Passing from the problem of the nature of error to that of the forms actually assumed by philosophic error, Croce accepts Vico's definition of error, as an improper combination of ideas, and therefore defines such forms, by deducing the number of possible improper combinations from his own conception of the legitimate forms of theoretical activity. This phenomenology of error is one of the main tasks of logic, while the refutation of particular philosophical errors is the task of philosophy as a whole. We shall rapidly survey these general forms, in which it will be easy for the reader to recognize the logical (or illogical) structure of many particular errors criticised in the preceding chapters. The pure concept can be improperly combined with, or exchanged for, the pure intuition (art), or the empirical and abstract concept (the natural and mathematical sciences); or it can be improperly split in its unity of intuition and concept (_a priori_ synthesis), and arbitrarily put together again, either as a concept which simulates an intuition or as an intuition which simulates a concept. Hence the five fundamental forms of error: æstheticism, empiricism, mathematicism, philosophism, and historicism or mythologism. To these must be added other forms originated from combinations of the preceding ones: dualism, scepticism, and mysticism. We have dealt elsewhere with both æstheticism and empiricism. Of the first, the most recent form is that which pretends to build a philosophy of pure intuition or of pure experience, that is, of an experience which, not being touched by any intellectual category, is also pure intuition. Empiricism is practically all the current philosophy of our times, from the positivism of Comte and Spencer to the more modern types of the so-called philosophic elaboration of scientific knowledge. Mathematicism is a rarer and more aristocratic form of error: it does not consist in the application of the mathematical method to the exposition of philosophical concepts, which is a mere didactic expedient, more or less convenient, but insufficient to characterize the quality of the concepts themselves; its true exponents are those philosophers or mathematicians who take mathematical fictions, such as the dimensions of space, for realities, and proceed to speculate on such a foundation. The near future seems to promise a great extension of this kind of philosophy, through the prevailing interest in the theory of relativity, which is fondly supposed to contain the germs of a revolution in thought. Both empiricism and mathematicism lead to a dualistic conception of reality, by opposing either the facts of scientific and historical knowledge, that is, a collection of facts limited in space and time, to an infinite reality beyond that knowledge, or our actual world of space and time, to worlds, spaces and times mathematically conceivable, but of which we have no experience. The passage from this dualism to