The Critique of Pure Reason– A Summary

In a famous passage toward the end of the Critique of Practical Reason, Kant says that two things fill the mind with ever increasing wonder: the starry heavens above and the moral law within. Through Copernicus, Galileo, Newton and others, incredible progress had been made about understanding the "starry heavens above." But skeptical philosophers like David Hume maintained that the scientific success could not be extended to other areas such as theology or morality.

Hume said that what we see in the natural world might have all kinds of causes. Inferring a Creator, let alone a particular kind of Creator, goes beyond the evidence. In fact, the very concept of causality is merely a habit of the mind that we form by constantly seeing two things happening together. If we did not repeatedly observe that a billiard ball moved when hit by another billiard ball, we would not bring the two events in relation to each other. And we certainly would not be able to infer from the movement of the one ball that another ball had struck it, unless we have constantly observed the two together.

Likewise, we cannot infer anything about supposed metaphysical causes by looking at the physical world, because causal relations only form in our minds through repeated experience. But no one in his right mind claims, for instance, that he constantly observes God creating the world. God as a cause is inferred from the effect, but that is precisely what, according to Hume, we cannot do.

These and other thoughts by Hume awoke Kant, as he himself said, out of his "dogmatic slumber." Essentially, Hume raised in him the following questions:

1. Given what Hume said about causality, how can I affirm the validity of Newton’s physics, which is built on the concept of causality? What makes it possible for natural science and mathematics to give us apparently reliable knowledge of the world?
2. Why is it so difficult to make similar progress in metaphysical questions about God, the soul, free will, and morality? Is knowledge about these things possible at all? And if so, in what way and to what degree? Clearly, Reason itself compels us to ask these questions, but then Reason seems to be unable to answer them. Why is that?

In Kant’s long and laborious answer, laid out in his Critique of Pure Reason, he essentially harmonizes Hume with Newton. Science and mathematics are so successful, he says, because they only describe reality as it appears to us, not as it is in itself. Science only studies the world that we can touch, feel, see, hear, and smell—the experiences of our senses. Even with the aid of technology such as a telescope or, nowadays, a particle accelerator, we take in all scientific data through our senses. But the way that we experience our senses—the way our mind puts together what we touch, feel, see, hear, and smell—depends on certain forms in which our mind is structured. We cannot help thinking in terms of space and time, cause and effect, quantity and quality, modality and relation. These ways of thinking are what Kant calls a priori, that is, they come before experience. In fact, all coherent experience is dependent on them.

The problem of dogmatic metaphysics is that it pretends we can free ourselves from these necessary preconditions of our experience and get direct, unfiltered knowledge of ultimate reality. Not so, says Kant. Even space and time are not a reality that we perceive without a human filter. On the contrary, it is impossible for us to think of anything without picturing it in time and space. Space and time are, so to speak, mental cookie cutters. They are forms of the human mind that the dough of our experience has to conform to in order to experience anything at all. In Kant’s terminology, they are "forms of intuition" or "forms of sensibility."

Does that mean, then, that space and time are completely subjective and do not exist at all except in our minds? Do we live in some kind of illusory world, like in the Matrix? No, that would be to misunderstand Kant. Space and time are real for Kant. Objects do not merely seem to exist in time and space; they are in time and space. But since space and time are necessary concepts for any experience whatsoever, the concepts only apply to things as they appear to us. In what way and to what degree space and time apply to reality apart from our experience of reality, is unknowable to us. All we can say is they are necessary concepts for experiencing reality. Therefore, while all objects of our experience are in time, not all of reality must necessarily be in time as we understand it. While all objects of our experiences are in space, not all of reality must necessarily be in space as we understand it. On an ultimate level, reality might be quite different from the space-time framework from which we cannot free ourselves.

That is why, Kant thinks, mathematics and geometry have truths that can be definitely proven. They are about the necessary forms of all our experience, which is why they are internally coherent. Geometry takes place in space, and mathematics is done in time. Thus, they must conform to our a priori intuitions of space and time.

This makes arithmetic and geometry "synthetic a priori truths." "Synthetic" means that they are truths not merely about the meaning of words, which would be "analytic" truths, but about the real world. At the same time, however, these truths are a priori in that they are not based on our experience of the real world.

Kant’s conception of time and space as they relate to arithmetic and geometry is a good example of why he called his philosophy a new "Copernican Revolution." Just like Copernicus had reverted our understanding of the universe by proposing that it is us who move, even though it looks as if the sun moved, so Kant tried to show that it is really the structure of our minds that "moves" in a certain way and lets reality appear to us according to these "movements." Empiricists such as John Locke had thought that objective reality impressed itself on the blank slate of our minds. Kant proposed that it was the other way round: Our minds impressed themselves on objective reality. All our experiences of the outer world must necessarily conform to the a priori forms of our intuition and fundamental categories of our understanding. If Locke and Hume had been right, all our ideas about the world would arise as a result of our experience. They would come "after" experience, a posteriori. In contrast, Kant thought that a priori knowledge—knowledge prior to experience—was possible, namely the knowledge of the categories of our understanding to which our experiences conform.

Kant divided these categories as follows:

1. Quantity: unity, plurality, and totality.
2. Quality: reality, negation, and limitation.
3. Modality: possibility, existence, and necessity.
4. Relation: inherence, causality, community, and correlation.

While there was nothing particularly new about this list as such, as Aristotle and the Scholastics had already made similar categorizations, the revolutionary move on Kant’s part was to say that they are a priori: that they precede experience and are necessary conditions for it. In the longest and probably most difficult part of the Critique of Pure Reason, called the "Transcendental Deduction of the Categories," Kant tries to prove that these categories are in fact a priori.

Having, in Kant’s mind, provided this proof, he is now ready to answer his initial questions more explicitly. (1) What makes it possible for natural science and mathematics to give us apparently reliable knowledge of the world? (2) And why is it so difficult to make similar progress in metaphysical questions about God, the soul, free will, and morality? The answer is that science, arithmetic, and geometry stay within the framework of what is possible for us to experience—a framework that is set by the forms of intuition and the categories of the understanding. This is why science is so effective, but it also means that science is limited. It shows us only the “phenomenal” world, not the “noumenal” world. That is, it only shows as the world as it appears to us, not as it is in itself. The world as it is in itself is the realm of metaphysics, and this is why we cannot give scientific answers to metaphysical questions.

The last third of the Critique of Pure Reason attempts to show, as Robert Kane has put it, “how we get into trouble when we try to press the human mind beyond possible experience into the realms of metaphysics.” Take the existence of God, for instance. Trying to prove his existence has failed, Kant says, because such proofs take the categories of the understanding that only apply to the physical world of appearances and impose them on matters that exceed the bounds of our possible experience. We cannot infer what caused the universe to come into existence based on our way of thinking, because our way of thinking is only fitted for inferences about the physical world of appearances.

Or take the soul. We cannot, Kant stresses, know the soul as such, only the self as it appears to us—our “phenomenal” self, not our “noumenal” self. We do not and cannot know what the soul is in itself, apart from the way our sense of self appears to us. Neither can we say anything of scientific certainty about the mortality or immortality of the soul. We may have faith and hope in eternal life based on what Kant calls “practical” Reason, but not scientific certainty.

Nor can we scientifically resolve the conflict between determinism and free will. Science is based on the view that everything works by determined laws, but our understanding of morality is based on the view that we have free will. Without the concept of free will, none of our moral practices would make any sense: no commands or punishments, no blame or excuses, no forgiveness or justice. But how can we reconcile the determined world of science with the free world of morality? Science itself cannot resolve this contradiction, says Kant. It cannot be resolved by “theoretical” Reason, only by “practical” Reason.

And it is this practical Reason that Kant tackles in his second Critique, the Critique of Practical Reason.

Is Enlightenment Totalitarian?

In their book Dialectic of Enlightenment, Theodor Adorno and Max Horkheimer make the startling statement that “Enlightenment is totalitarian.” Now one may ask if they are committing a category mistake when calling the Enlightenment, science, technology or even the whole Western philosophical tradition “totalitarian.” Do they misapply a political term to non-political entities? After all, only because there are banana republics, it does not follow that there are Republican bananas.

Well, first of all one has to realize that the term totalitarian was still quite new when Adorno and Horkheimer penned their work in the 1940’s. It was invented a mere twenty years before to differentiate Italian Fascism from traditional dictatorships. Prior to the rise of science and technology, dictatorship were never able to achieve total control, total guidance, or total representation of the people. Caligula was an insane despot, no doubt, but most people throughout the various provinces of the Roman Empire felt little effect of the succession from Tiberius to Caligula to Claudius. Rome and other older dictatorships were not modern police states with the technological capability to achieve the total union of a totalitarian state. Therefore, it is precisely the scientific and technological aspect of 20th-century dictatorships that demanded a new term like totalitarianism. I think Adorno and Horkheimer recognized this, plus, the term still being new, the meaning was perhaps more flexible than it is now.

Still, one might say that this does not make science and technology in itself totalitarian as we understand the term today. But in the very least, one has to admit that they were a necessary precondition for totalitarianism. Enlightenment and the resulting Industrial Revolution were the magic wand that turned old-fashioned dictatorships into totalitarian states. There is a close connection between the two.

Adorno and Horkheimer, however, would definitely not be satisfied with as small a concession as this. Their critique is much more fundamental, and, if true, much more devastating. In fact, they are even willing to say that their own critique of calling the Enlightenment “totalitarian” is rubbish—because this critique, too, is voiced from within the Western tradition, and Auschwitz has shown, they maintain, that the whole Western tradition is rotten at its core. Perhaps they would even admit that, on strictly linguistic terms, their use of “totalitarian” is not quite accurate. But what are we in the West to do? We cannot pull ourselves up by our own hair; we can only scream somewhat incoherently that we are stuck in the mud.

“Auschwitz,” writes Adorno in his Negative Dialectic, “has demonstrated irrefutably that culture has failed. That it could happen in the midst of the philosophical traditions, the arts and the enlightening sciences says more than just that these failed to take hold of and change the people. The untruth lives in those very categories, in their emphatic claim of autocracy. All culture after Auschwitz, including its urgent critique, is rubbish.”

I think Adorno might sadly laugh at someone calling his use of language a category mistake. He might say: “Don’t you get it? I’m questioning the whole Western tradition, and because I am part of this tradition, I think that my own critique is rubbish as well.”

How can someone come to such a devastating conclusion about his own cultural heritage? In a word, through the Holocaust, whose deathly sting was no doubt felt much more sharply by German Jews of the period, such as Adorno, than by us nowadays. But even we have to admit that universal education, which was the chief goal of the Enlightenment, was not able to prevent the rise of totalitarianism in Europe. The great masses of people in Europe were better educated than ever before in the history of the world, many receiving a classical education based on the Great Books, and yet they were swayed to participate in Fascist regimes and murder millions of innocents.

How did the people of the Dichter und Denker (poets and thinkers) turn so quickly into the people of the Richter und Henker (judges and executioners)? Otto Thorbeck, the SS judge who condemned Dietrich Bonhoeffer, had received the same classical education as Bonhoeffer, read the same Great Books of the Western tradition that I like to read. But apparently he saw nothing in those books that kept him from doing what he considered his duty, whereas Bonhoeffer felt it necessary to resist. Alas, there were too few Bonhoeffers in Germany at the time, though there were millions of enlightened and educated people. It is surely no coincidence that one of the greatest philosophers of the 20th century, Martin Heidegger, was a Nazi who never disavowed his Nazism, even after the war.

Obviously, pre-WWII thinking was not adequate enough for preventing the Holocaust, and, Adorno and Horkheimer believed, one of the chief aims of ideologies after WWII should be to prevent such a ghastly event from ever happening again. The main objective of many German philosophers since WWII, most famously the Frankfurt School and offsprings of the school such as Jürgen Habermas, has been to create a framework of thought in which totalitarian tendencies would be resisted at their very root. As Adorno writes in his Negative Dialectic: „Having robbed them of their freedom, Hitler has imposed a new categorical imperative on people, namely to construct their thoughts and actions in such a way that Auschwitz would never happen again, that nothing similar would ever occur.”

How to construct such thoughts and actions? That is the big question, though I don’t think that Adorno necessarily arrived at a definite answer. He primarily pointed out the failure of the Western tradition, including—or even especially—its philosophy and science.

The original project of philosophy has been to understand reality—without limits. In a lecture entitled “Philosophizing after Auschwitz,” the German contemporary philosopher Wolfgang Welsch asserts that Western philosophy, at its root, wants to understand the whole of reality. It is totalitarian in the literal sense of the word; it wants to encompass the total, and as long as it has not achieved this, it keeps striving toward it. It does this by creating a system of thought that encompasses everything, a one-fits-all method. Anything that does not fit or seem to fit into this system is being explained away, pushed aside or deemed unimportant.

Welsch compares this to Poseidon’s son Procrustes in Greek mythology. Procrustes made an iron bed of a certain length, and the guests that stayed in his house were supposed to fit exactly on the bed. If some guests were too big for the bed, he cut off parts of their legs to make them fit, and if some were too small, he stretched them.

Now if it is true that the attempt to understand the whole of reality with one single method (such as the scientific method) inevitably leads to the exclusion of certain parts of reality, then there seems to be a structural similarity between science and totalitarianism. Just as totalitarianism attempts to fit all people into a single political system and annihilates everything that does not fit, likewise science attempts to fit everything into a single method and disregards everything that does not measure up to that method.

Perhaps it is wrong to say that therefore science is totalitarian, but a case could be made for both science and totalitarianism being Procrustian.

Thus, according to postmodern critics, Western philosophy and science are marked by megalomania. They are head over heels in love with the idea of greatness in one form or another, and this love blinds them. Like the French philosopher André Glucksmann writes in his book Les maitres penseurs (“Master Thinkers”): Even though you cannot say that leading philosophers like Fichte, Hegel or Nietzsche are the direct cause of the Holocaust, nevertheless they made people non-resistant to totalitarianism because they were too much in love with the idea of Greatness.

People influenced by the Western tradition are often eager to jump on the bandwagon of anything “great,” quite irrespective of its moral worthiness. As long as it’s great and gives us a feeling of being part of something momentous, we are game. Like Dorothy in Middlemarch, we are willing to marry the otherwise unfit Mr. Casaubon, because we think that his obsession with finding the one key to all mythology will give us a sense of being part of something great. That is a dangerous tendency, and philosophy after WWII should caution people against it.

This divorce of greatness from the checks and balances of values is another aspect that Wolfgang Welsch points out in his lecture. It is called instrumental rationality. Instrumental rationality is the kind of use of reason that does not ask what something is ultimately good for, but merely looks for the most efficient way of achieving … well, of achieving what? Anything one wants. The goal is a blank that may be filled in by the strongest. Instrumental Reason focuses on how to get things done, but does not spell out what it is that ought to be done. It is Reason devoid of a teleology and an axiology.

And, as Horkheimer and Adorno write, the nature of such knowledge is technology. Technology becomes ever more efficient, but efficient for achieving what? It is pure power, which is very dangerous if devoid of good values. Technology wants to make everything faster, better, and more powerful. Worries about what those technologies might be used for come too late—usually in the form of regret rather than wise foresight. The Holocaust is a stark example of Instrumental Reason being employed for a highly unworthy goal.

Thus far Horkheimer, Adorno, Welsch, and Glucksmann. I still haven’t gotten around to saying what kinds of questions I find most worthwhile considering from these people, and I am much more hesitant to damn the whole Western tradition than Adorno, but I think I have an inkling of how Jewish German thinkers during the Holocaust would arrive at such conclusions. Whether or not I was able to communicate my inkling is another matter.

Is William James’ Pragmatism Different from “Saving the Appearances”?

In my last two posts, I talked about William James’ Pragmatism in relation to religion. But it could also be applied to science. The Pragmatic conception of scientific theories would be that they “work.” They cover the empirical data, but they might still not be true in a more objective sense. If a theory no longer “works,” it has to be abandoned for another theory.

Now I am wondering whether this Pragmatic conception of scientific theories differs at all from the ancient conception of “saving the appearances”? The Neoplatonist Simplicius (c. 490-560) writes that Plato instructed his students to “save the appearances” of the seemingly irregular planetary motions by coming up with the simplest possible hypothesis of regular motion that would explain the observed motions. Whether or not the hypothesis is true on an ultimate level is another question, but it is an approximation to truth because it is the simplest possible hypothesis that “works” with the observed data.

Like I discussed here, one contention between Galileo and certain Church leaders centered around their respective correspondence theories of truth. Galileo, it can be argued, was a “naïve realist” who thought that the Copernican system revealed absolute truth, whereas some of the Church leaders had a correspondence theory of truth closer to James’ Pragmatism, at least when it came to science. The Copernican system “worked.” It saved the appearances. But so did the system of Tycho Brahe. At the time, both systems worked equally well. They both saved the appearances. Therefore, Galileo chose the Copernican system for subjective reasons. As James said, “Our theories are wedged and controlled as nothing else is. Yet sometimes alternative theoretic formulas are equally compatible with all the truths we know, and then we choose between them for subjective reasons.” The mistake that Galileo made was not to admit the subjectivity in his choice.

My main question is: Does James introduce any new thought to the concept of “saving the appearances,” or is it basically just a rehashing of an ancient idea?

Leibniz: Why Did We Stop Asking Why?

The Greek philosopher Aristotle (384 – 322 BC) believed that there were four kinds of causes:

1. A material cause (the laptop on which I’m writing consists of certain matter, and in that sense the matter is the cause of my computer’s existence)
2. A formal cause (my laptop has a certain shape and form)
3. An efficient cause (a certain company has made my computer, using various technologies to do so, and this “art of computer-making” is the efficient cause; the “how”)
4. A final cause (that for which the computer was intended by the company, namely for me to sit here and write this post; the “why”)

Now I recently read the Discourse on Metaphysics by Gottfried Leibniz (1646 – 1716). In it, he laments the fact that Newton and his followers (“our new philosophers”) decided to banish all discussions of final causes from “Physics” (more or less equivalent with what we now call “science”). Newton famously said, “I will not feign a hypothesis,” by which he meant mostly that he would not try to explain why gravity exists, but only concern himself with how it worked.

This decision to limit science to the question of how and excluding the question of why is still with us today—quite to the dismay of Leibniz, I think, if he were alive. He would ask: “Why do we stick with this decision to banish final causes from scientific discussions? Let’s bring them back in. Explaining efficient causes is good. Let’s retain that. But explaining final causes is also good. Why did we throw them out? The best plan would be to join the two ways of thinking.”

What do you think? Was Newton right to banish final causes from science, or should we attempt to bring efficient causes and final causes together, not just in religious and philosophical discourse, but actually in science? I am inclined to think that science should confine itself to the “how” questions, but it’s not a conclusion one should reach lightly.

Hand-Drawn Video: Explaining Einstein (lots of fun!)

I couldn’t resist indulging my creative self during the Christmas break, starting on a hand-drawn video that explains Einstein’s Special Relativity. It will probably take a while to complete it, but I’m done with the first quarter now. Here it is, a work in progress:

Newton’s Greatest Achievement

Among Newton’s many achievements was the invention of calculus. However, when he wrote his groundbreaking Principia, he did not present his revolutionary theories in the form of calculus but in the form of Greek geometry. Why did he do that? Wasn’t calculus more adequate for what he was trying to say?

The reason might have simply been this: Since Newton had just invented calculus in order to come up with his calculations, it was not yet well known as a mathematical language. And among those familiar with it, calculus was not yet very reputable (to say the least). Not wanting to unnecessarily confuse his readers or put them off, Newton therefore chose to present his findings in the well-established language of classical geometry. He wrote the Principia twenty years after his eureka experience; it was a book to present his findings to the public, not a notebook of his actual work.

Some people, though, see greater significance in Newton’s use of ancient geometry, pointing out that he was obsessed with everything ancient. For instance, he thought that Jesus Christ had come to restore the true religion of Noah. He might have used ancient geometry, the thinking goes, because he considered it a more adequate vehicle for truth.

Perhaps. But I doubt that Newton’s belief in ancient truth (and the more ancient, the truer) was the reason for using Greek geometry in the Principia. In fact, I don’t think Newton had to have a reason at all. There was simply no good reason for using calculus; ancient geometry was still pretty much the only game in town, or at least the default. And you don’t need to have a reason for using the default.

Nevertheless, Newton was steeped in antiquity. Just like he thought that Jesus wanted to recover the true religion of the ancients, Newton thought he was merely rediscovering what had been lost to natural philosophy. He did not think that he was coming up with anything particularly new, only restating what had been known in antiquity.

Maybe that is why he considered his lifelong celibacy his greatest achievement instead of such inconsequential ideas as, say, gravity or the nature of light.

What is Science? What is Pseudoscience? Karl Popper’s Solution

In several of my recent posts, I have been discussing the question to what degree science reveals reality. But an even more fundamental question is: “What is science?” It is somewhat ironic to discuss particular achievements or difficulties of science if we are not even clear on what exactly science is. For instance, some confidently assert that (Super)string Theory is not science, but obviously the proponents of the theory would not agree.

So, what distinguishes science from a pseudoscience? In this post, I asked whether Freud’s psychoanalysis really was a genuine science, as he strongly asserted. But I am not the only one who asked these questions. People with far greater expertise have wondered about what exactly it is that distinguishes a genuine from a counterfeit science. One of these great minds was Karl Popper.

In what follows I heavily rely on Jeffrey L. Kasser’s treatment of Popper and the attempt to determine the demarcation line between science and pseudoscience. Go here if you want to get more from Kasser on the philosophy of science.

Karl Popper was especially interested in Einstein’s theory of relativity, Karl Marx’s theory of history, and the psychological theories of Sigmund Freud and Alfred Adler. It was widely believed at the time that the work of Marx, Freud, and Adler was genuinely scientific, but Popper became disenchanted with such theories. He, instead, argued that Einstein’s theory was distinguished from those of Marx, Freud, and Adler by its openness to criticism. This provides the key to Popper’s solution to the problem of demarcation.

Popper’s emphasis on criticism stems from his rejection of the most straightforward criterion of demarcation, according to which scientific claims are special because they are confirmed by observational evidence and because they explain observations.

Kasser explains Popper’s view that pseudosciences, such as astrology, are chock full of appeals to observational evidence. Hence, Popper thought, observation is cheap. It is essentially interpretation of experience in terms of one’s theory. The pseudoscientist finds confirming evidence everywhere (for example, in the many case studies of Freud and Adler).

Furthermore, apparent counterevidence can be turned aside or even turned into confirming evidence by a clever pseudoscientist. Freud and Adler had ready explanations for any observational result. For Popper, no evidence falsifies a pseudoscientific claim and almost everything confirms it. As a result, Popper came to see the two standard virtues of scientific theories as explanatory power and confirmation by a large number of instances as closer to being vices than virtues.

Fitting the data well is, thus, not the mark of a scientific theory.

What, then, is the mark of a good scientific theory? According to Popper, a good scientific theory should be informative, surprising, and in a certain sense, improbable.

Popper saw Einstein’s theory of relativity to perfectly exemplify these three criteria for genuine science. General relativity led to the surprising prediction that light would be bent by the gravitational field of the Sun. It was a great triumph when Arthur Eddington’s expeditions verified that light was bent by the amount that Einstein had predicted. For most observers, what mattered was the fit between Einstein’s predictions and the evidence, but not for Popper. What mattered to him was that the theory had survived a severe test. The mark of a genuinely scientific theory is falsifiability. Science should make bold conjectures and should try to falsify these conjectures.

I could end my post here, but Kasser goes on to stay that though Popper’s theory is admirably straightforward, it nevertheless requires some clarification. First, Popper generally writes as if falsifiability and, hence, scientific standing come in degrees. This suggests, however, that pseudosciences differ more in degree than in kind from genuine sciences. Second, Popper’s theory is both descriptive and normative, i.e. he claims both that this is what scientists do and that it is what they should do. Third, Popper is not offering a definition of science but only a necessary condition. He is not saying that all falsifiable statements are scientific but only that all scientific statements are falsifiable. Falsifiability is a pretty weak condition. Fourth and last, to call something unscientific is not to call it scientifically worthless.

To elucidate the fourth point, Popper thought that Freud, Marx, and Adler said some true and important things, even though he considered their theories unscientific. Furthermore, Popper maintained that metaphysical frameworks, such as atomism (which was not testable for centuries after it was proposed), can help scientists formulate testable hypotheses. Popper even thought for awhile that Darwin’s principle of natural selection was an ultimately unscientific doctrine. He later changed his mind about this, arguing that the Darwinian claim about survival of the fittest is not a mere definition of fitness (and, hence, unfalsifiable) but instead implies historical hypotheses about the causes of traits in current populations.

So far, then, Popper’s views. On to the criticism. Critics of Popper pointed out that statements such as “There is at least one gold sphere at least one mile in diameter in the universe” do not seem to be falsifiable on the basis of any finite number of observations, but they do not seem unscientific either. More important, statements involving probabilities appear unfalsifiable. A run of 50 sixes in a row does not falsify the claim that this is a fair die. Another criticism is that Popper does not adequately distinguish the question of whether a theory is scientific from the question of whether a theory is handled scientifically. Are theories scientific in themselves or only as a function of how they are treated?

Also, there have been several theories in the history of science that at first seemed to be falsified by observed results. But due to the perceived internal coherence of the theory, scientists persisted to experiment until they finally found confirmation for their theory. Should theories be abandoned at the first apparent falsification? This seems to be too rash.

If falsification rather than confirmation is the mark of science, should we accept the idea that being highly confirmed and having wide explanatory scope are not virtues of a scientific theory at all? Was it not a striking feature of Newton’s physics that it could explain the tides, planetary motion, and so on?

Thus, it is not exactly clear how Popper’s view should be expressed: Is it about the logical form of scientific statements or about the way they are treated by their advocates? However it is formulated, it is not clear that it provides a necessary condition for science.

(Super)string Theory: A Purely Mathematical Science

In 1959, the physicist Eugene Wigner published an essay on "The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” That is indeed one of the great wonders of the universe: that mathematics, which at first sight seems to a be a purely theoretical human invention, should correlate so closely to the actual world.

Superstring Theory is a good example of a current scientific endeavor that is purely mathematical. The theory tries to examine the nature of matter on a sub-atomic level, much smaller even than quarks. The problem is that we have (yet) no instruments to examine that level empirically. But given the “unreasonable effectiveness of math” in the past (such as in Einstein’s case), some scientists are confident that they can gain knowledge about the sub-quarkian level by purely mathematical reasoning. The result: (Super)string Theory.

Scientists even produce computer-generated images of their “findings,” even though they are based on nothing but mathematical deductions. So confident are some people in the effectiveness of math that they are willing to invest millions of dollars to build instruments that might eventually confirm the math more empirically.

I am not qualified enough to make any value judgment on the theory, but as someone interested in the philosophy of science, it seems that these forms of contemporary science are much closer to Descartes’ deductive method than to Bacon’s inductive method.

Science: A Constant March Forward or a Repeated Reversal?

Last month, I wrote a few blog posts inspired by a teaching course on the philosophy of science. The lecturer was Prof. Stephen Goldman. A correspondent of mine had also listened to the course and thought that Goldman was too much of an anti-realist in his position, i.e. that Goldman was too pessimistic about the ability of science to let us know reality. In defending the success of science, my correspondent compared the scientific project over the past few hundred years to a map of the world that has become ever more accurate.

This is (part of) what I wrote in reply:

Hi …,

I have been pretty distracted myself in the past weeks, getting lost in my spare time on Mann’s Magic Mountain, in Goethe’s Walpurgisnachtstraum and on the adventures of Don Quijote, among other things.

All right, then, back to more prosaic—though not any less interesting—endeavors …

First of all, a word in defense of Goldman. If I only read your descriptions of him, I would think him much more of an anti-realist than the impression I got from him by listening to his course (but perhaps my impression was wrong). Don’t you think that he mostly describes the history of scientific realism and anti-realism? I did not think that he constantly laid out his own position, and when his position did come through, it seemed to be an attempt to live in the tension between the two. What Goldman did contend was the claim of some scientists in the past to give us necessary, certain, and universal knowledge, while the history of science clearly shows that scientific knowledge is always contingent, revisable, and particular. I did not feel that Goldman himself defined all knowledge as necessary, certain, and universal; rather, he criticized those who have done so. That is why Goldman frames his whole course within Plato’s analogy of the gods vs. the earth giants. Only the gods can give us universal knowledge. Science, by its very nature, is a project of the earth giants. Man might not be the measure of all things, but in science, he (or she!) is the measurer of all things. And since humans themselves are contingent, particular beings, their measurements will also be contingent and particular rather than universal.

So it is not the case that science does not give us any knowledge; it is a question of what kind of knowledge science gives us. To put it differently, it is wrong for science to claim that it gives us something akin to divine revelation about nature (“Nature and nature’s laws lay hid in Night. / God said, ‘Let Newton be!’ and all was light”). Unlike what many post-Newtonian scientists and deists have thought, Nature is not the new Bible and the examiners of nature are not the new Priests.

Is the map a good analogy for the kind of knowledge science gives us? In some respects, I think yes. (By the way, does not Goldman himself use the analogy of the map, or have I heard/read that example somewhere else?) The map is an excellent analogy for the fact-gathering aspect of science. Take the many amazing facts we know about the human body, for instance. Here is a list of 22 of them that I made the other day.

All these things are fact, and the scientific project since Bacon should be applauded for uncovering them. I heartily do so. I love reading my children’s big Factopedia and marvel at everything science has found out in the last few hundred years. The facts on our “map” of the world have become ever more detailed and exact.

However, when it comes to the theoretical framework that puts all these facts together, the metaphor of the map breaks down. The revolution in physics in the early 20th century did more than just confine Newton to the realm of human experience; it completely altered our conception of time and space, and time and space are not exactly side issues. They are the most fundamental building blocks for our thinking. Without picturing time and space, no conception is possible. When we try, like Descartes, to think the most basic thought possible, namely “I think, therefore I am,” what we really think is “I think, therefore I am in some kind of time and space.” We think that our thoughts relate to each other in a time sequence, and we think that the “I” exists in some kind of space. We cannot imagine anything without reference to time and space. And now, in the last century, these conceptions have been changed! This is not a mere addition to our map of scientific details; this is an entirely new map! It’s as if we thought that we had a map of Venice, when in fact it was a map of Florence. We are in a different town now.

The same goes for the shift from direct creation to evolution. To think that incredibly intricate complexity can arise out of utter simplicity is not a simple add-on to a map; it’s a reversal of our thinking, a 180-degree turn of our premises. Evolution gave us a new map.

Given that these new maps of scientific theory have been laid in our hands repeatedly in the scientific process, it is not unreasonable to suppose that this will continue to happen, even while we gather many facts that will remain indisputable for ages to come.

As an example of how radically our picture of reality might change in the future, a few years ago I read a thesis by some (wacko?) physicists who hypothesized that we live in fact on the inside of a sphere and that the universe that we see is a projection into that sphere. I don’t believe any of it, and I do not remember now how he explained the obvious objections to his hypothesis, but it goes to show that radically different theoretical frameworks can arise and supposedly explain the facts.

In summary, I’d say that:

1. The fact-gathering aspect of science can be very well described as a map that becomes ever more accurate.

2. The big theoretical frameworks of science (sometimes? most of the time? always?) come about by paradigm shifts that give us a new map to draw on.

In addition, I would like to differentiate between description and comprehension, as well as between ontology and, for lack of a better word, observability.

1. Description and comprehension: Only because we can scientifically describe reality, it does not yet mean that we have comprehended reality. Description does not equal comprehension. In fact, the more elaborate the description, the better it masks our possible lack of comprehension.

2. Ontology and observability: Only because we can scientifically observe reality, it does not mean that we know what the thing observed actually is. What is matter? What is energy? What is magnetism? We can observe them. We can describe what we observe. But we never get quite to the ontological level of things. Or do we?

These two differentiations are of course related and could probably be expressed in a single point, which I am too lazy to attempt now.

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Was Newton Wrong?

Francis Bacon had little room for human creativity in the scientific method. He thought that the right method would make genius obsolete. But if there is anything that Newton has shown us, it is that genius has remained as essential to the scientific process as ever. Put somewhat simplistically, the genius of Aristotle ruled until the genius of Newton came along, and the genius of Newton ruled until the genius of Einstein came along, and now Einstein rules until the next genius comes along.

So, Newton did not strictly employ the Baconian method. It is sometimes assumed that he did—that he was a firm Baconian and anti-Cartesian (that is, opposed to Descartes). But it can be argued that his method was much more indebted to Galileo than to Bacon, though his assumptions were very different from Galileo’s. That raises the question again whether scientists discover truths about nature or whether they construct interpretations of experience. Are the standards for their interpretations derived objectively from nature or formulated by the scientists themselves? In other words, do scientists not only play by certain rules, but also make the rules?

We know what Newton thought about these matters due to a correspondence between one of his followers and the famous German philosopher/mathematician Leibniz.

I, myself, have not read this correspondence and rely once again heavily on Steven Goldman for what I express here. What you read in the following paragraphs are basically just his lecture notes, interspersed with a few of my own wild ideas. (Bear with me; I’m on a Goldman kick right now. Don’t worry, it’ll pass. I won’t be writing Goldman posts for the next few years.)

The first thing to notice about Newton was that his genius in various fields of research was neither due to Baconian induction nor Cartesian deduction, but due to creativity. Whether it was in theology, biblical interpretation, ancient history, world chronology, alchemy, physics, mathematics or chemistry—Newton was first and foremost creative. He left us 5 million words of creative thought.

One of his most famous creative achievements was the invention of the three laws of motion. They were soon adopted pretty much universally as laws of nature and did, in fact, function as the foundation for modern science until Einstein came along and showed that they were not universally true. None of these laws could be derived from experience. They were explanatory fertile presuppositions, creatively projected onto nature as principles of nature.

Saying that they were not derived from experience is not to say that they were not consistent with experience. They were, and they successfully predicted the behaviors of material objects moving under a wide range of forces, which encouraged their acceptance as truths of nature.

Nevertheless, the law of inertia, for example, never was, nor ever could be, confirmed experimentally. It stipulates as a universal law what early modern nature philosophers believed: that matter was inanimate, that is, that matter could not move itself. The third law, that for every action on a material object there must be an equal and opposite reaction, also is effectively stipulative.

In effect, the conceptual elements of Newtonian mechanics are Newton’s recognition of what must be accepted as true in order to have a mathematical theory of matter in motion. Newton needed to define space and time, matter, motion, and force in ways that would make relatively simple predictive algebraic equations of motion possible.

However, he did not state in such pragmatic terms that this is what he was doing. Rather, he defined space and time in absolute terms, as “things” existing in their own right and with eternal, uniform natures. How could he know this? He defined motion, too, in absolute, as well as in (Galilean) relative terms. These conceptual “ingredients” of Newtonian mechanics were, in effect, invented by Newton and were neither inductively nor deductively derivable from experience. But Newtonian mechanics works, and so does Newton’s universal theory of gravitation.

Think about it: How could Newton know that the same force of gravity applies throughout the Universe? Can such a claim be justified experimentally? Empirically?

What Newton demonstrated, deductively, was that assuming his particular form of the gravitational force, he could accurately predict the orbits of the Moon and all the planets and the periodicity of Earth’s ocean tides. In the process, he demonstrated that Kepler’s three “laws” of planetary motion were necessary consequences of the force of gravity. Reinforcing the claim that Newton’s physics, notwithstanding its nonempirical definitions, gave us knowledge of reality was the 19th-century prediction of the existence of the planet Neptune based on deviations of the known planetary orbits from the values predicted by Newton’s equation, as well as the roughly contemporary discovery that the orbits of binary stars observed Newton’s equation.

Newton’s physics works and, for more than 200 years, was lauded as finally giving man knowledge of at least physical reality. But, on an absolute level, Newtonian physics is wrong, in spite of “working”!

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