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Foundations of Analytical Philosophy, Part 2: Logical Atomism and Logical Positivism

Daniel Hutto continues to explore the Analytic jungle.

“The way to understand reality is by examining language.” This claim of analytical philosophy is still important to many thinkers today. In the last issue of Philosophy Now I tried to give a guided tour around some of the events that were responsible for the genesis of this way of thinking. My aim here is to continue that tour by looking at the way in which the tradition matured between the time of its birth and its ‘middle period’.

1. Russell’s Road to Logical Atomism

I will start by picking up a thread I left hanging at the end of the last instalment by giving a very brief exposition of the theory known as Platonic Atomism. On that view the building blocks of reality were terms (e.g. cat, door, etc.) which combined to make up whole propositions (e.g. the cat is by the door) – the objects of thought. When we are acquainted with these objects of thought, we are directly related to the world. Hence true thoughts, which were called facts, simply were the bedrock of the world.

According to Bertrand Russell’s early metaphysics everything that could be thought was a kind of term. Since these terms were the building blocks of whole thoughts (which if true were called facts) they all had equal status. This meant that anything that could be thought of as a term was somehow real. One attractive feature of this rather simplistic metaphysics was that it coped well with our intuition that when I am thinking (i) “My stomach hurts” or (ii) “I haven’t paid all my bills” I am thinking about different things.

This can be contrasted with Frege’s opinion that whole propositions should be seen as referring to either the True or the False. This view is particularly counter-intuitive; if we take Frege seriously all true propositions refer to the same object (i.e. the true) just as all false propositions refer to the same object (i.e. the false) [see last instalment, p.17]. It is an outrage against common sense to suggest that propositions such as (i) and (ii) above refer to the same thing simply because both are true.

But Russell’s account had a few problems of Rs own. First of all, Russell was hard pressed to explain what gave propositions their property of being either true or false. Just why did certain propositions happen to be true and others not? Another big problem for this more ‘object-based’ account was that it was difficult to see what false propositions were supposed to be. The paradox was that if the false proposition was treated as a real entity of our acquaintance then how could it be regarded as essentially a non-existent state of affairs?

Furthermore, there were other problems with this account concerning issues such as: (a) Generality, (b) Paradoxes and (c) Impossible Objects. In essence these problems were an unavoidable outgrowth of Russell’s adoption of the naive metaphysics of Platonic Atomism (i.e. everything is a term and all terms have equal status). To take just one example, it was a puzzle on Russell’s early view if we were to say something like (1):

(1) “There is no such thing as a round square.”

The trouble was that Platonic Atomism committed itself to the existence (or at least the subsistence) of impossible objects like the round square since such objects can appear as terms in true propositions. That is to say, if we treated ‘the round square’ as a name (for an object) then we would be committed to the existence of the object it named. By the time Russell had come to write his Principles of Mathematics in 1903 he had recognised this problem. His first proposed solution was to introduce the notion of ‘denoting concepts’. Denoting concepts were terms which could effectively stand for other terms.

By introducing ‘denoting concepts’ into his metaphysics he could allow a term that appeared within a proposition to refer to some object or collection of objects other than itself. For example, the ‘denoting concept’ all did not refer to a single entity any longer but rather to many other entities (with the proviso that said entities formed a complete set). But the very idea of one term standing for another was anathema to the vision of Platonic Atomism – so much so that it eventually led to the development of the famous view he published in On Denoting. The work was a landmark in Russell’s own thinking and analytic philosophy as a whole.

In it he began to treat the objects of denoting concepts (or phrases) not as real objects at all but as descriptions or incomplete symbols. This allowed him to take a harsh line with regard to some troublesome definite descriptions which picked out non-existent entities or impossible objects. In this sense although it sometimes appears as if we have used a name, in fact we have only made an assertion that makes mention of certain properties in relation to a ‘prepositional function’, such as x in (1) below. Very informally, what we have proposed is something like:

(1) “There is no unique thing (x) which has both the property of being /round/ and /square/.”

This is very different from saying something like (1) which is clearly paradoxical:

(1) “There is no unique thing (The Round Square) which has both the property of being /round/ and /square/.”

We can now see how Russell dealt with the problem that arose from the belief that “…if a word means-something, there must be some thing that it means.” (Russell, 1959, p.63).

To repeat, on Russell’s new account we could treat propositions like (1) as making true assertions without having to take ‘round squares’ and their brethren seriously at the ontological level (i.e the level of what there is). The illusion that there were such things as general terms (e.g. objects like ‘some’, ‘all’, or ‘every’) or impossible objects was now to be regarded as a trick of language.

This realisation gave Russell a newfound, albeit negative, respect for the need to pay attention to natural language. This change in thinking shifted his opinion of the way in which our thoughts are related to reality. He abandoned the idea that language simply reveals thought. He even went so far as to extend his theory of descriptions beyond just general terms and impossible objects to many of the things we normally treat as names (e.g. Mark Twain, New York, etc.).

It is important to note, however, that many aspects of his older view remained intact. Hence, he continued to think reality was composed of the true objects of our acquaintance. As he said, you cannot name anything you are not acquainted with (Russell, 1924, p.201). But if we accept his later view, we are nor directly acquainted with most of the things we ordinarily think we are. Thus, alleged names like ‘Socrates’, ‘London’, etc. do not stand for real things - they are descriptions and not names at all. Hence what there is could no longer be gleaned from a simple look at language. The real things with which we can be acquainted, those bits which go to make up the descriptions, were logically simple. Thus a logically pure language would show the true form of thought and thereby the form of reality (e.g. logical form = reality). But since ordinary language was not, and wasn’t going to be, a logically perfect language, ordinary language needed to analysed to reveal the true form of thought (i.e. misleading grammatical form ≠ logical form).

2. Tractarian Metaphysics

Ludwig Wittgenstein’s early position on these matters was developed as a response, in part, to the views of Russell. For example, they agreed about the way that ‘language disguised thought’ and that thought revealed the nature of reality. Nevertheless, there were many important differences between the views of these two thinkers.

For example, compare Russell’s views about the furniture of the universe in his mature period with those the early Wittgenstein expressed in his Tractatus Logico-Philosophicus (1922). As we have seen, Russell argued that we could get down in theory, if not in practice, to ultimate ‘simples’ (Russell, 1918, p.270). These simples-logical atoms - were supposed to be the basic constituents of the world. They were the only objects or things which could be given true names. But Russell also realised this was not a satisfactory, or complete, inventory of the world’s warehouse since facts could not be named in the same way logical simples could be. Let me explain why. The natural candidate to be a name for a fact would be a proposition, but a proposition can’t simply be a name for a fact because, as Russell says, “…there are two propositions for each fact. Suppose it is a fact that Socrates is dead. You have two propositions: ‘Socrates is dead’ and ‘Socrates is not dead’. And of those two propositions corresponding to the same fact, there is one fact in the world which makes one true and one false. [This] illustrates how the relation of proposition to fact is totally different from the relation of name to thing named” (Russell, 1918, p.187).

Apart from highlighting that propositions have this dual nature, Russell did little to provide an account of the nature of this duality. It was Wittgenstein’s ‘picture theory’ that filled this need (amongst others) – but before we examine that theory in more detail we must first get to grips with the metaphysics that lay behind it.

Near the very beginning of the Tractatus we find this famous proposition:

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

In reading this it is important to realise that Wittgenstein was not saying that there were no ‘things’ in the world – only that things needed to combine together (i.e. to form facts) in order to make up the world (see the Tractatus, section 2.011). He was also saying that things did not exist independently of facts, and vice versa. The way things happen to be arranged is what makes a fact. For an ordinary example, imagine how a book, a table and a room standing together in a certain way forms a fact like (∂) while the same objects standing together in a different way forms a fact like (ß).

(∂) The book is on the table in the room.

(ß) The table is on the book in the room.

We can now see why facts depend on things (and their arrangements). But in a similar way Wittgenstein thought things depended upon facts. Hence, it would be impossible to imagine some thing outside of all possible situations (i.e. all factual contexts) since our understanding of the nature of a thing depends upon knowing in which kinds of scenarios it can exist and in what capacities (Tractatus, 2.0123). Whenever we come to think of an object we must think of it in the context of some possible state of affairs – we cannot even imagine what it would be for a thing to exist outside of every and all possible state of affairs. For example, if you consider a object like a book its essence seems to depend upon what possible situations it might (or might not) inhabit – i.e. it could be read, burned, dropped, dusty, open, closed, etc. It cannot be drunk, driven, shattered, etc.

This view about the mutual interdependence of facts and things allowed Wittgenstein to hold that it is the essences of objects that fixes the form of the world (which is more than just a collection of things). The essential nature of objects is the bedrock of everything and determines which facts can and cannot be (Tractatus, 2.012). So to use our example, given the nature of objects mentioned, it is not possible to have an arrangement of things (i.e. a fact) like (γ ):

(γ ): The room is on the book in the table.

Whatever happens to be the case with the world (i.e. the facts) is underwritten by the world’s underlying essence which determines how things might possibly be arranged. This essence of the world is thus fixed by the nature of its objects (and their combinational possibilities) (Tractatus, 2.0124). The objects, by their very nature and the way they happen to combine, make the world one way or another – yet, even in doing so, they underwrite a multitude of different subsisting possibilities (or possible worlds). That is to say, behind the contingent way the world happens to be lies a fixed, unchanging, logical form of the world. (Tractatus, 2.022).

To use a simplistic analogy, it would be as if the world were made of lego pieces. Until the legos are arranged in a particular way there is no world of which to speak. However, all the possible worlds we might make with the legos are fixed by the nature of the particular legos we have to work with. More precisely, their individual shapes determine what possible constructions we might make. The logic of lego construction would be revealed by describing all the permissible combinations. And note also that such a ‘logic of lego construction’ would itself by given by the individual blocks themselves. Such a set of rules ‘of combination’ would be ‘determined’ by the nature of the legos themselves.

Let us stop for a moment and survey the progress we have made so far. We have learned that, according to the early Wittgenstein:

The facts of the world are nothing but how simple objects actually stand in relation to one another (out of the range of possible ways they might have stood in relation to one another).
These simple objects form the indestructible substance of all possible worlds.

3. Propositions as Pictures

We are now in a position to discuss the early Wittgenstein’s views on the general nature of propositions – i.e. his notorious picture theory of propositions. According to the picture theory all genuine propositions (the objects of thought) are composed of elements that ‘picture’ some possible state of affairs in the world (i.e. propositions say how things stand). This sounds like a simple idea but if we consider it against the background of the rise and fall of the ‘nametheory’ of propositions we will begin to appreciate the elegance of Wittgenstein’s novel contribution.

In effect, Wittgenstein took Russell’s work to its logical conclusion by proposing a theory of propositions which was tailor-made for the view that the world was composed of atomistic facts. Basically, he held that we make pictures of these ‘facts’ to ourselves by using pictorial elements ordered in various ways which allowed them to ‘represent’ the fact in question. His idea is said to have been inspired by the use of small scale models to represent traffic accidents in the Parisian Law Courts. In those cases model cars were arranged in various ways so as to represent the way in which the accidents might have happened in the hope of discovering how it actually did happen.

In Paris they would have used miniature cars for this purpose, but the accident could have been represented using apples and oranges, water-colours or even co-ordinates on a grid. The minimal requirement for a picture to represent a state of affairs is: (i) that we know what the individual ‘elements’ stand for (e.g. “This apple is my Toyota”) and (ii) that the elements are ordered in a way that corresponds to the way in which things might be ordered. It is in this way that a proposition arranges names (its elements) in such a fashion that they will agree or fail to agree with reality.

We can see this most vividly by examining the abstract structures in figures 1 and 2, below. If you look closely you will see that the very same ‘objects’ are arranged differently to form different shapes. Notice, that the possible shapes we might form would be constrained by nothing over and above the way in which the objects themselves might link together.

All this brings us to the inventive way that Wittgenstein dealt with Russell’s problem concerning the duality of propositions. He wrote:

2.21 The picture agrees with reality or not: it is right or wrong, true or false.

This point should be transparent enough. I could represent the world accurately or inaccurately in a picture. I could draw my hand with only two fingers or represent it similarly using the sentence “My hand has only two fingers.” Since my hand has more than two fingers these ‘representations’ would be false. Nevertheless, despite their falsity (in this instance) they remain intelligible – they make sense. It is not a nonsensical remark like “My finger only has two hands” – which represents nothing. The natural connection therefore in the case of any genuine picture and the world is that it makes sense of some possible state of affairs. An overview of Wittgenstein’s early position can be seen schematically in figure 3.

4. Positivistic Epistemology

One question that was deliberately left open in the Tractatus was: How do we know when any given picture succeeds in depicting the world or not? As Wittgenstein said this is not something we can gather from the picture itself. Nothing in the picture itself gives us grounds for saying whether or not it agrees with reality. We would need to stand outside our medium of representation in order to compare our picture and the world. This we cannot do. Wittgenstein was silent on such matters of epistemology since he believed such questions belonged to the speculative domain of psychology, not to philosophy. According to him, all we need to know is that pictures are sometimes true and at other times false. How we come to know when a given proposition is true or not is an empirical matter to discover.

Other philosophers were more concerned to give details about how and when we can know a proposition is true. The group known as the Vienna Circle developed a position they called logical positivism. At first glance their view of language bore more than a superficial resemblance to that of the early Wittgenstein. One of their number, Moritz Schlick, wrote: “To state the circumstances under which a proposition is true is the same as stating its meaning and nothing else” (Schlick, 1932-33, p.41). But the positivists went further than Wittgenstein would have wanted to go and combined this idea with what they called the verification principle. According to this principle, if a proposition was to have meaning then it must be possible, in principle, to say under what empirically testable conditions it would be true. Propositions which failed to meet this requirement – those which allowed of no test – were seen as strictly nonsensical. The thought was that any statement or idea which attempted to transcend the bounds of sensory experience was literally meaningless.

Why did the positivists take this view? Well, the issue turned on their idea that, in the end, all meaning was grounded in sensory experience. To borrow another quotation from Schlick: “…The meaning of a proposition obviously consists in this alone, that it expresses a particular state of affairs. This state-of-affairs must actually be pointed out in order to give the meaning of the proposition.” (Schlick, 1932-33, p.40, emphasis mine).

It is here we find the infamous analytic/ synthetic distinction of the positivists. Compare these statements:

(2) “A goose is a feathered biped”

(3) “A goose is a bird”

Both of these statements are true by definition and not made so by experience. They are what the positivists would call analytic. They are trivially true – but meaningful all the same. Ultimately, however, their meaning depended on experience. This can be illustrated in the following way. Suppose that I do not already know what a ‘feathered biped’ or ‘bird’ means – then your saying to me either (2) or (3) tells me nothing. If I am to learn what the concept or word ‘goose’ means, says the positivist, I will eventually have to have a goose pointed out to me. As in the case of (4) below:

(4) “A goose is one of those”

This is why the positivists claimed that to understand the meaning of analytic statements we cannot re-define them indefinitely – eventually we will need to rely on sensory experience to provide the meaning. Such statements which relate solely to sense experience were called synthetic. At this point I hope it is somewhat clear how the positivists saw themselves as ‘adding’ to the Tractatus-type philosophy.

I can only hope this short and woefully incomplete discussion of analytical philosophy’s ‘middle period’ will enable the unacquainted to have a least a sense of the issues at hand and the agenda that was set in place for others to follow. In my final contribution to this topic I will be discussing the last stages of the tradition’s development and the various directions in which analytic philosophy seems to be currently heading.

Dr. Daniel Hutto lectures in philosophy and cognitive science at the University of Hertfordshire.

References:

Ayer, A.J. 1936: Language, Truth & Logic. (Penguin); 1955: The Foundations of Empirical Knowledge. (Macmillan)
Coffa, J. A. 1991: The Semantic Tradition From Kant to Carnap. (CUP)
Hylton, P. 1991: Russell, Idealism and the Emergence of Analytic Philosophy. (OUP).
Hutto, J.D.D. 1992: “A Job For Philosophy” in Philosophy Now, No.4; 1993: “Foundations of Analytical Philosophy I: Early Analytical Philosophy” in Philosophy Now, No.8.
Russell, B. 1903: Principles of Mathematics. (Routledge); 1905: “On Denoting” in Logic & Knowledge (Routledge); 1918: “The Philosophy of Logical Atomism” in Logic & Knowledge (Routledge); 1924: “Logical Atomism” in Logic & Knowledge (Routledge); 1959: My Philosophical Development. (George, Allen & Unwin).
Schlick, M. 1932/33: “Positivism and Realism” in Erkenntnis III. (trans. Heath)
Wittgenstein,L. 1922: Tractatus Logico-Philosophicus (trans. Pears & McGuiness) (Routledge)