POSTULATE. This word occurs in geometry, and signifies something that is re manded, and must be granted before the demonstrations of the science can be wrought out. The postulates of Euclid have reference to certain constructions indispensable to the reasoning. They are these three: "A straight line may be drawn from one point to another;" "A line already drawn may be produced ;" and " A circle may be described from a given center, with a given radius." The object of laying down these in the shape of demands, is to fulfill one great condition of demonstrative science, which is, that nothing shall be proceeded on, in the course of the reasoning, without being explicitly stated at the outset. It has been noticed by critics that the three postulates of Euclid do not exhaust the demands actually made in the course of his demonstrations. Thus, in the 4th and 5th propositions, Book I., this postulate is assumed: " Any figure may be re moved from place to place without alteration of form, and a plane figure may be turned round on the plane." The postulate is something different from the axiom. An axiom is a general and fundamental principle, such as no one can deny, and serving as the ultimate foundation (in logic, the major premise) of deductive inferences; as, for example, "Things equal to the same thing are equal to one another." The postulate, in Euclid's sense, is a special accessory to the reasoning, different from the axioms.
But in philosophy, the postulate takes a much wider sweep, and expresses the most fundamental concessions implied in all reasoning, being pm-requisite in order to the astablish tnent of the axioms themselves.
Thus, it is a postulate necessary to reasoning and discussion that a reasoner shall be consistent with himself—that he shall not affirm a thing one minute and deny it the next. The so-called laws of thought—identity, contradiction, and excluded middle—are so many forms of the postulate of consistency. These laws are tantamount to demanding that the same thing shall not be maintained in one form, and denied in another. • If we say this room is hot, we must not, at the same time, say that it is not hot. So the ordi nary law of the syllogism, "Whatever is true of all members of a class, is true of each," is not so much an axiom as a postulate of consistency; we must be prepared to repeat individually the statements that we have affirmed collectively.
The ultimate premises of all truth and reasoning may be put in the form of postulates, as follows: 1. Present consciousness must be admitted as a ground of certainty. " I am thirsty," "I hear a sound," as facts of present consciousness, are to be held as trust worthy in the highest degree, or as amounting to the highest certainty. 2. But present consciousness is not enough; it must further be conceded that past consciousness is a ground of certainty. Present consciousness does not amount to an experience of value for future purposes, unless taken with past. Now, although a remembrance that is long past is often uncertain, a recent remembrance must be pronounced absolutely certain, not less than a present consciousness. That " I was thirsty a short time ago," I must be certain of, in order to establish the induction, "that water quenches thirst." 3. It must further be conceded, that " What has been iu the past, all circumstances holding the same, will be in the future." That a thing has been, does not imply that it will be. We may admit that the sun has risen to-clay, and rose yesterday, and so on, and without inconsistency, refuse to admit that it will rise to-morrow. People are generally well enough disposed to treat this as a certainty; indeed, there is a strong natural tendency of the mind to expect that the future will resemble the past, which, when corrected and regulated by experience, constitutes our belief in causation and the uniformity of nature. Still, a blind instinct is no guarantee for truth; and as the asser tion of the future is a distinct position, it should be formally assumed in a separate postu late. However often a thing may have happened, we still make a leap, and, so to speak, incur a risk in venturing to predict its future recurrence. Our confidence no doubt increases with repetition, but nothing can obliterate the line between what has been, and what is to be.
These three postulates of experience, coupled with the postulate of consistency, seem adequate as a basis of all the recognized axioms and truths of experience. In other words, the concession of them is enough to commit any one to the reception of all inductive and deductive evidence.