Accordingly what is in one sense the revival of classical learning is in
another a recourse to what inspired that learning, and so is a new
beginning. There is no place for a reformed Aristotelian logic, though
the genius of Zabarella was there to attempt it. Nor for revivals of the
competing systems, though all have their advocates. Scientific discovery
was in the air. The tradition of the old world was too heavily weighted
with the Ptolemaic astronomy and the like to be regarded as other than a
bar to progress. But from the new point of view its method was
inadequate too, its contentment with an induction that merely leaves an
opponent silent, when experiment and the application of a calculus were
within the possibilities. The transformation of logic lay with the man
of science, hindered though he might be by the enthusiasm of some of the
philosophers of nature. Henceforth the Aristotelian logic, the genuine
no less than the traditional, was to lie on the other side of the
Copernican change.
The demand is for a new organon, a scientific method which shall face
the facts of experience and justify itself by its achievement in the
reduction of them to control. It is a notable feature of the new
movement, that except verbally, in a certain licence of nominalist
expression, due to the swing of the pendulum away from the realist
doctrine of universals, there is little that we can characterize as
Empiricism. Facts are opposed to abstract universals. Yes. Particulars
to controlling formulae. No. Experience is appealed to as fruitful where
the formal employment of syllogism is barren. But it is not mere
induction, with its "unanalysed concretes taken as ultimate" that is set
up as the substitute for deduction. Rather a scientific process, which
as experiential may be called inductive, but which is to other regards
deductive as syllogism, is set up in contrast to syllogism and
enumeration alike. This is to be seen in Zabarella,[95] in Galilei,[96]
and in Bacon. The reformed Aristotelian logic of the first-named with
its _inductio demonstrativa_, the mathematico-physical analysis followed
by synthesis of the second, the _exclusiva_, or method of exclusions of
the last, agree at least in this, that the method of science is one and
indivisible, while containing both an inductive and a deductive moment.
That what, e.g., Bacon says of his method may run counter to this is an
accident of the tradition of the quarrel with realism. So, too, with the
scholastic universals. Aristotle's forms had been correlated, though
inadequately, with the idea of function. Divorced from this they are
fairly stigmatized as mental figments or branded as ghostly entities
that can but block the path. But consider Bacon's own doctrine of forms.
Or watch the mathematical physicist with his formulae. The faith of
science looks outward as in the dawn of Greek philosophy, and
subjectivism such as Hume's has as yet no hold. Bacon summing up the
movement so far as he understood it, in a rather belated way, has no
theory of knowledge beyond the metaphor of the mirror held up to nature.
Yet he offers an ambitious logic of science, and the case is typical.
Galilei.
The science of the Renaissance differs from that of the false dawn in
Greek times in the fact of fruitfulness. It had the achievement of the
old world in the field of mathematics upon which to build. It was in
reaction against a dialectic and not immediately to be again entrapped.
In scientific method, then, it could but advance, provided physics and
mathematics did not again fail of accord. Kepler and Galilei secured it
against that disaster. The _ubi materia ibi geometria_ of the one is the
battle-cry of the mathematico-physical advance. The scientific
instrument of the other, with its moments of analysis and construction,
_metodo risolutivo_ and _metodo compositivo_, engineers the road for the
advance. The new method of physics is verifiable by its fruitfulness,
and so free of any immediate danger from dialectic. Its germinal thought
may not have been new, but, if not new, it had at least needed
rediscovery from the beginning. For it was to be at once certain and
experiential. A mathematico-physical calculus that would work was in
question. The epistemological problem as such was out of the purview.
The relation of physical laws to the mind that thought them was for the
time a negligible constant. When Descartes, having faithfully and
successfully followed the mathematico-physical inquiry of his more
strictly scientific predecessors, found himself compelled to raise the
question how it was possible for him to know what in truth he seemed to
know so certainly, the problem entered on a new phase. The scientific
movement had happily been content for the time with a half which, then
and there at least, was more than the whole.
Bacon.
Bacon was no mathematician, and so was out of touch with the main army
of progress. By temperament he was rather with the Humanists. He was
content to voice the cry for the overthrow of the dominant system as
such, and to call for a new beginning, with no realist presuppositions.
He is with the nominalists of the later Scholasticism and the
naturalists of the early Renaissance. He echoes the cry for recourse to
nature, for induction, for experiment. He calls for a logic of
discovery. But at first sight there is little sign of any greater
contribution to the reconstruction than is to be found in Ramus or many
another dead thinker. The syllogism is ineffective, belonging to
argumentation, and constraining assent where what we want is control of
things. It is a mechanical combination of propositions as these of terms
which are counters to express concepts often ill-defined. The flight
from a cursory survey of facts to wide so-called principles must give
way to a gradual progress upward from propositions of minimum to those
of medium generality, and in these consists the fruitfulness of science.
Yet the induction of the Aristotelians, the dialectical induction of the
_Topics_, content with imperfect enumeration and with showing the burden
of disproof upon the critic, is puerile, and at the mercy of a single
instance to the contrary. In all this there is but little promise for a
new organon. It is neither novel nor instrumental. On a sudden Bacon's
conception of a new method begins to unfold itself. It is inductive only
in the sense that it is identical in purpose with the ascent from
particulars. It were better called exclusiva or elimination of the
alternative, which Bacon proposes to achieve, and thereby guarantee his
conclusion against the possibility of instance to the contrary.
His three Methods.
Bacon's method begins with a digest into three tables of the facts
relevant to any inquiry. The first contains cases of the occurrence of
the quality under investigation, colour, e.g., or heat, in varying
combinations. The second notes its absence in combinations so allied
to certain of these that its presence might fairly have been looked
for. The third registers its quantitative variation according to
quantitative changes in its concomitants. The method now proceeds on
the basis of the first table to set forth the possible suggestions as
to a general explanatory formula for the quality in question. In
virtue of the remaining tables it rejects any suggestion qualitatively
or quantitatively inadequate. If one suggestion, and one alone,
survives the process of attempted rejection it is the explanatory
formula required. If none, we must begin afresh. If more than one,
recourse is to be had to certain devices of method, in the enumeration
of which the methods of agreement, difference and concomitant
variations[97] find a place, beside the crucial experiment, the
glaring instance and the like. An appeal, however, to such devices,
though a permissible "first vintage" is relatively an imperfection of
method, and a proof that the tables need revision. The positive
procedure by hypothesis and verification is rejected by Bacon, who
thinks of hypothesis as the will o' the wisp of science, and prefers
the cumbrous machinery of negative reasoning.
Historically he appears to have been under the dominance of the
Platonic metaphor of an alphabet of nature, with a consequent belief
in the relatively small number of ultimate principles to be
determined, and of Plato's conception of Division, cleared of its
dialectical associations and used experientially in application to his
own molecular physics. True it is that the rejection of all the
cospecies is a long process, but what if therein their simultaneous or
subsequent determination is helped forward? They, too, must fall to be
determined sometime, and the ideal of science is fully to determine
all the species of the genus. This will need co-operative effort as
described in the account of Solomon's House in the _New Atlantis_.[98]
But once introduce the conception of division of labour as between the
collector of data on the one hand and the expert of method, the
interpreter of nature at headquarters, on the other, and Bacon's
attitude to hypothesis and to negative reasoning is at least in part
explained. The hypothesis of the collector, the man who keeps a
rain-gauge, or the missionary among savages, is to be discounted from
as a source of error. The expert on the other hand may be supposed, in
the case of facts over which he has not himself brooded in the course
of their acquisition, to approach them without any presumption this
way or that. He will, too, have no interest in the isolation of any
one of several co-ordinate inquiries. That Bacon underestimates the
importance of selective and of provisional explanatory hypotheses even
in such fields as that of chemistry, and that technically he is open
to some criticism from the point of view that negative judgment is
derivate as necessarily resting on positive presuppositions, may be
true enough. It seems, however, no less true that the greatness of his
conception of organized common effort in science has but rarely met
with due appreciation.
Forms.
In his doctrine of _forms_, too, the "universals" of his logic, Bacon
must at least be held to have been on a path which led forward and not
back. His forms are principles whose function falls entirely within
knowledge. They are formulae for the control of the activities and the
production of the qualities of bodies. Forms are qualities and
activities expressed in terms of the ultimates of nature, i.e.
normally in terms of collocations of matter or modes of motion. (The
human soul is still an exception.) Form is bound up with the molecular
structure and change of structure of a body, one of whose qualities or
activities it expresses in wider relations. A mode of motion, for
instance, of a certain definite kind, is the form of heat. It is the
recipe for, and at the same time is, heat, much as H2O is the formula
for and is water. Had Bacon analysed bodies into their elements,
instead of their qualities and ways of behaviour, he would have been
the logician of the chemical formula. Here, too, he has scarcely
received his meed of appreciation.
His influence on his successors has rather lain in the general
stimulus of his enthusiasm for experience, or in the success with
which he represents the cause of nominalism and in certain special
devices of method handed down till, through Hume or Herschel, they
affected the thought of Mill. For the rest he was too Aristotelian, if
we take the word broadly enough, or, as the result of his Cambridge
studies, too Ramist,[99] when the interest in scholastic issues was
fading, to bring his original ideas to a successful market.
Bacon's Logic, then, like Galilei's, intended as a contribution to
scientific method, a systematization of discovery by which, given the
fact of knowledge, new items of knowledge may be acquired, failed to
convince contemporaries and successors alike of its efficiency as an
instrument. It was an ideal that failed to embody itself and justify
itself by its fruits. It was otherwise with the mathematical
instrument of Galilei.
Descartes.
Descartes stands in the following of Galilei. It is concurrently with
signal success in the work of a pioneer in the mathematical advance that
he comes to reflect on method, generalizes the method of mathematics to
embrace knowledge as a whole, and raises the ultimate issues of its
presuppositions. In the mathematics we determine complex problems by a
construction link by link from axioms and simple data clearly and
distinctly conceived. Three moments are involved. The first is an
_induction_, i.e. an exhaustive enumeration of the simple elements in
the complex phenomenon under investigation. This resolution or analysis
into simple, because clear and distinct, elements may be brought to a
standstill again and again by obscurity and indistinctness, but patient
and repeated revision of all that is included in the problem should
bring the analytic process to fruition. It is impatience, a perversity
of will, that is the cause of error. Upon the analysis there results
_intuition_ of the simple data. With Descartes intuition does not
connote givenness, but its objects are evident at a glance when
induction has brought them to light. Lastly we have _deduction_ the
determination of the most complex phenomena by a continuous synthesis or
combination of the simple elements. Synthesis is demonstrative and
complete. It is in virtue of this view of derived or mediate knowledge
that Descartes speaks of the (subsumptive) syllogism as "of avail rather
in the communication of what we already know." Syllogism is not the
synthesis which together with analysis goes to constitute the new
instrument of science. The celebrated _Regulae_ of Descartes are
precepts directed to the achievement of the new methodological ideal in
any and every subject matter, however reluctant.
It is the paradox involved in the function of intuition, the acceptance
of the psychological characters of clearness and distinctness as
warranty of a truth presumed to be trans-subjective, that leads to
Descartes's distinctive contribution to the theory of knowledge. In
order to lay bare the ground of certainty he raises the universal doubt,
and, although, following Augustine,[100] he finds its limit in the
thought of the doubter, this of itself is not enough. _Cogito, ergo
sum._ _That_ I think may be admitted. _What_ I think may still need
validation. Descartes's guarantee of the validity of my clear and
distinct perceptions is the veracity of God.[101] Does the existence of
God in turn call for proof? An effect cannot contain more than its
cause, nor the idea of a perfect Being find adequate source save in the
actuality of such a Being. Thus the intuition of the casual axiom is
used to prove the existence of that which alone gives validity to
intuitions. Though the logical method of Descartes has a great and
enduring influence, it is the dualism and the need of God to bridge it,
the doctrine of "innate" ideas, i.e. of ideas not due to external causes
nor to volition but only to our capacity to think, our disposition to
develop them, and finally the ontological proof, that affect the thought
of the next age most deeply. That essence in the supreme case involves
existence is a thought which comes to Spinoza more easily, together with
the tradition of the _ordo geometricus_.