Lehrer & Taylor on the doubly time-indexed nature of ‘can’

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In their 1965 article ‘Time, truth and modalities’, Keith Lehrer and Richard Taylor suggest that the term ‘can’ needs to be doubly time-indexed.  There is the time at which the ability or capacity is ascribed to the agent, and there is also the time at which the result of the action is achieved.

Here is the example Lehrer and Taylor present to help make their point:

Smith, who works in the country, has promised his wife to be in the city at four o’clock. It is now shortly before half past three, and Smith is seated at a small table in the country airport not far from a plane that is about to depart for the city. At the present time, this plane, which leaves at half past three, is the swiftest possible means of transportation to the city, and the plane arrives non-stop in the city at precisely four o’clock.  Finally, let us imagine that although there is nothing to prevent Smith from leaving on the plane at half past three, he in fact does not do so (Lehrer & Taylor 1965, p.390).

This example produces the following puzzle.  It seems correct to say that (1) if Smith doesn’t catch the plane, he cannot arrive at 4:00pm.  At the same time, we want to be say that (2) if Smith does leave at 3:30pm, he’ll arrive at 4:00pm.  Moreover, (3) Smith can leave at 3:30pm (there’s nothing stopping him).  Finally, we’re stipulating that (4) he doesn’t leave at 3:30pm.  Statements (1)-(3) all seem like things we want to say, and yet with hypothesis (4) they entail a contradiction.  This is because (2) and (3) appear to imply that (5) Smith can arrive at 4:00pm, whilst (1) and (4) appear to imply that (6) Smith cannot arrive at 4:00pm (Lehrer & Taylor 1965, pp.390-1).

The contradictions we encounter when considering this set of statements ((1)-(6)) are the result, Lehrer and Taylor argue, “of the fact that ‘can’ does not have ordinary tenses,” and a large step in the direction of a solution is to recognise this talk of ‘can’ is standing in for talk of ‘being able’ which we can see is amenable to standard tensing (was able, is able, will be able) (Lehrer & Taylor 1965, p.394).

In the present piece I do not want to discuss the solution offered by Lehrer and Taylor to this apparent problem; rather, I want to look at the interesting claim that ‘can’ has a double time-index.  This is easily arrived at once we see that ‘can’ (with its lack of ordinary tenses) is being used to refer to abilities (‘is able’, etc).  This can then be made explicit in our analyses of ‘can’.  A statement such as (3) then, will become (3c) Smith can, at 3:00pm, leave at 3:30pm.

There is something right about this proposal. And attending to these details more widely would, I suggest, bring greater clarity to various philosophical debates (Frankfurt-style cases being the obvious target). However, there appear to be at least two ambiguities in Lehrer and Taylor’s suggestion.  Consider statement (5) of their own example, which when explicitly indexed becomes (5c) Smith can (at 3:30pm) arrive at 4:00pm.

Here we have the ability being explicitly time-indexed, as well as the arriving being time indexed.  But what is this arriving?  Lehrer and Taylor say that we need to distinguish between “the time of an event that is possible from the time of the possibility of the event” (Lehrer & Taylor 1965, p.396).  So they see the arriving as an event, which is straightforward, but how do they conceive of this event?  Is it an action?  Or perhaps the consequence of an action?  It seems clear that in their example it is a consequence of an action.  For when Smith arrives at 4:00pm, he is not then and there performing any action which could be said to be the action by which he arrives.  Arguably he has done such an action, namely, his boarding of the plane.  But Smith’s arriving is an event which, although something he is part of, and although he may be acting at the time, his acting at the time of arrival is not the action by which he arrives.

In a later paper Lehrer (1976) applies and develops this point into a more complete semantics for ‘can’, and there he says that “statements affirming that a person can do something have a double time index, one time reference being to the time at which the person has the capability, and the second being to the time of action” (1976, p.243).  This would imply that Lehrer and Taylor did mean to suggest the second time index attached to the action, as opposed to any consequence of the action.

But as we’ve seen from Lehrer and Taylor’s own example, it is clear that we often use ‘can’ to talk about consequences of actions.  If we want to provide a unified semantics of ‘can’ then, we’ll need it to be able to handle both kinds of cases.  Is this a problem for Lehrer and Taylor’s account?  That is unclear.  We should at least be aware of the distinction, for it is plausible that the relation an agent bears to an action will be different in kind to the relation they bear to a consequence of an action.  On the standard view (which I take to be the Causal Theory of Action with something like a Davidsonian theory of individuation) actions are events, just like the consequences of actions, so it is likely that this ambiguity is benign.

A second ambiguity might be more problematic for their view, however.  Here is the problem: the second time-index refers to the event (which we’re assuming for now might be an action or a consequence of an action), but which part of the event?  We might identify two types of option: we could refer to one moment of the event (the start or the finish being obvious candidates here), or we could refer to some portion of the event (the entire event being the obvious candidate here).  Lehrer and Taylor take the first option: the time-index refers to a moment or instant, rather than an extended period.  And in the example they use to present their ideas it is the end of the event that is referred to: the arriving is complete by 4:00pm.  But it is not clear this is always how ‘can’ is used.  Here’s an exchange where the reference seems to be to the start of the event:

A: How about dinner tonight?

B: Sound’s lovely.

A: Great, I can pick you up anytime between 7:30 and 8:00.

B: 8 would be perfect.

In this exchange A seems to be saying that it would be possible for the event of picking B up (i.e. the action or consequence of action) to start anywhere between 7:30 and 8:00pm. The time chosen by B was 8:00pm, and this refers to the start of the event.  The time-index on A’s ability is left implicit, but it would have to range over some time prior to 7:30 and would end at some time before 8:00; how much prior would depend on how long it takes for A to get to B.  The important point, however, is that the time at which the picking B up ends, i.e., the time at which they arrive at the restaurant (or wherever) doesn’t really matter.  The crucial time is the start time.  This would suggest that an adequate semantics needs to be capable of referring either to the start time or to the end time.  And this might be evidence for the view that we need two time indices for the event itself (to specify the start and end times), as well as an index for the ability.

It would not be a problem for such a view that we rarely make explicit both time indices.  For the same is true of the time-index on the ascription of the ability.  As Lehrer and Taylor state, when an utterance does not make explicit a particular time index it will be provided by context.

Bibliography

Lehrer, K., 1976. ‘Can’ in theory and practice: A possible worlds analysis. Action theory, 242–271.

Lehrer, K. and Taylor, R., 1965. Time, truth and modalities. Mind, 74 (295), 390–398.