Re: Re: Grice and conditionals (long, no Greek)

Date: Mon Sep 21 1998 - 16:55:06 EDT

In a message dated 9/21/1998 4:38:30 PM, wrote:

<<In formal logic, the following are all equivalent:

        if A then B
        if not B then not A
        not B or not A
        A or not B

There may be others. At any rate, "if not B then not A" is one of the
standard transformations. However, I'm a little bit worried about using the
"if not B, then not A" transform as a general device for understanding "if
A then B" sentences that contain negations. In order to make that work
properly, I agree with Grice that you have to bring in a number of
propositions that are implied but not stated, and that some of these things
may be implied by the context in which the statement is made. The result is
that you need many more propositions, not just A and B, if you want to use
formal means to understand conditionals. If Grice is correct - and he is at
least brilliant, whether or not he's correct, and in spite of his
impenetrable writing style - then bringing in all of these propositions
would give you a framework in which formal logic could be used effectively
to understand such statements.

My formal logic is *extremely* rusty, but let me try to use some examples
to illustrate what I mean:

Statement: If he does not come on time then we will wait for him.

A = he does not come on time
B = we will wait for him
If not B then not A = if we will not wait for him then he will come on time.

I'm skeptical that the propositional value of the original statement and
the transformation are the same in this case. Grice says that the reason
for this is that there must be some reason the person is telling us this,
which implies a number of propositions that are implied, but not stated,

1. There is a likelihood that he will not arrive on time
2. We need a plan for dealing with the contingency that he arrives late
(perhaps we were all planning to go somewhere together, and he wanted us to
give him a ride)
3. His tardiness is beyond our control, or if it is within our control,
there is some reason that we prefer not to negotiate with him in order to
get him to come on time, or perhaps there has been negotiation and it was
agreed that we would wait if he comes late

If we do not take these into account, then our formal analysis of the
statement will not be adequate. (If our formal analysis *is* adequate, then
we took it into account (grin!)) In this particular case, I think the
proper analysis requires an understanding that the statement is really
intended to be limited to a plan for handling the contingency that he is
late, and is not intended to be applied if he arrives on time. The "if not
B then not A" transformation took the statement out of context and
broadened its scope. Within the right scope, incidentally, the
transformation might make sense - e.g. perhaps we are formulating a policy
of leaving on time even if some people are not yet there, and we expect
that the result of this policy will be that people arrive on time.

You say that the "if not B then not A" is a good general tool for
understanding conditionals with negatives in both the protasis and the
apodosis. Consider this statement, which is similar to the first, but has
negatives in both the protasis and the apodosis:

Statement: If he does not come on time then we will not leave before he

A: he does not come on time
B: we will not leave before he arrives
if not B then not A = if we leave before he arrives he will come on time

Again, the result of the transformation is a little surprising, and seems
to have a different propositional value than the original statement.

I think that Grice is pretty important for understanding conditionals in
human language. He's also very hard going. I'm not sure who else is
important to read (perhaps Wittgenstein? but I'm not sure which works), but
perhaps some of the linguists on the list will know. At any rate, I think
that there's a fair amount of literature on the treatment of human language
conditionals, written largely by philosophers and linguists, and I know
that I haven't read much of it except for Grice and a little Wittgenstein.>>

A lot to deal with here and I only want to make a few points. First, in the
logical transformation, we are not really saying they are making the exact
same statement, only that the logic of the statement is the same. Second, in
the logical transformation,we need to becareful how we handle the tenses. They
may need some adjustment.

Statement: If he does not come on time then we will not leave before he

A: he does not come on time
B: we will not leave before he arrives
if not B then not A = if we leave before he arrives he will come on time

I'm not sure how to handle this. John Baima do you want to tackle it?

<<EI MH occurs twice in Matt 11:27 - nobody knows the son EI MH the father,
and nobody knows the father EI MH the son, and those to whom the son
chooses to reveal him. At least some translations (the first few I looked
at) translate this with "except" or "but". Why do you think this changes
the meaning?>>

All the examples were drawn from John Baima's thesis. One of his points is
that this translation makes knowledge of the Son more obscure than knowledge
of the Father since the Son reveals the Father to some. The logical
transformation would be: If anyone knows the Son, the Father does, and if
anyone knows the Father, the Son does, and those to whom the Son chooses to
reveal Him. It seems that the Father knows the Son preeminently as opposed to
exclusively, since the Son has revealed himself to the diciples. The Son
knows the Father preeminently, as opposed to exclusively since the Son reveals
the Father to others.

<<In Matt 13:57, Jesus says that a prophet is not without honor EI MH in a
home game. Now I assume your point is that this statement, taken as literal
truth, is false if a prophet is also dishonored outside of his home town.
Your solution is probably to interpret EI MH as something other than
"except". My solution (off the top of my head) is to bring in the larger
context in which the statement was made, and probably to treat this as a
hyperbolic statement - and I do think that Jesus uses hyperbole on other
occasions as well. Of course, hyperbole and other figures of speech are
pretty rough on formal logical analysis, but I'm sure that someone
somewhere has written on this in a useful way.>>

On could handle it this way, but it still seems that the meaning is: "If a
prophet is without honor anywhere then he is without honor in his home town
and in his own household." The idea is that the prophet is without honor
preeminently in his hometown.

<<In John 3:13, the statement is that nobody has ascended into heaven EI MH
him who descended from heaven, the Son of Man. I assume your point is that
there are a couple of people in the Old Testament who ascended into heaven.
In this case, I think you need to look at the scope of the statement -
Jesus is saying that there is only one person who can tell Nicodemus about
heavenly things, the one person who has been to heaven and has descended
from heaven. Now if you want to be strictly literal, yes, there are a
couple of prophets sitting in heaven who have ascended into heaven, but
they aren't on earth anymore, and are not available to explain things to
Nicodemus. If you want to be that literal, Jesus has not yet ascended into
heaven at that point either. (I think there are a lot of uses of "everyone"
and "nobody" in the NT that only make sense with the right scoping.)>>

The point is that Jesus is preeminently the one from heaven and therefore
preeminently qualified to speak about heaven.
One could also add Matt 12:39: No sign shall be given to this generation
except the sign of Jonah.
Logical equivalent: and if any sign shall be given to it then the sign of
Jonah will be given to it. Will the sign of Jonah be the only sign given to
Israel or will it be the preeminent sign? If the latter then translating EI MH
as "except" or "but" obscures the meaning. I wish to extend my thanks again to
John Baima for his work in this area. I wanted to see if this method could be
applied to all the EI MH clauses in the NT.

Charles Powell

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