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Copyright © Interdisciplinary Encyclopedia of Religion and Science ISSN: 2037-2329 and Alberto Strumia
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To refer to the content of this article, quote: INTERS – Interdisciplinary Encyclopedia of Religion and Science, edited by G. Tanzella-Nitti, P. Larrey and A. Strumia, http://www.inters.org
 Matter
Alberto Strumia
I. What is Matter? - II. Matter as a Philosophical-theological
Concept. 1. The Physical Approach. 2. The Mathematical
Approach. 3. The Metaphysical Approach. 4. Matter and Spirit:
Philosophic-theological Aspects. - III. Scientific Inquiry
into the Nature of Matter 1. The Atomic Theory of Matter.
2. Matter and Radiation. 3. The Theories of Relativity of Einstein.
4. Quantum Mechanics. 5. Organization of Matter: Information
and Complexity. 6. Matter and Mind. - IV. Between Science
and Philosophy - V. Matter and Mass, Field and Energy 1. The
Tendency of Substantialization of Mass and Energy in Classical Physics.
2. Special Relativity. 3. Quantum Mechanics. -
VI. Vacuum, Matter, and Energy. - VII. Matter and the Problem of
the Whole and of the Parts. 1. Positions and Problems of Approach.
2. Some Examples taken from the Sciences. VIII. Matter, Intelligence,
and Abstraction.
I. What is Matter?
In common, everyday language, we usually designate as “matter”
everything which falls under the direct perception of our external senses: we call
“material” that which one can see, touch, smell, taste and hear. This is
an adequate working definition on the macroscopic level, that is, on the human scale. In
everyday language we call “bodies” material objects (entities),
especially if solid, but in a wider sense also liquids, gases, and such things which can
be observed indirectly with measuring instruments. By the term matter, we mean
indiscriminately a sort of constituent fabric of corporeal bodies without reference to how
this fabric differs in different types of corporeal objects.
The need of introducing a similar terminology arises at first glance from the need of
distinguishing that which causes a sense experience from that which lies at the origin of
an experience of a non-sensorial nature, such as the internal experiences of thinking, of
feeling emotions, of remembering and willing, experiences which appear as fundamentally
imponderable and immaterial.
The matter becomes complicated when one goes over to a more detailed analysis involving
phenomena such as light, or areas of research encompassing the microscopic, biological, or
psychological worlds. As we shall see later, only a careful examination allows one to gain
a better understanding of the characteristics of these “worlds” and to
develop a more precise meaning of the word “matter”, independently and
in relation to them.
Historically, two approaches to the problem of matter have been
adopted: an approach which we can call “philosophical-metaphysical”
and an approach which today we qualify as “scientific”.
Each of these two ways of approaching the problem, if carried out
correctly, offers us very significant elements for answering the
question, «what is matter?». Such approaches are mutually
complementary in so far as they consider the same object from different
points of view: the “quantitative-relational” (scientific)
and the “entitative” (philosophical) points of view. I
will attempt to examine both as much as I can.
II. Matter as a Philosophical-theological Concept
In this section, I will consider the qualitative, or better yet,
metaphysical differences between different ways of approaching the
subject of matter, and I will also indicate those aspects which
concern theology more directly and which are treated at length in
other relevant entries referred to in the text.
1. The Physical Approach. In classical antiquity, when science
and philosophy were not yet separate subjects and rational and demonstrative
thinking began to develop (approximately around the 6th century
B.C.) beyond the mythical culture (
MYTH) which aimed more at communicating fundamental truths than
at analyzing the structure of the cosmos, Ionian philosophers —
such as Thales, Anaximenes, and Anaximander, etc. — later known
as “physicists” because they studied
nature (gr. physis), posed the problem of the constituent
elements of the sensible world (cf. Daumas, 1957). The exigency
of the human mind was then as it is now that of reducing the description
of the world to a few unifying, constitutive elements. Just as physicists
today ascertain that the quarks of the “standard model”
(cf. H. Firetzsch, 1983; Cohen-Tannoudji and Spiro, 1988) are the
fundamental components of the universe — even if they
are ready to change the model if it should prove inadequate or if
someone should find a better theory — these ancient inquirers
into the physical world explained, in a more simple way, every degree
of weight and density as well as every qualitative property, as
a mix of more or less dense concentrations of the four elements
of earth, water, air, and fire. Empedocles thought instead of a
mix of properly chosen amounts of the above elements. However naive
this description may sound today, and for that matter, too “qualitative”,
it does not, from the philosophical and methodological point of
view, differ substantially from the current way of proceeding. In
fact, just as today, the ancients looked for constituent elements
homogeneous with the thing they were supposed to describe and explain.
We call “reductionist” this method which is in essence
the simplest which one can adopt. To explain the nature of different
corporeal objects, we call to mind a description of these as composed
by yet smaller (microscopic) corporeal objects which cluster together
and which are none other than the minimum portions of the elements
which can be found in nature, even if in macroscopic amounts. For
these ancient inquirers into nature, a particle of “earth”
was made of the same “earth” as the ground we step on,
just as, for us, a particle is “matter” in the same way
as the table on which we lay a book. No one would say that a proton
or a quark is not matter. The problem, instead, becomes that of
understanding the nature of the matter common to all microscopic
and macroscopic objects, whether it is a primary and irreducible
constituent, or if, in turn, it is an effect of something else.
Not by chance are these elementary constituents sometimes called
the “building blocks” the universe is made of. And the
building blocks of a house are made of the same matter as the house
as a whole. As a proof of this substantial continuity of posing
the problem, there is a certain kinship that a scientist of today
feels for a thinker such as Democritus (460 B.C.- 370 B.C.) who
came up with the first atomic theory of matter.
2. The Mathematical Approach. The position of Pythagoras
(570-490 B.C.) and followers is particularly interesting, even from
the modern point of view, because it places mathematics at the foundation
of any explanation of nature (cf. Daumas, 1957). According to this
view, there are “points” in place of matter, a view which
brings us back to a geometrical description of physical space. We
would be led to think of “material points” of modern rational
mechanics, but the Pythagoreans were less concerned with describing
the ponderable aspect of nature than grasping its order, harmony,
and musicality through numerical ratios. In this sense, they went
from a “materialistic” to an “abstract” or “ideal”
description of the cosmos. And, once the Pythagoreans discovered
the correspondence between points of a line and numbers, the description
became at once geometric and arithmetic, or as one is oft to say,
“arithmo-geometric”. The crisis of “irrational”
numbers however, was not fully overcome until many centuries later
and this mathematization, on which the entire way of life and thought
of the Pythagoreans was based, reached a crisis and fell into a
lengthy period of stagnation.
3. The Metaphysical Approach. At this point, the time was
ripe for a shift from the physical and/or mathematical approach
to the metaphysical approach. The problem of understanding reality
no longer involved the question, «what are the constituent
elements» but «how is change possible?» that is,
the question of becoming. We
experience at the same time change and identity in things. Philosophical
inquiry shifts its focus from the investigation of the constituents
(“building blocks”) of the universe to the “principles”
which explain its existence and change. These principles cannot
be reduced to components which are corporeal and hence observable,
as they are of an entirely different nature from that of corporeal
bodies. Yet, they must be hypothesized for logical reasons in order
to explain the behavior of things and of corporeal bodies in particular.
Better yet, each of these principles are indispensable for understanding
reality since one runs into contradictions or finds it no longer
possible to go past a certain degree of knowledge, if such principles
are ignored ( METAPHYSICS,
I).
Every corporeal body — and this is particularly evident in living
bodies — changes partly during its existence and partly remains the same and
maintains its identity. If there were only one principle behind being, if there were only
“building blocks” (matter), a corporeal body would not remain the same,
should these “building blocks” be replaced by others. Thus, one would no
longer be able to say that a human or a living being is always the same living being
during the course of his life, as soon as the particles which comprise him are replaced.
Therefore another principle is necessary in addition to that of matter which guarantees
identity and permanence within change of constituent matter. Aristotle (384-322 B.C.)
called “substantial form” this immaterial principle, which makes an
entity be and remain what it is for its entire existence. Our conception of
information is most likely the closest to the Aristotelian concept of
form.
We find ourselves face-to-face with a description of corporeal bodies as a synthesis
(gr. synolon), as the result of two constitutive principles (co-principles, in so
far as they operate together) which are not themselves bodies, but of entirely different
nature, and are neither “observable” nor homogeneous with corporeal
objects, but make the existence and change of these possible: “matter”,
which is the common ground of corporeality, and “form”, which puts the
necessary information into matter so that it becomes this particular object with its
particular properties. This is the basis of the “hylemorphic” theory. At
this point, it is necessary to be more precise, even in the linguistic sense. Up to now, I
have used the word “matter” to indicate something which is of the same
nature, of the same “stuff” as bodies, while in Aristotle, matter
appears as a “principle” of a different nature, a pure potentiality to
receive the active and informative principle, which is “form”. It is
therefore necessary to distinguish between two types of matter; one needs to speak of
“primary matter”, which is the “principle” (the pure
potentiality to receive forms), and a “secondary matter”, which is
matter already actuated by form, of the same nature as observable corporeal objects, and
the fabric which they are made of. This “secondary matter” is none other
than what we call today simply “matter” in both common and scientific
language. It is homogeneous with corporeal bodies, and is a “thing”
(lat. ens quod), whereas the “primary matter” (just like the
“form”) is not a “thing”, but a principle through
which (lat. ens quo) things are as they are.
This kind of metaphysical inquiry into the nature of the constituents
of the corporeal world requires a conception of entity according
to several different modes ( ANALOGY)
such as an ens quod, or an ens quo, and not according
to a single homogenous (univocal) mode, such as that of the being
of Parmenides, which is always identical to itself and free of change,
or that of the pure being of Eraclitus, which is free of permanent
identity. Such a conception requires, instead, a gradation of modes
of being an entity which includes “potential” principles,
such as primary matter, “active” principles such as form,
and “things” already actuated in different degrees.
4. Matter and Spirit: Philosophic-theological Aspects. Philosophy,
unlike physics and the natural sciences, has involved throughout
its history not only the study of the sensible world but also the
analysis of the interior experience of man as characterized fundamentally
by his intelligence and will. This analysis has led one to introduce,
in addition to the concept of primary and secondary matter, a completely
immaterial principle, often known as
spirit or
soul. Aristotle had just used the term “soul” to indicate
the substantial form of living beings, distinguishing in it the
vegetative, sensitive, and rational faculties, the former two being
faculties shared with the other animals, the latter unique to human
person.
The term “spirit” was later used for the most part in the generic
sense, whereas the term “soul”, used more and more frequently to
indicate the human soul, denoted the spiritual principle a rational individual, such as a
human person, is endowed with. Again, the term “Spirit” is used in
philosophy and theology to indicate the nature of higher and completely immaterial beings
such as Angels and God. We refer to other related entries for a
more complete treatment of these subjects and of their relationship with the subject of
matter.
In the history of human culture in its relation with religious thought, matter has
often been considered an element related to corruption, degradation and evil, as it was
seen in opposition to the spirit and to immaterial realities in general. The philosophy of
Plato was not foreign to this vision: the body, for example, is viewed as the
“prison” of the soul. One of the original contributions of Christianity,
taking after Judaism, is to consider the intrinsic goodness of matter. The dialectic of
good and evil shifts its focus from the paradigm spirit/matter, which is, in a certain
sense extraneous to the moral dimension, to human heart, that is to his and her interior
life. In this regard, the reflection, of the Fathers of the Church (Ireneus,
Tertullian, Augustine), who opposed to Manicheism and dualist doctrines in general, is
well known. Matter and corporeality are good, because they are created, as the spiritual
realities are, by one God ( CREATION, III.1). The theological significance
of matter and its ordering towards God are then reflected in the very work of
sanctification of the Church. Indeed, she entrusts to the “matter” of
the sacraments the function of signifying in an efficacious manner the order of grace, as,
for example, the water in the sacrament of baptism; and even of actualizing it, as it
happens in the transubstantiation of the bread and wine into the flesh and blood of Jesus
Christ in the sacrament of the Eucharist.
From the philosophical-theological perspective, matter can in several
cases be associated reductively to the idea of
materialism, from which it must be properly distinguished. The fusing
of the attributes of the spirit into those of matter, or, conversely,
the spirtualization of matter, can lead to various forms of
pantheism. Christian teaching, in this regard, exhorts not to view
the entire world as matter only, and to dispose oneself to recognize
the works of the Spirit. These works, even though they are realized
through visible and sensible matter, transcend matter in their origin.
III. Scientific Inquiry into the Nature of Matter
Modern science, which is based on Galileo’s method, abandons
the metaphysical approach in order to resume both the physical approach
of the Ionian philosophers and the mathematical approach of the
Pythagoreans, restating and in a certain sense unifying the two.
The intent of this section is not so much to give a complete description
of the different scientific theories of matter as to put into relief
the changes of the concept of matter which the passage from one
paradigm to the other has entailed (for the by now classical concept
of “paradigm”, cf. Kuhn, 1966).
1. The Atomic Theory of Matter The success of Galilean and
Newtonian mechanics seems naturally to suggest a mechanical description
(mechanism) of all of corporeal reality. In this viewpoint, the
simplest unifying scheme capable of accounting for different densities
of corporeal bodies, from solids to liquids and gases, was the atomism
of Democritus. After Dalton (1766-1844) devised the first experimental
proof of the atomic theory, atomism gained enough scientific merit
to be placed side-by-side with the already well-established Newtonian
mechanics. Thus, while the atomic theory gave a description of the
“structure of matter”, on the basis of which all of chemistry
was developed, Newtonian mechanics was the tool with which the “dynamics”
was described, that is a system’s evolution in time. On the
basis of the latter, the kinetic theory of gases, and more generally,
statistical mechanics, was developed, which was the first microscopic
mechanical model explaining the macroscopic theory of thermodynamics.
The development of classical physics can be therefore examined from
two points of view: from the point of view of the “structure”
of matter, which I address in this entry, and from the point of
view of its “dynamics” (
MECHANICS).
2. Matter and Radiation. Successively (beginning from the
19th century), classical physics was faced with other phenomena
to describe, such as light, electricity, and magnetism. What is
the physical nature of light? Is it made up of corpuscles of matter,
in which case, such corpuscles would be so small as to appear practically
immaterial to the observer? With his corpuscular theory, Newton
(1642-1727) proposed this material model of light, but it did not
agree completely with experience (experiments measuring the speed
of light, for example, made clear that light propagates in a refractive
medium with a velocity of c/n, where c is the velocity
of light in a vacuum, approximately 3 ¥ 108 m/sec, and n
is the index of refraction of the medium, instead of the velocity
c n required by the Newtonian theory). With his wave
theory of light, Huygens (1629-1695) explained the phenomenon of
light as a mechanical periodic vibration which propagates in a nearly
imponderable “aether” and predicted (in addition to the
correct speed of propagation in refractive media) the phenomenon
of interference later observed experimentally by Young in 1810.
The equations of Maxwell (1831-1879) which govern electromagnetic phenomena, allowed
an interpretation of the nature of light as a wave phenomenon, but
of an electromagnetic, and not mechanical, nature. Therefore, if
the nature of light is reduced to that of an electromagnetic wave,
the problem shifts from mechanics to the nature of electricity and
magnetism, two distinct phenomena which were unified by Maxwell.
The concept of “field” began to make way, as a vehicle
transporting energy in a form not conceptually reducible to the
kinetic energy of particle mechanics, even if the two are convertible.
The concept of radiation was the first to be placed alongside and
later in opposition to that of matter and thus even the concept
of energy associated with radiation is seen in opposition to that
of matter. One begins to speak of energy no longer as a property
of “something”, as an attribute of the field which transports
it, but as “something”, as if it were an autonomous entity
like matter, and of a nature in a certain sense different from the
latter. This conception of energy is favored also by the fact that
it is subject to a conservation law like that of mass: if «nothing
is created and nothing is destroyed», as Lavoisier (1743-1794)
had posited for mass-matter, this was true also for energy which
is conserved even if it transforms from one form to another. How
do matter and energy differ according to 19th century classical
physics? Certainly on account of two easily identifiable characteristics.
The first of these two is the fact that matter possesses “mass”,
whereas energy does not; in fact, it is this property which allows
one to define matter itself, interpreting mass as a “quantity
of matter”. Matter is what has mass, whereas energy can subsist
independently of matter in the form of an electromagnetic field
which has no mass, in addition to being able to be transported by
masses in the form of kinetic energy. In the second place, matter
appears in discrete form, like atoms and particles (ions, electrons),
whereas energy appears as a “continuum”, whether it is
associated with the motion of a particle (kinetic energy) or takes
the form of radiation.
3. The Theories of Relativity of Einstein. With the theory
of «special relativity» (1905) of Albert Einstein (1879-1955)
the famous equivalence of mass and energy was established ( RELATIVITY,
THEORY OF, I), quantified by the formula E = mc2 and, thus,
the first of the two properties stated above, which distinguished
mass from energy, as it was then understood, begin to break down.
On the one hand, the “mass” of a particle at rest appears
itself as a “concentrated” form of energy (energy at rest),
on the other hand, radiating energy proves its material character,
as soon as it gets inertial and gravitational properties according
to the mass E/c2 associated with it. At the same time, the
discrediting of Lorentz’s aether by Einstein as unobservable
and its replacement with the “vacuum”, gives energy a
character of yet starker self-sufficiency. The energy of radiation
no longer needs a support, that is, a vehicle which transports it
(substantiation of energy).
The theory of «general relativity» (1916) allows one
to make another interesting step in our inquiry into the nature
of matter. It associates the “metrical” (curvature) properties
of space-time — already unified by the geometrical space-time
representation of special relativity, developed by Minkowski —
to the distribution of mass-energy present in space-time itself,
in the form of matter and non-gravitational fields ( RELATIVITY,
THEORY OF, II). The absolute space and time of Newton, understood
as an empty pre-formed container in which matter is later placed,
is replaced by a space-time whose metrical properties are defined
by the presence of matter itself. Already, with special relativity,
space and time are no longer described as two independent entities
but as a single four-dimensional geometric structure (of which three
are spacelike and one is timelike); with general relativity, space-time
is curved near masses and is no longer described by means of Euclidean
geometry but instead, with the help of the geometry of Riemann (1826-1866),
in such a way that the inertial trajectories (geodesics) of heavenly
bodies, which move within it, are the same in a flat space-time
in which gravity however is present. In such a way, curvature replaces
and describes the effects of gravity itself.
4. Quantum Mechanics. Quantum
mechanics — even though it brings with it many problems
to clarify, related to the paradoxes it gives rise to (cf. for example,
Selleri, 1987) — makes further steps towards unification.
On the one hand, the non-relativistic formulation of quantum mechanics,
with the equation proposed in 1926 by Schrödinger (1887-1961) attributes
wave-like properties even to matter, following the discovery in
1922 by De Broglie (1892-1987). On the other hand, the relativistic
formulation of quantum mechanics, introduces, with the concept of
the “photon”, the discretization of the energy spectrum
of the electromagnetic field (quantum electrodynamics) — already
hypothesized by Einstein in his famous interpretation of the photoelectric
effect (1905) which earned him the Nobel Prize — and of
fields in general (quantum field theory).
In this picture, the matter of wave-particles and the energy of wave-photons, appear
conceptually indistinguishable. But quantum mechanics now introduces a criterion of
distinction which is both new and old: new, on account of its mathematical formulation,
and old, for its philosophical content. From the mathematical point of view, the criterion
is given by the different statistics the wave-particles obey. Some of these,
(“fermions»”, particles of half-integer spin), which obey
Fermi-Dirac statistics — unlike the others (“bosons”,
particles with integer spin) which obey Bose-Einstein statistics — are subject
to the Pauli “exclusion principle” which does not allow two identical
particles to have identical quantum numbers at the same place and time. This fact is
interpreted as the impossibility for two fermions to overlap. It is recognized,
philosophically speaking, as the property characteristic of matter, while bosons are not
subject to this constraint and behave like radiation. Fermions, in fact, are the particles
which make up matter (protons, neutrons, electrons, etc.), whereas bosons are the field
particles that transport the energy of interaction (photons, gluons, W and Z0
particles, and also gravitons, whose existence is not yet experimentally confirmed).
It is worthy to note that one of the most important consequences
of relativistic quantum mechanics was the prediction of the existence
of the “antiparticles” — the so-called “antimatter” —
about which much was speculated. The prediction was the work of
Paul Dirac (1902-1984) who discovered, in addition to the solution
to his famous equation which corresponded to the electron, then
experimentally well-known, another solution which turned out to
be identical to that of the electron with the difference of a sign-change
in t (same properties: mass, electric charge, spin, etc.).
At first, this solution was interpreted as an electron which travelled
backward in time ( TIME,
II.3). This interpretation, however, turned out to be non-physical;
in fact, scientists realized that, alternatively, one could interpret
the same solution as a particle identical to the electron, which
travelled forward in time, but which had opposite electric charge.
This positive electron, or positron, was discovered experimentally.
Later, antiparticles corresponding to all known particles were discovered,
even for the electrically neutral particles, which however were
described by other quantum numbers of opposite sign and which were
capable of annihilating with the corresponding particles and giving
off energy in the form of radiation. There remained the problem
of understanding why our universe is made up almost exclusively
of matter instead of antimatter. This problem of “symmetry
breaking” is probably one of the most researched problems of
particle theory and cosmology
in the past few decades.
5. Organization of Matter: Information and Complexity. The
study of matter in living organisms is the subject of biology.
Nevertheless, the overlap with chemistry
and physics has always been significant for various reasons, chief
among which, the fact that a certain reductionist methodology required
that one reduce all of the natural sciences to physics, the Galilean
science par excellence ( REDUCTIONISM).
For this reason, the link between biology and physics was expected
to be represented by organic chemistry. Another reason for this
was that the great experimental and theoretical discoveries of molecular
biology, as the genetic code of DNA and the double-helix
model of Watson and Crick (1953), was in essence a confirmation
of great importance in this sense.
Recently, that is, ever since physicists and mathematicians have resumed systematic
study of non-linear systems — a field of study begun by Poincaré and later
abandoned for many decades after his death — and from the conception of science
of complexity, which gradually involved all sciences with its
problematic, the reductionist process encountered a halting point and the relationship
between physics and biology changed radically. In a certain sense, one can say that today
it is the biologist who proposes an epistemological model to the physicist and not vice
versa.
The fact that in a non-linear differential equation the sum of two or more solutions is
not generally a solution, forms the mathematical basis of the crisis of reductionism in
that it does not allow the decomposition of a solution describing a complex structure, or
the “whole” into simpler solutions which describe its parts seen as
isolated from each other. The former, elementary, non-reductionist characteristic of
non-linear physical systems, finds its counterpart in practically all sciences (see below,
VII). Other aspects of complexity concern instead the dynamics of systems which because of
their non-linearity, behave “unpredictably”, and, if they are
dissipative, can be shown to be capable of “self-organization”, due to
the fact that they are open systems which interact with the external world with which they
exchange matter, energy, and entropy (cf. Nicolis and Prigogine, 1989).
A decisive role seems to be played by information
which, coming into play on different levels of organization of matter,
determines in each level several characteristics which differ qualitatively
and not only by quantitative amounts, becoming in this manner irreducible
with each other.
6. Matter and Mind. Another scientific problem which involves
living matter and which has developed considerably in recent times
is that of the mind-body
relationship: here one deals with an investigation which directly
concerns the sciences such as biology, physiology, psychology, together
with philosophy and theology, in an interdisciplinary context which
goes under the name, by now of common usage, “cognitive sciences”.
Parallel with the mind-body relationship, we find the problematic
of the so-called field of artificial
intelligence which involves, in place of the sciences of living
matter, computer science and information theory.
Cognitive sciences deal with how intelligent knowledge is formed in our mind in its
relationship with the brain and more generally with the body, in view of its at least
partial reproduction by the computer. It is clear that scientific problems related
to this kind of research ask in an unavoidable manner philosophical questions with
theological implications of great importance. We will indicate two of these which seem to
be among the most relevant: a) is it possible for a corporeal brain (or a computer)
to form universal abstract concepts only from its material resources and therefore think
like a human being? Or is it necessary to require the intervention of a non-material
function, like that performed by a spiritual soul? b) is it possible for a corporeal
brain (or computer) with its material resources alone, to be conscious of its activities
and therefore to possess a self-consciousness like a human being? Or is it necessary to
let a non material function performed by a spiritual soul intervene?
The two preceding questions are by now the subject of scientific
and meta-scientific discussion between physicists, mathematicians,
engineers, and computer scientists, not to mention, philosophers
and theologians. From the point of view of the philosopher, these
questions directly involve the classical problems of “abstraction”
and “reflection”, functions which the human mind habitually
performs (see below, VIII).
IV. Between Science and Philosophy
I will now delve into some philosophical questions related to scientific
theories, such as those which have surfaced in the preceding section,
making more precise, among other things, the meaning of the terms
and looking out for frequent misunderstandings related to an improper
usage of terminology which easily arise when one goes from the scientific
domain to the philosophical domain and vice versa.
The first observation concerns the scientific method. In the 20th century, one has
witnessed a particularly significant step in the understanding of the scientific method
which has had notable repercussions in the way matter is conceived. This step involved a
shift from a fundamentally positivist attitude to an attitude which revised the
foundations of scientific theories. This change of position was in part the result of a
free decision, and in part, dictated, in a certain sense, by the very evolution of
scientific research.
An example of the first type, in which a change of methodological attitude was the
fruit of careful reflection and of a free decision, was offered by Albert
Einstein. The Einstein of special relativity — an “operationist”,
in the sense of Bridgman’s operationist theory — defined quantities through
operations corresponding the experimental procedure used to measure such quantities. The
beginning hypotheses with which Einstein constructed the special theory of relativity are
none other than codifactions, in terms of laws, of what results from experience. The
Michelson-Morley experiment (1887) did not imply any modification of the laws of
electromagnetism due to the translational motion of the earth with respect to the aether,
therefore: a) the principle of Galilean relativity is valid not only for mechanical
phenomena but also for electromagnetic phenomena; b) the speed of light is invariant
under uniform translations of the observer’s reference frame The reason why Lorentz
(1853-1928), who had also deduced the correct transformations, had not succeeded in
arriving at a complete theory of relativity lies in the fact that he unwittingly added to
the two preceding principles, elements not derived from experiment, as the mechanical
explanation of the contraction of rods during their motion.
General relativity was discovered, instead, not from pressing experimental problems,
that is, not because Newton’s gravitational theory did not agree with experience (not
by chance did the experimental verification of general relativity require extremely
precise measurements), but from a need to revise the foundations of Newtonian mechanics, a
revision yet incomplete even with special relativity. What seemed unsatisfying was the
fact that the laws of Newtonian mechanics were not completely independent from the choice
of the observer, as it has happened with the laws of electromagnetism, but were related to
inertial frames of reference. How can one make two frames of reference equivalent? Making
them equivalent would have meant making them, in an appropriately generalized sense, all
“inertial”. The mathematical solution was found in the idea of the
curvature of space-time described by Riemannian geometry which made possible inertial
motion along geodesic trajectories which are not straight in the Euclidean sense.
Even Werner Heisenberg (1901-1976), at the beginning of his
“matrix mechanics”, adopted the operationist method: in his theory, only
observable quantities were supposed to appear. An undoubtedly certain criterion which is
however incapable of being absolutized in that some variables which cannot be observed are
sometimes required for the logical consistency of the theory. And these variables, in
Heisenberg’s mechanics, are the eigenvectors of the orthonormal basis of the
functional space l2 which correspond to the initial conditions of the
eigenfunctions of Schrödinger. In giving up the absolute criterion of exclusivity of
non-observable quantities, Heisenberg was lead by the very structure of the theory instead
of by an epistemological reflection.
The preceding considerations defer the question of the metaphysical foundations of
scientific theories. Every scientific theory, with is mathematical formalism, establishes
“relations” (equations, laws) which relate different
“quantities” with each other: relations and quantities are none other
than “properties” of physical objects which one wishes to describe. The
fact that a physical object has certain properties instead of others is sufficient ground
for excluding a determined way of conceiving the object as a whole. And this is so because
“quantity” and “relations” are not only the object of
the sciences, but also of metaphysics, which considers them in so far as
they are entities, and in particular, in so far as they are “properties”
(accidents) of other entities (substances). Thus we can say that a scientific theory can
be in fair agreement with a certain “metaphysics” and exclude others.
The elements of metaphysics (metascience) with which a scientific theory agrees best are
at the same time: a) the background of philosophical foundations (logical or
ontological) which it implicitly assumes b) the philosophical background in which
what is usually called “interpretation” of the theory is conceived.
In the following sections, I will examine certain assumed metaphysical
aspects which are useful for the interpretation of scientific theories
of matter, which I have referred to in the preceding section.
V. Matter and Mass, Field and Energy
1. The Tendency of Substantialization of Mass and Energy in
Classical Physics. In the mechanistic interpretation of classical
mechanics, one frequently confuses, from the philosophical point
of view, “substance” with “accident”, that is
between physical objects and their properties. From the philosophical
point of view, for instance, matter is “substance” in
so far as it is capable of subsisting by itself. Mass and energy,
on the other hand, are not “things”, they are not themselves
substances, but properties of matter, that is to say “accidents”.
With the advent of the field concept and its interpretation as something
real and not just mathematical, the tendency arose, in classical
physics, of identifying the energy carried by the electromagnetic
field with the field itself, that is, of treating filed energy as
a substance and not as a mere field property. It can be legitimate,
if one wishes, to call radiation “electromagnetic energy”,
but it is necessary to be careful in clarifying what one means by
the term “energy”, energy, in so far as it is “a
field property” or the field itself. An ambiguous terminology
is always risky, especially if one is interested in making science.
Besides, even before the substantialization of the concept of energy,
there existed, in the interpretation of classical physics, the substantialization
of the concept of mass which was often considered synonymous with
“quantity of matter”. Quantity is what is measurable in
a substance, observable par excellence and then easy to identify
with the object itself, with the substance itself. In this way we
have mass-matter, on the one hand, and energy-radiation, on the
other. Energy is found to have a dual aspect: it is treated as “accident”
in so far as it is the kinetic energy of material masses and “substance”
when it is in the form of radiation. Vice versa, mass exists only
in the form of matter because radiation is massless.
The extremization of these processes of ontologizing interpretation, of mass-matter on
the one hand, and energy-radiation, on the other, has lead to a two-fold reductionism:
first, towards materialism, and later to energetism. All of this has a historical motive.
I will begin with a few considerations on materialism. As R. Masi
has rightly observed, in his classical study of the structure of matter, «The
concept of form at the basis of the hylemorphic theory and of all of Aristotelian physics
had been misunderstood by the Scholastics of the decadent period: form which, in the true
thought of Aristotle and Thomas Aquinas is an incomplete and partial reality, an
“ens quo”, was instead described as a complete substance, an
“ens quod”, leading to a host of contradictions» (Masi, 1957,
p. 85). The nominalist thought of the mediaeval Oxford school (13th century) had
completely stripped the notion of analogy of meaning, making univocal the
search for principles on which to base the understanding of the universe. From this point
of view, the method of research had been led back to where the Ionian philosophers left
off, even if the instruments of observation and mathematical tools were clearly in a much
more advanced stage. For this reason, once the univocalized and no longer genuinely
Aristotelian notion was rejected, the new “natural philosophers”, as
they were then called, had no other alternative than to adopt as an interpretative
principle of the physical universe “matter”, understood in a simply
univocal manner. Consequently, Newtonian physics could not be anything else but
“materialist” as far as the structural description of the cosmos was
concerned, and “mechanistic”, as regards the dynamical and causal
explanation of its becoming and, finally, “reductionist”, in its
approach to the relationship between the whole and the parts. Aristotelian and Thomistic
thought so misunderstood, it became the principal enemy to combat in view of a rigorous
and certain science, which could be only mathematical and experimental. Faced with the
obscurity of Aristotelian forms, mechanism represented clarity without equal: all of
natural phenomena was conceived as a combination of material particles, bound together and
in relative motion: the universe became a big machine, decomposable in smaller ones. With
the development of thermodynamics, the concept of energy acquired notable importance, in
parallel with that of matter, but the reduction of thermodynamics to mechanics, brought
about by the kinetic theory reaffirmed the primacy of matter and motion.
The true alternative to the materialism of Netwonian mechanics is related to the
electromagnetism of Maxwell: the concept of field was developed without using the concept
of particle; the field of Maxwell is not made of particles, though being real. The fact of
substantializing field energy, which leads to “energetism”, entails
misunderstandings and conceptual errors which I spoke of above, but also: after a certain
point, there arose the tendency, in the field of classical mechanics, to reverse the
direction of reductionism. Instead of explaining everything in terms of
matter and particle motion, a new reductionism arose which tends to view energy, instead
of matter, as a founding principle to which even the notion of matter can be reduced,
conceived as a condensed form of energy. This gave rise to energetism whose first
proponent was the chemist, W. Ostwald (1895): the distinctive character of energetism
is the abandonment of matter-energy dualism which has reigned supreme up to now. Energy
becomes the most general concept. Not only does matter have to sustain the prevailing of
energy, but it has to yield unconditionally to it its place (cf. Masi, 1957).
The misunderstandings were engendered by a two-fold conceptual
error: the first consists in conceiving the electromagnetic field
as something which is not “material substance”; the second
consists in attributing a “substantial” character to energy,
in place of the substantiality removed by the field.
2. Special Relativity with its equivalence of mass
and energy restores the symmetry: not only matter but also radiation
(electromagnetic field) is endowed with a “mass”, which
is revealed by its inertial and gravitational properties (deflection
of light rays in a gravitational field). Several times people say
of conversion of matter into energy and vice versa in nuclear processes.
If it is intended that a “substance” (a part or all the
matter of some particles) has become an “accident” (some
amount of energy), an incorrect use of philosophical terms is made.
Since a property (accident) like energy can exist only as a property
of something, and matter (substance) can convert itself only into
another substance (substantial mutation), and not into an accident
(without a supporting subject: an energy of what?). Otherwise it
is correct to say that a substantial mutation has taken place during
which some particles released a part or all their “rest mass”
which was acquired by the reaction products (particles and/or radiation)
as kinetic and electromagnetic energy.
3. Quantum Mechanics. If special relativity has unified
the two properties (accidents) of mass and energy, quantum mechanics,
in its relativistic version called “quantum field theory”,
tends to compose the unit of matter and radiation, in that it presents
us a set of wave-particles in which the distinction between what
is classically denoted as “matter” and “energy”
became more drastically subtle. Matter and radiation (in the wide
sense of field of interaction: gravitational, electromagnetic, strong
and weak, which one seeks to unify) constitute no longer two opposed
entities, but rather two ways of actuating, or two “species”,
of the same reality, endowed with mass-energy, which is in a certain
sense its “genus”. From the point of view of the philosophical
tradition, it would seem natural to call this single genus “matter”,
meaning that it can actuate itself in the two species which obey
the two quantum statistics: fermions, endowed with half-integer
spin, which represent matter in the classical sense of the word,
and bosons, of integer spin, which constitute the field of interaction.
From the contemporary physical point of view, it is more usual to
denote this “genus” as “field”, which actuates
itself in two “species” of fermionic and bosonic fields.
VI. Vacuum, Matter, and Energy
At this point of the discussion, yet another old problem appeared:
that of the “vacuum” (cf. A. Strumia, Il problema della
creazione e le cosmologie scientifiche, 1992). What is the vacuum?
Can it exist? A more precise use of terminology can spare many misunderstandings
which have more than once lead many illustrious persons astray.
From the metaphysical point of view the vacuum, in the absolute
sense, is “the vacuum of entity” and as such can be identified
with “nothingness” (“non-entity”, “no-thing”),
a concept coined in order to identify things that do not exist.
Metaphysically, the vacuum does not exist by definition, because
that which exists, by the very fact that it exists, is an entity.
The vacuum, understood in the absolute sense, is therefore an absolute
and total negation of being. The vacuum in a relative sense, not
as an absolute negation, but only relative, is the “privation”
of something in a certain subject and not the total negation of
the subject. In scientific language we say “vacuum” in
the privative sense of “absence of matter”: in this case,
however, the step from this relative meaning to the absolute one
is not legitimate, if one wishes to draw conclusions of a philosophical
and theological character which do not follow logically.
According to classical physics, in the area of pure mechanics, the vacuum is a region
of space in which matter is absent (vacuum of matter): where atoms and particles are not
present, there is a vacuum. The planetary model of the atom of Rutherford confirms the
fact that empty space is prevalent in the physical world. Where there is no matter,
classical physics admits, however, there can be space, as a pure empty extension and not,
therefore, nothingness. Space assumes its identity, becomes a kind of substance, can exist
in the absence of matter, and is in fact the container of matter which is in a certain
sense pre-existent. This is the Newtonian concept of absolute space. Electromagnetism
fills this empty space with the aether which supports the field and is responsible for
electromagnetic interactions between material charged particles and transports
electromagnetic radiation energy. The vacuum, therefore, is “vacuum of
matter”, but not an absolute vacuum, in that it is filled by the aether.
Special relativity eliminates both the aether and absolute space of Newton and
re-establishes the vacuum as “something” which, however, has the
property of transmitting radiation. In fact, the vacuum, is in a certain sense the best
“means” in that, through it, all signals travel at the maximum allowed
velocity c, which is precisely the velocity of light in vacuum. The vacuum of
special relativity, therefore, is “vacuum of matter”, but not of
“radiation”. It is a vacuum which has at least one property: that of
transmitting radiation, and as such, it is not nothingness, because that which has
properties is a substantial being. It is nevertheless neither the aether, nor the absolute
space, since measurements of space and time are not absolute as in non-relativistic
physics. Relativistic vacuum is, in a certain sense, the field itself, which is never
exactly vanishing, because of the presence of corporeal bodies, over which the vacuum
extends, which exchange continually their mutual interactions. And if there were no
corporeal bodies nor radiation, would special relativity allow us to affirm that the
vacuum of both is something real? We recall that special relativity is a theory which
defines operationally its concepts: if there were no corporeal bodies nor fields it would
not be possible to define neither the observer, nor the measurement, because these require
corporeal objects to identify the coordinate axes, rulers to measure the lengths, and
clocks to measure the times. The vacuum of matter and fields would therefore not be
observable and definable and would be only a being of reason.
General relativity identifies the gravitational field with the metrical properties of
space-time (metric tensor) and makes the latter depend on the distribution of mass-energy,
that is on the presence of matter and non-gravitational fields. In this way, the
geometrical properties of space-time are determined by bodies and external fields (which
are significantly called cumulatively “matter”) and on their motion. It
is a concept of space and time far from the Newtonian one and, as it has been emphasized
by various authors, very close to the Aristotelian one. In Aristotle’s view, in fact,
space is defined through the notion of contact (today we speak of interaction) between
bodies, which allows one to introduce the concept of distance and time defined as the
number which measures motion. Clearly the two conceptions are not comparable on the
mathematical level, but only on the qualitative, metaphysical level. Something of this
kind can be found in Lobachevskij: “contact” is an attribute
characteristic of bodies; to bodies owe the name of “geometrical”
bodies, as soon as we fix our attention on this property and we do not consider instead
all the other properties, be they essential or accidental. In this way, we can conceive of
all corporeal objects of nature as parts of a single global body, which we call space (cf.
Lobachevskij, New Principles of Geometry with the Complete Theory of Parallels, Russian
edition 1835-38).
General relativity is not only incompatible with the absolute space and time of Newton
(and with their philosophical transposition brought about by Kant), just as special
relativity is not: in addition, it tells us that space and time are determined by the
presence of matter, by corporeal objects and by their mutual interactions. What is then
the “vacuum” of general relativity? The vacuum is “vacuum of
matter”, where by matter one means both corporeal objects and non-gravitational
fields. The vacuum is a free gravitational field described as a Riemannian space-time: it
is a pure abstraction because the universe is filled with matter-radiation. Nevertheless,
the Einstein equations of general relativity can be described by eliminating the presence
of matter and external fields, by means of free gravitational fields. And they even admit
a solution in which the gravitational field is zero, which corresponds to the space-time
metric of special relativity. But in the absence of fields and corporeal bodies, as one
has observed, it is not possible to speak either of the observer or of a measurement and
therefore it is not possible to speak of space-time, for which the vacuum understood in
this way appears as a pure abstraction, or a limit concept.
Quantum electrodynamics and quantum field theory further substantialize the vacuum, in
that it is conceived as an entity in which there are “virtual” pairs of
particles and anti-particles which can be brought to an observable (real) state at the
cost of an appropriate amount of energy. The vacuum so understood is certainly not
nothingness, but simply “vacuum of observable matter”. With the help of
Heisenberg’s uncertainty principle, such matter can become observable on the
condition that the energy DE required is extracted from the vacuum itself in a time
less than h/DE, where h is Planck’s constant. A similar quantum fluctuation of the vacuum, according
to certain authors, would be responsible for the generation of the entire universe from
the “quantum vacuum”, which is not “nothingness”, but
a pre-existent entity, in which pairs of particle-antiparticles (matter) and the act
necessary to extract them are virtually present ( CREATION. III).
Someone wished to interpret the quantum vacuum as the “primary
matter” of Aristotle, but this does not seem to be true, if
not for the fact that primary matter, in addition to not having
extension in that it is not yet “signed” by quantity (unlike
the vacuum which is however a space-time region), is a pure potency
and requires an adequate “external” cause to be actuated
into “secondary matter”, whereas the quantum vacuum would
seem to include in itself the capability of actuated matter.
VII. Matter and the Problem of the Whole and the Parts
From the point of view of metaphysical analysis of the structure
of matter, the problems which arise from the physics of nonlinear
systems, and more generally, from the science of complexity, brings
us directly back to the classical problem of the “whole”
and the “parts”. The other aspects related to complexity,
such as “unpredictability”, “deterministic chaos”,
and “self-organization”, concern for the most part the
evolutionary “dynamics” of matter. ( COMPLEXITY,
V; DETERMINISM/INDETERMINISM, II; UNIVERSE, IV.1).
1. Positions and Problems of Approach. In the contemporary
sciences the problem of the “whole” and of the “parts”
(which is presented at times as the problem of “holism”)
can be formulated at first glance in the following way. We consider
a given object (the whole) which we will call “complex”
in that it appears to us as very articulated and difficult to examine
as a whole. We decompose (on the basis of an assigned rule) the
source object into other objects which we call “parts”
and which turn out to be simpler to examine because they are scientifically
well-understood. There are two alternative possibilities: a) the
complex object is exhaustively explained, at least within certain
limits, with a study of its parts taken as self-standing; b) the
complex object manifests properties and behavior which cannot be
explained with an examination of its component parts alone.
The first case is equivalent to the typical assumption of the reductionist approach:
the whole is completely explained through its component parts. We could say by a formula
which makes scientific sense only when the terms are explained exactly, but which has
however a certain expressive power, that “the whole is the sum of the
parts”. The second case emphasizes the insufficiency, or the impossibility, of
the reductionist approach and points to a holistic approach. We distinguish
“insufficiency” and “impossibility” because both
situations can arise.
We encounter insufficiency when we find that the complex whole is not exhaustively
explainable through the study of the component parts, since it is characterized by
properties typical of the “whole” in itself. These properties elude
scrutiny if one does not consider the general whole, because they cannot be found in the
single separate parts. One can say then, using a rough formula, that in this case
“the whole is more than the sum of its parts”, or that it contains new
information in addition to that contained in the parts, information which characterize it
as a “whole” taken together. In the Aristotelian scheme, one would say
that the “whole” has a form which makes it “one”, with
new properties not present in the juxtaposition of the parts. It is not by chance that the
term “form” reappears in the language of biologists and mathematicians
(cf. e.g., Thom, 1989)., together with a new interest in the writings of Aristotle.
One encounters “impossibility” when the complex whole is not
divisible into simpler parts. In this case, some parts, or every part, have identical
properties, or have a degree of complexity comparable to that of the
“whole” and, consequently, the subdivision does not lead to any
simplification. It is a little like what happens when a magnet, cut in half, does not
become simpler in its structure, but gives rise to two new magnets similar to the original
one. Using a rough formula, we can say that in this case “the whole is contained
in its parts” and in a certain sense “replicated in all its
parts”. It is interesting to note how these parts are not necessarily identical,
but possess enough similarities to permit an application of the same definition to both
the whole and the parts. In philosophical language, we would say that the parts are of the
same nature as the whole.
Clearly, these statements regarding the insufficiency of the reductionist
approach do not have to lead to exasperation. Reductionism is always
in a certain sense legitimate, otherwise knowledge would be impossible.
Human intelligence needs to break up and put together in order to
understand: it is not always indispensable to study the entire universe
as a whole to understand one of its parts, even if in certain cases
it is necessary to do so. An example of this is the recent dialogue
between cosmology and particle physics aimed at solving the problem
of the so-called “first instants” of the universe ( COSMOLOGY,
III, VI.1).
2. Some Examples taken from the Sciences. Given the importance
for both the analysis within the sciences and for potential dialogue
with other fields, we outline briefly how the subject of the whole
and of the parts is viewed and approached in a few of the main scientific
disciplines.
In biology, one finds that a living organism manifests properties
which, even from the chemical-physical point of view, are not shared by inanimate objects.
Even the simplest living organism cannot be entirely described by analyzing its component
parts. In a reductionist mindset, a statement of this kind is met with suspicion and
accused of vitalism because it seems to introduce an animistic factor into life. But this
is not the real problem: the point is rather that of seeing if, in the organization of
matter, the matter itself, if stimulated in the right way by an adequate external cause,
tends to manifest a new level of order, which was not present in the components taken
separately, once a certain degree of organic structuralization (complexity) has been
reached. On this level, an analysis of the component parts is no longer sufficient
— it has been however useful and necessary up to this point — but
there is a need for an inquiry of a different level of the whole and of the whole itself.
An in-depth study of a relatively complex molecule, as crystalline lattices in solids
or electrical conductors (to cite only a few examples), have pointed out how even in the
chemistry of inanimate objects the properties of the whole of a composite
complex structure is not completely deducible from the properties of the constituent
atoms. The existence of molecular orbitals with completely shared electrons does not allow
one to think of electrons which belong to a single atom. In an electric conductor, the
conduction electrons are shared even among all the atoms. Therefore, there exist, even on
the chemical level, properties of the whole which the progress of research reveals to be
more and more significant.
In the field of physics, we must take into account two classical aspects which
characterize it: that inherent in the “mathematical tool” in itself and
that having to do with the “explanation of observation”. From the
mathematical point of view, as soon as physics uses more and more mathematics to formulate
its laws in the form of equations, new problems arise. Such problems come about when new
mathematical results give unexpected results to these physical questions. I will deal with
this subject shortly, when I treat the subject of mathematics (cf. here below). As far as
the agreement between hypothesis and observation is concerned, we are faced at the same
time with a vast array of unsolved, and perhaps, unsolvable, problems in classical
mechanics, deemed too complicated. In quantum mechanics, problems still remain which are a
source of paradoxes in their formulation and understanding.
In classical mechanics, it suffices to consider, for example, the complexity of
turbulent motion in fluids. The classical model of Landau (1959), which superposes several
convective motions associated with increasing frequencies, does not correctly predict the
transition to turbulence which appears as a completely new property in addition to that of
convection. In quantum mechanics, certain events appear as “non
separable” even if they occur at great distance. It appears to be a question of
those cases in which the whole seems to be located in one of its parts.
In the field of mathematics, the problem of the whole and of the parts
appears with great clarity in the two aspects alluded to above. As far as the aspect of
insufficiency is concerned, the problems related to the non-reducibility of the whole to
the sum of the parts gain for the theoretical physicist and for the mathematician a clear
formulation, when the evolutionary laws which govern the near totality of physical
processes are formulated in terms of non-linear differential equations. Now, in
“linear” equations, the sum of two or more solutions (let us call them
“parts”) is also a solution (let us call it “the
whole”) of the system, and vice versa, a general solution
(“whole”) can be written as the sum of several solutions
(“parts”); in physics, this law is known as the “principle of
superposition”. A well-known example is the case of waves which interfere as
their oscillations are summed. In “non-linear equations”, the preceding
statement is no longer in general true. It follows, in the sense indicated above, that the
whole is not generally obtainable as the sum of the parts. Let this reference suffice to
indicate the relationship between all the different types of behavior inherent in
non-linear theories which constitute different aspects of a single problem. Our
considerations lead us to the second aspect of the problem, that of the impossibility of
using an adequate reduction, or, also, of the indistinguishability of the parts from the
whole: the whole is replicated in all of its parts. A typical example of this second
aspect is given to us by “fractal geometry”, (cf. Peitgen and Richter,
1986). Fractals, among other things, have the property of being
“self-similar”, that is of reproducing infinitely, in all of their
parts, geometrical forms similar to that of the whole; for this reason, it is not possible
to isolate the forms which are structurally less complex than the whole by subdividing
them into smaller and smaller parts. It is interesting to note that in the Mandelbrot set,
the form of the parts is not exactly identical, but is similar to the shape of the whole
and maintains the degree of complexity, which can be quantified with the so-called
“fractal dimension”.
In logic, the problem of the relationship between the whole and the
parts arises mainly in the second of the two aspects already mentioned, that for which the
whole can be found, in a certain sense, as a part of itself. This problem appears, for
example, in the “logic of sets”. The set of all sets is a typical
example of a set which contains itself as an element: in this case a part of the set
coincides with the whole. In the first phase, the logic of classes, developed by Russell and Whitehead has turned over the problem by
excluding from the definition of “class” the sets which contain
themselves as an element in order to avoid the usual contradictions which can arise from
their consideration. It is known that Russell’s paradox arises when one tries to
define an object as «a catalogue of catalogues which do not refer to
themselves». It therefore seems possible to construct a theory of collections
which contain themsleves as elements. Computer scientists nevertheless deserve the credit
for having made current the by now classical problems of mathematical logic, such as those
related to Godel’s theorem on the consistency and completeness of axiomatic systems. Another merit of computer science is that of making possible
the representation on the computer screen of Julia sets the beauty and
elegance of which was unknown and were considered as mathematical
“monsters”, due to their infinitely windy boundary. Research in
artificial intelligence has led to the understanding that information can
be nested on various levels and that there exist several hierarchies of information: the
lower level resides in the hardware structure of the machine, and the higher levels in the
software; the programming language, in turn, contains information which is significant for
the programmer. Such information falls into lower-level instructions which are
mechanically executable by circuits which do not perceive them as significant. The program
itself and its whole contain information on a higher level related to the goal it was
written for, it resides in the mind of the programmer and of the user, and so on and so
forth.
In all of the sciences, therefore, there seem to appear a hierarchical
structure of information related to the degree of complexity and
therefore to the unity of the structure in question. In Aristotelian-Thomistic
philosophy, as has been said earlier, the unitary principle of a
being is its form. Even if it is not yet clear what course the sciences
will take, it seems relatively indicative of the shift from the
univocal scheme of reductionism towards that of the new and more
satisfying vision. Today we are witnessing, curiously, an interesting
change, due to which mathematics itself, and with it the other sciences,
seem to show a genuine interest towards a broader rationality which
opens to the sciences the horizon, up to now scorned, of analogy.
VIII. Matter, Intelligence, and Abstraction
Cognitive science deals with how intelligent knowledge is formed
in our mind, in its relationship with the brain and with the body
in general, even in view of at least partial reproduction of the
latter through the use of the computer ( ARTIFICIAL
INTELLIGENCE; MIND-BODY, RELATIONSHIP). In observing, for example,
the methodology of current scientific research in artificial intelligence,
we are confronted, from the philosophical point of view, with a
two-fold approach: roughly speaking, we can take a “Platonic”
route and an “Aristotelian” one, excusing my somewhat
schematic, but very significant, use of this terminology. As A.
Koyré has suggestively observed: «If you claim for mathematics
a superior status, if more than that you attribute to it a real
value and a commanding position in Physics, you are a Platonist.
If on the contrary you see in mathematics an abstract science, which
is therefore of a lesser value than those — physics and
metaphysics — which deal with real being; if in particular
you pretend that physics needs no other basis than experience and
must be built directly on perception, that mathematics has to content
itself with the secondary and subsidiary role of a mere auxiliary,
you are an Aristotelian. What is in question in this discussion
is not certainly — no Aristotelian has never doubted the
certainty of geometrical propositions or demonstrations —
but Being; not even the use of mathematics in physical science — no
Aristotelian has never denied our right to measure what is measurable
and to count what is numerable — but the structure of
science, and therefore the structure of Being.[...] It is obvious
that for the disciples of Galileo just as for his contemporaries
and elders mathematicism means Platonism» (Koyré, 1943, pp. 421,
424).
From the technical point of view, the results obtained suggest, in the future, what
type of approach to prefer and how to correct it in order to make it better.
a) The approach which we call, in a certain sense, “Platonic”,
is also reductionist: it is based on a theory of knowledge as
“anamnesis”, the memory of innate ideas which are revived from its
contact with sensible experience. In this point of view, the intelligence is led back to
that operation which brings to the fore “memory” up to a superposition,
at least approximate, of the idea with the sensory datum of experience. From the point of
view of computer science, this conception suggests the technique of “letting
in”, on the part of the user, of as much information as possible, in the
hardware: the information plays a similar role to that of the innate ideas, or, as one
prefers to call them, in this case, of concepts. One cannot deny that the term
“concept” is used more than once in a rather ambitious way by those who
deal with artificial intelligence and often indicates simply a certain codification stored
in memory, which makes the recognition of objects not completely identical to each other,
recalling vaguely the notion of universals. With this strategy, the system works well as
long as one does not depart from the set of stored data, but it does not recognize certain
similarities and does not succeed in establishing analogies. One obtains a scarce level of
universality with such concepts.
b) A second way of approach is based on a methodology upturned with respect to the
former and which is more similar to the “Aristotelian” conception, or at
least to an empiricist one, in that it is based on the hypothesis that knowledge is not
innate, but is learned from experience through a process which goes from the external
senses to the brain and to the mind. It is a question of a methodology which attempts to
emphasize techniques of machine “learning” of concepts.
But what is a concept? In both of the preceding approaches, there is a tendency to make
recourse to two techniques, that of approximation on the one hand, and that of
modelization on the other. The “technique of approximation” connects
back, in a certain sense, to the empiricist notion of David Hume
(1711-1766): the concept would be a kind of “singular vague” datum and
one tries to realize this vagueness of the singular in view of a generalization by
introducing an allowed margin of error, which allows several objects to fall into the
approximate scheme and not just one. The “technique of modelization” is
certainly less rudimentary than the one of approximation and it is based on a process of
“abstraction” (performed first, however, by human mind) aimed at
identifying elements common to several singular data.
A comparison with the cognitive science of Thomas Aquinas, based on that of Aristotle,
seems useful and also interesting. Such science identified, basing itself on common
experience, three operations characteristic of human understanding: the first operation
was called simplex apprehensio and we could agree to translate this diction from
Latin into English as “simple apprehension”; the second operation is
“judgement” (lat. iudicium); the third is
“reasoning” (lat. ratiocinium). Each of these operations acts on
the source material and elaborates its own product which is the object of the study of
logic. Simple apprehension begins with the sensory datum furnished by the senses and by
the brain, we shall say generally from the body, and furnishes as a final result (or
product) the concept. The judgement has as source material the product of the first
operation and works, by connecting together appropriately the concepts, by elaborating a
proposition or enunciation. Finally, the reasoning connects the propositions elaborated by
the second operation, following the rules of inference which guarantee the correctness of
the deduction (cf. for example, Thomas Aquinas, In “Peri hermeneais”,
Proem., n. 1). The theory of abstraction lies on the level of the first operation, in
so far as by “abstraction” we mean that process which the mind performs
on the datum elaborated by the body, starting from a sensory singular element and
extracting from it an informative universal product, that according to this theory is
precisely the concept (cf. Summa Theologiae, I, q. 85, a. 1).
This operation is of a cognitive character: it releases, in a certain way, the
information from a physical signal which transports it, from the physiological
representation which is found in the body and the brain and, from the logical point of
view, has the effect of furnishing a datum in the form of a “universal”
(concept), removing it from the material context which delimited it and made it a
“singular” concrete. And it is just this characteristic of universality
that qualifies the concept as a principle of knowledge, of a nature qualitatively
different from that of the sensory material datum present in the senses, in the nerves, in
the brain, as an electrical polarization, as a chemical alteration, or other, or in an
electric circuit such as a state of a binary system. The concept appears with a different
nature, which is not reducible to sensible material datum: it is not reducible to the
cerebral state, even if it is tied to it. From this point of view, universality is not
obtainable from genericity, in the sense of indeterminacy, as Hume intended to: the
universal is not an approximate singular, with a margin of error in its boundary, but is
something qualitatively different, being non-material information.
The content of information does not coincide, properly speaking, with the signal which
it transports, even if one cannot ignore the physical vehicle (of electrical nature,
chemical, or other). To be known by the human mind, information needs to be in a certain
sense extracted (“abstracted”) from its vehicle and possessed by the
mind in an immaterial form (“intentional”). One then asks the question
of how the mind must be made to perform this operation of abstraction of non-material,
universal, information from sensory data, elaborated up to its cerebral state. The
standard response given by this theory is that in order to perform an operation of
abstraction of a non-material principle, such as information, a non-material mind is
necessary, for reasons of fitting causality. All of this is based on the conception of
universal as immaterial information, since matter is by its very nature individualizing
(principle of individuation). If this way of approaching the problem is correct, it does
not seem that a computer by itself, in so far as it is material — or a brain by
itself, in so far as it is material — can elaborate a universal abstract
concept, even if it can manage information related to it, when it is made to work by an
operator who is endowed with an immaterial mind. What the machine or the brain-body can at
most produce is an electromagnetic or an electrochemical representation, or something
else, which does not contain the matter of the observed object, but which is however still
tied to the matter-energy of the physical signal, and, as such, is not yet universal. In
the Aristotelian-Thomistic conception, this representation is called phantasma and
abstraction of the universal concept from the particular phantasma cannot be
performed by a corporeal, material organ, but has to be the work of an immaterial
intellect, which, in so far as it performs such an operation, is called “active
intellect”. The machine can, however, manipulate (singular) symbols which for the
human operator has a universal meaning which furnishes elaborations of reasoning and
calculations, whereas the processes of human intelligence seem to be irreducible to the
processes of calculation (cf. Penrose, 1995).
Alberto Strumia
(translated by Eric Chang)
See also: CHEMISTRY;
COMPLEXITY; EPISTEMOLOGY; MATERIALISM; MECHANICS; QUANTUM MECHANICS;
REDUCTIONISM; SPIRIT.
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