From 1900–1930, the greatest revolutions in physics since the 17th century had a manifold effect on philosophy: some thinkers came to take philosophy now to be the handmaiden of science; a few try to form their own scientific metaphysics; and many decide that the new science has become too abstract for philosophy to combine with human experience, and they turn against any attempt to incorporate science into philosophy. The most famous and most influential response is the first, which we call positivism. The logical positivists all embraced the first book of a young genius named Ludwig Wittgenstein. After briefly reviewing some of the new science, we will examine positivism and Wittgenstein’s early classic, his Tractatus Logico-Philosophicus.

Special relativity, general relativity, and quantum mechanics—the three great discoveries of the early 20th century—not only change the scientific view of the world, but essentially make a metaphysical picture of the world difficult to achieve. The special theory of relativity shows that there is no “ether” for light to propagate through—as it was believed necessary before that, that for any kind of electromagnetic radiation to propagate, it had to have a medium; but that seemed not to be true—furthermore, relativity showed that space and time are interdependent, they’re part of one phenomenon called space- time, and space-time measurements are relative to the movement of reference frames. There is no simultaneity at a distance anymore: Measurements of lengths of space and time are objective; they’re not dependent on our subjective experience, but they’re relative to the relations and relative velocities of what we measure and what we measure with.

General relativity expands these notions of special relativity and shows that space itself is altered by the bodies in it. This means that Leibniz was at least partly right in his argument with Newton; he wasn’t completely right because he thought (Leibniz thought) that space-time was internal to substances, whereas Einstein’s field equations in general relativity have vacuum solutions, meaning that there is space-time for Einstein’s theory of general relativity even where there is no matter or substance at all. Leibniz wasn’t all correct. The invariance of space-time measurements appear only in highly abstract mathematical formulae. But then there’s quantum mechanics: Quantum mechanics shows that the small components of matter do not behave like scaled-down versions of macroscopic material objects; they exhibit wave and particle features depending on our interaction with them. They do not have trajectories at all, and as individuals they are indeterministic. What we have now is on the one hand from special and general relativity; you have what you might call a very weird picture of the universe. On the other hand, from quantum mechanics, it seems likely that one can’t even picture what’s happening at the microphysical level.

The banishing of the ether and the substitution of relativistic formula for Newton’s laws seem to imply something else as well: that science does not try to know the ultimate underlying entities that cause observable phenomena but merely create mathematical models for predicting observable phenomena. Let me say a bit more about that: The way Einstein was interpreted by scientists was one thing, but the way Einstein was interpreted by philosophers was a little different; that is, philosophers of science were particularly concerned with the way he came to his conclusions, and it certainly appeared that what Einstein had done was to look at the observations and to change the picture of the physical reality to match the observations. In other words, experimental data showed that measured phenomena—for example, the velocity of an object in its time measurements would change as the velocity approaches the speed of light—didn’t make sense to anyone in terms of their picture of the real world, but the observation showed that it was true; the observation showed that there was no ether, so he banished the ether. The general picture that philosophers of science took from Einstein was that we should forget about trying to model or picture things themselves, and focus instead on explaining and predicting observations.

This meant that in a mathematical model—and all scientists, especially in physics, are employing mathematical models—the terms in the model do not need to refer to existences, they only have meaning in the sense of being placeholders that translate observations into predictions. In other words, the presence of a particular variable or a particular concept of an entity in a physical law needn’t imply that the entity really exists as something independent of the law; it merely has to make the equation work out in the end. This was one way of interpreting Einstein’s achievement.

This particular way of interpreting it was, in fact, the view of logical empiricism, or logical positivism. This movement was created by members of what was called the Vienna Circle: Moritz Schlick, Otto Neurath, perhaps most importantly Rudolf Carnap, and several others. They had been influenced by the earlier philosopher of science, Ernst Mach, and by what they took to be, as I said, the methodological implications of Einstein’s theory of relativity. Certainly the positivists disagreed with each other; they were each different philosophers with their own views. But they agreed more or less on the following, self-consciously revolutionary program, and it was revolutionary. For the positivists, all positive—and the term “positivism” and the adjective “positive” simply go back to Auguste Comte’s 19th-century work, it simply means empirical, dealing with empirical data—or empirical data, all knowledge of them, hence all knowledge of facts, come from sense experience narrowly construed, without theoretical additions. This is clearly a kind of empiricism. These statements of observations are supposed to be expressed in atomic statements, or “protocol sentences,” of the most primitive data we have.

Let me give you an example: We might in everyday life say—and even a scientist might say—when we ask, “What do I observe here?” I observe the lectern. But that’s not quite good enough for the positivist, because “lectern,” after all, is a term of everyday language. Suppose we brought in someone here who had never seen a lectern and we ask, “What are you observing?” They cannot say, “We see a lectern.” But what you and the person who has never seen a lectern before can agree on is you both see the color brown, you see an object this high, you feel something solid, you feel something with a certain texture. The protocol sentences—the sentences in the theory that actually state just what’s observed—would not say, “I observe,” or “a lectern was observed at a certain moment in time,” but rather, “A brown patch covering a rectangular object with high density was observed.” Calling it a “lectern” is not a primitive statement of the sheer data we’re receiving.

The theories of science exist to explain and predict the occurrence of such observations. The entities posited by the theories, as I’ve said, need not exist in themselves; they may only serve to facilitate predictions. The philosopher’s job is to produce a system of logic that can be used to construct such theories and justify their inferences. This is, in effect, an ideal, logical language, and it’s precisely what Russell and Whitehead had tried to formulate. What’s

happening is the positivists are trying to take advantage of the great logical revolution that started with Frege and was brought to a fairly high level by Russell and Whitehead; to take this new logic and use it now in science or to clarify science, particularly physics and what physics is achieved. All scientific claims should, in principle, prove to be reducible to claims about the most basic science, hence physics; in this sense, science itself should be unified. Perhaps we can’t do it yet; perhaps right now we’re unable to see how biological claims can be reduced to chemical claims, which can be reduced to physical claims. But in principle, we should be able to do that; so the positivists were also physical reductionists by and large.

Continuing our discussion of positivism, statements have meaning only in two ways, as I hope is clear by now: They have meaning as logical statements, which reveal logical structure; and as verifiable empirical claims about observations. In fact, verifiability—famously for the positivists—is the criterion of meaning, not merely of truth. Statements incapable of test or verification are simply meaningless. This is an enormous thing to say, because what the positivists took from this was simply that ethics, aesthetics, political philosophy, and metaphysics are meaningless uses of words. In a sense, you might say they’re going back to Hume’s old dictum: If you can’t show that it’s true logically or mathematically—in other words, through relations of ideas—and you can’t show that it’s true as matters of fact, which is now being interpreted as true in terms of the protocol sentences that summarize actually observed data, if it’s not true by those criteria then there’s nothing to be said at all; and it’s not something we can claim to be rationally true, although the positivists are going one better and saying it’s not even meaningful at all.

Carnap (one of the positivists) did, however, entertain what he called a “principle of tolerance,” and eventually accepted a bit of pragmatism; that is, he admitted that there is no one ontological language that is determined by sense data, but several. What does that mean? It means that in principle, if you were to gather up all the statements of observation we can about whatever is happening in the world and whatever scientists are experimenting on, it’s by no means clear that there’s only one theory of reality, one ontology, that would explain all those; there could, in fact, be several different types of ontologies, several different theories of reality. For example, on the one hand, an ontology of mere phenomena in Hume’s sense, just of sense data themselves; or on the other hand, an ontology of physical objects or events. They might hold equally well. So Carnap accepted that it might be the case that the data themselves in the form of protocol sentences did not singularly determine one ultimate metaphysically theory.

Last, before we move on in this discussion, I want to emphasize that one of the most crucial distinctions for the positivists remains the distinction between observation statements and theory statements. This is another example of a very old program in the history of philosophy—I’ve mentioned in earlier lectures—namely that even Aristotle thought that there must be some level of experience that essentially can’t be doubted; it’s indubitably true in the sense that it’s simply the shared data that we get from our senses. Then we may make errors when we interpret that. When you are driving on a long road and in the distance you see something by the side of the road, and you think you’re seeing a person; you get closer and you realize it’s a sign. The mistake was not that you actually saw a person instead of a sign, the mistake was that based on a very limited amount of data that you actually were receiving, and that was being caused by the object in the world that you were looking toward, you leapt to interpret that as something; it’s the interpretation that was wrong. In the same sense, positivism absolutely requires that we can separate statements of sense data—the facts, ma’am; just the facts—from any theoretical interpretation of it. We then try to pick the best, most reliable, most predictive theoretical interpretation, but we have to keep the two separate.

While the positivists were just starting up and gaining ground in Vienna, an odd thing happened. A young man from a wealthy Viennese family, born in 1889, had gone to Manchester, England, to study aeronautical engineering. But he found himself caught up in conceptual problems about the mathematics he was learning. He eventually read Russell’s 1903 book, The [Principles] of Mathematics, along with Frege’s book The Foundations of Arithmetic, and he became so obsessed with the questions of mathematical logic that he dropped his interest in aeronautics and engineering, and he decided to go to Cambridge to study logic with Russell in 1911. A year later, Russell said, this 23-year-old knew so much logic that Russell had nothing left to teach him. That was Ludwig Wittgenstein. In 1914, Wittgenstein enlisted in the Austrian army and saw action during the First World War.  

During his four years of service, he composed much of the only book that he would publish during his lifetime, his Tractatus-Logico Philosophicus.

I’ll just say in general something that’s useful, because we’ll be coming back to Wittgenstein later in the course. Wittgenstein is one of those philosophers, same thing is true of Heidegger, of which we typically speak of his early work and his later work; because while everybody’s work changes over the course of their lifetime—at least one hopes it hopes it does as they grow and mature—in Wittgenstein’s and Heidegger’s case, the later work is in some ways very different than the early work. In this lecture, we’re looking at his early work, his first book, the Tractatus, and the picture it presents. One might say that the Tractatus is an attempt to clarify—and this is a rather abstract way of putting it, but it’s probably the best way to put it—just what Frege’s Begriffsschrift (remember his new logic, his new logical notation) does and what it does not accomplish; in effect, the meaning of the new logic that Frege developed; that’s what Wittgenstein is after. While Wittgenstein’s work ultimately differed from the work of the Vienna Circle and hence the positivists in some significant ways, the circle looked on this book as a crucial, kindred achievement; so it’s perfectly appropriate to give our analysis of the Tractatus along with logical positivism.

What Wittgenstein did in the Tractatus—which, by the way, is a little book organized into, in effect, atomic statements; little statements that are numbered on the side—Wittgenstein analyzed all phenomena as states of affairs or facts; so everything we see in the world is a state of affairs. Language represents or “pictures” those facts, those states of affairs. So we have the states of affairs, and we have language. But then there’s logic: Logic gives language the structure that makes this representation possible. The logical forms of propositions match the logical form of the world. Logic is then the form that is shared by both the language that we use to describe the world and the states of affairs that are the world, and that’s what makes possible linguistic representation, or true representation. Some philosophers put it this way: How does language hook onto the world? The way language hooks onto the world, and hence has the possibility of being true, is that there’s an underlying form shared by both—the world, the states of affairs, and our language—and that’s the rules of language. The rules of logic reveal the scaffolding of language and hence of states of affairs.

Wittgenstein then made a bold statement: Logic is pure syntax, a structure necessary for meaning, but by itself is meaningless. As you know, when we speak in language, we not only say words that have meanings, but those words have to be organized in a specific patter or order or you get no meaning. Syntax is the pattern, the rules for structuring sentences. In the case of logic, Wittgenstein is saying logic is just pure syntax; it’s a structure necessary for anything to be meaningful. But that means—and Wittgenstein is thinking like a real philosopher here—if logic is the structure that makes meaning possible, that structure itself is meaningless, as he said; sinnlos, has no meaning. Logical truths, tautologies—for example, “all bachelors are bachelors”—do not say anything; rather, what he says, they show or exhibit logical form. This is Wittgenstein’s say/show distinction. The reason he’s saying this is he has to give a way to distinguish: If logic is the structure held in common by language that means and states of affairs that are meant, then logic can’t be like language; it has to be something else, and hence it can’t mean. But it has to do something; and so he says logic displays or shows structure, but does not say it. “Saying” is something language does.

The statements of logic that portray the logical structure are therefore sinnlos or meaningless; however, they are to be distinguished from metaphysical and ethical statements. Remember, the positivists say that ethical and metaphysical statements, and aesthetic statements—statements about values, and about things that can’t be observed—that these are meaningless. Wittgenstein here had another category of meaninglessness: Statements of ethics or metaphysics are not senseless, sinnlos in German, but rather they are nonsense, unsinnig; they don’t say anything, nor do they exhibit any logical structure, they neither say nor show.

Wittgenstein did not, however, think that ethics or metaphysics, or religion, was unimportant nonsense. In fact, he thought it was doubtless more important than science or logic, but it was still outside the bounds of rationality. It is das Mystische; the mystical. Wittgenstein is a remarkable figure in his early life, also in his later life; but in this remarkable book, he concludes it talking about the mystical. As he concludes his book, he finally says, “Whatever can be said, can be said logically. Beyond that, one must be silent.” For Wittgenstein’s perspective, whatever can be said can be said clearly. He thinks he’s displayed how it is that what we say can mean states of affairs because of the shared structure of logic; he’s shown that logic, by itself, of course, doesn’t say because it’s not language, but it does show; and yet he said that there are all sorts of other things in the world that we try to talk about, but there is no rational meaning to what we’re saying. But in that case, when we’re talking about ethics, metaphysics, and religion, Wittgenstein literally says, “Those are the most important things, but they cannot be discussed rationally.” He meant this quite seriously: Ethics and religion are far more important than logic, science, and philosophy of science, but there’s nothing we can say about them; they’re outside the realm of rational, meaningful speech.

In the succeeding 30 years, much important work was done by the positivists and their offspring. The fundamental features of positivism, we could say are the belief that science is the last word on fact; the empirical sciences, operating with a scientific method, are our best shot at understanding facts or states of affairs. Second, that all such facts ultimately reduce to the facts of physics; we may not be able to reduce them at this point in time, we may not know enough, but in principle they must be reducible to the most basic atomic facts, you might say, about physics; and that the observation language and the theoretical language of science must be kept strictly separate. The reason they must be kept separate is we want the data, the protocol statements that say what’s been observed at what time, that’s how we adjudicate between which theoretical statement is true or false. If the observation statements were mixed together with theory, they could not act as a fair judge of which theoretical statement is true; so these have to be separate. Lastly, what is the job of philosophy in all this? The job of conceptual clarification and the formulation of logic; metaphysics is pointless. From the point of view of the logical positivists, the proper aim of philosophy is to explain how science, mathematics, and logic work. These are the realms where we can talk about rational meaning and about fact, about truth about the world; and they’re inspired to do this by the great achievements in physics, really the unparalleled achievements, from 1905–1930. Outside the realm of science, philosophy really has no other role.

But one part of the scheme failed early; and that is even during the heyday of logical positivism. If you remember from an earlier lecture, the logicist project—started by Frege and which Russell and Whitehead tried to fulfill in their Principia Mathematica—was to derive all mathematics from simple logical notions. This project faltered, as I mentioned before, on the shoals of the paradoxes of set theory that Russell himself had discovered. In 1931, the great genius Kurt Gödel eventually showed that it was impossible for any logical system rich enough to include arithmetic—and that’s the kind of system that Principia Mathematica tried to portray—will not be able to prove all the statements made in it to be true or false, and not be able to prove that contradictions can never occur in the system. That’s a big problem: If our logical system could generate, if our language can generate the worst possible thing, the extreme form of falsehood, a contradiction; if we can’t prevent that, then the language has a problem in it.

Consequently, Gödel showed that the paradoxes of set theory that we talked about earlier with the barber of Seville in an earlier lecture were ineliminable. However useful advances in logic might be in serving to clarify philosophical arguments—and this should be mad clear, that usefulness is not in doubt; first and second order of logic remain for the rest of the 20th century ways by which many philosophers, analytic philosophers in particular, try to clarify arguments in order to then examine them. However, the attempt to form a complete logical language that would be self-enclosed and self- contained, that hope died in 1931 with Gödel. We cannot find a complete, ideal language.

As for Wittgenstein, on the last page of the Tractatus, he famously declared that the proper method in philosophy would be to say everything that “can be said,” meaning, say all facts as determined by the natural sciences; and then, he said the best way to teach philosophy would be to simply sit in the seminar room and wait until somebody said something metaphysical, and show them that their statement was nonsensical. In other words, there is nothing else for philosophy to do. This is how radical 20th century philosophy is becoming. In his mind, Wittgenstein resolved the only problems philosophy could resolve and showed that it could do nothing else. True to his word, at the height of his celebrated youthful fame, he felt he had solved the problems of philosophy that could be solved, the rest are completely unsolvable, they are mystical; and so he quit the university and found work as a school teacher.