From: Jim Pryor <jim.pryor@nyu.edu>
To: X <X@nyu.edu>
Date: Tue, 15 Oct 2013 6:13 PM (6 days 14 hours ago)

On Tue, Oct 15, 2013, at 03:11 PM, X wrote:
> Hi Professor Pryor,
> I was just going over some of the readings and lecture notes and I came
> across the analogy of being able to conceive a world in which pigs can
> fly, but not being able to conceive a world in which 2+2=5
> I don't fully understand why this kind of analogy works - can't I
> conceive
> a world in which the latter is true? I can imagine a universe where what
> we define the properties of 2 to be actually amount to the value of 2.5 - in
> which case 2+2 (in that universe) would equal the value that I equate to
> be 5.
> I understand that in doing this I am changing the properties of the
> number
> 2, so arguably 2 is no longer 2, but is now 2.5 - however aren't we doing
> that for the pig situation as well? Pigs can't fly, but I'm imagining a
> situation where their properties have changed to allow them to fly.
> This is just something that I always wondered but forgot to mention in
> class, and as I am keying in on my arguments for my paper, I figured I'd
> send you an email to get your input on this somewhat unrelated question.
> Thanks, and I'll see you in class tomorrow,

Hi X, the important difference to keep track of is the difference
between imagining using some words differently, and imagining the things
you NOW IN FACT use those words to describe having different properties.
It's clear that I can imagine using the words "two" and so on
differently, so that "two plus two is five" comes out meaning something
true --- something different than I now would mean by those words. That
is also true of "pigs" and "fly". I can imagine using "pigs" to mean
"pigeons," then what I then expressed with the words "pigs can fly"
(namely, that pigeons can fly) would be true. The difference is that
there is SOMETHING ELSE I can also do in the second case, but CAN'T do
in the first case, at least not without some kind of contradiction or
incoherence. What I CAN do in the pig case is that I can imagine
pigs---the things I in fact use the word "pig" to mean---being able to
fly. I CAN'T imagine the numbers two and five and addition and equality
being such that two plus two equals five. You didn't describe such a
universe. You described a different universe, where two plus two---what
I actually mean by those words---still equaled four but IN THAT UNIVERSE
WE TALKED DIFFERENTLY, and used those words to say something different.
Of course what you describe is possible. (We don't even have to use the
words "two" and so on to mean something mathematical. We could use the
words "two plus two equals five" to mean what we now mean by "hello, how
are you.")

I hope that helps.