The meaning of metaphysics

`Meta' in Greek means over, and -- since when you jump over something you find yourself behind it in space and after in time -- it is also understood as behind and after. The word `metaphysics' is said to originate from the mere fact that the corresponding part of Aristotle's work was positioned right after the part called `physics'. But it is not unlikely that the term won a ready acceptance as denoting the whole field of knowledge because it conveyed the purpose of metaphysics, which is to reach beyond the nature (`physics') as we perceive it, and to discover the `true nature' of things, their ultimate essence and the reason for being. This is somewhat, but not much, different from the way we understand `meta' in the 20-th century. A metatheory is a theory about another theory, which considered as an object of knowledge: how true it is, how it comes into being, how it is used, how it can be improved, etc. A metaphysician, in contrast, would understand his knowledge as a knowledge about the world, like that of a physicist (scientist, generally), and not as a knowledge about the scientific theories (which is the realm of epistemology).

If so, metaphysics should take as honorable a place in physics as metamathematics in mathematics. But this is very far from being the case. It would be more accurate to describe the situation as exactly opposite. Popularly (and primarily by the `working masses' of physicists), metaphysics is considered as something opposite to physics, and utterly useless for it (if not for any reasonable purpose). I will argue below that this attitude is a hangover from the long outdated forms of empiricism and positivism. I will argue that metaphysics is physics.

A detractor of metaphysics would say that its propositions are mostly unverifiable, if intelligible at all, so it is hardly possible to assign any meaning to them. Thales taught that everything is water. The Pythagoreans taught that everything is number. Hegel taught that everything is a manifestation of the Absolute Spirit. And for Schopenhauer the world is will and representation. All this has nothing to do with science.

But Democritus, and then Epicurus and Lucretius taught that the world is an empty space with atoms moving around in it. In due time this concept gave birth to classical mechanics and physics, which is, unquestionably, science. At the time of its origin, however, it was as pure a metaphysics as it could be. The existence of atoms was no more verifiable than that of the Absolute Spirit. Physics started as metaphysics. This is far from an isolated case.

The question of verifiability is a part of our understanding of the nature of language and truth. What is the meaning of words and other objects of a language? The naive answer is: those things which the words denote. This is known as the reflection theory of language. Language, like a mirror, creates certain images, reflections of the things around us. With the reflection theory of language we come to what is known as the correspondence theory of truth: a proposition is true if the relations between the images of things correspond to the relations between the things themselves. Falsity is a wrong, distorted reflection. In particular, to create images which correspond to no real thing in the world is to be in error.

With this concept of meaning and truth, any expression of our language which cannot be immediately interpreted in terms of observable facts, is meaningless and misleading. This viewpoint in its extreme form, according to which all unobservables must be banned from science, was developed by the early nineteenth-century positivism (August Comte). Such a view, however, is unacceptable for science. Even force in Newton's mechanics becomes suspect in this philosophy, because we can neither see nor touch it; we only conclude that it exists by observing the movements of material bodies. Electromagnetic field has still less of reality. And the situation with the wave function in quantum mechanics is simply disastrous.

The history of the Western philosophy is, to a considerable extent, the history of a struggle against the reflection-correspondence theory. We now consider language as a material to create models of reality. Language is a system which works as a whole, and should be evaluated as a whole. The job the language does is organization of our experience, which includes, in particular, some verifiable predictions about future events an the results of our actions. For a language to be good at this job, it is not necessary that every specific part of it should be put in a direct and simple correspondence with the observable reality.

A proposition is true if, in the framework of the language to which it belongs, it does not lead to false predictions, but enhances our ability to produce true predictions. We usually distinguish between factual statements and theories. If the path from a proposition to verifiable predictions is short and uncontroversial, we call it a factual statement. A theory is but only through some intermediate steps, such as reasoning, computation, the use of other statements. Thus the path from a theory to predictions may not be unique and often becomes debatable. Between the extreme cases of statements that are clearly facts and those which are clearly theories there is a whole spectrum of intermediate cases.

The statement of the truth of a theory has essentially the same meaning as that of a simple factual statement: we assert that the predictions it produces will be true. There is no difference of principle: both factual statements and theories are varieties of models of reality which we use to produce predictions. A fact may turn out to be an illusion, or hallucination, or a fraud, or a misconception. On the other hand, a well-established theory can be taken for a fact. And we should accept critically both facts and theories, and re-examine them whenever necessary. The differences between facts and theories are only quantitative: the length of the path from the statement to verifiable predictions.

This approach has a double effect on the concept of existence. On the one hand, theoretical concepts, such as mechanical forces, electromagnetic and other fields, and wave functions, acquire the same existential status as the material things we see around us. On the other hand, quite simple and trustworthy concepts like a heavy mass moving along a trajectory, and even the material things themselves, the egg we eat at breakfast, become as unstable and hazy as theoretical concepts. For to-day's good theory is to-morrow's bad theory. We make and re-make our theories all the time. Should we do the same with the concept of an egg?

Certainly not at a breakfast. But in theoretical physics an egg is something different from what we can eat: a system of elementary particles. This makes no contradiction. Our language is a multilevel system. On the lower levels, which are close to our sensual perception, our notions are almost in one-to-one correspondence with some conspicuous elements of perception. In our theories we construct higher levels of language. The concepts of the higher levels do not replace those of the lower levels, as they should if the elements of the language reflected things "as they really are", but constitute a new linguistic reality, a superstructure over the lower levels. We cannot throw away the concepts of the lower levels even if we wished to, because then we would have no means to link theories to observable facts. Predictions produced by the higher levels are formulated in terms of the lower levels. It is a hierarchical system, where the top cannot exist without the bottom.

Recall the table describing four types of langage-dependent activities in our discussion of formalization. Philosophy is characterized by abstract informal thinking.

The combination of high-level abstract constructs used in philosophy with a low degree of formalization requires great effort by the intuition and makes philosophical language the most difficult type of the four. Philosophy borders with art when it uses artistic images to stimulate the intuition. It borders with theoretical science when it develops conceptual frameworks to be used in construction of formal scientific theories.

Top-level theories of science are not deduced from observable facts; they are constructed by a creative act, and their usefulness can be demonstrated only afterwards. Einstein wrote: "Physics is a developing logical system of thinking whose foundations cannot be obtained by extraction from past experience according to some inductive methods, but come only by free fantasy".

This "free fantasy" is the metaphysician's. When Thales said that all is water, he did not mean that quite literally; he surely was not that stupid. His `water' should rather be translated as `fluid', some abstract substance which can change its form and is infinitely divisible. The exact meaning of his teaching is then: it is possible to create a reasonable model of the world where such a fluid is the building material. Is not the theory of electromagnetism a refinement of this idea? As for the Pythagoreans, the translation of the statement 'everything is number' is that it is possible to have a numerical model of the Universe and everything in it. Is not the modern physics such a model?

When we understand language as a hierarchical model of reality, i.e. a device which produces predictions, and not as a true picture of the world, the claim made by metaphysics is read differently. To say that the real nature of the world is such and such means to propose the construction of a model of the world along such and such lines. Metaphysics creates a linguistic structure -- call it a logical structure, or a conceptual framework -- to serve as a basis for further refinements. Metaphysics is the beginning of physics; it provides fetuses for future theories. Even though a mature physical theory fastidiously distinguishes itself from metaphysics by formalizing its basic notions and introducing verifiable criteria, metaphysics in a very important sense is physics.

The meaning of metaphysics is in its potential. I can say that Hegel's Absolute Spirit is meaningless for me, because at the moment I do not see any way how an exact theory can be constructed on this basis. But I cannot say that it is meaningless, period. To say that, I would have to prove that nobody will ever be able to translate this concept into a valid scientific theory, and I, obviously, cannot do that.

It takes usually quite a time to translate metaphysics into an exact theory with verifiable predictions. Before this is done, metaphysics is, like any fetus, highly vulnerable. The task of the metaphysician is hard indeed: he creates his theory in advance of its confirmation. He works in the dark. He has to guess, to select, without having a criterion for selection. Successes on this path are veritable feats of human creativity.