DESCARTES
745
DESCARTES
understanding of problems — and consequently its
method cannot be external, it must be essentially im-
manent. The true method is to seek for reasonable
evidence and the norm of such evidence is to be found
in the science of mathematics (Discours de la
mcthode, 2" partie). "It is not that arithmetic and
Koometry are the only sciences to be learned, but that
he who would progress on the road to truth must not
delay over any object about which he cannot have a
certainty equal to that given by arithmetical and
geometrical demonstrations" (2" Regie).
Is everything, then, capable of being known in this way, antl consequently can human knowledge become the complete coimterpart of reality? Descartes says so over and over again; it is his controlling idea; [ind he endeavours to prove it both from the nature of 3ur thought and from the universal connexion of things. The mind is equally intelligent however di- verse the objects it considers; and those objects be- cause of their perfect enchainment are always equally intelligible. There is, therefore, no question "so far removed from us as to be beyond our reach or so deeply hidden that we cannot discover it", provided 3nly that we persevere and follow the right method (Disc, de la meth. 2" partie; 4" Regie). Such is the rationalism of Descartes, surpassing even that of Plato, in which under the name of "the Infinite" three-fourths of reality remains for ever imknowable.
How then is this mathematical evidence to be ob- tained. Tn'o methods, dangerous at once and sterile, must be avoided. We cannot build on the experience af our senses; "for they are often fleceptive", and con- sequently need a control which they have not in them- seh-es. Bacon was misled on this point (2" Regie). Neither can we adopt the syllogistic method; for this is not, as was formerly thought, a means of dis- covery. It is simply a process in which, two terms being given, we find by means of a third that the former two are linked together, i. e. that they have some common characteristic. Now if they have this common characteristic it is useless to search for it with my light other than their own. Let them pass under direct scrutiny; let their natures be studied, and in time the common trait will reveal itself. This is the mind's straight road to discoverj', passing on from one idea to another without the aid of a third. The syllo- ^sm is of no use until the discoverj' has been made; it simply .serves the purpose of exposition (14" Regie). There are but two ways leading to mathematical pvitlcnce: intuition and deduction (3" Regie). Intui- tion " is the conception formed by an attentive mind, so clear and distinct that it admits of no doubt: or, what amounts to the same thing, it is the clear con- ception of a soimd and attentive mind, the product of unaided reason" (3^ Regie). Intuition is not, there- fore, perception by the senses — it is an act of the understanding brought to bear on an idea. The senses do not supply the object but merely the occa- sion. A movement, for instance, awakens in us the idea of motion, and it is that idea we must regard as the object of intuition. In very simple matters in- tuition acts quickly; thus "everj'one can know in- tuitively that he exists; that a triangle is terminated by three angles, neither more nor less, and that a globe ha,« liut one surface" (.3" Regie; 12" Regie; K6p. aux deux objections). In the case of objects more or less complex, intuition proceeds by way of analysis. Since it deals with ideas, and ideas are but one aspect of thought, everj-thing must be reduced to clear and distinct elements, to ultimate or "indecomposable" parts. The.se ultimate parts must be inspected one after another, until the object is exhausted. " by pas.s- ing from those that are easilj' known to those that are less easily known" I'fi" R^gle). In the long run every- thing will be spread out in full light.
Dedurtion is the process in which by a continuous movement of thought we draw from a thing that we
certainly know the conclusions that of necessity flow
from it. This procedure may be carried on in two
ways. " If, for instance, after various calculations I
discover the relation between the quantities A and B,
between B and C, between C and D, and lastly be-
tween D and E I do not yet know the relation be-
tween A and E"; but I can infer it by retracting the
several steps of the series. This is the first form of
detluction (7" Regie). There is a second form in
which, the connecting links of the series being too
numerous to enter the mental field of vision all at once,
we are content to draw conclusions from the general
impression we have of the series (7" Regie). De-
duction is an intellectual process, but it differs from
intuition by bringing in memory as a factor. And
this is noteworthy in view of the important role that
memory plays in the Cartesian explanation of certi-
tude, and the desperate effort he makes to defend this
procedure. From the conspicuous place that reason
holds in the Cartesian method, one might infer that
there was no room for experience. Nothing could be
less true. For Descartes, as for Bacon, the one pur-
pose of science is utility. He also expects from it a
continual betterment of the conditions of human life,
and his hopes in that direction go very far, as, for in-
stance, when he says of medicine that in the end it
would procure us the boon of immortality (Disc,
de la m(?th. 6" partie). And as he who wills the end
wills the means also, Descartes accepts in its entirety
the experimental part of the Baconian method (let-
ter to Mcrsenne, 1631), and acts accordingly. He
put himself in touch with all the experimental work of
his day (letter, April, 1632), urged others to take up
research (letter to Mersenne, 1632), and carried on
experiments of his own that covered a wide range of
subjects: the weight of air (letter, 2 June, 1631), the
laws of sound and light (letter, 1633); the essential
differences between oils, spirits, eaux-de-vie, common
waters, aquafortis, and salts. He dissected the
heads of various animals to show the workings of mem-
ory and imagination (cf. letters to Mersenne, 1633;
April, 1637; 13 November, 16.39; 4 Januarj-, 1643,
ed. Cousin, Paris, 1826). There was hardly a fact
that escaped this apologist of Reason nor anything
into whose hidden nature he did not inquire; even the
"Chasse de Pan" he followed with his accustomed
ardour.
But if the mind, moving as it does in the realm of intelligible objects, have a power of intuition sufficient to master them all, why these researches? Are they not a hindrance rather than a help? Let deduction but go on to the end, and it must assuredly attain that exhaustive knowledge which is the goal of investiga- tion, but such is not the case. Experiment helps rea- soning in more ways than one. It supplies the fact that calls forth in our intelligence the idea of the prob- lem to be solved. That idea once aroused, the intelli- gence takes hold of it, and may produce many others, according to the nature of which experience and rea- son play reciprocal, yet different, roles. The idea of a problem may be so simple as to allow a mathematical deduction of the properties of the object in question, and nothing more. In this case experiment is called in only by way of illustration, as happens, for in- stance, in the study of the laws of motion. (Cf. Principes, 2" partie.) But again the idea of a prol> lem may be so complex as to suggest various hy- potheses, since principles as a rule are so fruitful that we can draw from them more than we see in the world around us. We must then choose from among the hypotheses presented by the intellect that which cor- responds most nearly to the facts: and experiment is our only resource. It acts as a sort of guide to ra- tional deduction. It sets up, so to say, a number of sign-posts which point out, at the cross-roads of logic, the right direction to the world of f.-icts. Finally, we may be confronted with two or more hypotheBes
