Chapter C: The Renaissance

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_.