[FOM] Mathematical explanation

mjmurphy 4mjmu at rogers.com
Mon Oct 31 18:56:45 EST 2005

I wrote:

>> It seems to me that the latter passage here supplies the very
>> assumption (condition of applicability) you ask for: that no Fs should
>> be Gs.

Richard responded:

> This misses both my points. (i) That no Fs should be Gs is not a
> condition for the applicability of "3+4=7", since "3+4=7" neither says
> nor implies that if there are three Fs and four Gs, then there are seven
> F-or-Gs. What it says is that three plus four is seven, and the most it
> implies is: (*) If there are three Fs and four Gs, and no F is G, then
> there are seven F-or-Gs. is what I wrote above. (ii) If that doesn't
> seem convincing, then consider (*): I claim that it has no "conditions
> of applicability". It is certainly not a condition for its applicability
> that no F is G, since it can be used in /modus tollendo/ reasoning.


I am still missing your point, I guess.  Can you tell me what proposition 
the utterance "3+4=7" expresses when it is, say, being uttered by a 
mathematician and is expressing a necessary proposition?

I also wrote:

The point, as I read it, is that utterances of "3+4=7" can be true or
false while its literal meaning remains the same (contra your remarks and 
remarks of several other posters).

To which Richard responded:

Obviously that is the point of the example. I've argued above that the
example fails to make that point. But let's assume I'm wrong. Then the
question at issue is what, even if Searle were correct, would follow
about the necessity of *the //proposition expressed* by "3+4=7" on
various occasions of utterance. I am conceding, for the moment, that
this sentence may express different propositions on different occasions.
In that case, it is correct that the literal meaning of the sentence is
not necessarily true, but that is because the literal meaning of the
sentence is not a complete proposition.


It is not merely a matter of making explicit unarticulated semantic
constituents in order to transform an incomplete proposition into a complete 
one.  Take the non-mathematical
example again, "The ink is blue."  Firstly, what is incomplete about the
proposition it seems to express, that the ink is blue?  But perhaps, in
order to be more precise, we say, "The ink is blue on the page."   Is
this any more complete?  I don't know, but let's assume it is, and that
now we have a complete proposition--that the ink is blue on the page.
But then, is the ink blue on the page under natural light, or ultraviolet
light, or etc.?    Once again, we have to appeal to a series of assumptions
etc. etc., ie to context, to determine the truth value of the proposition. 
So here we have a completed
proposition that differs in truth value depending on context.

This pertains to Searle's claim that context should not be taken as part
of semantic content, as some (in relevance theory, for example) have
suggested.  Do this and you get an infinite regress, and never a
completed proposition.  So for example we could find a context in which the 
proposition that the ink is blue on the page under
ultraviolet light is true, and another where it was false, and so forth. 
This is one reason that views like Searle's are
often referred to radical contextualism or radical pragmatism (all 
pragmatic enrichment; no semantic core).

Finally, I doubt that anything of interest in the philosophy of
language was definitively settled during the 60's and 70's.   In any case, 
the kind of context sensitivity Searle is talking about persists even after 
we have dealt with the kind of indexicality that Lewis was concerned with.



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