AXIOM

AXIOM, ἀξίωμα, a self-evident truth; or a proposition whose truth every person perceives at first sight. See TRUTH and PROPOSITION. Thus, that the whole is greater than a part; that a thing cannot give what itself has not; that a thing cannot be and not be at the same time; that from nothing, nothing can arise; etc. are axioms.—The word is Greek, ἀξίωμα, q.d. dignitas, auctoritas, or even effatum: whence Cicero in lieu thereof uses the word pronuntiatum. By axioms, called also maxims, are understood all common notions of the mind, whose evidence is so clear and forcible, that a man cannot deny them without renouncing common sense and natural reason. See MAXIM, EVIDENCE, etc.



The rule of axioms is this, that whatever proposition expresses the immediate clear comparison of two ideas without the help of a third, is an axiom.—On the other hand, a truth which does not arise from an immediate comparison of two ideas, is no axiom. See IDEA, RELATION, etc. Wolfius assigns the essence of an axiom thus: Whatever proposition arises immediately from the consideration of a single definition, is an axiom—Thus it necessarily following from the genesis of a circle, that all right lines drawn from the centre to the circumference thereof, are equal; inasmuch as they all represent the same line in different situations: This is an axiom. See DEFINITION.

Hence, the truth of axioms being perceived by the mere intuition of a definition; they need no demonstration: since they are necessarily as true, as the definition is just. See DEMONSTRATION. Several authors abuse this property of axioms, and obtrude for axioms the premises of syllogisms, which they are not able to prove—Euclid himself lies liable to exception on this account, having assumed the equality of figures which mutually agree, or are congruous to each other, as an axiom. See CONGRUENCY. Axioms, in effect, strictly speaking, are no other than identic propositions.—Thus to say that all right angles are equal to each other, is as much as to say, all right angles are right angles: such equality being implied in the very definition, the very name. See DEFINITION.

My Lord Bacon proposes a new science, to consist of general axioms, under the denomination of philosophia prima. See PHILOSOPHY, KNOWLEDGE, etc.

AXIOM is also an established principle in some art or science. See PRINCIPLE, etc. Thus, it is an axiom in physics, that nature discovers herself most in the smallest subjects; that nature does nothing in vain; that effects are proportional to their causes, etc. Thus it is an axiom in geometry, that things equal to the same third are also equal to one another; that if to equal things you add equals, the sums will be equal, etc. So it is an axiom in optics, that the angle of incidence is equal to the angle of reflection, etc. It is an axiom in medicine, etc. that there is no sincere acid in the human body, etc. In this sense the general laws of motion are called axioms; as, that all motion is rectilinear, that action and reaction are equal, etc. See LAWS OF NATURE.

These particular axioms, it may be observed, do not immediately arise from any first notions or ideas, but are deduced from certain hypotheses: This is particularly observable in physical matters, wherein, as several experiments contribute to make one hypothesis, so several hypotheses contribute to one axiom. See HYPOTHESIS, etc.

AXIOM