A metalanguage is still a language, and a metatheory a
theory. Metamathematics is a branch of mathematics.
Is metaphysics a branch of physics?
`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attitude is a hangover from the long outdated forms of empiricism and positivism.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.