Recession of the galaxies indicates a repulsive force and suggests that Newton's formulation of gravitation is not complete. A possible modification is proposed, and this Neo-Newtonian equation allows a quantitative treatment of Mach's principle. It also limits the velocity of matter to c and gives a correct prediction for the perihelion of Mercury.

The lessons of “logical empiricism” still need learning by scientific philosophers who continue to give ultimate descriptions of ultimate things. Even attempts to assign some basic transformative role to language must fail, as this role can always be reversed on some higher language level. Final philosophical characterizations of the universe collapse when we see their arbitrary linguistic nature. Similarly, the effort to force scientific philosophy into an ontology, as shown by a recent example, turns out to be only a conventional way of talking, rather than a legitimate appeal to something in the universe. More vulnerable recent examples of scientific metaphysical descriptions of “reality” reveal a deceptive linguistic superfluity in no way necessary for science or scientific philosophy. Within the inevitable circularity of language, semantic analysis can still fasten to the goal of predictability; and predictability can do without uneconomical symbolism.

Two initially different arguments for indeterminism are often based either upon the Uncertainty Relations or the statistical interpretation of the wave equation of quantum mechanics. Both arguments ultimately involve three factors: (1) the assumption that elementary entities are enough like classical particles for it to make sense to say they are either determined or indetermined, (2) the fact that no exact measurements are possible of quantities supposed to characterize elementary entities, (3) the pragmatic supposition that determinism is false unless exact predictions are theoretically possible.

If it is legitimate to use (3) to prove indeterminism, then an equally legitimate argument can be based upon (2) which denies (1). Thus, it is doubtful that quantum mechanics supports indeterminism, though it may show that the concepts of ‘determined’ and ‘indetermined’ are inapplicable to the world.

There are three points which Professor Schlesinger makes in his criticism of my discussion of the principle of simplicity.

1. (1) He holds that the principles of simplicity and verifiability may in actual use contradict each other. The simpler hypothesis will be rejected, he maintains, if it leads to unverified consequences.

2. (2) He holds that it is legitimate to add auxiliary hypotheses to one's theory, if it is desired to allow, let us say, for the creation of the universe by a deity, or to exclude the possibility for all time of such events as a pail of water freezing on fire.

3. (3) He maintains with Bridgman that the cosmogonists' use of the simple notion that the same laws of nature hold throughout space-time leads to “perfectly hair-raising extrapolations” which a verificationist will reject.

A new semantical antinomy, the antinomy of designation, is introduced into a metalanguage M with respect to a modal object language L. Carnap's device of restricting the principle of interchangeability for L does not suffice to prevent occurrence of this new antinomy. To achieve this result it seems most natural to replace the rules of designation for L by more complicated rules. This replacement suffices to prevent occurrence of the antinomy with respect to L. Moreover, it seems likely that analogous replacement will suffice to prevent occurrence of the antinomy with respect to languages which in means of expression are richer than L.

Professor S. F. Barker has recently argued that the theory of the status of theoretical concepts in natural science put forward by Hempel and Braithwaite is mistaken. Essentially this “formalistic” theory says that these concepts “take on” meaning from their place in a total theoretical system which as a whole implies testable observation statements. In the paper it is argued that Barker's criticism of the Hempel-Braithwaite theory is mistaken because (a) he does not sufficiently consider the operative empirical restrictions on concept formation in scientific theorizing, and (b) his criticisms are based on an acceptance of a narrow empiricism which would reject most existing theoretical natural science as empirically meaningless.

Two ideal standard clocks, effectively isolated from interaction with other physical systems, and in a region of the universe free of gravitational fields, are assumed to move in any arbitrary manner so that they coincide on at least two occasions. In general, the reading of one of them will become retarded relative to the other in the interval between successive coincidences. This relative retardation is predicted by the restricted theory of relativity, taken together with the assumption that the ‘rate’ of a clock depends only on its velocity and not on its acceleration. The recognized procedure for calculating the retardation in terms of clock ‘rates’ is set out, and is illustrated by its application to a simple hypothetical experiment in which one clock remains at rest and the other travels away from and back to it with constant speed in a straight line.

There is nothing paradoxical in the predicted retardation as such. The so-called 'clock paradox' arises because an alternative, and apparently valid, calculation procedure, also based on clock 'rates', leads to a contradictory result. The term ‘paradox’ is something of a euphemism since the two predictions are contradictories.

It is shown that the paradox does not arise when direct use is made of the Lorentz transformation without introducing the additional, and non-essential, step in reasoning involved in utilizing the clock ‘rates’. It is then shown that the paradox arises only through using these clock ‘rates’ without due regard to the exact significance of the quantities so described; once this is recognized the paradox is resolved completely within the framework of the restricted theory, which then provides a unique and unambiguous prediction of the relative retardation.

Once the paradox is thus resolved, the general theory of relativity can add nothing significant to the analysis. It is shown that the application of the principle of equivalence is essentially trivial; in effect, Einstein and Tolman evaded the real logical issue raised by the contradictory predictions by denying the applicability of the restricted theory and then utilizing, by means of the principle of equivalence, results obtained from it. This tortuous procedure succeeded in evading the paradox rather than in resolving it; it would obviously be quite invalid were the restricted theory indeed inapplicable to the problem.

The twin paradox of relativity theory is reviewed. A distinction is made between physical clocks and biological ones. It is suggested that metabolic activity might be a better measure of aging than physical time. Further it is suggested that entropy changes representing metabolic activity would be a good way to describe aging. Using the above criterion it appears that a traveling twin will be older than his brother.

The passage criticized by Mr. Linhart as “misleading” may be clarified as follows. Linhart is quite right that a method of interval estimation including a formula equivalent to my VI may be based on inverse probability, and that probability values considerably greater than zero may be thus obtained. The method of inverse probability to which I refer in the criticized passage, however, is that of Carnap, according to which (as indicated in the preceding paragraph of my paper, and on p. 16) the inverse probability of a law on the basis of finite evidence is zero. My statement that “... our method of interval estimation is superior to that of inverse probability, in that the probability values yielded by the former are considerably greater than those given by the latter...” remains true, since it is Carnap's method, which is not an interval method, of which I am speaking.

The author discusses Professor Darlington's recent paper “On the Confirmation of Laws.” He criticizes Professor Darlington for not writing out in full the evidence sentence in formula III of his paper, and expresses doubts as to whether Professor Darlington's solution to the problem of the confirmation of laws follows from the complete version of that formula.