By dialectical fundamentalism I mean the view that maintains the inerrancy of the orthodox classical scriptures of dialectical materialism; by flexible scientific naturalism I mean the view recognizing the past heuristic value of dialectical materialism, but also the realization for the need to develop and change it along lines suggested by complementary philosophies relevant to the scientific outlook.

Moral philosophers have often felt the need of a concept which would cover all those cases where we are prevented from achieving our ends through no fault of our own: a criterion for saying when failure is not blameworthy. The deontologists thought we were not to blame for actions done in genuine ignorance of the facts. Kant declared in a famous passage that we were not morally responsible for failures due to the “niggardliness of stepmother nature.” In this article I want to introduce into moral philosophy a new concept for clarifying the failures for which we are not to blame: the notion of scarcity, taken from economic theory.

We will be dealing with “sequential circuits” in the sense of E. F. Moore and G. H. Mealy. Each such circuit is assumed to have a finite number of input wires (possibly none) and a finite number of output wires (but at least one). Each element of such a circuit will be assumed to be an and-circuit, an or-circuit, a not-circuit, or a delay circuit, for some specified temporal delay. Each element has one output wire which, however, may branch in order to serve several purposes simultaneously. (Similarly the inputs of the total circuit may be allowed to branch.) The and-circuits and or-circuits have two input wires each, while the not-circuits and the delay circuits have one input wire each.

The year 1897 saw the publication of the first of the modern logical paradoxes. It was published by Cesare Burali-Forti, the Italian mathematician whose name it has come to bear. Burali-Forti's own formulation of the paradox was not altogether satisfactory, as he had confused well-ordered sets as defined by Cantor with what he himself called “perfectly ordered sets” (“Classe parfettamente ordinata”). However, he soon realized his mistake, and published a note admitting the error and making the correction. He concluded the note with the observation that his result could be established on the basis of the correct definition of well-ordered set as easily as for the “perfectly ordered sets” for which it had first been obtained. We shall reproduce his results in their corrected form.

Of the many cosmological models developed during the past forty years, none is completely satisfactory; so work continues in the development of new models and in the checking of their predictions against the growing mass of experimental evidence. The validity of a model rests on its agreement with experimental data, particularly the data on distribution of galaxies and on redshifts.