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Date: Fri, 17 Oct 2014 21:14:19 -0400
From: John Cowan <cowan@mercury.ccil.org>
To: bpfk-list@googlegroups.com
Subject: Re: [bpfk] {ro}, existential import and De Morgan
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Riley Martinez-Lynch scripsit:

> Which is to say, {ro} has existential import. This is the position of 
> classic/Aristotelian logic, but not modern logic.

As pc explained it to me, Aristotelian and Fregean (modern) logic don't
actually contradict one another in this area.  However, the *translation*
from Aristotelian "All As are Bs" to Fregean "For all x, if A(x) then
B(x)" is not quite truth-preserving.  "All A is B" is taken to be false
if there are no As, whereas "For all x, if A(x) then B(x)" is vacuously
true if there does not exist x such that A(x).  Lojban expresses each
of these differently: the Aristotelian claim is "ro broda cu brode"
whereas the Fregean claim is "ro da poi broda cu brode".

Now these can be reconciled in their interpretation if we assume that
"ro" has existential import: then "ro broda cu brode" requires that
there are brodas, whereas "ro da poi broda cu brode" requires only that
there are das.  The latter is true except in a completely empty universe,
which is not really worth talking about.

> Can anyone show me where and how this problem was resolved? Failing that, 
> would anyone care to take this up and once and for all settle the matter?

In answer to both questions:  probably not.

-- 
John Cowan          http://www.ccil.org/~cowan        cowan@ccil.org
What has four pairs of pants, lives in Philadelphia,
and it never rains but it pours?
        --Rufus T. Firefly

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