Re: Nonfirstorderizability

Eddie Cantor wrote:
> What's nice about it? There's a very dodgy argument towards the end
> (which the writer appears to endorse) as follows
>
> A) "Ontological Innocence" is the claim that terms referring to
> pluralities "have no new ontological commitments to any kinds of
> entities over and above the individual objects that compose the
> pluralities in question. (This defines "Ontological Innocence")
>
> (B) But plural locutions are committed to plural entities and
> Ontological Innocence is false. (This states the "house view")

Since that's the argument's conclusion, I'll comment on it at the end.
>
> (C) For (beginning of argument) a semantic theory assigns to each
> significant expression a unique semantic value which constitutes this
> expression's semantic contribution to the sentences in which it occurs.

That sounds non-controversial.

> (D) For instance ... a plural term (say "Peter and Paul") is assigned
> as its semantic value a certain plurality.

Not always. The standard view, as I see it, is that eg. "Peter and
Paul are yelling" means nothing more than "Peter is yelling and Paul is
yelling," and it's perfectly reasonable to translate it that way.

But suppose Peter and Paul are movers, and the sentence is (R1) "Peter
and Paul carried the refrigerator". R1 *can* be interpreted as (R2)
"Peter carried the refrigerator and Paul carried the refrigerator"; but
R1 can be true even where it's physically impossible for Peter to carry
the refrigerator, and also physically impossible for Paul to carry the
refrigerator (in which case R2 would have to be false).

Or suppose that Peter and Paul (and Tom, ***, and Harry) are workers
on an assembly line, and the sentence is (C1) "Peter, Paul, Tom, ***,
and Harry built some cars." It would be absurd to translate C1 as (C2)
"Peter built some cars, Paul built some cars, Tom built some cars, ***
built some cars, and Harry built some cars.", because C2 is clearly
false: Peter, for one, did not build any cars.

In order for R1 and C1 to be true, then, they arguably have to be
interpreted as assertions that there are collective entities ("Peter
and Paul" or PP, and "Peter, Paul, Tom, ***, and Harry" or PPTDH that
do things that the individual objects don't do, and even things that
the individual objects cannot do.

> (E) The semantic theory regards this plurality as one entity: it is
> the contribution of one syntactic expression.

PP and PPTDH obviously are things that exist; after all, something
carried the refrigerator and built the cars. And they're different
existents from Peter, Paul, or any of the other objects; as some
assertions are true of them that are false of any of those objects.
There's an implication that the existence of PP and PPTDH depends on
the existence of Peter, Paul, etc.; but that's not a logical
implication - substitute equivalent terms for PP and PPTDH ("The
movers" and "The assembly line workers") and it vanishes.

The above briefly summarizes the case for ontological 'realism'
regarding plural or collective entities. I don't think that the
semantic theory makes a case for this realism so much as reflect it:
when it comes to collectives, ontological realism is pretty much the
'house view' in both philosophical and common thought.

> (F) This plural entity is not an object, if with Frege we mean by
> 'object' the referent of a singular first-order term.

PP (or "the movers") is clearly not an object in the same way that
Peter and Paul are objects; it's neither one of them, but it's also not
another, third, object existing alongside them; and it's not reasonable
that anyone would think it was. If the homeowner wanted to provide
lunch for the movers, for instance, he'd provide lunch for Peter and
lunch for Paul, and not make a third lunch for "the movers" (or just
one for "the movers," while not feeding either Peter or Paul).

That's the type of paradox that (it looks to me) would come from
treating plural entities as separate objects.

> (G) Nevertheless, this plural entity does represent an ontological
> commitment. (End of argument).

Which says the same as B:

> (B) But plural locutions are committed to plural entities and
> Ontological Innocence is false. (This states the "house view")

I see what you mean by the argument being a bit dodgy. I believe I see
what the author means, though, so I'll try to fill it in:

Suppose that one rejects the idea that plural entities are
ontologically real - that there are any plural entities existing
anywhere or doing anything. In that case, what appear to be the acts
of plural entities are nothing more than the acts of the individual
objects that constitute them; and assertions about these plural
entities are just different ways to express assertions about those
individual objects.

That would be ontological 'nominalism' wrt plural entities. A
nominalist would interpret R1 not as a proposition about PP, but a
shorthand way of expressing propositions about Peter and Paul - not R2,
but something more like, (R3) <Peter carried his end of the
refrigerator, and Paul carried his end>. Similarly, he'd interpret C1
not as a proposition about PPTDH, or as C2, but as a shorthand way of
expressing conjunct propositions about the individual objects like (C3)
<Peter assembled the chassis for some cars, and Paul put wheels on
those chassis, and Tom welded frames to those chassis, etc.>

If plural entities are not ontologically real, then all sentences like
R1 and R2 assert propositions like R3 and C3. Propositions like R3 and
C3 can be translated into FOPL without using plural quantifiers.
Therefore, plural entities are not ontologically real only if all
statements involving plural entites can be translated into FOPL without
using plural quantifiers. Conversely, if some statements can be
translated into FOPL only by using plural quantifiers, then at least
some plural entities are ontologically real.

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