The modern corpuscular theory of radiation was born in 1905 when Einstein advanced his light quantum hypothesis; and the steps by which Einstein's hypothesis, after years of profound scepticism, was finally and fully vindicated by Arthur Compton's 1922 scattering experiments constitutes one of the most stimulating chapters in the history of recent physics. To begin to appreciate the complexity of this chapter, however, it is only necessary to emphasize an elementary but very significant point, namely, that while Einstein based his (...) arguments for quanta largely on the behaviour of high-frequency black body radiation or ultra-violet light, Compton experimented with X-rays. A modern physicist accustomed to picturing ultra-violet light and X-radiation as simply two adjacent regions in the electromagnetic spectrum might regard this distinction as hair-splitting. But who in 1905 was sure that X-rays and γ-rays are far more closely related to ultra-violet light than to α-particles, for example ? This only became evident after years of painstaking research, so that moving without elaboration from Einstein's hypothesis to Compton's experiments automatically eliminates from consideration an important segment of history—a segment in which a major role was played by William Henry Bragg. (shrink)

In "Logical consequence: A defense of Tarski" (Journal of Philosophical Logic, vol. 25, 1996, pp. 617-677), Greg Ray defends Tarski's account of logical consequence against the criticisms of John Etchemendy. While Ray's defense of Tarski is largely successful, his attempt to give a general proof that Tarskian consequence preserves truth fails. Analysis of this failure shows that de facto truth preservation is a very weak criterion of adequacy for a theory of logical consequence and should be replaced by a stronger (...) absence-of-counterexamples criterion. It is argued that the latter criterion reflects the modal character of our intuitive concept of logical consequence, and it is shown that Tarskian consequence can be proved to satisfy this criterion for certain choices of logical constants. Finally, an apparent inconsistency in Ray's interpretation of Tarski's position on the modal status of the consequence relation is noted. (shrink)

We consider connections between number sense—the ability to judge number—and the interpretation of natural language quantifiers. In particular, we present empirical evidence concerning the neuroanatomical underpinnings of number sense and quantifier interpretation. We show, further, that impairment of number sense in patients can result in the impairment of the ability to interpret sentences containing quantifiers. This result demonstrates that number sense supports some aspects of the language faculty.

In a recent number of Philosophy of Science, Mr. C. D. Hardie offers some interesting suggestions concerning the problem of other minds. In his view the fact that we feel certain of their existence constitutes a problem; and he wishes to find a rational justification for this certainty. “What grounds have I for believing in the existence of other minds?” he asks. He is attracted by the traditional argument from analogy, but finds it incomplete; for “any conclusion arrived at by (...) analogy and induction is at best only probable,” and “I am certain that other minds exist.” Again we find him remarking that “there is room for an account which makes our knowledge of them depend in some way on analogy... but which is such that we can be certain that other minds exist....”. (shrink)

Recent advances in quantum physics have led to a renewal of interest in the problem of human freedom and in the wider problem of indeterminism. It is important to recognize, however, that if every denial of determinism is to be called indeterminism, the latter term covers a wide range of logically distinguishable positions. We should perhaps speak in the plural number of indeterminisms rather than of indeterminism. For determinism may be defined, simply, as the doctrine that every event has a (...) cause; or we may add that the effect is always uniquely determined; or that when the effect is complex it can always be exhaustively analyzed into components each of which is the effect of a component of the cause; or that every cause directly or indirectly includes the entire universe. And in the case of each of these, or of still other interpretations of determinism, the denial would be a form of indeterminism. (shrink)

According to the Laplacian definition, the probability of an event is the ratio of “favorable” cases to possible cases. It is obvious that the definition presupposes the equal probability of the possible cases; and to make the definition of probability depend upon the conception of equal probability has the appearance, at least, of a vicious circle. Moreover it is hard to see how we can assure ourselves that each possible case is really no more and no less probable than any (...) other. But even if we define probability as the relative frequency of occurrence of events under a given set of conditions, or of true conclusions from premises of a given type, we still require the conception of equal probability, unless indeed we choose to renounce entirely the mathematical expression and calculation of probabilities. (shrink)