In theories of the mobilities of ions in gases a rather precise knowledge is required of the forces which are called into play when an ion approaches a neutral molecule; for it is by virtue of these forces that ions are deflected from their paths and that their drift along the electric force is impeded. Again, the current question whether ions, in their motion through a gas, form “clusters”, that is, whether they surround themselves by one or even more layers of neutral molecules, can be decided theoretically only on the basis of a rather precise knowledge of the interactions.

Quantum mechanics was initiated with the object of allowing only observable concepts to enter into the theory. The new mechanics has, however, inherited the old difficulty with the conservation laws involved in beta decay, and this led Pauli, about 1931, to introduce the idea of the neutrino, with the object of reconciling the facts of beta decay with the conservation laws. The neutrino, as it was proposed by Pauli and as accepted today, is a particle devoid both of mass and charge, but having a spin 1/2 and obeying the Fermi statistics. In 1934 Fermi founded his theory of beta disintegration based on the neutrino. The Fermi theory assumes that this hypothetical particle is emitted simultaneously with the disintegrating electron and carries off the excess energy, thereby reconciling the conservation laws with beta disintegration. It will be remembered that the continuous distribution in energy of the beta particles is such that, except at the maximum energy end point of the beta spectra, there is more energy available from the disintegration than is emitted in the form of beta particles.

The aim of this contribution is to trace the transformation of the meanings of certain terms as the order of the logics in which they appear is raised. By “order of the logic” we simply refer to the number of truth-values characterizing the logic, so that if the number of truth values shows symptoms of traveling to infinity we may speak of the goal as a logic of infinite order.

In our discussion of rigidity, we agreed to set external differential forces equal to zero, or to correct our instruments for the effects of such forces. Let us suppose that we were in the presence of an electrostatically charged gravitational body. That is, the gravitational body (e.g. the sun) would have some electrostatic charge (as is probably the case for the sun). If we corrected our rods and clocks for the effect if any of this differential force (which would certainly be negligible in any case, so far as spatial geometry is concerned), we might then expect that the geometry of the field would be the same as when the gravitational body is uncharged. But is this the case? Not at all! And the explanation is not far to seek: the charge contributes energy to the field; but energy, by relativity theory, is equivalent to mass, and mass always modifies the gravitational potential. Hence, the geometry of the charged gravitational field (which depends on the potential) must be different from the uncharged.

It is well known that, in classical theory, Liouville's theorem shows that if an ensemble of systems is distributed over a small element of volume in phase space, the ensemble fills a region of equal volume at all later instants of time. In quantum mechanics, the uncertainty principle is associated with the products of the errors in conjugate coordinates and momenta, and such products can be interpreted in terms of volume elements in phase space. Comparison of these two facts leads to the assertion in the interesting volume on “Statistical Mechanics” recently published by J. E. and M. G. Mayer that “The Liouville theorem is essential for the complete understanding of the uncertainty principle.