The axiom of Cartesianism is, therefore, the Cogito ergo sum.
The fact is that the uniformity of nature stands to induction as the axioms of syllogism do to syllogism; they are not premises, but conditions of inference, which ordinary men use spontaneously, as was pointed out in Physical Realism, and afterwards in Venn's Empirical Logic. The axiom of contradiction is not a major premise of a judgment: the dictum de omni et nullo is not a major premise of a syllogism: the principle of uniformity is not a major premise of an induction.
Hence arises the compatibility of philosophy and theology which was the fundamental axiom of scholasticism, and the possibility of a Summa Theologiae, which is a Summa Philosophiae as well.
Moreover, it was a diplomatic axiom in Denmark, founded on experience, that an absolute monarchy in Sweden was incomparablymore dangerous to her neighbour than a limited monarchy, and after the collapse of Swedish absolutism with Charles XII., the upholding of the comparatively feeble, and ultimately anarchical, parliamentary government of Sweden became a question of principle with Danish statesmen throughout the 18th century.
That the executive and legislative powers ought to be absolutely separate The had been an axiom throughout the Revolution.
Assuming as an axiom that the centre of gravity of any number of interdependent bodies cannot rise higher than the point from which it fell, he arrived, by anticipating in the particular case the general principle of the conservation of vis viva, at correct although not strictly demonstrated conclusions.
An axiom based upon this view has been formulated, and although paradoxical it may well be quoted here.
He laid most stress upon this axiom when, in September 1886, Ruiz Zorilla suddenly sprang upon Sagasta a military and revolutionary movement in the streets and barracks of Madrid.
Another commonly received axiom was that no body could be affected by more than one movement at one time, and it was thus supposed that a cannon ball, or other projectile, moves forward in a right line until its first impulse is exhausted, when it falls vertically to the ground.
The appearance, in September 1604, of a new star in the constellation Serpentarius afforded him indeed an opportunity, of which he eagerly availed himself, for making an onslaught upon the Aristotelian axiom of the incorruptibility of the heavens; but he continued to conform his public teachings in the main to Ptolemaic principles, until the discovery of a novel and potent implement of research in the shape of the telescope placed at his command startling and hitherto unsuspected evidence as to the constitution and mutual relations of the heavenly bodies.