[D. H. Mellor] Kant's claim that our knowledge of time is transcendental in his sense, while false of time itself, is true of tenses, i.e. of the locations of events and other temporal entities in McTaggart's A series. This fact can easily, and I think only, be explained by taking time itself to be real but tenseless. /// [J. R. Lucas] Mellor's argument from Kant fails. The difficulties in his first Antinomy are due to topological confusions, not the tensed nature (...) of time. Nor are McTaggart' s difficulties due to the tensed nature of time. The ego-centricity of tensed discourse is an essential feature of communication between selves, each of whom refers himself as 'I', and is required for talking about time as well as experience and agency. Arguments based on the Special Theory are misconceived. Some rest on a confused notion of 'topological simultaneity'. In the General Theory a cosmic time is defined, as also in quantum mechanics, where a natural present is defined by a unique hyperplane of collapse into eigen-ness. (shrink)

Much of the progress in the fields constituting cognitive science has been based upon the use of explicit information processing models, almost exclusively patterned after conventional serial computers. An extension of these ideas to massively parallel, connectionist models appears to offer a number of advantages. After a preliminary discussion, this paper introduces a general connectionist model and considers how it might be used in cognitive science. Among the issues addressed are: stability and noise‐sensitivity, distributed decision‐making, time and sequence problems, and (...) the representation of complex concepts. (shrink)

We discuss saturating ultrafilters on N, relating them to other types of nonprincipal ultrafilter. (a) There is an (ω,c)-saturating ultrafilter on $\mathbf{N} \operatorname{iff} 2^\lambda \leq \mathfrak{c}$ for every $\lambda and there is no cover of R by fewer than c nowhere dense sets. (b) Assume Martin's axiom. Then, for any cardinal κ, a nonprincipal ultrafilter on N is (ω,κ)-saturating iff it is almost κ-good. In particular, (i) p(κ)-point ultrafilters are (ω,κ)-saturating, and (ii) the set of (ω,κ)-saturating ultrafilters is invariant under (...) homeomorphisms of $\beta\mathbf{N\backslash N}$ . (c) It is relatively consistent with ZFC to suppose that there is a Ramsey p(c)-point ultrafilter which is not (ω,c)-saturating. (shrink)

The basic concepts appropriate for anS matrix theory for classical nonlinear physics are formulated here. These concepts are illustrated by a discussion of shock wave diffraction patterns. Other information concerning solutions of non-linear conservation laws is surveyed, so that a coherent picture of this theory can be seen. Within thisS matrix framework, a number of open problems as well as a few solved ones will be discussed.