The story of deductive logic is well known. Until the beginning of the nineteenth century, deductive logic as a subject was represented by a finite and rather short list of well known patterns of valid inference. The paucity of the subject did not discourage scholars, however – there were professorships in Logic, courses in Logic, and volumes – fat, fat volumes – in Logic. Indeed, if anyone wants to see just how much can be made out of how little subject matter, I suggest a glance at any nineteenthcentury text in traditional logic. The revolution in the subject was brought about by the work of the English logician Boole.

Boole's full contribution to the mathematics of his time has still to be fully appreciated. In addition to creating single handed the subject of mathematical logic, he wrote what is still the classic text on the subject of the calculus of finite differences, and he pioneered what are today known as ‘operator methods’ in connection with differential equations. To each of the subjects that he touched – calculus of finite differences, differential equations, logic – he contributed powerful new ideas and an elegant symbolic technique. Since Boole, mathematical logic has never stopped advancing: Schröder and Pierce extended Boole's work to relations and added quantifiers; Behmann solved the decision problem for monadic logic; Löwenheim pioneered the subject that is today called ‘model theory’ Russell extended the system to higher types; and by 1920, the modern period in the history of the subject was in full swing and the stage was set for the epochal results of Godel and his followers in the 1930s.

I think that if we attempted to set out the ‘man on the street's’ view of the nature of time, we would find that the main principle underlying his convictions on this subject might be stated somewhat as follows:

(1) All (and only) things that exist now are real.

Future things (which do not already exist) are not real (on this view); although, of course they will be real when the appropriate time has come to be the present time. Similarly, past things (which have ceased to exist) are not real, although they were real in the past.

Obviously, we shall have to make some assumptions about the concept real if we are to discuss the ‘man on the street's’ view at all. The assumptions I shall make are as follows:

1. I. I-now am real. (Of course, this assumption changes each time I announce that I am making it, since ‘I-now’ refers to a different instantaneous ‘me’.)

2. II. At least one other observer is real, and it is possible for this other observer to be in motion relative to me.

And, the most important assumption, which will be referred to (when properly understood) as the principle that There Are No Privileged Observers:

1. III. If it is the case that all and only the things that stand in a certain relation R to me-now are real, and you-now are also real, then it is also the case that all and only the things that stand in the relation R to you-now are real.

There is no doubt that the examination into the structure of physical geometry and relativity theory initiated by Reichenbach and continued by Grünbaum has extended our understanding and called our attention to matters of philosophical importance. Unfortunately, I find myself unable to agree with Grünbaum on a number of central points. I do agree that the ordinary standard of congruence in physical geometry is the solid rod. I do not agree that one can define ‘congruent’ in terms of solid rods in such a way as to make possible an empirical determination of the metric, especially if the need for correcting for perturbational or differential forces in accordance with some not exactly known system of physical laws is to be taken into account. The prevalent assumption to the contrary is due to an error committed by Reichenbach and frequently found in the literature of the past thirty years (the error of supposing that there must be ‘universal forces’ in any non-standard metric). What appears rather to be the case is that the metric is implicitly specified by the whole system of physical and geometrical laws and ‘correspondence rules’. § No very small subset by itself fully determines the metric; and certainly nothing that one could call a ‘definition’ does this.

Secondly, I believe that it is misleading to say, as Grünbaum does, that physical geometry provides ‘the articulation of the system of relations obtaining between bodies and transported solid rods quite apart from their substance-specific distortions’ (p. 510). What Grünbaum means is not really ‘quite apart from their substance-specific distortions’, but after proper correction has been made for their substance-specific distortions.

Before we say anything about quantum mechanics, let us take a quick look at the Newtonian (or ‘classical’) view of the physical universe. According to that view, nature consists of an enormous number of particles. When Newtonian physics is combined with the theory of the electromagnetic field, it becomes convenient to think of these particles as dimensionless (even if there is a kind of conceptual strain involved in trying to think of something as having a mass but not any size), and as possessing electrical properties – negative charge, or positive charge, or neutrality. This leads to the well-known ‘solar system’ view of the atom – with the electrons whirling around the nucleons (neutrons and protons) just as the planets whirl around the sun. Out of atoms are built molecules; out of molecules, macroscopic objects, scaling from dust motes to whole planets and stars. These latter also fall into larger groupings – solar systems and galaxies – but these larger structures differ from the ones previously mentioned in being held together exclusively by gravitational forces. At every level, however, one has trajectories (ultimately that means the possibility of continuously tracing the movements of the elementary particles) and one has causality (ultimately that means the possibility of extrapolating from the history of the universe up to a given time to its whole sequence of future states).

The philosophy of physics is continuous with physics itself. Just as certain issues in the Foundations of Mathematics have been discussed by both mathematicians and by philosophers of mathematics, so certain issues in the philosophy of physics have been discussed by both physicists and by philosophers of physics. And just as there are issues of a more epistemological kind that tend to concern philosophers of mathematics more than they do working mathematicians, so there are issues that concern philosophers of physics more than they do working physicists. In this brief report I shall try to give an account of the present state of the discussion in America of both kinds of issues, starting with the problems of quantum mechanics, which concern both physicists and philosophers, and ending with general questions about necessary truth and the analytic-synthetic distinction which concern only philosophers.

The problem of ‘measurement’ in quantum mechanics

Quantum mechanics asserts that if A and B are any two possible ‘states’ of a physical system, then there exists at least one state (and in fact a continuous infinity of states) which can be described as ‘superpositions of A and B’. If A and B are the sorts of states talked about in classical physics – definite states of position, or momentum, or kinetic energy, etc. – then their superpositions may not correspond to classically thinkable states.