On the dynamics of Alper and Bridger (Q1863947)

In 1996 the author published a paper [Mind 105, 81--83 (1996)] where he discussed how indeterminism may be entailed in classical dynamics by means of supertasks, systems in which an infinite number of individual actions are performed in a finite time. In 1998, \textit{J. S. Alper} and \textit{M. Bridger} (AB) [Synthese 114, 335--369 (1998)] made a critical analysis on Pérez Laraudogoitia's (PL) paper, rejecting his conclusion. In the next year, PL replied to AB [Synthese 119, No. 3, 313--323 (1999; Zbl 1032.70003)], arguing that AB did not solve the problems created by his supertask systems. Still in 1999 AB replied [Synthese 119, No. 3, 325--337 (1999; Zbl 1032.70002)] to PL's criticisms. In the present paper the author gives a new reply. This reviewer thinks that PL and AB are speaking different languages and/or about different subjects. Supertasks do not make sense from the physical point of view, since there is no such thing as infinite systems. So, supertasks are just a logical and philosophical curiosity, which may be interesting for the foundations of physics from a formal point of view. But from this formal point of view, a clear and precise language and framework should be made explicit. Philosophers should be more careful than physicists in discussions like this. And neither authors seem to be concerned with this aspect, namely, the statement of a common framework which is supposed to be the basis for any kind of discussion. If PL and AB obtain different results in different frameworks, what is the big surprise? This is just an example on how different people understand classical physics in an intuitive way. PL recognizes that his approach is local (in a sense) and that AB's approach is global (in a sense). The results obtained by all three authors are interesting in principle. But a precise language and a correct use of an axiomatic framework is demanded.