THOMAS AQUINAS’ COMMENTARY ON THE DE TRINITATE OF BOETHIUS, QUESTION V.
INTRODUCTION
Thomas Aquinas holds that scientific
knowledge is attained when observable phenomena and their properties are
accounted for in terms of their relations to their causes. On establishing the
divisions of the sciences, Aquinas follows the threefold division of the
speculative sciences as proposed by Aristotle and handed on to the Middle Ages by
Boethius, namely: Natural Philosophy, Mathematics, and the Divine Science. With
the intention of building up our familiarity with the content of the work of
Aquinas, we are set to discuss his division of speculative science using his Commentary on “Super Boethium De Trinitate”
Quaestione V[1]
(Commentary on the Trinity of Boethius, Question V) as our primary source
and guide.
With this in mind, we shall proceed to discuss, firstly,
the appropriate division of speculative science; then, we shall discuss the
subject matters of Natural Philosophy. Afterwards, we shall present Thomas’
position on Mathematics and the Divine Science. Also, it is important to note
that the names Thomas and Aquinas will be used interchangeably at the course of
this work.
1.0 THE APPROPRIATE DIVISION OF SPECULATIVE
SCIENCE
In this article,
Aquinas sets out to give a clear cut distinction between the two divisions of
speculative science. The first according to Aquinas is concerned with the work which
we seek to retrieve, while the second concerns the method it attributes to the
parts of speculative science.
Among
the objections to the question whether speculative science is appropriately
divided into these three; natural, mathematical and divine,
is the view that, since rational philosophy or logic was not mentioned in its
division, the division of science is inadequate. Also, that philosophy is commonly divided into seven
liberal arts, which include neither natural nor divine science. Hence, natural
and divine should not be called parts of speculative science.[2]
Apparently, these views are erroneous.
Aquinas
possesses a more splendid view on these questions. For him, we do not seek to
know those things studied by logic for themselves. Rather, we study them to
enable us understand other sciences. Thus, logic is not included under
speculative philosophy as a part but as something brought under speculative
philosophy as furnishing speculative thought with its instruments, namely,
syllogisms, definition, and the like, which we need in the speculative
sciences.[3]
Thomas,
further illustrates the divisibility of speculative science, first, on the
level of nature. In his reply, he writes that:
The theoretical or speculative intellect
is properly distinguished from the operative or practical intellect by the fact
that the speculative intellect has for its end the truth that it contemplates, while
the practical intellect directs the truth under consideration to activity as to
an end.[4]
These
(that is, the speculative and the practical intellect), according to Aquinas as
stated by the Philosopher in the De
Anima, differ from the other by means of their ends. While the end of the
speculative science (or knowledge as Thomas puts it) is truth, the end of
practical knowledge or science, according to Thomas is action.[5] Simply
put, the use of the theoretical or speculative intellect leads to the operational
or practical intellect. Thomas further explains that, given that matter are
inevitably proportionate to their end, the subject matter of the practical
science are necessarily things made by man, so as to direct their knowledge to
an end. Speaking on the central theme of the speculative science, Thomas posits
that, this form of science are necessarily things that cannot be made by man,
thus, our knowledge of them cannot be directed to activity as to an end.
Thomas
further distinguishes speculative science on the theme that some objects of
speculative science depend on matter for their being; hence they can exist only
in matter. This division Thomas asserts first, that some objects of speculative
science depend on matter on dual bases. The first is that, some depend on
matter both with respect to their existence and their concept. For instance, we
cannot define a tree without necessarily including the roots, stems and leaves
in its definition. Aquinas posits that it is of this sort that physics and natural
science studies.[6] On the other hand, the
second reason is for these speculative science objects being understood. This,
Thomas defines as those things whose definition contains sensible matter and
can be understood without them. Put differently, although these objects depend
on matter with respect to their existence, they do not depend on it with
respect to their concept, given that sensible matter is not included in their
definition. This is the case with lines and numbers. For Thomas, it is this
kind of objects that mathematics studies.[7]
Moreover,
another level of speculative science is that, which do not depend on matter
with respect to their existence because they can exist without matter. Thomas continues
by stating that:
Either they never exist in matter, as in
the case of God and the angels, or they exist in matter in some instances and
not in others, as in the case of substance, quality, being, potency, act, one
and many, and the like. The science that treats of all these is theology or
divine science, which is so called because its principal object is God.[8]
What
is more, this level of speculative science according to Aquinas is called
metaphysics or beyond science. Hence, it ought to be learned after physics.
Like Aristotle, Thomas inferred that before we understand what is metaphysical,
we have to proceed from that which is sensible to that which is non-sensible.
Thomas further responded to the erroneous views that,
given that all other science depends on divine science; the divine science
ought to have placed before the others.[9]
According to Aquinas, although the divine science is by nature the first of all
sciences, it should also be learned after mathematics. For in other to know the
separate substances, metaphysics has to know the number and disposition of the
heavenly spheres and this is impossible without astronomy, which presupposes
the whole of mathematics.[10]
2.0 THE SUBJECT MATTER OF NATURAL PHILOSOPHY
The objections
raised regarding this discourse echo the view that natural science does not
treat things that exist both in matter and motion. Among other objections is
the view that, since science pertains to the intellect, the intellect knows by
abstracting from matter; therefore, science cannot treat what is not abstracted
from matter. Also, things which the natural sciences treat are not subject to
motion; for instance, the soul. Lastly, all creatures are mutable, since for
Augustine, it is only in the office of God to be immutable. As such, if it is
the task of natural science to consider what is in motion, it will be its
business to consider all creatures, which for them clearly appears to be false.[11] Although
the premise to their argument (objections) is true, the conclusions which led
them into holding such views stand false.
On the contrary,
Thomas responds that natural “things are those, in which there is a principle
of motion. Hence, wherever there is motion there must be matter.[12] Consequently,
forms and natures, though belonging to things existing in motion, are without
motion when they are considered in themselves; and so they can be the objects
of sciences and of definitions. Natures
of this kind, which are the objects of the sciences of real beings, are thought
of without motion; and so they must be thought of without those conditions by
reason of which motion belongs to mobile things. Since every motion is measured
by time, and the primary motion is local motion, a thing must be subject to
motion inasmuch as it exists.[13] And
as such, Thomas posits that natural science treats of what is in motion and
matter.”[14]
In the De Anima, Thomas responds that the
object of the intellect is the essence of a thing. Thus, the intellect
abstracts from a limited or restricted matter and its conditions. Meanwhile,
within the scope of natural science, the intellect does not abstract from
common, limited or restricted matter.[15] What
is more, Thomas sagaciously, responds to the last objection mentioned above in
the following words:
The
mutability characteristic of all creatures is not with respect to any natural
motion, but with respect to their dependence on God, separation from whom
entails destruction of their very being. And that dependence falls under the
consideration of metaphysics rather than under that of natural philosophy.
Spiritual creatures, moreover, are mutable only with regard to choice; and this
sort of motion is not the concern of the natural philosopher but rather of the
metaphysician.[16]
3.0 THE SUBJECT MATTER OF MATHEMATICS
In the third
article of question five, Aquinas sets out to correct the negative impression that
since truth consists in the conformity of the intellect, there must be
falsehood whenever we think of something other than that which is. So, if in
mathematics we consider what is in abstraction from matter, we will consider it
falsely. Thus, for these Philosophers, mathematics should not be considered
science, for every science is concerned with what is true.[17]
In his response, Thomas replies that when the mathematician abstracts, he does
not consider anything outside its domain. He does not think that a line exists
without sensible matter; rather, he treats a line and its properties without
considering sensible matter. Thomas continues that there is no disagreement
between his intellect and reality, thus (even in reality), what belongs to the
nature of a line does not depend upon that which makes matter sensible, but
vise versa.[18]
Responding to the
objections, Thomas adds that the intellect has two operations. The first called
the understanding of indivisibles, by which a thing is known by what it is. And
the second operation by which it joins and divides; forming negative and
affirmative statements. In relation to these operations as they correspond to
their principles, the first is concerned with the nature of a thing itself, by
which the object of a thing holds a certain rank among beings (as with the case
of a complete thing like a whole or an incomplete thing like a part or
accident).
Thomas further
maintains that, given that the truth of the intellect results from its conformity
with what is in reality, it is evident that in the second operation, the
intellect cannot abstract what is united in reality. Through the first
operation, however, we can abstract some things that are not separate in
reality. Consequently, the intellect consists of two forms of abstractions. The
first which is concerned with the abstraction of form from sensible matter, corresponds
to the union of matter and form or accident and subject. The second, as it
concerns the abstraction from the whole, corresponds to the union of the whole
and part; and this corresponds to the abstraction of the universal from the particular.
In concluding his
third article, Thomas distinguishes the operations of the intellect into three
distinct parts. One through which the operation of the intellect is separated
from reality, and this belongs to the science of the divine or metaphysics. The
second is through the operation by which the quiddities of things are conceived
which is the abstraction of form from sensible matter, and this belongs to
mathematics. The third is concerned with the abstraction of a universe from a
particular; and this belongs to physics and all other science in general.[19]
4.0 THE SUBJECT MATTER OF DIVINE SCIENCE
The fifth article
treats on the question “whether divine science treats of what exists without
matter and motion”. Thomas begins his
argument by presenting that the most excellent science deals with the most
excellent beings. Thus the most excellent science is the divine science. Besides,
since immaterial and immobile beings are the most excellent, divine science treats
both.[20]
Thomas further affirmed that since science is perfected only through the
knowledge of principles, we must realize that if a science considers the
subject of a genus, it must invariably, investigate the principles of that
genus.
These principles
are categorized in two forms. The first principles are complete natures in
themselves, and also serve as principles to other things, such as the heavenly
bodies are principles of lower bodies and simple bodies are principles to mixed
bodies. The second principles however, are
not complete natures in themselves, but only principles of natures, as unity is
the principle of number, point the principle of line, and form and matter
principles of natural bodies. Principles of this sort, for Thomas, are
investigated only in the science that deals with the things of which they are
principles.[21]
Again, in answer
to the question of the subject matter of the divine science, if it treats what
exists without matter and motion, Thomas writes that:
Since
the principle of the being of all things must be being in the highest degree as
the Metaphysics says, these principles must be most perfect and therefore
supremely in act, so that they have no potentiality whatsoever, or the least
possible, because actuality is prior to, and more excellent than potentiality,
as the Metaphysics says. For this reason they must be free from matter, which
is in potency, and free from motion, which is actuality of that which exists in
potency. Divine beings are of this sort, “because if the divine exists
anywhere, it exists especially in such a nature” (that is to say, in a nature
that is immaterial and immutable), as is sad in the Metaphysics.[22]
Consequently,
given that divine beings are the principles of all things and they are complete
natures in themselves, they can be studied in two ways: first, insofar as they
are the common principles of all things and second, in so far as they are
beings in their own right. Although the first principles are most evident in
themselves, we can reach them by the light of natural reason only to the extent
that their effect reveals them.
What is more,
according to Thomas, is that, there are two kinds of divine science, namely,
that which treats of divine things, not as the subject but as the principle of
the subject, this kind of science is pursued by the philosophers and is also
called metaphysics. Secondly, that which investigates divine things for their
own sakes as the subject of the science, this is taught in Sacred Scripture.[23]
CONCLUSION
So far, we have
tried to duly retrieve Thomas’ thought in his Commentary on the Trinity of Boethius, Question V, with good sense
of understanding. Summarily, we presented Thomas’ affirmation of Aristotle’s
three division of speculative science as Natural Philosophy, Mathematics and
Divine Science and discussed their subject matters. Also, we saw Thomas’
distinction of speculative science from the practical science or intellect. Hence,
while the speculative science has for its end the truth that it contemplates,
the practical science directs the truth under consideration to activity as to
an end.
In the division of
speculative science which forms Thomas’ central thesis here, the natural
science has as its subject matter, those things which depend on matter for
their being and for their being understood. The mathematical science on its
part, has its subject matter those things which although depend on matter for
their being, do not depend upon it for their being understood, given that
sensible matter is not included in their definitions. Lastly, the contemplative
science or the divine science studies those things whose beings neither depend
on matter for their existence nor for their being understood. This is because
they exist without matter; as with the case of God and Angels.
BIBLIOGRAPHY
Aquinas,
Thomas. Super Beothium De Trinitate. Transl.
by Armand Mauer. Toronto, 1953
[1]
Thomas’ commentary on Boethius’ De
Trinitate was written at Paris at the end of the 1250s. the work is divided
into six questions, and three parts. Part I (question 1 and 2) concerns human
knowledge of God and the manifestation of divine truth. Part II (question 3)
concerns the knowledge possessed by faith and (question 4) the nature of
numerical identity and difference and the causes of individuation. Part III
(question 5 and 6) concerns the division and the methods of speculative science
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