§ 16. Before, however, we attempt to delineate the logical ideal of
the discoverer, it will be necessary to encounter a serious objection
which protests on principle against such an undertaking, and urges
that discovery by its very nature must elude logical treatment. It
is contended, in the supposed interests of logic, that discovery is
a process so inherently and incurably psychological that no logical
account can ever be given of it. Discoveries are windfalls, and come
as ‘happy thoughts’ to the gifted geniuses that make them, in a manner
neither they nor any one else can account for or describe: they are
therefore logically fortuitous, and to set forth the ideal of proof by
which the truth of discoveries is tested is all that need, or can, be
the concern of logic.
Certainly the great majority of deductive logicians have taken up some
such attitude towards the process of discovery. Aristotle contents
himself with a bare mention of ‘sagacity’ (ἀγχίνοια), which is defined
as the instantaneous apprehension of the suitable middle term for
constructing a demonstrative syllogism.[390] When one recollects the
weary centuries of painful effort and continual failure which elapsed
while the _élite_ of the human race were seeking for clues to, e.g.,
the mysteries of disease and of physical happenings, before they hit
upon the notions of microbes and the mechanical theory, this naïve
underestimate of the most difficult and essential of scientific
procedures sounds like a mockery. Yet the whole Aristotelian school
pass over the problem as lightly. They all seem to believe that, while
it is merely low cunning to make a discovery, it is a real proof of
mental capacity to arrange it ‘in logical order’ after it has been
made, and to show how far short it falls of the logical ideal. Even the
inductive logicians may be said to have participated in this attitude.
For they were not more anxious to propound methods of discovery than
to contend that their conclusions were just as rigidly proved and just
as formally valid as those of syllogisms. They did not see that they
were thereby accepting the demonstrative ideal of proof and giving away
their own; what they should have shown was that this ideal was utterly
nugatory, and that their own methods could never conduct to ‘proof’,
but only to something vastly superior.
§ 17. In spite, however, of this wonderful consensus of logicians the
above argument depends essentially on a confusion. It has confused
two things which are perfectly distinct, the actual procedure of
the individual discoverer, and the generalized description of the
attitude of mind and procedures of discoverers, as they appear to
subsequent logical reflection. Both present problems to the logician,
but the problems are not the same. To anticipate the process of actual
discovery may well be left to the prophets; it will transcend the
powers of logic and indeed of any science, unless it be individual
psychology, if it exists, or history, if it be a science.[391] It may
readily be admitted that anecdotes about the bath which fomented in
the mind of Archimedes the idea of specific gravity, and the streets
of Syracuse through which he ran and cried ‘_Heureka!_’, or about
the apple-tree which shed its fruit upon Newton’s receptive head,
and stimulated his brain to frame the law of universal gravitation,
are beneath the dignity of science. Their narration belongs to
history, which can go as deeply into their details as the scale
of the history and the purpose of the historian demand; but the
particular circumstances of a particular discovery may well be treated
as ‘accidental’, and be smoothed out of the scientific record. But
why does it follow that no common features can be traced in these
histories of discovery, and that there cannot be compiled out of a
sufficient number of them a generalized account of what appears to be
the ‘essential’, i.e. really relevant, procedure of discoverers, which
may serve as a guide and model to subsequent discoverers? Why should
this be more difficult than to describe the method of lion-hunting
from the records of lion hunts, or the treatment of a disease from the
history of a number of cases? Indeed, it would seem that the thing has
been done. Any discoverer may reflect upon his own discoveries, and,
like Poincaré,[392] formulate the method he has found successful. And
if discoverers are not all perfectly unique in their methods, important
uniformities will probably be found by comparing the methods of a
number of discoverers.
Why again should it be assumed that the general account thus extracted
from a retrospective study of discoveries must at once coincide with
the logical ‘ideal of proof’? Why should it even point to this, or
be related to it otherwise than by contrast? Surely the possibility
should be discussed that there are _two_ procedures for logic to
consider, of which the one describes how human knowers, starting
from what they believe themselves to know, set about it to fortify
and extend their knowledge, while the other moves on a superhuman
plane and describes, with Platonic fervour, how ideal demonstration,
descending from absolutely certain principles, moulds into a closed
and inexpugnable system all the truths which are deducible from these
and alone intelligible. The two accounts must be distinct, for they
have different starting-points and work upon different material. Nor
need they ever have any point of contact. For it may well be that human
knowing never attains to an absolute certainty and a completed system,
while deductive proof never condescends to notice mundane fact.
This was certainly so in the first rapturous vision of _a priori_
‘proof’ which solaced Plato amid the elusiveness and opacity of the
flow of happenings. The deduction of the intelligible order of the
ideal ‘Forms’ from their supreme ground and (_sole_!) premiss in the
‘Idea of the Good’ stopped short of facts and events at the _laws_ of
minimum generality,[393] and recognized in all the happenings of the
sensible world an ineradicable taint of ‘not-being’ which rendered
their stability impossible and their prediction vain. Aristotle
similarly distinguished between the procedure which started from the
_notiora nobis_, the apparent facts of perception, and that which
began with the _notiora naturae_, the self-evident principles which
could form the ultimate premisses of demonstrations. But that these two
methods must somehow coincide was assumed rather than proved, in a way
that should have discredited the doctrine. For Aristotle also was not
able to explain how ‘science’, being of ‘universals’, could apply to
particulars, which nevertheless he would not with Plato stigmatize as
‘unreal’, while the ascent from the sensible fact to the ‘universal’,
which was called the ‘induction’ of the ‘principle’, is hardly
validated by the naïve allegation of a mental faculty of ‘intuitive
reason’ (νου̑ς) endowed with the special function of apprehending
principles in their particular exemplifications. It is high time,
therefore, that this whole assumption that a necessary congruity exists
between the logic of discovery and of proof should be subjected to a
thorough examination.