[FOM] Mathematical explanation

Richard Heck rgheck at brown.edu
Thu Nov 3 00:34:48 EST 2005

This will be my last message on this topic, since the discussion isn't
going anywhere and isn't likely to go anywhere soon.

mjmurphy wrote:

> Your argument has been to explain examples in which an utterance of
> "3+4=7" is false by claiming that they express a proposition different
> from the one expressed when mathematicians use it.  But why not look
> at it this way. Assume that any utterance of the sentence means the
> same thing or expresses the same proposition (for instance as you have
> given above). But then why is the utterance false in the case of the
> overlapping circles?  Treat whatever it takes to make the utterance
> false as contextual assumptions that are not part of the proposition
> expressed, but could always be written out as extra clauses appended
> to the proposition expressed. [etc] 

These comments utterly fail to come to terms with the dialectical
situation. I am /not/ granting, except for the sake of argument, that
"3+4=7" is ever false. When I do grant this claim, I argue, as noted,
that it doesn't always express the same proposition. Why on earth would
I then want to assume, within the scope of said supposition, that it
does always express the same proposition?

If one wants to use the word "proposition" in such a way that every
sentence always expresses the same proposition on any occasion of use,
there is no stopping him, presumably. But then one has to recognize that
no-one else uses the word that way, /including so-called radical
contextualists/. To use it in that way is to cut the term loose from the
theoretical anchors that give it a point.

> Richard said:
> This slip [which involved asking whether "the ink [is] blue on the
> page under natural light, or
> ultraviolet light"] is very revealing: The ink might /look/ different
> colors under different lighting conditions, but surely you do not
> really think that changing the lighting conditions changes the ink's
> color.
> Me:
> I sure do.  Not its physical chemical or physical makeup, obviously.
> Let's say that we have an ink which is blue under natural light, but
> red under ultraviolet light. [etc]

That begs the question at issue. I'm not prepared to say any such thing.

> Imagine that we all normally live under ultra-violet light.
> Furthermore, imagine that we are in the habit of coloring things for
> display under ultra-violet light. The "real" color of the ink would be
> red, because ultra-violet light provides the natural conditions under
> which we see the ink in this context.  What the ink looks like under
> non-ultra-violet light, and even if it remains the same color or
> rapidly changes color under those conditions, is irrelevant.

These comments do not address the question at issue, which was whether
the color of the ink changes /as lighting conditions change/. You are
assuming that the context has changed in certain ways. That is a
different matter. My point was that you slide back and forth, near
constantly, between claims about objective facts of the matter---what
color the ink is---and claims about how context affects what is
said---what claim "the ink is blue" expresses under certain
circumstances. To fail to appreciate the distinction between these two
sorts of issues is to confuse use and mention quite horribly. What we
have here is just another example of that confusion.

These comments also seem to assume a dispositional theory of color,
which is a pretty hefty assumption. For what it's worth, even with that
assumption, this example seems to me not to be very impressive. I see no
reason to suppose that, even in these conditions, "the ink is red" would
express a truth. Perhaps it would be /uttered/ under those
circumstances---perhaps---but it seems to me that it is pretty easy to
tell a Gricean story about why, in those circumstances, its utterance
might /communicate/ a truth even if it does not /express/ one.

> Lets' say that sentences are made true by their truth conditions. 
> Being blue under natural light, being blue under ultraviolet light,
> are two such conditions.  I think they are two wo different ones.  Do
> you think that being blue under natural light is the same thing as
> being blue under ultra-violet light?

I think asking "What color is the ink under different lighting
conditions?" is like asking "What temperature it is in Topeka in Tulsa?"
or "What is 3+4 on Tuesdays?"

> Philosophers of mind or language don't have a clue as to what their
> talk of cognitive states amounts to in any terms that go beyond the
> vaguely metaphoric.

I guess psychologists are equally clueless, too. They should return
their grant money.

Richard Heck

Richard G Heck, Jr
Professor of Philosophy
Brown University
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