Wittgenstein's Picture Theory and Logical Positivism

Introduction

Welcome to the first lesson of our module on Logical Positivism. In our last lesson, we explored G.E. Moore's philosophy, which championed common sense and viewed philosophy's role as the analysis of ordinary language propositions we already know to be true. This was one major direction that early analytic philosophy took. Today, we turn to another, far more radical path, forged by Ludwig Wittgenstein.

Wittgenstein, a student of Bertrand Russell, was deeply immersed in the problems of logic and language that occupied both Frege and Russell. His first great work, the Tractatus Logico-Philosophicus, presented a stark, powerful, and unified vision of the relationship between language, thought, and reality. This book had a tremendous influence, particularly on a group of philosophers known as the Vienna Circle, who formed the core of the Logical Positivist movement.

Our learning outcome for this lesson is to explain Wittgenstein's 'picture theory' of meaning from the Tractatus and its influence on logical positivism. We will dissect his theory of how language hooks onto the world and see how this led him to draw a sharp boundary between meaningful discourse and what he considered nonsense.

1. A World of Facts

To understand Wittgenstein's theory of language, we must first understand his view of the world. He opens the Tractatus not with a statement about language, but with a statement about reality.

The book begins with the famous propositions:

1. The world is all that is the case.
2. The world is the totality of facts, not of things.

This is a fundamental departure from traditional metaphysics. For Wittgenstein, the basic components of reality are not individual objects (like chairs, trees, or electrons) in isolation. If you just had a list of all the things in the universe, you wouldn't have described the world. You need to know how those things are configured. You need the facts. A fact is the existence of a "state of affairs" (e.g., the fact that the book is on the table).

To delve into this foundational idea, which sets the stage for everything that follows, please watch the first part of the following video.

This metaphysical groundwork—a world composed of structured facts—is the reality that language must represent. The question then becomes: how can language do this?

2. The Picture Theory of Meaning

Wittgenstein's answer is the picture theory. In essence, a meaningful proposition functions like a picture of a possible state of affairs.

For a proposition to be a picture of a state of affairs, they must share a common structure. Wittgenstein argued that this works as follows:

1. Elements: The simple names within the proposition correspond one-to-one with the simple objects in the state of affairs.
2. Structure: The way these names are arranged in the proposition—its logical or grammatical structure—mirrors the way the objects are arranged in the state of affairs.

This shared structure is what Wittgenstein calls logical form. The proposition and the fact it represents must be isomorphic; they must have the same logical shape. Because your background is in mathematics, you can think of this as a kind of mapping that preserves structure, similar to an isomorphism between two groups or vector spaces.

Let's explore this theory in more detail. First, a high-level overview, and then a more granular explanation.

Now for a more detailed look with a helpful analogy.

A proposition has a sense if it pictures a possible state of affairs. It is true if that state of affairs actually exists (i.e., is a fact). It is false if that state of affairs does not exist, but is still possible. A string of words that does not picture a possible state of affairs has no sense; it is nonsense.

3. The Limits of Language: Saying vs. Showing

The picture theory has a dramatic consequence: it draws a very sharp limit around what can be said meaningfully. If meaningful propositions are pictures of facts, then the only things we can talk about are contingent states of affairs in the world.

So, what about logic, ethics, or metaphysics?

Wittgenstein introduces a crucial distinction between saying and showing.

• Saying: A proposition says that a certain state of affairs exists. It pictures a fact. This is the realm of natural science.
• Showing: A proposition shows its logical form. We can see the logical structure in the proposition, but we cannot say what that structure is with another proposition, because we would have to step outside of logic to do so.

Propositions of logic (e.g., "It is either raining or it is not raining") are a special case. They don't picture a specific state of affairs. A tautology like this one is true under all possible states of affairs. It doesn't exclude any possibility, so it doesn't "say" anything about the world. Wittgenstein calls such propositions senseless (sinnlos). They are not nonsense, but are empty of factual content. They show the structural properties—the "scaffolding"—of language and the world.

Propositions of ethics, aesthetics, and metaphysics, however, are another matter. They do not picture any possible state of affairs. A statement like "Murder is wrong" does not describe an arrangement of objects in the world. According to the strict criteria of the Tractatus, such statements are nonsense (unsinnig).

This leads to the book's startling conclusion. The Tractatus itself, being a work of philosophy, is composed of such nonsensical propositions. Wittgenstein uses the famous metaphor of a ladder: we must use the propositions of the book to climb up and see the world correctly, but then we must throw the ladder away.

The book ends with the final, cryptic proposition: "Whereof one cannot speak, thereof one must be silent."

The following reading from the Stanford Encyclopedia of Philosophy provides a dense and precise summary of these points.

4. The Influence on Logical Positivism

The Tractatus, with its sharp critique of metaphysics and its rigorous, logical foundation, was a revelation to the philosophers of the Vienna Circle (e.g., Moritz Schlick, Rudolf Carnap). They saw in it a powerful weapon to demolish traditional philosophy.

They embraced Wittgenstein's conclusion that metaphysical statements are nonsense. However, they interpreted his project through their own empiricist lens, leading to a crucial divergence.

• Wittgenstein's view: A proposition is meaningful if it pictures a logically possible state of affairs. Verification is a separate issue. For him, the "unsayable" (ethics, aesthetics, the mystical) was not trivial; it was profoundly important, something that could only be shown. As John Searle mentioned in the first video, Wittgenstein thought the most important part of his book was the part he left out.

• The Logical Positivists' interpretation: They fused Wittgenstein's logical framework with a strong empiricism. They argued that for a proposition to be meaningful, it must be, at least in principle, empirically verifiable. They interpreted "picturing a fact" to mean "corresponding to a possible experience." They had little patience for Wittgenstein's "mystical" realm of the unsayable; for them, if it couldn't be verified, it was simply meaningless garbage.

This reinterpretation gave rise to the verification principle of meaning, which became the central doctrine of logical positivism.

This final video clip explicitly addresses this influential, and arguably mistaken, interpretation of the Tractatus.

Conclusion

In this lesson, we have explored one of the most ambitious and influential theories in 20th-century philosophy. Wittgenstein's early work attempted to solve all the problems of philosophy at once by showing their linguistic nature.

Key Takeaways:

• The Picture Theory: Meaningful propositions are logical pictures of possible states of affairs. They are meaningful because they share a logical form with the reality they represent.
• Saying vs. Showing: Language can say how things are in the world (the domain of science), but it can only show its own logical structure.
• The Limits of Sense: This theory consigns traditional metaphysics, ethics, and aesthetics to the realm of nonsense, as their propositions do not picture facts. Propositions of logic are senseless because they are empty of factual content.
• Influence on Logical Positivism: The Vienna Circle adopted the Tractatus's anti-metaphysical stance but reinterpreted the picture theory through an empiricist lens. This led them to formulate the verification principle, which equates meaning with empirical verifiability, a position more radical than Wittgenstein's own.

Preview of the next lesson:

Having seen how Wittgenstein's work inspired the logical positivists, we will now turn our full attention to their central doctrine. In the next lesson, we will explain the verificationist criterion of meaning in detail and analyze its powerful use as a tool for attacking metaphysics. We will also begin to examine the serious problems this principle faces, including the famous objection that it refutes itself.