The so-called no-rate argument argues that time cannot flow or pass in the literal sense of that term, because its motion can be assigned no meaningful rate. This paper examines a yet unexplored objection to the no-rate argument, which consists in showing that the argument itself is based on an extended conception of motion, according to which it is meaningful and consistent to say that time flows at no well-defined rate.
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The distinction between dynamists and anti-dynamists is therefore transversal to the more notorious distinction between A-theorists and B-theorists, who respectively assert and deny that tenses are objective, irreducible, and non-relational features of time. Moving spotlight theorists are examples of dynamists subscribing to the A-theory, while Prior (1958, 1968) and Zeilicovici (1989) are examples of non-dynamist A-theorists. The overwhelming majority of B-theorists are non-dynamists, but Zwart (1976) and Maudlin (2002, 2007) are exceptions. Similarly, the question whether or not time literally flows is logically independent of the debate concerning McTaggart’s argument against the reality of time, even if the two issues have been traditionally conflated. See, for instance, Craig (2000, 219–22).
The phrase “well-defined” should be understood here as “compatible with the accepted definition or understanding of speed”, and not as “having a definite or precise value”. This means that the no-rate argument is concerned with the form of the purported speed of time, rather than with its value.
The no-rate argument can also be phrased in modal terms, so as to lead to the conclusion that time cannot possibly flow.
The hypothesis of the hyper-time, in particular, has been recently revived by Skow (2012b), though it should be noticed that he considers the hyper-time only a heuristic fiction.
Tallant (2010) appears to endorse a similar strategy. However, his argumentation is ultimately directed towards defending an anti-dynamist conception of time. Notice, in fact, that he explicitly refers to the flow of time as a metaphor (2010: 139, fn 19), and that what he calls ‘dynamic theory of time’ should not be confused with dynamism, as he roughly equates it with the A-theory.
Notice that this remains true independently of which strategy the dynamists employ to resist the no-rate argument, and in particular even if they choose to deny premise (3), which will play a major role in the discussion to follow. For instance, the hyper-time strategy requires that time should move with respect to a temporal dimension that is not the one with respect to which all ordinary movers flow or pass. Similarly, to argue that the speed of the flow of time should be the multiplicative inverse of ordinary speeds evidently implies that the roles of time and speed should be exchanged in either case.
The adequacy of this analysis is confirmed by the fact that one of the logical objections to the flow of time, due to Grünbaum (1973, 315–6), is specifically directed against the meaningfulness of this claim. Grünbaum argues that this claim is in fact a plain tautology, which, as such, can have no empirical content. To properly address Grünbaum’s objection would go beyond the scope of this paper; should it suffice to mention that at least some dynamicists consider the flow of time empirically evident (cfr. for instance Maudlin 2007, 114).
Evidently, in this context we are referring to a conceptual or logical possibility. Therefore, to argue that it is not epistemically or practically possible for anyone to go through an infinite chain of conceptual implications is no objection to the present argument.
This, of course, does not exclude that the anti-dynamist could construct a logical argument along the lines of the variation-rate argument or on the basis of some of its premises. For instance, they may argue that no quantity can vary with respect to itself, rejecting the extended at-at theory of motion and hence the dynamist conception of the flow of time on that basis. However, what matters to our present inquiry is that no such argument could be adduced in order to establish premise (2).
Incidentally, this should prevent any van Inwagen-style replies such as: “I cannot make sense of the claim that time flows by covering one second at each second without moving at a rate of one second per second”. To those who are tempted to advance similar objections, I simply reply that they are relying on the wrong intuition.
©2014 by Walter de Gruyter Berlin / Boston