Tuesday, May 20, 2008

Countercurrents

I have been thinking about certain temporal sentences like the following:

1. When I go to the store, I will get milk.

and

2. When I went to the store, I got milk.

I do not know anything about the literature on this topic (if there is any). So, what I am about to say might have been said by someone else or definitively disproven. If anyone has any information about the literature on this topic, I would be happy to hear it.

Here is an initial idea that seemed plausible to me:

3. Necessarily ((when I go to the store, I will get milk is true) iff (the
nearest future time during which I am going to the store is a time at which I get milk))

Unfortunately, there are several counterexamples to this suggestion. Here is one. Suppose I utter sentence (1) and then set out to get milk. One time during which I am going to the store is a time that ends the moment I step through the grocery store doors. But, that is not a time during which I get milk. However, if I get milk shortly after stepping through the door, then it seems spoke truly when I uttered (1).

Here are two modifications. The first is my lame suggestion and the second is Andrews more interesting suggestion:

4. Necessarily ((when I go to the store, I will get milk is true) iff (the
nearest future event during which I am go to the store is an event during which I get milk))

This might be subject to the same sorts of objections as (3). It all depends on what you think about events. Here is a variant of Andrew's suggestion:

5. Necessarily ((when I go to the store, I will get milk is true) iff (the
nearest future continuous time every subinterval of which is a time during which I am going to the store and no continuous superinterval of which includes more times during which I am going to the store is a time during which I get milk))

There are similar accounts of the (2) involving past times which I will not spell out here. What do you guys think of this suggestion? Are there any obvious counterexamples? I have had at least one person tell me that these accounts are too narrow because (1) is true if I get milk at any time in the future while I am going to the store. Does anyone else share that intuition about (1)?

UPDATE: Please note that I have revised (5) in my comments below and ignore the formulation in the post.

5 Comments:

Blogger Andrew Cullison said...

(5) is a bit difficult for me to comprehend - is it worded the way you want it to be worded?

Also, I think I know what you mean by superinterval - but could you give me a quick defintion so I know we're on the same page.

2:06 PM  
Blogger Joshua said...

This comment has been removed by the author.

5:02 PM  
Blogger Joshua said...

(5) is not quite right. I screwed something up in it. Let me try to fix it as follows.

Let's say that T is a maximally continuous F-ing time for S is a time that meets the following conditions: (i) T is a continuous time during which S is F-ing, (ii) Every subinterval of T is a time during which S is F-ing, and (iii) there is no continuous superinterval which is such that each of its subintervals is a time during which S is F-ing.

A superinterval of a time T is a time that includes T as a subinterval.

Now (5) should read as follows:

5. Necessarily ((when I go to the store, I will get milk is true) iff (the nearest future maximally continuous store going time for me is a time during which I get milk))

That's a better. Does it make sense now?

5:04 PM  
Blogger Andrew Cullison said...

Got it.

Now I've got some thoughts.

First Stab at a Counterexample:
Suppose I go to the store. I leave to get alleviate some crisis (with the intention of returning after I go be Superman for a bit).

I go back and get the milk. Consider my utterance "When I go to the store, I will get the milk" prior to my adventure. This view seems committed to saying it's false.

Second Stab:

I go to the store and the terrorists blow it up. After pulling myself up from the rubble I go across the street to the other store (insert a sufficiently long pause - so we don't have a maximally continuous store going interval). When I return with the milk and we evaluate whether what I uttered was true or not - It seems we should say true.

I don't think these are terribly decisive, but they're stabs.

6:54 PM  
Blogger Joshua said...

These are the same kinds of counterexamples I have considered. I am inclined to say that spoke falsely in the first circumstance. If Bree were to stop me when I am in superman gear and say "you said you would get milk when you went to the store", I am inclined to respond "but, I had to help these people out" and not "yes and I will". The former seems like an appropriate response but I am not sure that the latter is.

In the second case, I guess I am not sure whether my journey after the explosion counts as a second maximal store going time for me. Maybe there is just one big store going time. If I hang out in the rubble for a while and help out survivors, then I am more inclined to say that there are two store going times, but less inclined to believe that I spoke truly prior to any of my trips.

These are the kinds of counterexamples I've been thinking about, though, and I guess overall I have very week intuitions about these cases.

6:45 PM  

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