Subject: Re: [jboske] Quantifiers, Existential Import, and all that stuff

From: [email-masked]
Date: Sun, 3 Mar 2002 20:32:02 EST

In a message dated 3/3/2002 2:57:20 PM Central Standard Time, 
[email-masked] writes:

> Each object that is not identical with itself...
> Any object that is not identical with itself...
> Every object that is not identical with itself...
> All objects that are not identical with themselves...
> 
> Nope, no existential import in sight in MY ontology. I get the 
> membership of the empty set in each case, and accordingly in "all 
> universally quantified statements where the quantifier has 
> existential import." A false statement implies anything, and so all 
> members of the empty set have any property you care to name.
> 

Putting a generous interpretation on your remarks, I take it that you think 
all universals have their subject term in the antecedent of a conditional and 
are therefore true whenever nothing fits that subject term. A fairly large 
group of people (I think Zeno Vendler wrote a paper on this once that may be 
substantially in the Encyclopedia of Philosophy) even since the free 
quantifier became the norm have held that a sentence starting "each member of 
the empty set..." was ipso facto false, ditto for "every," but not for "any" 
and "all." Even if we have brainwashed most folk (not likely, I think), the 
long tradition in logic deserves some attention in a logical language. And 
notice that what makes your interpretation work is not the quantifier, but 
the conditional. 

<I believe that some Lojbanists have severely overinterpreted English 
semantics. English is ambiguous, and is used in quite different ways 
by different speakers and writers.>

And we ought to be able in Lojban to match anything they say.