UNITY OF METHOD
According to Aristotle there is not a single method
applicable to all subject matters, but each has its own
appropriate method (Metaphysica 995b; De anima
402a; Ethica 1094b). While this was being reiterated
by Saint Thomas in the thirteenth century, two of his
contemporaries formulated conceptions of a universal
method of discovery applicable in all the sciences;
Roger Bacon in his scientia experimentalis, and
Raymond Lully in his ars magna, the one empirical,
the other a priori. Bacon calls his experimental science,
“this great mistress of the speculative sciences,”
attributing to it “the same relation to the other sciences
as the science of navigation to the carpenter's art and
the military art to that of the engineer.... It directs
other sciences as its handmaids, and therefore the
whole power of speculative science is attributed espe-
cially to this science” (Opus maius, Part VI, p. 633).
Knowledge is acquired in two ways, either by reasoning
or by experience. Experience includes what is learned
not only through the external senses but also through
internal illumination or divine inspiration, the latter
being important for both religion and for the principles
of the speculative sciences. Bacon worked out no rules
of operation for his new experimental science and it
is not a precursor of his namesake's logic of induction.
However, he assigned to it three prerogatives. The first
is that of verifying conclusions deduced from princi-
ples. This is not so much a method of testing hypotheses
as of giving certainty to conclusions and removing
doubt, and is not therefore properly a method of
discovery. But in its second and third prerogatives it
is one of discovery. In the second it discovers new
truths
within a science which are incapable of being
deduced from the principles of that science, and in
the third it operates without reference to the limits
of any of the particular sciences, but by its own power
investigates the secrets of nature.
Like Bacon, and those in the tradition of Aristotle,
Lully believed that each branch of inquiry rested on
a limited number of principles and basic concepts. To
this he added the notion that if letters of the alphabet
were substituted for these elements, and combined in
every possible way in a purely mechanical fashion,
everything which it is possible to know in that subject
could be discovered. Thus the great art was capable
of yielding universality of knowledge. Lully enjoyed
as great a following among his contemporaries as
Thomas Aquinas and the basic idea underlying the
great art continued to exercise a fascination until the
seventeenth century, when it became incorporated in
the ars combinatoria of Leibniz. But where Lully
assumed that each branch of knowledge had its own
simple elements, Leibniz believed it to be possible to
find a single set of irreducible concepts common to
all the sciences. Once all these concepts were given
their characteristic numbers or signs, their combina-
tions could generate a complete “demonstrative
encyclopaedia”:
Now since all human knowledge can be expressed by letters
of the Alphabet, and since we may say that whoever under-
stands the use of the alphabet knows everything, it follows
that we can calculate the number of truths which men are
able to express, and that we can determine the size of a
work which would contain all possible human knowledge,
in which there would be everything which could ever be
known, written, or discovered; and even more than that,
for it would contain not only the true but also the false
propositions which we can assert, and even expressions
which signify nothing
(ed. Wiener, p. 75).
Leibniz claimed to have derived the basic idea of the
art of combinations from the study of Aristotle's formal
logic, but it was, he says, arithmetic and algebra which
revealed to him the role of signs or characters in
making demonstration in the sciences possible. “It is
as if God, when he bestowed these two sciences on
mankind, wanted us to realize that our understanding
conceals a far deeper secret, foreshadowed by these
two sciences” (trans. Loemker, p. 340).
Descartes too had drawn his inspiration for a uni-
versal method for the sciences from the study of math-
ematics, but what he saw as significant was not, as with
Leibniz, the use of symbols in algebra, but the logical
interconnections of all the parts of geometry. These
“had caused me to imagine that all those things which
fall under the cognizance of man might very likely
be mutually related in the same fashion” (Discourse
on Method, Part II). This conviction is expressed in
an early opuscule: “All the sciences are interconnected
as by a chain; no one of them can be completely
grasped without the others following of themselves and
so without taking in the whole of the encyclopaedia
at one and the same time” (Oeuvres, X, 255). Descartes
began his first work on method, the Regulae, with an
explicit attack on the Aristotelian specialization of
methods according to subject matter. He did so on two
grounds, first, that the mind in its cognitive exercise
is no more differentiated by its subjects than is the sun
by what it illuminates, and, second, that everything
knowable is logically linked. The logical order, or
“order of reasons” which proceeds from the simpler
to the more difficult, runs directly counter to the “order
of subject-matters,” the latter being “good only for
those for whom all reasons are detached” (ibid., III,
266f.). To isolate a branch of knowledge by subject is
to deprive it of its scientific character and render it
a mere collection. There can therefore be no plurality
of sciences but only one universal science, whose parts
are undifferentiated by subjects. Leibniz took the same
view of his demonstrative encyclopaedia, pointing out
that as in geometry the demonstrative order does not
permit everything belonging to the same subject to be
dealt with in the same place. Because the encyclo-
paedia would result in the dissolution of the divisions
of the sciences by subject, an index would be an essen-
tial part of the project in order to make it possible
to bring together all propositions bearing on any one
subject (New Essays, Book IV, Ch. XXI).
In the eighteenth century the most insistent voice
on the identity of method in all the sciences was
Condillac's. Like Leibniz, he saw the perfect existing
example of this method in algebra, with its use of signs.
Algebra provided “a striking proof that the progress
of the sciences depends uniquely on the progress of
language, and that well constructed languages alone
can give analysis the degree of simplicity and pre-
cision of which it is susceptible” (
Oeuvres, II, 409 b).
He did not, like Leibniz, conceive the possibility of
a single language for all the sciences; each would have
its own, while using exactly the same method of analy-
sis. The more radical part of Leibniz' ideal, that of
a universal language, emerges again, however, with
Condorcet. This language would, he says, be like alge-
bra, “the only really exact and analytical language yet
in existence,” containing within it “the principles of
a universal instrument applicable to all combinations
of ideas,” and as easily available to all as the language
of algebra itself (
Sketch, pp. 197f.).
