Cartesian. Geometry in Vico's opinion is the one hypothesis by which metaphysics passes over into physical science. But while making this advance it remains a hypothesis, a probability, something intermediate between faith and criticism, imagination and reason; which indeed is the eternal character of metaphysics and human science in general according to Vico's point of view in this first phase of his theory of knowledge. Just as mathematics cannot be the basis of metaphysics, the science from which it is itself derived, so it cannot provide a foundation for the other sciences, although they follow it in order of derivation. All objects other than number and size are beyond the reach of the geometrical method. Physical science is indemonstrable: if we could demonstrate the physical world, we should be creating it (_si physica demonstrare possemus, faceremus_): but we do not create it, and are accordingly unable to demonstrate it. The introduction of the mathematical method into natural science has not helped it. Without the mathematical method, science makes great discoveries; by its means it has made none, whether great or small. The physical science of to-day is in fact like a house, sumptuously furnished by former owners, to which their heirs have added nothing, but have occupied themselves merely in moving and rearranging the furniture. Accordingly, we must reintroduce and maintain the experimental method in physical science, as opposed to this mathematical method; the English tendency as opposed to the French; the cautious use made of mathematics by Galileo and his school, as against the Cartesians' reckless and presumptuous employment of it. The English are right in not allowing physical science to be taught in the mathematical style. Such a style admits of progress only when the terms are defined, the axioms established, and the postulates granted. In physical science we have to define not terms but things: we can make no unchallenged statements; and the complexity of nature forbids our forming any postulates. Thus in the more favourable instances this method results in a mere harmless verbalism. Observations of nature are expounded with the phrases: "By definition IV.," "By postulate II.," "By axiom III.," and concluded with the pompous abbreviation "Q.E.D." But all this carries no demonstrative conviction. The mind retains as much freedom of opinion as it had before listening to such noisy methods. In these circumstances Vico could not refrain from satirical comparisons. The geometrical method, he says, in its proper sphere works unnoticed; when it makes a noise, it shows that it is doing no work; just as a coward's attack consists of much shouting and no blows, while a brave man holds his tongue and strikes home. Again, the man who upholds the geometrical method in subjects where it fails to carry conviction, when he pronounces this to be an axiom, or that to be a demonstrated truth, is like a man who