If their view is correct, the theory appears to be a remarkable example of deductive reasoning.
Really, he urged, there could be only one substance - Descartes himself had dropped a passing hint to that effect - and the bold deductive reasoning of Spinoza's Ethics, in process if not in result, betrays its kinship to the ontological argument, with its affirmation of what must be.
Whatever be the historical worth of this story, it may safely be said that it cannot be disproved by deductive reasoning from the premisses of abstract logic. The most we can do is to assert that a universe in which such things are liable to happen on a large scale is unfitted for the practical application of the theory of cardinal numbers.
Aristotle's analysis of the syllogism showed man how to advance by combining his thoughts in trains of deductive reasoning.
Thus, while arithmetic may be defined as that branch of deductive reasoning concerning classes and relations which is concerned with the establishment of propositions concerning cardinal numbers, it must be added that the introduction of cardinal numbers makes no great break in this general science.
