de re and de dicto
I said a couple of things hastily in my earlier message on modal logic
regarding the de re/de dicto distinction that it might be useful to
tighten up, especially in light of a couple of recent posts.
I said earlier that a de re context is one "in which a free variable
occurs in the scope of a modal operator." That is not well put. Here
is a more precise statement. A _context_ of a given formula A is just a
subformula of A. Thus, a _modal context_ in a formula A is just a
subformula of A of the form (Nec B) or (Poss B). Given this, we say
that a formula A contains a _de re_ context just in case it contains a
modal context -- i.e., a subformula of the form (Nec B) or (Poss B) --
in which a variable occurs free. To illustrate, the sentence
"necessarily, rocks do not speak", i.e.,
(1) (Nec (forall (?x))
(=> (rock ?x)
(not (speaks ?x))))
contains no de re contexts; all of the variables occurring in the
modal context (which, in this case, is the entire formula) are bound.
(It is, we might say, _purely de dicto_.) By contrast, "all (existing)
rocks necessarily do not speak" is de re:
(2) (forall (?x)
(=> (rock ?x)
(Nec (not (speaks ?x)))))
Here, "?x" occurs free in the context (Nec (not (speaks ?x))) and so the
context is de re.
Conceptually, in terms of possible worlds, the difference is that, in a
sentence that is purely de dicto, one is talking only about the
properties that the objects in a given possible world have *in that
world*. Thus, in (1), the idea is that if we look at the rocks in any
given world, we will find that they do not speak in that world. By
contrast, in a sentence with a de re context, one first "picks out" an
object in some given world and then considers the properties which *that
very object* possesses in some *other* possible world. Thus, (2) above
tells us that, if we consider some existing rock, i.e., some rock in the
actual world, then, if we consider any other possible world w, we will
find that *that very object* does not speak in w. You can see that this
proposition, unlike (1), involves us in essentialism -- (2) commits us
to the thesis that anything with happens in fact to be rock is
*essentially* speechless; it couldn't possibly have been something that
speaks. For if a rock could have been, say, a human being, then (2)
above is false, whereas (1) can safely be assumed to remain true -- we
can still assume that, necessarily, anything that *happens* to be a
rock is unable to speak (even if it *could* have been something that
*can* speak).
-chris
--
Christopher Menzel # web: philebus.tamu.edu/~cmenzel
Philosophy, Texas A&M University # net: chris.menzel@tamu.edu
College Station, TX 77843-4237 # vox: (979) 845-8764