In the mathematical sciences, the principle of the conversion of the true with the created had been applied in appearance only. The principle itself was original and sound: so was the theory of mathematics. But the connexion between the two truths was altogether artificial and false. What was lacking was, unless we are mistaken, an effective relation between the concept of God who creates the world and, as creating it, knows it, and that of the man who arbitrarily constructs a world of abstractions, and in doing so either knows nothing at all, or else, when he ceases to be a geometer or arithmetician and becomes a philosopher, when he is composing not Euclid's Elements but the theory of knowledge in the De antiquissima, knows merely that his procedure is arbitrary. If the mathematical sciences construct their concepts as they please, if they produce not truth but definitions, they are as a matter of fact not sciences at all, nor any form of knowledge, and cannot be compared with the divine knowledge, the knowledge of actual reality. In mathematics, says Vico, "man, holding within himself an imaginary world of lines and numbers, operates in this world by abstraction just as God operates in the universe by reality." It is a luminous comparison; but perhaps its light is that of metaphor rather than logic.

In the moral sciences, on the other hand, the comparison is so entirely logical that it should frankly be called coincidence. Human knowledge is qualitatively identical with divine, and knows the world of man equally well; it is, however, quantitatively more restricted, and does not extend like the divine to the world of nature. In the human field we no longer find the expedients of weakness, definitions and falsifications; knowledge is here at its highest point of concreteness. Man creates the human world, creates it by transforming himself into the facts of society: by thinking it he re-creates his own creations, traverses over again the paths he has already traversed, reconstructs the whole ideally, and thus knows it with full and true knowledge. Here is a real world; and of this world man is truly the God.

It seems undeniable, then, that the application of the "verum-factum" made in the New Science is the only one which corresponds to the criterion previously formulated. The earlier attempt at an application of it to mathematics, though important in other respects and well calculated to free the mind from mathematical prejudice, cannot be considered a true or strict use of it. It is possible that Vico was sometimes vaguely conscious of the difference between the two applications, the strict and the metaphorical, which as a rule he confused and treated as identical. The science of the world of man, he says, proceeds exactly as does geometry, which while it constructs out of its elements or contemplates the world of quantity, itself creates it; but with proportionately greater reality, since order has no connexion with human affairs, containing as they do neither points, lines, surfaces, nor figures. Another indication of his gradually dawning consciousness that he had now for the first time in his doctrine of the world of man discovered a true and proper knowledge, not a mere fiction of knowledge, may perhaps be seen in the much greater conviction, warmth, and enthusiasm with which he now uses the epithet "divine": quite a different thing from the chilly, if not absolutely ironical, ad Dei instar of the De antiquissima. The proofs of the New Science, he says more than once, with fervour, "are divine in their nature, and should give thee, Reader, a divine joy: since in God knowledge and creation are one."

The conversion of the true with the created was bound to react upon the treatment of certitude in one, perhaps the chief, of the various meanings in which Vico uses the word, namely, historical fact: the peculiare, certum, as opposed to the commune or verum. This forms the other important section of Vico's second theory of knowledge. In the former theory these cognitions were, as we saw, legitimised and protected by being put on a level with all other kinds of knowledge, all of them equally weak or equally strong, being all alike founded on probability or authority, whether of the individual (autopsy) or of mankind.

But now that the knowledge of the human mind and its laws was rescued from the region of authority and probability, historical fact, although still in a sense, by its very nature, founded upon authority, was placed in a new light. The certain must enter into a new relation, confronted as it now was not by another certainty, that is, mere probable knowledge of the human mind, but by a truth, a piece of philosophical knowledge.

This relation is also called by Vico the relation between philosophy and philology: the former dealing with necessities of nature, necessaria naturae, and contemplating the reason from which issues the science of truth; the latter with decisions of the human will, placita humani arbitrii, and following the authority whence comes knowledge of the certain. The one considers the universal, the other the individual; the one, as Leibniz would have said, the vérités de raison, the other the vérités de fait. With Vico the distinction is not so clearly expressed: in fact, authority as opposed to reason sometimes, according to him, becomes a part of reason itself, or is confused with the knowledge of the human will as opposed to that of rational volition; but the general sense is none the less quite plain. By philology Vico means not only the study of words and their history, but, since words are bound up with the ideas of things, he means also the history of things. Thus philologists should deal with war, peace, alliances, travels, commerce, customs, laws and coinage, geography and chronology, and every other subject connected with man's life on earth. Philology in a word, in Vico's sense, which is also the true sense, embraces not only the history of language or literature, but also that of events, philosophy, and politics.

It is true that philology, the truth of fact or certitude, had not always been so brutally treated as it was by the Cartesians. Grotius had given evidence of immense historical learning employed on behalf of his doctrine of natural right. Gravina, Vico's contemporary and fellow-countryman, demanded as necessary to the student of law not only "the art of reasoning" (ratiocinandi ars) but "skill in the Latin tongue" (Latinae linguae peritia) and "knowledge of history" (notitia temporum). And Leibniz, whom we have just named, reasserted the value of learning as against the Cartesians, and extended his patronage, en grand seigneur, to the varied collection of historical anecdotes which he scattered freely over his pages. But Vico observed that the philosophy and philology of his time always remained external to one another, as they had been almost entirely in Greece and Rome. All the quotations from historians, orators, philosophers, and poets accumulated by Grotius were a mere embellishment. Perhaps Vico would have passed the same judgment upon the liberal use made of history by Leibniz, if he had known of it and expressed his opinion. In reading the works of philologists he was conscious of such a sense of vacuity and weariness in the unintelligent jumble of historical observations, that he was almost led to agree with Descartes and Malebranche in their hatred of scholarship: for a time, in fact, he did entirely agree with them. But these two philosophers—so his later thought ran—ought, instead of despising erudition, rather to have asked whether it were possible to reclaim philology to philosophical principles; and the philologists for their part, instead of marshalling facts for a display of learning, ought to strive to make them the aim of science. Philology must be reduced to a science. This was Vico's idea of the relation of certitude to truth, or philology to philosophy.

What was the meaning of reducing philology, or history, which is the same thing, to a science or philosophy? Strictly speaking, the reduction is impossible: not because they deal with subject-matter different in kind, but because their subject-matter is in point of fact homogeneous. History is already essentially philosophy. It is impossible to make the most insignificant historical statement without moulding it with thought, that is with philosophy. But since the existence of this philosophical basis of philology was not at that time realised, indeed it was none too often realised in later times, and in consequence easily denied; and since most people, as we have seen, imagined either an aristocratic geometrical philosophy, hating and avoiding the "profane mob" of facts, or else, as at first Vico did, a philosophy and a history equally devoid of cogency, and merely matters of opinion: for these reasons Vico, after the change of his philosophical point of view, now that he had attained to the consciousness of the speculative method in the science of man, and understood more deeply the human mind, was bound to see how much current history stood in need of reform and extension; to feel the lack of an improved philology as a consequence of the improved philosophy, and to express it in terms of the theory of knowledge by the formula reuniting philology to philosophy: "that this second science, as is fair, should be the consequence of the first" (ut haec posterior, ut par est, prioris sit consequentia). He was bound, in other words, to rescue history from its condition of inferiority, where it was a mere slave to caprice, vanity, moralising and precept-making, and other irrelevant aims, and to recognise its own true end as a necessary complement of eternal truth. Philosophy nowadays is full of and intimate with historical fact: and this gives it greater breadth and a more lively sense of dealing with concrete reality. This is no doubt one meaning of Vico's formula concerning the union of philosophy and philology, and the reduction of the latter to a science.

It is, however, certain that in propounding this formula he had in view a further and, as often happened, a different meaning. This other meaning might be most simply illustrated by comparing it, as Vico himself did with Bacon and his "more certain method of philosophising": that method which Bacon expressed in the title of his work by the words Cogitata et visa, and Vico proposed to "transfer from the natural to the human or political world." In a word, he demanded the construction of a typical history of human society (cogitare) which was then to be discovered in the facts (videre). Thus the ideal construction would acquire certainty from the facts, and the facts truth from the ideal construction: authority would be confirmed by reason and reason by authority. He demanded a science which should be at once a philosophy of man and a universal history of nations. Now this structure which he required—something intermediate between cogitare and videre, thought and experience, this mixture of the two processes—is intrinsically different from the unity of philosophy and philology, in so far as that is a philosophical interpretation of factual data. Such an interpretation is living history: the other is neither philosophy nor history, but an empirical science of man and society, drawing its materials from schemata which are neither the extra-temporal categories of philosophy nor the individual facts of history: although it can never be constructed without philosophical categories and historical facts. It is an empirical science; and as such, neither exact nor true, but only approximative and probable, and subject to verification and correction from the side both of philosophy and of history.