United States or Cabo Verde ? Vote for the TOP Country of the Week !
Neither sense alone nor the understanding alone produces knowledge, but both cognitive powers are necessary, the active and the passive, the conceptual and the intuitive. Here the question arises, How do concept and intuition, sensuous and rational knowledge, differ, and what is the basis of their congruence?
Poincaré replied that the attempt to find reasons in nature for the selection of a definite congruence relation in space is like trying to determine the position of a ship in the ocean by counting the crew and observing the colour of the captain's eyes. In my opinion both disputants were right, assuming the grounds on which the discussion was based.
The absolute indetermination of nature in respect of all the relations of congruence is replaced by the indetermination of observation with respect to a small subgroup of these relations. Poincaré's position is a strong one. He in effect challenges anyone to point out any factor in nature which gives a preeminent status to the congruence relation which mankind has actually adopted.
The new theory provides a definition of the congruence of periods of time. The prevalent view provides no such definition. Its position is that if we take such time-measurements so that certain familiar velocities which seem to us to be uniform are uniform, then the laws of motion are true.
It follows that a certain subset of closely allied congruence relations can be assigned of which each member equally well agrees with that statement of observed congruence when the statement is properly qualified with its limits of error. This is an entirely different question and it presupposes a rejection of Poincaré's position.
The natural course of all waters is downward, wherefore of congruence they fall that way where they find the earth most low and deep: in respect whereof, it was erst said, the seas do strike from the northern lands southerly.
Such measurement does not follow from the mere serial property of time; it requires a theory of congruence which will be considered in a later lecture. In estimating the adequacy of this definition of the temporal series as a formulation of experience it is necessary to discriminate between the crude deliverance of sense-awareness and our intellectual theories.
The paradoxes of relativity arise from neglecting the fact that different assumptions as to rest involve the expression of the facts of physical science in terms of radically different spaces and times, in which points and moments have different meanings. The source of order has already been indicated and that of congruence is now found. It depends on motion.
In the case of the thread we can observe the loss of self-congruence. Thus immediate judgments of congruence are presupposed in measurement, and the process of measurement is merely a procedure to extend the recognition of congruence to cases where these immediate judgments are not available. Thus we cannot define congruence by measurement.
The first of these axioms, which is the third axiom of congruence, is that if ABC is a triangle of rects in any moment and D is the middle event-particle of the base BC, then the level through D perpendicular to BC contains A when and only when AB is congruent to AC. This axiom evidently expresses the symmetry of perpendicularity, and is the essence of the famous pons asinorum expressed as an axiom.
Word Of The Day