[FOM] Mathematical explanation
4mjmu at rogers.com
Sat Nov 5 16:03:00 EST 2005
This will also probably be my last message on the topic as well. I've
appended some brief remarks to A.R.D.Mathias message at the end. I
> 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]
Richard Heck wrote:
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?
Quite. What I am trying to do in the above passage is to show you how, in
the case of an arithmetical statement such as "3+4=7", assuming you
have already granted that the statement can vary in truth value from
occasion, it may do so very while expressing the same proposition. With
this in mind, try reading the passage again.
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.
I claim to be using the term in its accepted sense. Since you do not
actually argue the issue, neither will I.
I take it by some of comments that you would take you would say that
1) "The ink is blue under natural light but turns red under ultraviolet
...to be false, though it might manage to communicate, via Gricean
Implicatures for example, an informative and even perhaps a
I would say that in many contexts 1) is straight out true. It might even
constitute an "expert opinion", as it were, of someone whose job it was to
know how various inks behaved under ultra-violet light. The problem with
your approach is that Gricean pragmatics involves arguing that the vast
majority of assertions that people, even experts, would call true, are
actually false. For example, if the notion of domain is merely pragmatic,
then most quantified utterances are going to be false, though they may
manage to convey something true. Indeed this is one of the considerations
that has tilted philosophers away from Grice et al over the past ten years.
These comments also seem to assume a dispositional theory of color,
which is a pretty hefty assumption.
No, they just assume some good old fashioned, pre-theoretic linguistic
> 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.
There was a local psychologist in the paper yesterday claiming that a
particular bank robber "wanted" to get caught because he was not wearing a
may be true or not, but there is absolutly nothing about "intentional
"belief boxes" or "processing modules" that has
any bearing on its truth or falsity. Or are you arguing that solving
Frege's Puzzle would be a great advance in psychology?
It is true however that there are vast swathes of modern analytic
philosophy, cognitive science, linguistic semantics, and so on, from
which our tax dollars could fruitfully be diverted. And of all the
pseudo-scientific drivel being spouted in these fields, the debates and
puzzles surrounding beliefs, belief states, belief boxes and etc., are
surely the most silly. Put a bit crudely, the dominant view is that the
mind is a computer and, since a computer runs according to the rules of
some FOL variant, there must be some physical analogue in the brain to
premises, derivations, and so on. But, although the brain must operate
like this, philosophers have absolutely no idea what the physical side of
this equation would look like (though there is some vague talk of firing
neurons). Instead, it has generally been decided that the job of making
sense of and then verifying
the philosophical claims belongs to neurophysiology or neurobiology or, at
any rate, some
other field of endeavor. The philosophical claims all involve "loans
taken out on future research", as they say. Further, this situation has
been constant for nearly forty years, and there is no sign it will ever
change. Until it does, talk of "processing modules" and so on is just
children using big words because they think it will make them sound like
In another post, A.R.D. Mathias wrote:
I'd be inclined to think that the statement "the ink is blue" amounts to
a bundle of more detailed statements about the appearance of the ink under
various conditions, (so that changing the lighting means shifting from
one of these more detailed statements to another) together with a
Platonic belief in some objective global entity about which each of
these statements is giving partial information.
Well, the problem with putting it that way is that your bundle ends up being
an infinite disjunction. Also, you don't really need the objective global
entity if you have overlapping similarity relations (LWs example of the
string in which no thread runs the entire length).
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