Physicists did not at first concern themselves with these difficulties, but two new facts changed the face of things; the first is what is called the law of black radiation. A perfectly black body is one whose absorption coefficient is … Read More
Let us go back to the kinetic theory of gases; the gases are formed of molecules which circulate in all directions with great velocities; their trajectories would be rectilinear if from time to time they did not collide each other, … Read More
One wonders if Mechanics is not on the eve of a new upheaval; recently a meeting was held at Brussels, attended by some twenty physicists of various nationalities, and at each moment they might have been heard to speak of … Read More
A few years ago, I had the opportunity to expose some ideas about the logic of the infinite; on the use of the infinite in Mathematics, on the use made of it since Cantor; I explained why I did not … Read More
The antinomies to which certain logicians have been led come from the fact that they could not avoid certain vicious circles. It happened to them when they considered finite collections, but it happened to them much more often when they … Read More
Is it possible to reason about objects that can notbe defined in a finite number of words? Is it even possible to talk about it knowing what one is talking about, and by saying something other than empty words? Or … Read More
It is in a totally different direction that Mr. Zermelo is seeking the solution of the difficulties we have pointed out. He tries to establish a system of axioms a priori, which must allow him to establish all the mathematical … Read More
Russell introduces a new axiom which he calls axiom of reducibility. As I’m not sure I fully understood his thought, I will let him speak. “We assume, that every function is équivalent, for ail its value to some predicative function … Read More
Russell published in the American Journal of Mathematics, vol. XXX, under the title Mathematical Logics as Based on the Theory of Types, a memoir in which he relies on considerations quite similar to those which precede. After recalling some of … Read More
We must not forget the preceding considerations when defining the cardinal number. If we consider two collections, we may seek to establish a law of correspondence between the objects of these two collections, so that any object of the first … Read More
Can the ordinary rules of logic be applied without change, as soon as we consider collections taking an infinite number of objects? This is a question we did not ask at first, but we were led to examine when the … Read More
I would like to add a remark which relates only indirectly to the foregoing; we have seen above the importance of the Analysis Situs and I explained that this is the real domain of geometric intuition. Does this intuition exist? … Read More
