ABSTRACT
It is a common experience that the excellence of an artist’s mastery over his material, and the decisive certainty with which he judges and assesses works in his art, is only quite exceptionally based on a theoretical knowledge of the rules which prescribe direction and order to his practice, and determine the standards of value on which the perfection or imperfection of the complete work must be assessed. Normally the practising artist is not the man who can who can inform us rightly regarding the principles of his art. He follows principles neither in his creation nor his evaluation. In his creation he follows the inner activity of his harmoniously trained powers, in his judgement his finely formed artistic taste and feeling. This is not merely so in the case of fine art, of which one may first have thought, but in that of the arts generally, in the widest sense of the word. It therefore holds for the activities of scientific creation and the theoretical evaluation of their results, for the scientific demonstrations of facts, laws, theories. Even the mathematician, the physicist and the astronomer need not understand the ultimate grounds of their activities in order to carry through even the most important scientific performances. Although their results have a power of rational persuasion for themselves and others, yet they cannot claim to have demonstrated all the last premisses in their syllogisms, nor to have explored the principles on which the success of their methods reposes. The incomplete state of all sciences depends on this fact. We do not here mean the mere incompleteness with which the truths in a field have been charted, but the lack of inner clarity and rationality, which is a need independently of the expansion of the science. Even mathematics, the most advanced of all sciences, can in this respect claim no special position. Though often still treated as the ideal of all science as such, how little it really is such is shown by the old, yet never finally composed disputes as to the foundations of geometry, or as to the justification of the method of imaginaries. The same thinkers who sustain marvellous mathematical methods with such incomparable mastery, and
who add new methods to them, often show themselves incapable of accounting satisfactorily for their logical validity and for the limits of their right use. Though the sciences have grown great despite these defects, and have helped us to a formerly undreamt of mastery over nature, they cannot satisfy us theoretically. They are, as theories, not crystal-clear: the function of all their concepts and propositions is not fully intelligible, not all of their presuppositions have been exactly analysed, they are not in their entirety raised above all theoretical doubt.
