The philosophic concepts and the empirical and abstract concepts in Aristotle. Philosophy, physics and mathematics.
In Aristotle, the determination of the rigorous philosophic concept and its distinction from empirical and abstract concepts make great progress, although this does not amount to a solution of those Platonic embarrassments. Aristotle accurately traces the limits between Philosophy (and so the philosophic concept) and the physical and mathematical sciences. Philosophy, the science of God or theology (as he also calls it), treats of being in its absoluteness, and so not of particular beings or of the matter that forms part of their composition. The non-philosophical sciences, on the other hand, always treat of particular beings (περὶ ὄν τι καὶ γένος τι). They take their objects from sense or assume them by hypotheses, giving now more, now less accurate demonstrations of them. All the physical sciences have need of some definite material (ὕλη) because they are always concerned with noses, eyes, flesh, bones, animals, plants, roots, bark, in short with material things, subject to movement. There even arises a physical science that is concerned with the soul, or rather, with a sort of soul (περὶ ψυχῆς ἐνίας), in so far as this is not without matter. Mathematics, like philosophy, studies, not things subject to movement, but motionless being; but it differs from philosophy in not excluding the matter in which their objects are as it were incorporated (ὡς ἐν ὔλῃi): the suppression of matter is obtained in them by aphairesis or abstraction.[6]
The universals of the "always" and those of the "for the most part."
This divergence between philosophic and physical or mathematical procedure is the point upon which empiricism and mathematicism rely; but these, inferior here to Aristotle, deny the science of absolute being (περὶ ὅντος άπλῶς) and leave in existence only the second order of sciences, which deal with the particular and abstract. There is another important distinction in Aristotle, but to tell the truth it is impossible to say how far he connected it with the preceding distinction between philosophy and physics, with which it is substantially one. Aristotle knew two forms of universal: the universal of the always (τοῡ ἀεί) and that of the for the most part (τοῡ ὡς ἐπὶ τὸ πολύ).[7] He was well aware of the difference between the first, which is truly universal, and the second, which is so only in an approximate and improper manner; and he even asked himself if the for the most part alone existed and not also the always; but his interest was directed not so much to the comparative differences of the two series, as to the common character of universality which both of them asserted as against the individual and accidental. Science (he said) is occupied, not with the accidental, but with the universal, whether it be eternal and necessary (ἀναγκαῖον) or only approximately universal (ἐπὶ τὸ πολύ).[8] Philosophy, physics and mathematics felt at this period that they had a common enemy in sensationalism and sophism, and they formed an alliance against this common enemy, rather than as happened later, dissipate their energies in intestinal welfare.
Controversies concerning Logic in the Middle Ages.
Without dwelling upon the later scepticism, mysticism and mythologism, which represented the dissolution of ancient philosophy and the germ of a new life (especially in Christian mythologism, which had absorbed elements of ancient philosophy and was accompanied by a very developed theology), we must pass on to note the progress which the logical problem made in the schools of the Middle Ages. To look upon mediæval philosophy (as many do) as a negligible episode, a mere detritus of ancient culture quite unconnected with the later spiritual activity, is now no longer possible. Certainly in the disputes of the nominalists and realists, the problem of transcendence and of immanence was neglected. It could not be solved on the presumptions of a philosophy which had at its side a theology, of which it constituted itself the handmaiden. The Platonic transcendence was incurable in Christianity, and those who even to-day seek to purify Christianity from survivals of Greek thought, do not perceive that, in this purification effected by their philosophies of action and of immanence, they are destroying Christianity itself.[9]
Nominalism and realism.
But in those disputes, besides the question of the place that belongs to science in relation to religious faith, or to mundane science in relation to revealed and divine science, the question of the nature of the concept was also raised; that is to say, they continued the Platonic-Aristotelian enquiry into the doctrine of the concept in the second of the meanings that we have distinguished. But no true conclusion was reached in this enquiry. The conciliatory formula of the Arabic interpreters of Aristotle, accepted by Albertus Magnus and Thomas Aquinas, in which the universals were affirmed as existing ante, in and post rem, in so far as it is possible to confer upon it an exact meaning, was understood in a superficial manner, and therefore it has not unreasonably seemed too easy and too expeditious.[10] A dispute of this sort cannot be solved by summarizing discordant opinions, as in the formula we have mentioned, or by fixing a mean, as in conceptualism. But the realists, bravely maintaining the truth of the philosophic universal, maintained the rights of rational thought and of philosophy; and the nominalists, on their part, asserting in contradiction to the former, the nominalist universal, prepared the modern theories of natural science. Realism produced philosophic thought of high importance, as in the so-called ontological argument of Anselm of Aosta, which (though through the myth of a personal God) asserts the unity of Essence and Existence, the reality of what is truly conceivable and conceived. Gaunilo, who confuted and satirized that concept, by employing the example of a "most perfect island," thinkable yet non-existent, seems an anticipation of Kant; at least of the Kant who employed the example of the hundred dollars to illustrate the same case—if it is not more accurate to say that Kant was, in that case, a late Gaunilo. Anselm replied (as Hegel did to Kant) that it was not a question of an island (or of a hundred dollars of something imaginable that is not at all a concept), but of the being than which it is impossible to think a greater and a more perfect (the true and proper concept). On the other hand, the nominalists, who like Roscellinus maintained that the universelles substantiae were nonnisi flatus vocis, performed the useful office of preventing the sciences of experience from being absorbed and lost in philosophy. In Roger Bacon we see clearly the connection of nominalism with naturalism. He considered individual facts, so-called external experience, in its immediacy, as the true and proper object of science. Concepts were for him a simple expedient, directed towards the mastery of the immense richness of the individual. "Intellectus est debilis (he said); propter eam debilitatem magis conformatur rei debili, quae est universale, qitam rei quae habet multum de esse, ut singulare."
Nominalism, mysticism and coincidence of opposites.
But the nominalists, dialecticae haeretici (as Anselm called them), were heretics only in the circle of the dialectic. The truth remained for them something beyond; the concept, the secunda intentio, was certainly something arbitrary and ad placitum instituta; it was "forma artificialis tantum, quae per violentiam habet esse," but beyond it were always faith and revelation. God is the truth, and in God the ideas are real; hence Roger Bacon gave to inner light (as the positivists or neocritics of to-day give to feeling) a place beside sensible experience. Mysticism, being developed from mediæval philosophy, both from one-sided realism and from one-sided nominalism, extends its hand at the dawn of the new Era to the philosophy of Cusanus, to scepticism, to docta ignorantia. This was not a mere negation; so much so that in it (though in a negative form and mixed with religion) there appears in outline nothing less than the theory of the coincidence of opposites, that is to say, the cradle of that modern logical movement, which was destined definitely to conquer transcendence. The coincidence of opposites is the germ of the dialectic, which unifies value and fact, ideal and real, what ought to be and what is. This important thought reappears in German mysticism; and (significantly for its future destinies) rings out upon the lips of Martin Luther, who declared that virtue coexists with its contrary, vice, hope with anxiety, faith with vacillation, indeed with temptation, gentleness with disdain, chastity with desire, pardon with sin; as in nature, heat coexists with cold, white with black, riches with poverty, health with disease; and that peccatum manet et non manet, tollitur et non tollitur, and that at the moment a man ceases to make himself better, he ceases to be good.[11] And before it became dominant in Jacob Böhme it was stripped of its religious form and eloquently defended in Italy by Giordano Bruno.[12]