I’ve been interested on and off in the issue
of which argument forms involving natural language conditionals are reasonable
to use in everyday contexts. The importance of the everydayness is that we want
argument forms that not only preserve certain truth, but which don’t take us
from almost certainly true (or acceptable) premises to almost certainly false (or
unacceptable) conclusions. From that perspective, I’ve often wondered whether
all instances of this argument are good:

(1)      All Fs
are Gs.

(2)      So, if a
is an F, then a is a G.

Most instances of this sound pretty good to
me. But something came up today that made me wonder about it. Take the
following instance of the argument.

(3)      The Brown football team have won every
game they’ve played this year.

(4)      So, if the Brown football team have played
Notre Dame, they’ve beaten Notre Dame.

There’s some presuppositions involved in
saying that this is an instance of the form, roughly to the effect that if they
played Notre Dame and won the game, then they beat Notre Dame, but I guess that
is right. And, to put the example in context, Brown is not in the same division
as Notre Dame (they are Div I-AA and Notre Dame are Div I-A) but since teams do
play outside division from time to time, it is not out of the range of
possibility that Brown played Notre Dame. But you’d expect that if the teams
had played, Notre Dame would have won.

Anyway, the argument seems pretty good to
me, but maybe it isn’t. Maybe I could imagine coming to more or less accept (3)
and still be hesitant about (4). I don’t think I would – I think if I accepted
(3) I would also believe (4) and conclude on the basis of it that Brown hadn’t
played Notre Dame. But maybe I could accept (3) and reject (4).

What reminded me of this was a different kind
of argument, one used by V. H. Dudman in a 1994
paper. I’ve amended Dudman’s example a little bit.
Compare the following three arguments. (Background: it is extremely unlikely
that anyone will present a paper on pie-throwing at an APA. Indeed, for any
particular person, it is unlikely that they’d present a paper on pie-throwing
at a randomly selected APA.)

(5)      Someone presented a paper on pie-throwing
at the last APA.

(6)      So, if Brian didn’t present a paper on
pie-throwing at the last APA, someone else did.

(7)      Someone presented a paper on pie-throwing
at the last APA.

(8)      So, if Brian hadn’t presented a paper on
pie-throwing at the last APA, someone else would have.

(9)      Someone will present a paper on
pie-throwing at the next APA.

(10)    So, if Brian doesn’t present a paper on
pie-throwing at the next APA, someone else will.

Everyone agrees that the argument from (5)
to (6) is good, and the argument from (7) to (8) is bad. And everyone agrees
that this is the basis for positing some kind of difference between the kind of
conditional found in (6) (regularly called ‘indicative’) and the kind of
conditional found in (8) (regularly called ‘subjunctive’).

But what do we say about the argument from
(9) to (10)? Dudman thinks it’s bad. If you believe
(9), but believe it on the basis of evidence that some particular person will
present a paper on pie-throwing, and you have reason to believe that person is
me, and believe, as per the background assumptions that no one else is likely
to do this, he thinks you’ll still reject (10).

I’m not so sure. On the other hand, that it
doesn’t seem clearly good does seem
evidence for Dudman’s claim that future tense ‘indicatives’
like (10) do fall into the same logico-grammatical
category as past-tense ‘indicatives’ like (6). But on the third hand (or is it
fourth by now) that it doesn’t seem clearly
bad seems evidence against Dudman’s claim that there
is a natural class of conditionals, what he calls ‘projectives’
which includes both subjunctives like (8) and so-called future indicatives like
(10). After all, the argument from (7) to (8) is a howler, but the argument
from (9) to (10) is more problematic.

I don’t know what to make of all this, but the
issues seem murkier than I remember, and much murkier than I’d like them to be.
Much thanks (of a distinctively philosophical thought) to Chris Kane for
reminding me how confused I am about all this.