J. J. C. Smart's Encylopedia Entry on Time

I have been reading J. J. C. Smart's article on time (or a draft of that article or a draft of a revision of that article) which appears in The Encylopedia of Philosophy, edited by John Edwards (New York: Macmillian, 1967), Vol. 8, pp. 126-34.  Because this is an encylopedia, I was very surprised to find the tone of that article to be so polemical.  Rather than choosing to provide readers with a history of various the developments in the philosophy of time, Smart instead opts to (mostly just) assert that one particular view of time is correct.  In the course of setting forth this view, he tramples over anyone who disagrees with him.

For example, Augustine was "led to puzzle [over time] here [in the Confessions] because he demands, in effect, that non-analogous things [space and time] should be talked about as they they were analogous."  We then learn that Augustine is further confused because he happens to be a presentist:

This thought - that the present is real in a way in which past and future are not real - is part of the confusion of the flow or passage of time.  This is not to say that presentism has not recently been very intelligently defended, however implausibly, as by John Bigelow.  (We might regret that so fine a fellow as Bigelow should think of himself as only instantaneous.)

Is this encylcopedia material?  Smart limits himself to defending eternalism, the position according to which all times are equally real.  All sentences with express tense on their surface are to be translated into so-called tenseless sentences with added indexical referents to a tokened utterance.   So, for example, to say "Caesar crossed the Rubicon" is really to express the proposition otherwise expressed by the English sentence "Caesar crosses the Rubicon earlier than this utterance".  (I said "so-called tenseless" because it is not clear to me that "this utterance" does not itself involve a reference to the present, i.e., "the utterance I am now making".)  To flesh out this picture, Smart lays all his eggs in the four-dimensionalist basket.  This makes Caesar a four dimensional space-time worm who lies (tenselessly) along a world line in the space-time manifold.  According to Smart, Caesar didn't move through time.  In fact, Caesar may not have moved at all.  Rather, "Caesar moves (tenselessly) earlier than this utterance" is true in virtue of proper parts of Caesar's space-time worm lieing (tenselessly) at different portions on Caesar's world line.  Note that the worm which is Caesar exists both earlier, simultaneous with, and later than this utterance, as well as earlier, simultaneous with, and later than any other utterance.  In the common tensed idiom, Caesar's worm has always existed and will always exist.  Get the picture?

Most of this is layed out very articulately, but there are few arguments adduced in its defense.  For the most part, we're supposed to accept it because the "special theory of relativity has made it impossible to consider time as something absolute; rather, it stands neutrally between absolute and relational theories of space-time."  I'm not sure what Smart's point is, but it is clear that he's staking out a substantive anti-constructivist position in the philosophy of science.  For example, Michael Tooley is guilty of being "bold enough to consider modifying special relativity".  Unlike Smart, I prefer not to be hog-tied by scientific theories with counterintuitive entailments, especially when those theories contradict other well-received scientific theories.   This is not to say they should be ignored, but Smart's assurances all of this can be worked out as research continues fall a bit flat.

What of the obligatory treatment of Zeno and Cantor?  Here Smart says

Given the concepts available to him, Zeno rightly rejected the view that an extended line or time interval could be composed of unextended points or instants.

This has a very odd ring in my ears, but let's leave that aside.  The fallacy in Zeno's famous argument that one could never traverse a finite distance composed of infinitely many points is diagnosed by Smart as the mistaken belief that the points of the continuum are sequential.  Perhaps, although Smart doesn't clarify.  In any case, this is relevant because it relates to the structure and geometry of space-time.  How do we get dimension, and so space-time geometry, out of mathematics without avoiding Zenoesque paradox?  Easy.  Smart says:

The set of all rational points on a line has dimension 0.  So does the set of all irrational points.  In these cases an infinity of "unextended points" does indeed form a set of dimension 0.  Since these two sets of points together make up the set of points on a line, it follows that two sets of dimension 0 can be united to form as set of dimension 1... The modern theory of dimension shows that there is no inconsistency in supposing that an appropriate nondenumerable infinity of pints makes up a set of greater dimensionality than any finite or denumerable set of points would.

Smart has given us two sets of points, both of which he asserts have dimension 0.  These are the set of rationals and the set of irrationals.  Now this is interesting.  First of all, there are continuum many irrationals and only a countable infinity of rationals.  It's true that the set of rationals plus the set of irrationals yields the line, but assuming the Continuum Hypothesis, the set of irrationals has a cardinality one order of infinity higher than the cardinality of the set of rationals.  This means that two sets of the same cardinality, aleph one, can differ in their dimension.   What is going on?  This is itself suspect, but it seems to contradict Smart's last cited claim above.  On the theory Smart has so quickly sketched, it is only the case that a "non-denumerable infinity of points makes up a set of greater dimensionality than any finite or denumerable set would" if a set of a non-denumerable infinity of points can make up set with the same dimensionality as a denumerable set.  Now if  Smart hasn't erred, he certainly hasn't given us anything satisfying.

A major theme of Smart's entry is that we have to disabuse ourselves of the pernicious notion of the "flow of time".  Too many philosophers have been seduced and led into error by this relatively commonsensical view.  But these philosophers usually have their own reasons for rejecting Smart's picture, such as "dubious philosophical reasons connected with the notion of free will".  What of those who opt for a causal theory of time?  Well, "perhaps they could rely on causal connectibility and not on connectedness."  But "connectibility is a modal notion and so will not be liked by philosophers such as those influenced by Quine, who are suspicious of modality."  Or perhaps philosophers influenced by that dubious notion of free will won't like the fact that Smart holds that their entire worm already lies in the space-time manifold.  On this view, all propositions about parts of my worm lying past the part writing this sentence are either true or false.  No problem.  These concerns can easily be allayed by pointing out i) that this theory does not imply determinism because it is consistent with indeterminism, ii) indeterminism and free will are incompatible, and iii) compatibilism is possibly true.  Points (ii) and (iii) are unsatisfying and point (i) looks false.

The general point here is that Smart, in an encylopedia entry, presents a particular philosophy of time as the obviously correct view.  Yet this view is highly controversial.  Opposing views are hardly discussed, and when merely mentioned, they get dismissed with immensely philosophically unsatisfying one-liners.  Objections to the view Smart puts forth are presented tersely and treated as if they all stem from an archaic philosophical tradition.  To be fair, almost all objections to any view mentioned in the article, including views Smart doesn't favor, are presented in one line.  Thus we can skip a discussion of presentism because it has "difficulty... analysing cross-temporal statements such as 'Smith will have come before you have finished breakfast'".  The entry is a fun read, and it contains a lot of good information, but it's way too polemical and limited to be included in any encylopedia.

Comments

[Ken]

"...philosophers influenced by that dubious notion of free will won't like the fact that Smart holds that their entire worm already lies in the space-time manifold. On this view, all propositions about parts of my worm lying past the part writing this sentence are either true or false."

Very nice. It only remains to consider that no one pitches arguments to a machine (vs. a free deliberative agent) to round-off the pragmatic RAA of Smart's positivism, as elaborated to cover time.