Steven Savitt

Barry Dainton wrote Time and Space “to provide an introduction to the contemporary philosophical debate that presupposes little or nothing by way of prior exposure to the subject, but that will also take the interested and determined reader quite a long way”. He has achieved much of what he intended in this difficult enterprise. He covers the major arguments in a fair-minded way, writes clearly, and has found a good illustrator to provide a host of diagrams that his student readers in particular will find helpful. The book also has a helpful glossary and list of web resources, as well as a brief bibliography and index.

The distinction between presentism and eternalism is usually sought in some formula like ‘Only presently existing things exist’ or ‘Past, present, and future events are equally real’. I argue that ambiguities in the copula prevent these slogans from distinguishing significant opposed positions. I suggest in addition that one can find a series of significant distinctions if one takes spacetime structure into account. These presentisms and eternalisms are not contradictory. They are complementary elements of a complete naturalistic philosophy of time.

Wittgenstein's remarks in his Tractatus on mathematics are quite obscure. Benacerraf and Putnam wrote, "In his Tractatus Loqico-Philosophicus, Wittgenstein maintained, following Russell and Frege, that mathematics was reducible to logic." On the other hand, Max Black claims, "Wittgenstein does not regard mathematics as reducible to logic, in the manner of Whitehead and Russell." I offer a detailed commentary upon Wittgenstein's remarks, concluding that his views most likely do not follow those of Frege and Russell. I reject a criticism of Wittgenstein presented by Black but find severe shortcomings in the view I take Wittgenstein to be presenting.

One of the questions that is addressed, from various perspectives, is the origin of time-asymmetry. Given the time-symmetry of the dynamical laws, all inferences about the future that are derivable from a dynamical theory are matched by inferences about the past. For Huw Price, who discusses the origins of cosmological time asymmetry, this is reason to treat all time-asymmetric cosmological theories with caution. He dismisses both the inflationary model and Stephen Hawking’s proposal to account for time-asymmetry with his famous “no boundary condition.” Instead, on the basis of the fact that we have no a priori reasons to distinguish between initial and final conditions, he advocates Gold’s time-symmetric model for the universe, in which the thermodynamical arrow of time is tied to the expansion of the universe, so that in the contracting phase towards the big crunch, entropy decreases.