13. Scientific Truth in the Early 20th Century 
With this lecture, we move into the 20th century. As I mentioned before, centuries, of course, are artificial periods of time. Nevertheless, we do have certain expectations. Doubtless for psychological and social reasons, we tend to think that centuries represent breakpoints and that something different happens in the 20th century, because it's the 20th century and it's no longer the 19th century, as if the century could exert some kind of influence on the events that take place in that century.

As a matter of fact, what we're going to be looking at, in the next lectures, is the shift in the treatment of the knowledge problem in science, as we've been calling it, from the 19th century, in which the problem was dominated by scientists seeing this as a problem for science that needed to be addressed by scientists, to a problem that was perceived to be a problem in science to be addressed by philosophers. So there is going to be a shift, although it doesn't occur, obviously, on January 1, 1900. There's a transition.

I'm going to be speaking in this lecture in particular about three figures—about the French mathematician and mathematical physicist Henri Poincare, the American physicist Percy Williams Bridgman, and the English mathematical logician Bertrand Russell. They will be placed in the line of thinking that we have been exploring throughout the 19th century, beginning with John Herschel and his revival of the Baconian theory of scientific knowledge.

You'll recall his colleague, William Whewell, and his sort of historicized-Kantian view of scientific knowledge as critically dependent upon fundamental ideas that are creatively invented by scientists and which anchor the deductive character of scientific knowledge;

Auguste Comte and his developmental theory of mind and of the way we experience the world and the way we conceptualize the world;

John Stuart Mills's enhanced version of inductive logic in order to anchor the objective reality of scientific knowledge;

Ernst Mach's phenomenalism, the view that the object of scientific knowledge is not the world at all, but our experience;

Pierre Duhem's conventionalist version of that reaching effectively the same conclusion, or a similar conclusion;

the physicist Heinrich Hertz's theory of scientific knowledge as essentially logically consistent but not giving us a picture of the reality behind experience.

Now, before adding Poincare, Bridgman, and Russell to this line of thought, I want to share with you what seems to me in the context of this course a rather delicious irony, and one which is very important in terms of revealing the nature of what we have been exploring—what will eventually erupt explicitly as the Science Wars in the 1980s and 1990s—the way that the knowledge problem is anchored in an empirical reality about science.

By 1900, science mattered to society in ways in which it had never mattered before. Science was no longer an intellectual curiosity or a prestigious intellectual accomplishment. By the early 1900s, science mattered to society in quite practical and concrete ways. Science in the second half of the 19th century had developed theories in chemistry and in physics, for example, and also in biology, that were creating wealth, power and prestige at the national level for nations and also for individuals.

Industry was increasingly seen as driven by science-based technological innovation. Think of the chemical industry in the second half of the 19th century with its invention of synthetic dyes, new kinds of pharmaceuticals, synthetic fertilizers, the first synthetic materials—Bakelite, for example—and the first plastics; in physics, the relationship of physics to emerging electrical industry technologies—the telegraph, the telephone, radio; new transportation technologies and the role that thermodynamics played in improving the efficiency and the power of internal combustion engines, for example.

Government increasingly saw science as providing both military power and economic growth, through its stimulation of technological innovation. In the public mind as well, all of a sudden, science and especially science-based engineering and medicine were, in the early decades of the 20th century, perceived as being very important.

Of course, as the 20th century advanced, science mattered more and more to society and continues to matter more and more to us in more and more complex ways. So, science in the early 1900s was recognized broadly as being important.

Now, what's ironic about this, is that what made science matter to society in the early 1900s, was a consequence of the theories of the 19th century, some of which we referred to in earlier lectures—the mathematical physical theories, the thermodynamics, the chemistry, etc.—that turned out to be pregnant with important applications that were literally transforming our lives and the world.

Yet the opening decades of the 20th century were also the time when radical new scientific theories were being formulated—the special theory of relativity, the general theory of relativity, quantum theory, genetics. Those theories were throwing out the 19th-century theories. That's the irony.

That is, science mattered because of the fruits, as Francis Bacon predicted, that suddenly were flowing from the "cornucopia of scientific knowledge"—that when we had knowledge of nature, we would have control over nature, and we have it and we're proud and we know that science now is knowledge of nature. That's happening at exactly the time when scientists are saying, "You know those 19th-century theories of electromagnetism and Newtonian mechanics? All wrong!"

This is an irony that should remind us of Fourier's move. You recall, Fourier in 1822 published his analytical theory of heat in which he explicitly separated the functional value or the functional correctness of a scientific theory, namely a set of equations that correctly described the way that heat behaves without making any statements whatsoever about what heat is ontologically, what it really is. Separate those two issues. Forget trying to identify scientific equations with a picture of the world and say, "Do the equations generate logical consequences that parallel what we experience of the world?"

So this move, whose echoes in mathematical physics, thermodynamics, statistical mechanics, and the kinetic theories of gases we've talked about in previous lectures, manifests itself in this irony here. It's that science was being productive for society based on theories that the scientists themselves were in the process of disproving as knowledge.

So, as we had done in an earlier lecture in which I asked the question, "From the perspective of the 19th century, what did the pioneers of modern science in the 18th century really know, where by know we mean having universal, necessary and certain knowledge of the external world, of nature, of the causes of experience?" We have to say that they didn't really know it. They had developed a set of ideas that in some important respects worked, but did not really qualify as knowledge.

Here we see the same thing about 19th-century theories seen from the perspective of the early 20th century. We are going to explore this transition in the next few lectures and the implications of these new theories, which are not improvements of 19th-century theories, as we shall see, but create new realities—redefine reality in deep and significant ways.

In this lecture, though, I want to focus now on Poincare, Bridgman, and Russell, as three thinkers who, in some respects are transitional, but represent three mathematicians and scientists; and in the case of Russell a mathematical logician, who developed important theories of scientific knowledge, sort of the tail end of that movement we've been tracing since the early 1800s in which scientists felt that it was necessary for them to address this problem.

Let me begin with Henri Poincare 1854-1912, who was quite an elegant French mathematician and mathematical physicist. He was a bit unusual in that he not only was a world-class mathematician, but also made important contributions to mathematical physics and even to problems in engineering and engineering mechanics. He did not have any highfalutin notions about pure science being somehow superior to applied science, as if, if you did pure science brilliantly, then you didn't bother with applied science.

So, he actually made a wide range of very profound contributions. There is something in mathematics called the Poincare Conjecture, which is extraordinarily subtle and complicated even to describe qualitatively, having to do with three dimensionality and the properties of three-dimensional space. He then generalized this to the properties of any dimensional space—that there would be certain features of any dimensional space that could be generalized based on what he had been exploring as certain so called topological features of three-dimensional space.

Though the Poincare Conjecture remained a conjecture of Poincare's—he couldn't prove it—he conjectured that this theorem was true. Attempts by mathematicians to prove it, had systematically failed over the 20th century. Then just at the very end of the 20th, beginning of the 21st century, a young Russian mathematician named Grigori Perelman, offered a proof of the Poincare Conjecture, which is being tested and seems to be definitive that it is, in fact, finally a proof. It's very important from the point of view of developing certain aspects of differential geometry and topology.

Poincare himself, wrote an essay that he contributed to a congratulatory volume on the 60th birthday of the King of Norway and Sweden. They were then the same country with a single king at the time. It's interesting that the king thought that to celebrate his 60th birthday, it would be nice to have a collection of essays written by prominent scientists and mathematicians!

Interestingly, this essay had an error that was just caught in time to be corrected before publication. In the paper, he actually had what is now considered the first-known mathematical description of chaotic motion and chaos, so he's somewhat a founder of chaos theory.

Poincare was deeply committed to philosophy of science as an activity that was appropriate for scientists. Poincare's philosophy of science was a very distinctive one. For Poincare—this is why I've emphasized his practical contributions to pure and applied science, as well as his genius as a mathematician—the only objective reality was what he called the "internal harmony of the world," and that mathematics was a convenient language for articulating the internal harmony of the world.

What does this mean, the "internal harmony of the world?" Think of the game of chess. In effect, the game is the set of rules. It has nothing to do with the pieces. The pieces can have any shape whatsoever, as long as they're marked so that you know which a pawn is and which a knight is, so which piece is permitted to make which moves, which are derived of course from the rules of the game. So you could play chess with human beings taking the place of plastic pieces or ivory pieces or carved aluminum pieces. They could be any shape you want. They don't have to be in the shape of a king or a queen, or a horse and a bishop. All that matters in chess are the rules that determine the internal harmony, using Poincare's language, of the game.

Analogously, Poincare said, that what we can know, what we mean by objective reality, is the internal harmony of the world that we experience. In order to explicate this internal harmony and to articulate it, we need to use mathematics, because it is the language of relationships. It is a convenient language.

Now, Poincare is often called a conventionalist, but there's a big difference between what he meant by a convenient language and to say, for example, that the concepts scientists use are conventional—that they somehow vote on how you should define what space means, what matter means. For Poincare, the convenience of mathematics is somehow related to the fact that mathematics, in fact, captures the patterns of the internal harmony of the world—that the rule-based behavior of the world is captured in mathematics.

So the word convenience for Poincare means that there's a closer relationship between the mathematical equations in science and the world, than is suggested by the term convention. The only objective reality is the internal harmony of the world. What makes it objective? According to Poincare, what makes science—scientific knowledge—objective, is that it is a shared conceptualization of experience. This is a very powerful and profound notion, which we are going to see echoed in later thinkers in the course of the 20th century and it telegraphs what scientists perceived as a radical conception of knowledge in the 1970s and 1980s, the notion that scientific knowledge is socially constructed.

Yet Poincare was among the most eminent of all scientists and mathematicians. For him, what made scientific knowledge objective was that it was based on a shared conceptualization of the world—not the only possible conceptualization of the world, but a description of the world that is based on a group of concepts that are shared by anyone who's willing to make the effort to adopt those concepts, and to use them along with mathematics in order to describe experience.

In Poincare's view, then, the object of scientific knowledge is not a reality existing independent of experience. The object of scientific knowledge is experience under a particular kind of description, namely a description under the shared concepts that the scientific community uses because they turn out to be convenient for describing the internal harmony of the world—for capturing the internal harmony of the world.

For Poincare, science is truth and science is knowledge, but not in the sense in which philosophers have thought of it as absolute truth—as knowledge that is uniquely true in capturing what reality is like out there behind our experience.

The second thinker that I'd like to discuss is Percy Williams Bridgman 1882-1961, born and reared in Cambridge, Massachusetts. He went to Harvard as an undergraduate and earned his bachelor's degree there. He went to Harvard for his master's degree and doctoral degree. His first job was at Harvard, and he stayed at Harvard, in 1926 being appointed a full professor of mathematics and "natural philosophy."

That latter term hung on in many elite intellectual institutions—as opposed to science, a professor of mathematics and natural philosophy. Bridgman was an eminent experimental scientist. He was famous for, and won a Nobel Prize in physics, for his researches on the behavior of materials at very high pressures and at high temperatures. For example, if you subject a metal to pressures of thousands of pounds per square inch, what will its electrical conductivity be like? What will its thermal conductivity be like?

In order to do this, he had to develop, in many cases, new kinds of equipment that would achieve extremely high pressure and sensors, in order to measure the physical properties of materials under these extraordinary conditions. The reason he won the Nobel Prize is that this turned out to be very fruitful. Both the instruments that he helped pioneer and the studies that he made, turned out to be very fruitful in scientific theory, but also in technological applications.

So Bridgman was a first-rate experimental scientist and he was also, as Poincare was, committed to the view that as a professional scientist, he needed to articulate a theory of scientific knowledge, which he did in at least two books, especially one called The Logic of Modern Physics.

Bridgman was deeply impressed by the role that measuring operations played in the special theory of relativity and the general theory of relativity. Einstein in inventing the special and general theories of relativity asked some very simple questions about how you would measure a spatial interval. How would you, at rest in your laboratory measure the length of a moving body? How would you measure that two events occurred simultaneously?

Now, it turns out that these were fundamental measurement operations for the special theory of relativity. In the case of the general theory of relativity, it had been an assumption of Newtonian mechanics that gravitational mass, which is what we call weight, and inertial mass, the resistance of a material object to moving—to being accelerated—that they are equivalent. They are always equal.

Einstein made that a principle of the general theory of relativity—that they are equivalent, the inertial mass and the gravitational mass. That was based on a generalization by Einstein, on a series of experiments by a Hungarian physicist named Eotvos, showing that to a high degree of precision, these two numbers were in fact equal.

Bridgman looked at the theory of relativity. He felt that Einstein's line of reasoning here, revealed something very important about science and scientific knowledge. It was that measuring operations are capable of causing us to re-conceptualize reality, what we mean by reality.

Bridgman developed a philosophy of science—a theory of scientific knowledge—that he called operationalism, in which the meaning of the scientific concept, is the set of operations that must be performed in order to measure that concept. Every concept, to be meaningful, must be translated into a set of operations that are specified for how you measure it.

So what does momentum mean?
What does velocity mean?
What do we mean by space?
What do we mean by time?

You have to flesh that out by telling me how do you measure spatial intervals:

How do you measure temporal intervals?
How do you measure momentum?
How do you measure velocity, etc?

The meaning of the concept is associated with the set of operations that you must specify in order to measure that concept.

From Bridgman's point of view, then, the object of scientific knowledge again is not external reality. It's not a reality that is independent of experience. It is the product. So the object of scientific knowledge is the result of a network of concepts that scientists use, most of which are operationally analyzed, some of which they never have time to analyze operationally—that are left ambiguous operationally. The result of using this particular network of concepts, defines what science is about. Science is about objects that scientists themselves create through the concepts that they use.

We're going to be exploring this idea in much detail in the course of subsequent lectures, so it will become clearer exactly what this means, but that's a very powerful notion—that the object of scientific knowledge is somehow created by the activity of doing science. We don't find those objects in the world, but rather, the scientific community creates those objects through the concepts that they use.

The third thinker is Bertrand Russell, an Englishman with a rather checkered personal history. He was the son of a viscount and his mother was the daughter of a baron. He himself ascended to the earldom in 1931. He held very strong political beliefs and activism right from the First World War through the Vietnam War.

Russell was a very important contributor to modern mathematical logic, and he was also one of the founders of a movement in philosophy called analytical philosophy. That is part of his legacy, because in the next lecture we're going to be looking in detail at Logical Positivism, one of the dominant approaches to the philosophy of science, the theory of scientific knowledge, in the middle 20th century.

Russell's philosophy of scientific knowledge was based on his absolute conviction that the key to knowledge was logic. So, unlike Bridgman and Poincare, for Russell, science is knowledge of the external world. Scientific knowledge has a deductive logically necessary universal character. It is capable of doing that because, according to Russell's view, the world is an ensemble, a collection, of atomic facts.

This is "atomic," in the sense that every fact out there in our experience—what we experience through our senses—contains what's out there in the world and they are independent of one another. We cannot take one fact and from that fact find its relationship to another fact. Relationships among the facts of experience are themselves facts. Logic—if you have the right logical language, you could write a set of sentences in this logically, perspicuous, transparent language, that would stand in a one-to-one relationship to the world because the world is a collection of facts.

The facts can be captured. Facts and their relationships can be captured in logical sentences, sentences in which the logical connectives are either truth or false. That's called truth functional connectives. So, every statement you make about the world is either true or false. If it's based on observable facts that can be compared with the sentences—with the content of the sentences—then you can have a description of the world—a picture of the world, if you will—that is decisive.

This approach to knowledge and truth, in which logic is the key to our descriptions of the world, to our logic, to our knowledge claims, was also fundamental to Russell's attempt in the early decades of the 20th century—which, in fact, is what made him initially famous, first with Alfred North Whitehead and then on his own, to reduce all of mathematics to logic.

This was the project that Gottlob Frege at the end of the 19th century was attempting in the case of arithmetic, and published a large work in which he claimed to have reduced arithmetic to logic. He was then working on another volume to reduce geometry to logic. So those are the two foundational branches of mathematics. If you could reduce both arithmetic and geometry to logic, then mathematics reduces to logic.

Russell sent Frege a note indicating that there was a fundamental logical flaw in his book on reducing arithmetic. Gottlob Frege had to acknowledge it and said, "Well, you know, there goes my life's work." The book was published in any event, but the effort clearly had failed.

Russell then thought that he could repair the flaw, and that he could figure out how to reduce mathematics to logic. This was a very important move, because at the end of the 19th century, questions had arisen about the nature of mathematical truth and knowledge. For Russell, if you could reduce mathematics to logic, then these questions were resolved, because logic is what we mean by knowledge and truth. Knowledge is logical knowledge. Truth is logical truth. So he was doing for physics, for physical science, the same thing that he had attempted to do for mathematics.

The project, after many volumes and a tremendous amount of work, was perceived to be a technical failure, but it was enormously rich because it founded 20th-century mathematical logic, in some respects, along with the work of Frege. Yet for our purposes, Russell's book Our Knowledge of the External World, in a semi-popular way contains the germ of what we call analytical philosophy—an analytical logical approach to philosophical questions, which identifies as a central feature of philosophizing, analysis of language. Because many philosophical problems, Russell claimed, are the result of not having a perspicuous language—of not having a language that minimizes connotation and equivocation.

So he caused, in a certain sense, philosophers—he and others in England especially in the early 20th century—to become very sensitive to the analysis of language—rather than plunging into solutions to philosophical questions, to analyze the terms that were being used carefully. This is indeed related to the analytical philosophy of science—the idea that if one could use a logically perspicuous language, one could capture these atomic facts about the world that our senses give us. Sense data is the name given to these objective inputs from the world.

So, if we pay careful attention to them and to their relationships, then we would be able to have a science that was about the world, not just about experience—that actually captured the world and its relationships. It would be a deductive system and it would, therefore, give us true philosophical knowledge and not merely summarize experience.

This, as I said, was an important influence on the movement called Logical Positivism, but we will see how this story becomes more complex and unfolds in the next few lectures.