The fictitious or conventional character of mathematics is still more apparent than that of the natural sciences; and we shall not add anything to what we have said in the preceding chapter about the abstract concept, the non-concrete universal, which is the distinctive process of mathematical thought. The application of the mathematical processes, through the empirical concepts, to the historical datum, gives origin to what we have called the judgment of numeration (and mensuration), and to the mathematical sciences of nature. All that has been observed of the natural sciences in general is valid for these also. Their truth is still only the truth of the intuitive, historical datum of which the empirical concepts are practical elaborations; the addition of a further practical elaboration, the abstract concept, can add to their mnemonic or, as it is more often called, technical efficiency, but not to the value of their original content. This process, as the purely naturalistic one, can be applied to the human as well as to the natural reality, but it is evident that its usefulness decreases in the passage from the one to the other, following the same standards that apply to the natural sciences in general, those of the relative perceptibility and importance of the individual happening. It is at its highest in physics or astronomy, less notable in biology or economics; practically inexistent in psychology or sociology, the two sciences that suffer not less from the delusions of misapplied statistics than from the invasions of cheap philosophy. Croce's theory of science, as we have already remarked, differs from the generally accepted methodology of modern science only in its context, which is usually agnostic in, the pure scientist, while, in Croce, it consists in the affirmation of the pure concept, or of the autonomy of philosophy: a proposition with which the scientist qua scientist has no reason to quarrel. In both cases, the autonomy of scientific thought is only relative, and the difference of context is a difference in the determination of its limits. In both cases, scientific thought is recognised as thoroughly legitimate only within limits. The cry of the bankruptcy of science, of which we heard so much a few years ago, is as meaningless for Croce as for the pure scientist; science cannot become bankrupt except by over-stepping its logical limits, that is, by first ceasing to be science and becoming the ape of philosophy.
[1] See Logica, part ii, La filosofia, la storia, etc., pp. 171-269.
[VII. THE THEORY OF ERROR][1]
The practical origin of theoretical error—Confirmations of this doctrine—The forms of error—Æstheticism and empiricism; mathematicism—Philosophism: the philosophy of history and the philosophy of nature—Mythologism: philosophy and religion—Dualism, scepticism, mysticism—The conversion to truth—The function of error.
One of the most original developments of Croce's thought—a doctrine that does not owe its validity only to its connection with the system, since we can find it adumbrated already in such widely divergent philosophies as those of Socrates and Thomas Aquinas, of Descartes and Rosmini, but which in Croce's system acquires a new and wider meaning—is the theory of the practical origin of theoretical error, which we shall briefly discuss in this chapter.
From a strictly logical standpoint, every error is mere privation or negativity, the opposite of the logical value which is truth, and therefore inexistent outside the moment of opposition. As there are not two values in æsthetics, the beautiful and the ugly, but one only, beauty or expression, of which ugliness or non-expression is merely the negative aspect, so in logic also there is but one value, thought or truth, and error is non-thought, that which logically has no being or reality. There is no thought which is not a thinking of truth.
Let us pause for one instant to consider this last proposition, which at first sight undoubtedly has a somewhat paradoxical air. And yet it is impossible not to accept it, unless we are willing to fall into the most radical scepticism, which would imply a renunciation not only of every form of thought, but even, since there is no action which is not founded on knowledge, of every kind of action. If we believed that it were possible for our thought to think that which is not true, no external criterion or standard of truth could even be substituted for that which thought intrinsically would lack, since the apprehension of such external standards would in itself be an act of thought, and therefore suffer from the indetermination and uncertainty of thought itself. This belief in the validity of human thought is in fact, however disguised or even openly denied, present in every thinking and acting being: every thought, every action of man is an implicit declaration of this faith. And once we have consciously acquired it, as an inalienable, intrinsic characteristic of our whole spiritual activity, it is evident that it leaves no place for faith as such, for an obscure, independent faculty, a mystical intuition, different from and superior to our human thought, and which could mysteriously endow thought itself with the gratuitous gift of truth.
And yet, after we have denied the logical existence of error, we are still confronted with the mass of positive errors which we can more or less easily identify in the course of history and in our daily experience. Positive errors, that is, affirmations of knowing that which we do not know, are real products of our activity: but since the theoretical value, truth, is absent from them, they cannot be products of the theoretical activity. They must therefore be products of the only other form of spiritual activity, the practical. Ignorance or obscurity or doubt are not errors; they are the inexhaustible matter to which the spirit of man is perpetually giving form and reality. To be aware of one's ignorance is in fact the first stage in the research of truth, the initìum sapientæ. Thought and truth are affirmation; the positive error is an affirmation also, which simulates truth. We cannot think an error, but we can pass from thought to action, by making a false affirmation, a purely practical affirmation, which consists in the act of producing sounds to which no thought corresponds, or, which amounts to the same, only a thought without value, without coherence, without truth. What we have qualified in its negative aspect as a theoretical error manifests itself in its positive aspect as an act of will, directed to a certain end, a practical act, and, as such, having its own rationality, which is neither logical, nor moral, but purely economic, consisting in the adequacy of that particular affirmation to the individual purpose by which it has been prompted. Morality requires that the thinking spirit should realize itself as truth; and therefore the economic act which is error, though logically unreal, though economically useful, finds inevitably its ultimate sanction in a moral condemnation.