate. We can think of relational universals such as ‘is darker than’ or ‘loves’ as common features, not of several particulars, but of several pairs of particulars. If my table is red and your scarf is red, then on the Platonist ontology there is a common thing, the universal redness, that is present in both particulars. Similarly, on the amended version of the Platonist ontology, if William loves Kate and Barack loves Michelle, there is a common thing, the relational universal ‘loves’, that connects William with Kate and Barack with Michelle, and so which both couples share.

However, if this is how we are going to treat relational facts in general, it seems we must also extend this treatment to instantiation facts in particular, since instantiation is a type of relation. If my table instantiates redness and your car instantiates reliability, then by this reasoning there has to be a common thing – instantiation – connecting my chair with redness and your car with reliability. Instantiation will therefore have to be included in the category of relational universals. But this itself is the beginning of an infinite regress: if the form of ‘instantiation’ is itself instantiated both in the table-redness pair and in the car-reliability pair, then there has to be a common relational form, instantiation no. 2, connecting instantiation with the two pairs. The same reasoning will also call for the generation of instantiation no. 3; and so ad infinitum.

Aristotelian Strategies

Awareness of the difficulties faced by the Platonist ontology has led some philosophers to cut their losses by trying to reduce either universals to particulars or particulars to universals. On the one hand, the ‘bundle theory’ advocated by David Hume seeks to avoid particulars by reducing them to bundles of universals. On this position, my table is nothing but a collection of co-located properties: a shape, a size, a chemical composition… On the other hand, nominalists such as William of Ockham have sought to avoid universals by asserting that only particulars exist, with common features explained in terms of how we classify things, that is, in terms of how we use words. Both these projects face serious difficulties, and in the end, each still has to contend with the problems attending its fundamental category.

Another strategy for overcoming the difficulties with the Platonist ontology can be found in Aristotle’s work. For Aristotle, the source of the Third Man problem was Plato’s contention that universals enjoy independent existence (universalia ante res), and the problem can be solved by rejecting this view and accepting that universals are inextricably linked to the particulars that instantiate them (universalia in rebus). One thing this could mean is that there are no uninstantiated universals – there can’t be redness unless there are red things. But I can’t see how this claim would help with the Third Man Argument. To my mind, the only way to extract a promising strategy for dealing with the Third Man problem from Aristotle’s ideas, is to read him as advocating a wholesale rejection of the Platonist ontology. On this latter position, the world doesn’t ultimately consist of two categories of entities – bare particulars and universals – but of one single category of entity, encompassing both particularity and universality as aspects of a single item. On this account, what exists is not the bare chair on the one hand and its properties on the other, but a single item, the chair with its properties, which is not a compound produced by the combination of a particular and universals, but a fundamental, irreducible unit. Such objects are sometimes known as thick particulars.

This view faces its own challenges. It needs to make sense of our talk of an object changing properties, and of different objects sharing a property. I am not going to explore these issues here. I want to concentrate instead on the question of whether it offers a solution to the Third Man Argument. I think the answer is that in some cases it does and in some cases it doesn’t.

The problem is solved for subject-predicate facts. The fact that my table is red is not construed as arising from the combination of a particular and a universal, hence the threat that this combination might generate an infinite regress doesn’t get a grip.

However, it’s hard to see how this proposal could work for relational facts. Separately, William and Kate may both be indivisible units (people), encompassing both their particularity and their universal properties; but the fact that William loves Kate cannot be seen as an aspect of William independently of Kate, nor vice versa of Kate independently of William. The new view doesn’t offer an alternative to treating relational facts as combinations involving two thick particulars and a relation. And this is all we need to get the Third Man Argument going, since we now need instantiation to connect the relation with the pair of thick particulars.

Wittgensteinian Strategies

However, the central idea of the ‘thick particular’ proposal can be used to provide a general solution to the Third Man Argument. This strategy involves rejecting the idea that facts are produced by combining anything. As mentioned, an ontology of thick particulars achieves this for subject-predicate facts, but I have argued that it doesn’t work for relational facts. However, the no-combination approach can also be sustained by a different ontological framework, where the basic constituents of reality are simply facts. On this position, facts are what reality consists in, and a fact is a fundamental, indivisible unit, not arising from the combination of more basic items.

There is no clearer or more succinct characterisation of this view than the first two assertions of the Tractatus:

“1. The world is all that is the case.

1.1. The world is the totality of facts, not of things.”

These two sections, I submit, put forward an ontology of basic facts. By doing so, they constitute Wittgenstein’s solution to the Third Man Argument.

This fact-based ontology that I am now attributing to Wittgenstein faces important challenges itself. It needs to make sense of our talk of the constituents of facts – for example, concerning what the fact that my table is red has in common with the fact that your scarf is red, or with the fact that my table is rectangular. It would also need to make sense of our talk of unactualised possibilities – of what isn’t the case but could be, or at least can be represented as being the case. The Tractatus contains attempts to answer these questions, but I don’t have the space here to review this aspect of the work.

If my interpretation of this passage is along the right lines then Wittgenstein would be making a contribution to one of the central debates of Western philosophy. But how could that happen? Wittgenstein knew very little about the history of Western philosophy. He had received no formal philosophical training before he arrived in Cambridge in 1911, and in Cambridge his philosophical activity doesn’t seem to have included study of the classics of philosophy.

There is not mystery, however, about how Wittgenstein came into contact with the issue that, on my reading, is addressed by these opening sections of the Tractatus. A version of the Third Man Argument had been advanced by F.H. Bradley, a leading Oxford philosopher, in the last decade of the nineteenth century. Russell and Bradley had extensive interaction over this and there is abundant evidence of Russell’s concern with various versions of the problem; and Russell, of course, was Wittgenstein’s mentor at Cambridge.

Furthermore, Wittgenstein’s fact-based ontology can be seen as a natural extension of a view advocated by Gottlob Frege, to whose ‘great works’ Wittgenstein acknowledged a debt of gratitude in the Preface to the Tractatus. The question of the relative priority of facts and their constituent properties has has close parallels to a similar controversy concerning thoughts and their constituent concepts. On this latter issue Frege advocated a position very close to the view I’m ascribing to Wittgenstein concerning facts and their constituents. Frege characterises it in the following terms in 1919: “So I do not begin with concepts and put them together to form a thought or judgement; I come by the parts of a thought by analyzing the thought” (Posthumous Writings, p.253, 1979). The view that I am attributing to Wittgenstein could be expressed in very similar terms: “I do not begin with particulars and universals and put them together to form a fact; I come by the parts of a fact by analysing the fact.” So Wittgenstein’s contribution to the debate on the nature of reality can be seen as a translation to the analysis of facts of the position that Frege held on the analysis of thoughts.

José Zalabardo is head of the Department of Philosophy at University College London.