Popper on Science and Philosophy (Column 759)

With God's help

In the series of columns 155 – 160 I tried to sharpen and define what philosophy is, and in particular what distinguishes it from science. The conclusion was that although philosophy also deals with reality (and perhaps primarily with reality), and in that sense it is like science, unlike science it does not rely on observation, at least not in the simple sense (the use of the senses). Philosophy is grounded in observation with the 'eyes of the intellect,' that is, the use of intuition, against the background of my view that our intuition is a cognitive tool and not merely a thinking tool (see column 653). On the other hand, science too is not a product of observations alone, and besides the generalizations that are its daily bread, it also involves quite a few a priori assumptions that do not arise from observation and are not subject to observational falsification. I therefore tend to agree that the distinction between philosophy and science is far from sharp.

A few weeks ago I was sent an article by the philosopher Karl Popper entitled: "The Nature of Philosophical Problems and Their Roots in Science" (THE NATURE OF PHILOSOPHICAL PROBLEMS AND THEIR ROOTS IN SCIENCE). The very title of the article suggests that Popper is proposing here to blur the difference between science and philosophy, and that therefore interested me greatly. I read it and found in it quite a few problematic arguments, and I will try to present here a critical reading of it that will help me sharpen the meaning of the ideas presented in the above-mentioned series of columns.

The Nature of Philosophical Problems

Popper opens by saying that the division of fields of inquiry and science into different disciplines is anachronistic and unimportant. A researcher, he says, should be engaged in solving problems, and every problem requires tools from different disciplines. Thus, for example, a problem in geology requires tools from mathematics, chemistry, various fields of physics, the use of various engineering tools, and more.

This argument is very strange, since those tools would not have developed properly without disciplinary division. A discipline of fundamental science was built out of the understanding that those very same tools are used to solve problems from different fields. When people understood that infinitesimal calculus was used in countless fields, that area was formulated as an independent field. The same is true of mechanics, quantum theory and relativity, thermodynamics, field theory (different fields in physics). Had that not happened, in each of those fields we would have had to develop those tools separately, and it is doubtful whether enough geniuses like Newton or Leibniz would have been found in each of those fields to develop calculus a hundred times in parallel. Moreover, Popper's very ability to speak of a field such as geology (which is not a fundamental science), and certainly of physics or mathematics, stems from the fact that they were defined as distinct disciplines. Otherwise he would have had to speak about each concrete problem on its own, without resorting to the collective name that unifies them, such as 'geology,' 'calculus,' and so on.

The claim that there really is a field such as philosophy or physics is a matter of definition. It may be that it is only useful to define it for the purposes of our discussion. The question whether it "exists" is, in my opinion, not well defined. Exists in what sense? The important question is whether that definition is useful, and here the answer is plainly yes. Whether Plato was right that at the basis of each such field there is a Form floating somewhere in the world of Forms is not important on the practical level with which Popper is dealing. That is a question in metaphysics, not in the philosophy of science. Popper may need that question because it smells of Platonism, which, as is well known, was very much not to Popper's taste (the whole first part of his monumental book, The Open Society and Its Enemies, is devoted to attacking Platonism. See also columns 239 and 565).

His determination that we study problems and not fields is simply factually false. It is really not true. We certainly study both fields and problems. Fundamental science deals with fields, and non-fundamental science deals with problems (and even there it is divided into different fields, and that division is decidedly useful and necessary).

When Popper denies the distinction between fields, his intention is to open the door to blurring the boundary between philosophy and science. That is what he will address later in the article.

Wittgenstein's Claim Against the Existence of Philosophical Problems

At the beginning of his discussion, Popper invokes Wittgenstein[1] and some others from the school of logical positivism, according to whom there are no philosophical problems at all:

All real problems are scientific. What are called "philosophical problems" are nothing but pseudo-problems, and what are called "philosophical sentences" are pseudo-sentences — meaningless combinations of words, neither false nor true, but not even constructed as proper sentences. They are no less meaningless than a sentence like "Socrates is identical" — an expression that Wittgenstein himself gives as an example.

From this it follows, Popper claims, that one cannot create a philosophical theory. Philosophy is not a theory but an activity. An activity of exposing the faulty language that generates the supposed "philosophical problems," and of training people to speak properly in a way that will not give rise to such problems. Wittgenstein belonged to the movement known as "analytic philosophy," whose main toolbox consisted of linguistic analysis. They argued that the philosopher does not solve problems but dissolves them, by exposing the grammatical malfunction that gives rise to them. In particular, they argued that what are defined as the subject matters of philosophy, such as metaphysics or even political theory, are either empirical claims handed over to science, or pseudo-claims (that is, collections of words devoid of meaning. In their view, anything that cannot be empirically examined is a pseudo-claim)[2].

Popper strongly opposes this: he argues that there are real philosophical problems, and that philosophy lives only as long as there are such problems. If it should turn out that there are none, we should all stop doing philosophy.

I share Popper's view, but I am puzzled by his argument. After all, this is exactly what the analytic philosophers and logical positivists claim: that we should stop doing philosophy and focus on linguistic analysis that will dissolve the philosophical problems, that is, show that they are merely apparent. On their view, that is precisely the philosopher's task. In other words, their claim is that philosophy is not a distinct field of research but a methodology whose purpose is to clarify and sharpen all the other domains of our intellectual activity. Moreover, Popper himself explained in the previous section that the division between the different fields is anachronistic, so why is it so important to him to discuss the role of each discipline and to insist that there are distinct problems it is supposed to deal with?!

In my above-mentioned columns I explained why I too disagree with the positivist position, but Popper's argument against it fails.

Explanation, Partial Defense, and Critique of Wittgenstein's Position

Popper agrees that quite a few people talk nonsense, and that perhaps the philosopher's role is to expose this. But there are also people who said things that are not grammatically precise, yet they are fascinating, profound, and sometimes more important than the "common sense" of others. If we were to disqualify their words from the outset because of their lack of precision, we would lose a great deal of important content. For example, infinitesimal calculus in its early versions was undoubtedly sheer "nonsense" according to Wittgenstein's criteria, but it was precisely this that led to tremendous theoretical development. If Wittgenstein had succeeded in "eliminating" their meaninglessness in real time, he would have destroyed one of the wonders of mathematical thought. The physicist Erwin Schrödinger, one of the fathers of quantum theory, said in response to Wittgenstein's (early) statement at the end of his Tractatus, "Whereof one cannot speak, thereof one must be silent": "But that is precisely where speech begins to become interesting."

I will only note here that the fact that certain claims proved useful does not mean that there is substance to them or that it would have been wrong to dismiss them on grounds of vagueness. By that logic, we should leave every collection of words intact lest it produce interesting and useful results, and in that way you have pulled the ground out from under philosophical inquiry altogether. The claim that analysis is not everything (with which I fully agree) does not mean that there is no point in engaging in analysis.

In short, there is no doubt that maximum linguistic clarity is needed. Moreover, there is quite a bit of philosophical writing (he mainly means large portions of continental philosophy. See columns 140, 223, and others) that really is meaningless. In our time, the heap of nonsense, word games, and empty verbiage called 'postmodernism' has brought this to a truly marvelous peak. Popper agrees that the influence of Wittgenstein and linguistic analysis did indeed reduce, if only temporarily, this hollow discourse (that is, they were useful). Popper goes on to argue that every philosophical school can degenerate in this way, so that its problems become pseudo-problems and its language turns into meaningless gibberish. He explains that this happens when philosophy tries to exist within itself, detached from the extra-philosophical problems that give rise to it: mathematics, cosmology, politics, ethics, religion.

His claim is that the customary manner of teaching philosophy may lead the student to Wittgenstein's conclusions. When one reads the great philosophers without any knowledge of the scientific, mathematical, and institutional problems from which their ideas arose, what they say seems abstract, alien, and sometimes unnecessary, and then the natural conclusion is that "it's all nonsense." In his opinion this is a grave mistake, but it is unavoidable so long as philosophy is studied "from the books" rather than through the problems from which it grew. Here he implicitly returns to his (mistaken) remark about dealing with fields instead of problems. Beginning in the next section he brings examples for this claim.

Before we enter those examples, I will already say here that the fact that scientific background is needed in order to understand the novelty of a philosophical thesis and its implications does not mean that the distinction between the fields is meaningless. That is an entirely different claim. Below I will return to this distinction.

Pythagoras and the Birth of Platonism

Popper opens the discussion with the thesis that Plato's theory of Forms (his central philosophical doctrine) cannot be fully understood except in a non-philosophical context, and especially in the context of the critical state of problems in early Greek science, particularly in the area of the theory of matter. The crisis in question emerged following an important discovery in the history of mathematics: the square root of 2 is an irrational number.

He argues that Plato's theory of Forms has never been fully understood, and never will be understood, by philosophers who study philosophy in the accepted way, unless the necessary mathematical facts are presented to them first. He now begins to spell this out. The beginning of the matter lies in the Pythagorean conception according to which "all things are numbers."

The founder of the Pythagorean sect was deeply influenced by the fact that musical harmony is based on relations between whole numbers, and by the fact that the right angle too is based on numerical relations (especially within the triangle whose side ratios are 3:4:5, or other Pythagorean triples such as 5:12:13 and the like). These two discoveries led Pythagoras to the generalization that "all things are, in their essence, numbers or numerical relations. Number is the logos — the principle, the essence, the true nature of things." I would note that among some Greek thinkers atoms too were defined as "numerical units that cannot be divided."

I wonder what exactly is meant by the claim that things are composed of or made of numbers. I very much doubt that it has any meaning at all. One can perhaps argue that numerical relations can be found in every object in the world, but that is another claim, for which we do not need the Pythagoreans (though I have very serious doubts about that as well). Their claim is that entities are composed of numbers. That is a claim in ontology, not in epistemology or phenomenology. This is an example of a vague statement that Wittgenstein, and I myself as well, would dismiss as a pseudo-claim. This formulation really is a marvelous demonstration of bizarre nonsense)[3].

But Popper argues that this idea (so astonishingly vague) turned out to have great power. From it the Pythagoreans moved on to investigate geometric forms by means of series of numbers, and they arrived at genuinely interesting mathematical insights. Popper now goes on to describe the Pythagorean approach that represents geometric forms by means of points (like star drawings). Thus, for example, the sum of odd numbers is always the square of a natural number. In the figure below you can see that in the upper-left square there is one little circle. The second square contains 4 points, which are 1+3. The third square already has 9 points, which are the sum of 1+3+5, and so on.

Thus, the sum of n odd numbers is a square whose area is n².

If you want to sum the even numbers, in the same way you get rectangles:

That is:  2+4+6…+2n = n(n+1)

• By the same token, the sum of the first n natural numbers gives us a triangle, and if we duplicate it we get a parallelogram, whose number of points is 1+2+3+…n = n(n+1)/2:

And thus geometric forms were conceived by the Pythagoreans as equivalent to series of numbers, or to relations between numbers. Later, abstract properties as well, such as harmony, beauty, health, knowledge, and the like, were conceived as numbers, or as numerical relations. Thus there also arose a set of oppositions, which was likewise hung on relations between numbers, and I will not go into that here. The Pythagoreans were also influenced by the similarity between points in a geometric diagram
and points in the heavens and celestial formations, that is, constellations such as Leo, Scorpio, and Virgo. If "Leo" is an arrangement of points, then that arrangement necessarily has a number. From here grew the belief that the "forms" are in fact the celestial forms of things — numerical structures that exist in a higher space.

Although the Pythagorean claims have no real meaning in my opinion, this could be an example of Popper's claim above, according to which it would have been very bad had Wittgenstein (or little old me) been there to dismiss this sentence as a pseudo-claim. We would have lost all the richness that grew out of engaging with this vague claim. But even if such criticism might have been harmful, that does not mean it is not correct. There can be quite a few pieces of nonsense that gave rise to valuable insights. Does that mean we should not criticize nonsense?!

If we return to Popper's line of argument, what we have so far is a rather bizarre story. A strange claim as though all the entities in the world are composed of numbers or numerical relations is drawn from some sort of similarity between models. This situation leads to the crisis brought about by the discovery of irrational numbers, which destroyed their aesthetic structure. The Pythagoreans discovered that the number corresponding to the length of the diagonal of a unit square (the square root of 2) cannot be expressed as a ratio between whole numbers. This created a philosophical crisis, since a square is a very basic shape, and if within it there is something that is not a ratio between whole numbers, then Pythagoreanism as a whole is in trouble. This crisis threatened geometry, physics, music, cosmology, metaphysics, and in fact the entire framework of scientific explanation. Popper points out that the crisis was so severe that the Pythagorean disciple who exposed the irrationals — "Hippasus" according to tradition — was expelled from the sect and, according to some versions, even murdered.

And here Plato enters the picture. Popper argues that Plato's theory of Forms was born directly out of this Pythagorean-mathematical crisis. When it became clear that the square root of 2 is an irrational number, that is, one that cannot be written as a ratio between integers, not only did the numerical view of geometry collapse — an entire structure of philosophical conceptions collapsed with it. This crisis was especially severe because it was not a mistake or a computational failure; it was the result of a mathematical proof. A paradigm had to be replaced, and Plato offered his theory of Forms as a fitting substitute. Popper emphasizes that if we do not understand the scientific background, we do not understand Plato's inner movement at all. His theory of Forms is not a response to a purely philosophical perplexity, but a reaction to a real scientific crisis, the first in Western scientific thought.

In place of the numbers that, according to the Pythagoreans, constituted the foundations of reality, Plato proposed a system of pure forms as a superstructure that gives stability and meaning to the dynamic world around us. These forms are not numbers, but they create order and relations, and give form to our complex and restless reality, something that preserves the idea behind the Pythagoreans without yielding to the problems created by irrational numbers. According to Plato, the sensory world is not entirely "scientific," since it is strewn with contradictions, differences, and imprecisions, and therefore is very difficult to conceptualize. But above it and within it, Plato claims, there is a true world, a world of forms that is fixed and perfect, and therefore can be handled by rational and systematic thought. Science is supposed to deal with the world of forms and not with our world. The Forms do not compose our reality (as the numbers did for the Pythagoreans), but rather constitute abstractions of which our world is an embodiment and illustration.

I devoted several columns here to Platonism (383 – 385, 435, and others), so I will not continue explaining it. For our purposes here, this is enough. In later sections Popper brings a few more similar examples of philosophical doctrines being born from scientific crises. But they add nothing substantial to what we have seen so far.

A General Look at the Philosophy-Science Relationship

On the basis of the example we saw and those that follow it, Popper argues that real philosophical problems are born from real scientific problems; that philosophy degenerates the moment it disconnects from this ground; and that Plato is not a "mystic of forms," but a scientist trying to save a scientific system that has collapsed. At the same time he returns to the point that philosophy deals with real problems and not merely with creating proper language with pure and precise grammar (as Wittgenstein claimed). He further argues that science advances through finding solutions to problems, and not as the study of some 'field' or as an occupation with 'essences' (this is essentially a rejection of the Platonism that he used above as an example for his claim).

The fact that a certain problem was born in mathematics or science does not turn it into a "non-philosophical" problem. On the contrary, when a problem deals with questions of the nature of explanation, what reality is, how one can know, what the proper form of proof is, what the structure of the world is, and the like, it naturally becomes a philosophical problem. The boundaries between science and philosophy are not natural. They were created only for organizational purposes. Popper argues that problems migrate between fields, and their philosophical importance is determined not by the method by which we solve them, but by the kind of question they raise.

According to Popper, philosophy does not speak about science — it is part of the scientific effort to solve problems.
Every great philosophical problem rests on a great scientific problem that preceded it, and therefore if we wish to understand philosophy, we must understand the history of science not as folklore, but as a continuous chain of problem situations.

Critique

I must say that this article seems to me quite bizarre. I will not repeat here the a priori criticisms I raised at the beginning of the column, which dealt mainly with Popper's claims against the demarcation of different scientific fields and the demarcation between science and philosophy. Here I will only add to them points that arise from reading the course of Popper's argument in the article, and their main concern is a critique of his central thesis, according to which there is no real disciplinary difference between science and philosophy.

First, the example we saw, and those that followed it, were examples from early Greek science, which in our terms today (and in fact then as well) was really philosophy and not science. The claim that the objects in the world are composed of numbers, whatever its meaning may be, is a philosophical claim and not a scientific one, certainly according to Popper's own definition, which required a scientific theory to be falsifiable. So what is surprising about a philosophical crisis producing another philosophical system that tries to solve it?! How does one see from here that a new philosophy is born from a scientific crisis? True, later on he also touches on Kant's doctrine, but that is really a problematic example for his thesis, since Kant himself explains what gave birth to his critique: Hume's skepticism (which awakened him from his dogmatic slumber). In other words, this is a doctrine that was very clearly born from a philosophical problem and not from a scientific one.

Beyond that, what Popper did in his discussion was to offer his own interpretation of Plato's motivations for creating a new philosophical doctrine. Does that mean it is impossible to understand its meaning without understanding the 'scientific' crisis (which is actually philosophical, as we have seen) that preceded it? What difficulty is there today in understanding Plato's theory of Forms without knowing that once upon a time Plato himself was troubled by the irrationality of the square root of 2? Popper's thesis, even if it is correct, belongs to the history of philosophy and not to philosophy. A historian may be interested in knowing what gave rise to the Platonic doctrine, but a philosopher is supposed to examine it on its own merits.

This distinction recalls a similar distinction in the philosophy of science, between the context of discovery and the context of justification. When some scientist proposes a new scientific theory, we are not interested in what caused him to discover it, what his motivations were in formulating it, or who revealed the theory to him in secret or in a dream. Even if Einstein were to tell us that his late mother appeared to him in a dream at night and revealed to him the explanation for black-body radiation or the theory of relativity, that really should not interest scientists, and not even philosophers of science. That is the 'context of discovery,' namely a description of the path by which the scientist arrived at his theory. This belongs to the world of psychology or mysticism, and is not relevant to the discussion of the theory itself. Such a discussion should take place in the laboratory, in the face of findings that will confirm or refute the proposed theory. This is the 'context of justification,' and only it constitutes a substantive discussion of the theory. What Popper offers us here is a discussion of the context of discovery of Plato's theory of Forms, whereas a substantive discussion of it ought to deal with the context of justification (which in philosophical discussion is not empirical but rational-analytic).

There is no doubt that scientific crises, and scientific thinking in general, influence philosophical doctrines (determinism and quantum theory, discussions of free will in light of neuroscience, God in light of evolution, the Big Bang that ruled out an eternal universe, relativity and conceptions of time and space, and so forth). Quite often, knowing this background also contributes to understanding the philosophical doctrine itself. But from that to the claim that there is no place for demarcating science and philosophy, or that one cannot study and understand philosophy without the scientific background that preceded it and gave birth to it (if that is even true), the distance is enormous.

A Concluding Note: What Is Philosophy?

It seems to me that what led Popper to these strange claims is a misunderstanding about the definition of philosophy. This is indeed confusing. We are essentially trying to understand what place there is for a field of inquiry that makes claims about the world but is not connected to laboratory observations, and is also neither logic nor mathematics. If there is no reliance there on observations, how can one make claims about the world?! What could be the justification for such claims?! Beyond empirical observation, at most one can think of reflection on logical-mathematical structures (which in themselves say nothing whatsoever about the world).

This difficulty leads to empiricism, which recognizes only one way of accumulating information and making claims about the world: through observation. Notice that this is an extreme empiricism, since it views not only science in this way (as if it were wholly based on empirical observations), but essentially our entire ability to make claims about the world, even when these are not scientific claims. This is not true even of science, and certainly not of philosophy. To be sure, such a position fits Popper very well, since he sees scientific theories and generalizations as claims that do not really say anything about the world, but rather as claims that help us organize our thinking. He does not even recognize the ability of observations to confirm a scientific theory (only to refute it). In my assessment, this is probably what ultimately led him to deny the existence of the field of philosophy independently of science, and to make the very strange claims we have seen here.

In my above-mentioned series of columns on philosophy, I explained the mistake in this way of thinking, and I proposed a systematic definition of philosophical inquiry and discussion. I explained there that these are insights generated by non-sensory 'observation' (through intuition, or the 'eyes of the intellect'). This proposal neutralizes the categorical difficulty of locating philosophical discussions (they do indeed make claims about the world, and yet are not based on empirical observations, at least not in their accepted sense), and therefore makes Popper's discussion unnecessary, along with the need for the strange and untenable claims that arise in it.

[1] His bitter rival, with whom the dispute between them came almost to physical violence, in what later came to be called the "poker incident." It is worth noting that the quarrel there revolved precisely around this very question: are there real philosophical and ethical problems, or is all philosophy nothing but the removal of linguistic ambiguities.

I would note that I am actually very impressed by people who are prepared to brandish pokers over a problem like this rather than over road rage, a coveted job, money, interests, or a position of power. I once said to someone who had become religious and was astonished by the number of quarrels among rabbis in the religious world that, in my eyes, this is worthy of great appreciation. They are prepared to quarrel over spiritual problems (sometimes foolish ones), whereas others quarrel over nonsense. Moreover, I told him that the more things there are in your world that matter to you, the more quarrels you will conduct. People who do not quarrel — it may be because there is nothing in their world that matters to them and is worth quarrelling over. In many cases, the pursuit of peace is nothing but indifference and a vacuum of values, not a positive personal virtue. Of course, this is not always so, in either direction: quarrels are not always worthy of appreciation (sometimes the quarrels themselves are the goal, and not the values over which people are ostensibly quarrelling. The values are a fig leaf for a quarrel over positions of power), and the absence of quarrels is not always an expression of indifference and emptiness of values. In the current context, in my opinion the main problem in our society is not the quarrels. On the contrary, the quarrels are a symptom that there are values here and that they matter to people. The problem is the lack of mutual attentiveness, and the lack of willingness to conduct those quarrels on the merits (even if in a harsh and even painful way). I have no problem with harsh and blunt language, and not even with forceful steps. I only want that before you or I take such steps, we first conduct a clarification of the matter itself and formulate a position in a logical and substantive way. After that, one may quarrel and brandish pokers at one another. The focus of the criticism on the form of the discourse, on forcefulness, and on violence misses the real problematic focal point.

[2] There is no need to note that this claim itself is a pseudo-claim according to their own view.

[3] Strikingly similar to a claim that appeared not long ago on the site, to the effect that "God is logic." Here lies the explanation to the questioner as to why I did not answer him.