Even for mathematics itself Vico apprehends danger from the substitution of analytic for geometrical or synthetic methods. He doubts whether modern mechanics is really a product of analysis; for analysis blunts the inventive faculty or talent, and though infallible in, its results (opere) is confused in its processes (opera); while the synthetic method is turn opere cum opera infallible. Analysis presents its grounds by inquiring whether the equations of which it is in search happen to be present; it appears to be an art of guessing, a kind of mechanism rather than thought. For similar reasons Vico attached no value, to the more or less mechanical topics and arts of discovery and memory invented by Lulle and Kircher.

The sympathy with experimental methods which as we have seen estranged Vico from the French tendency of thought, that is from Cartesianism, and directed him towards the Italian and English schools of Galileo and Bacon, led him on the other hand to a hostile attitude towards Aristotelianism and scholasticism. Inculcating as he did the pursuit of the particular and the use of inductive methods, asserting that man possessed an inexhaustible wealth of physical knowledge which, thanks to fire, machinery, and tools, was able to issue in the creation of objects resembling the special products of nature, and praising his own metaphysic as one subservient to (ancillantem) the ends of experimental science, he was bound to realise how well deserved was the too universal discredit, as he calls it, into which Aristotelian science had fallen. If he disapproved of the introduction by Descartes of physical forms into metaphysics, and of his resulting materialistic tendencies, he accused Aristotle and the schoolmen of the opposite error of introducing metaphysical forms into natural science. Like Bacon he held that the syllogism and sorites produce nothing new, and only repeat what was already contained in their premisses. He emphasised the many ill effects of the Aristotelian universal in every department of knowledge; in jurisprudence, where empty generalities crush legislative wisdom; in medicine, which aims rather at propping up systems than at healing the sick; and in practical life, in which he describes the abusers of universals by the mocking title of "Thematists." The use of universals results in homonymies or equivocations which cause all kinds of errors. As against this distrust of universals in the sense of general or abstract conceptions, Vico showed a corresponding reverence for the Platonic ideas, the metaphysical forms, or as he also called them, kinds; the eternal and infinitely perfect patterns of things. A nominalist in mathematics, Vico was suspicious of nominalism in all other fields of knowledge. He asserts the reality of the forms or ideas, and tells how from his youth up he was attracted by this doctrine, which he learnt from a teacher of his, who as a Scotist was a follower of the scholastic system most akin to Plato's.

Taken as a whole Vico's first theory of knowledge is neither intellectualistic, sensationalistic, nor truly speculative. It contains all these three elements, harmonised to a certain extent, not by a hierarchical subordination of any two to the third, but by the subjection of all three to a recognition of the inadequacy of human knowledge. Its intention may have been to meet by a tactical manoeuvre dogmatics and sceptics at once, the former by denying that we can know everything, the latter by denying that we can know nothing at all. But its actual outcome is an assertion of scepticism or agnosticism, tinged, however, with a trace of mysticism. God's knowledge is the complete sphere of knowledge, the unity of which man's is but a series of fragments. God knows all things because he contains in himself all the elements of which he makes them: man tries to understand them by taking them to pieces. Human science is a sort of anatomy of the world of nature; it divides man into body and soul, and soul into intellect and will: from body it abstracts figure and motion, and from these existence and unity. Of these metaphysics studies existence, arithmetic unity and multiplication, geometry figure and its measurements, mechanics the motion of the circumference, physical science the motion of the centre, medicine the body, logic the reason, and ethics the will. But this anatomy meets with the same fate as that of the human body. In the latter case, the greatest physiologists doubt whether, owing to the effects of death and of dissection itself, it is possible at all to discover the true position, structure, and function of the organs. Existence, unity, figure, motion, body, intellect, and will are one thing for God, for whom they coalesce into one, and another for man, to whom they remain distinct. For God they live, for man they are dead. The clear and distinct perception is a proof not of the strength but of the weakness of the human understanding. Physical laws appear self-evident just until they are subjected to comparison with metaphysical. The Cogito ergo sum is absolutely conclusive when man considers himself as a finite being; but when he includes himself in God, the one true being, he realises that in truth he does not exist at all. By means of extension and its three dimensions we believe ourselves to establish eternal truths; but in fact coelum ipsum petimus stultitia, since the eternal truths exist in God alone. The axiom that the whole is greater than the part may seem eternal, but if we go back to the beginning, we find that it is false: we see that the centre of the circle contains in itself as much capacity for extension as the whole circumference. Wherefore, Vico concludes, "he has advanced in metaphysics who in the study of this science has lost himself."

To hold, as some have done, that these words show Vico a simple Platonist or a follower of the traditional Christian philosophy, would entail denying any importance whatever to his first theory of knowledge. It would be a confession of adherence to the fallacious method of philosophical criticism and history which looks only at the general conclusions of a system and ignores the particular content which alone gives it its true individuality. No doubt, any philosophy must always in its ultimate conclusions be either agnostic, mystical, materialistic, spiritualistic, or the like: in other words, it must have its place in one or other of the eternal categories in which thought and philosophical inquiry move. But to expound philosophers in this one-sided manner can only serve to perpetuate the mistakes repeated over and over again in the history of thought, when it passes fruitlessly from one error to another, leaving the old only to adopt the new, itself perhaps an old one born again or painted with the colours of youth. The Platonismi agnosticism, or mysticism of Vico is in the fullest sense of the word original, because it forms the accompaniment of doctrines not only not inferior to the average of contemporary thought, but greatly in advance of it.

The first of these doctrines is the theory of knowledge as the conversion of the true with the created, Vico's substitute for the otiose criterion of the clear and distinct perception. Though this conversion represents for Vico an ideal unattainable to man, it yet does not bring with it an exact definition of the condition and character of knowledge, the identity of thought and being, without which knowledge is inconceivable.

The second is the revelation of the nature of mathematics, as unique among the forms of human knowledge in origin, rigorous because arbitrary, wonderful but unfit to rule over and transform the rest of our knowledge.

Finally, the third doctrine is the vindication of the world of intuition, empirical knowledge, probability, and authority, all those forms of experience which intellectualism ignored or denied.

In these points Vico the agnostic, the Platonist, the mystic, was neither agnostic nor mystic nor Platonist. He achieved a threefold advance upon Descartes, and upon all these three heads criticised him conclusively.

The one thing in which Descartes was still in advance of Vico was precisely that dogmatism of which Vico would have none. Descartes, whether he succeeded or not, projected a perfect human science deduced from the internal consciousness. Vico, on the other hand, considering the French philosopher too confident and despairing of the success of his project, proclaimed the transcendent nature of truth, took his stand upon revelation, and contented himself with producing a metaphysic worthy of man's weakness, humana imbecillitate dignam. His was a philosophy of humility, as the Cartesian was one of self-confidence.