VII. A Rule for Axioms. This is a Rule of Axioms, That no Propositions be set up for Axioms, but such as are most manifest and evident.
For no body questions, but that there are some Common Notions of the Mind that are so clear and perspicuous, as to stand in need of no Demonstra∣tion, to make them appear more distinctly. For did they involve the least Doubtfulness, they could not be the Foundation of a certain Conclusion. And therefore they are called Axioms, or common E∣nunciations, because they are so clear and manifest, as to stand in need of no Demonstration.
VIII. The Evi∣dence of Axioms doth not arise from the Senses. But we are not to suppose, as some do, that the Certainty and Evidence of Propositions doth in any degree proceed from the Senses; for that is abso∣lutely false. For the Truth-discerning-Faculty is not placed in the Senses, which are often deceived by a Similitude of Things, and are not able to dive into the Difference that lies hid in them. Who is it that doth not experience how narrow and weak our Senses are, and how frequently they deceive us, when we go about to search out any thing by their means?
For altho' this Axiom, That the Whole is greater than any one of its Parts, be in some sort discer∣nible by the Senses, yet not with such a Certainty as is necessary to Science; because whatsoever our Senses discover to us concerning it, is only founded on the observations of ou•• Infancy, which cannot afford us an undoubted, but only a probable Cer∣tainty. For by Induction a thing cannot be cer∣tainly known, except we be certain of the fulness of the Induction; there being nothing move com∣mon, than for us to discern at last the falsity of those things, which from general Inductions we were persuaded to be most True. The whole Truth of this Proposition, the Whole is bigger than its Parts, doth depend on the clear and distinct Notions we have of the Whole and Parts, by which we judge that the Whole is greater than any one of its Parts, and that the Part is less than the Whole. For when we are discoursing of any thing that is firm and stable, we must not have recourse to the Senses, as Plato saith; but to constant, im∣mutable, and impregnable Reasons. Thus we clearly know, that a Triangle is a Figure, that the Number Two is an even Number; because the Notion of a Figure is contained in the Definition of a Tri∣angle; and in that of the Number Two, the Notion of an Even Number.
IX. The Cer∣tainty of Propositions depends on the clear Knowledge we have of them. Wherefore all the Certainty of our Knowledge in Natural things, depends on this Principle, Whatsoever is included in the clear and distinct Idea of any thing, the same may with truth be affirmed of it. Thus because Substance is included in the Conception of a Body, we may affirm a Body to be a Substance. Because it is involved in the Idea of a Circle, to have equal Diameters, we may assert of every Circle, That all their Diameters are Equal. Because it is included in the Idea of a Triangle, that all its Angles are Equal to two Right ones, we may affirm the same of all Tri∣angles. What must be the Qualifications of Axioms, appears from what we have said of the framing of Propositions that are necessarily true, in the Thirteenth Chapter.