In "Two Concepts of Modality", Alvin Plantinga argues that propositions
aren't sets of worlds, because "you can't believe a set, and a set can't be
either true or false" [208]. I think this argument is better than it might
appear in the rather Ungerian context of Plantinga's paper, where he uses
several arguments of the same kind to support completely crazy views, like
that Lewis is an antirealist about possible worlds.
The traditional job description for propositions says that they are a) the
ultimate bearers of truth-values, b) the content/object of propositional
attitudes, and c) the meanings of declarative sentences. Plantinga is
right that sets aren't the most intuitive candidates for this job: Is the
empty set an 'ultimate bearer' of the truth-value false? Is it the content
of Frege's belief in Axiom 5? Is it what you have to know in order to
understand Axiom 5? Well, intuitively not, but I don't think intuition is
to judge questions like these. More importantly, there are reasons
against the identification of sets with propositions.
I'm currently writing a chapter on modal realism.
I don't like this topic because it always confuses me. Here is one such
confusion.
In some world w, pretty much resembling our world, there are two
individuals A and B. Let 'A-in-w' be an extremely rich descriptions of A
that implies every qualitative truth about w, similarly for 'B-in-w'
and B. Now the following two sentences might both be true:
1) If I were A-in-w, I would do X.
2) If I were B-in-w, I wouldn't do X.
I often visited blogs and other websites just to see that nothing has changed there. No more. To save these wasted minutes I've wasted some hours on writing a little script that keeps track of the latest updates of all those websites and displays them using diff.
It is easy to overlook that David Lewis has revised his worm view of ordinary things in 'Tensing the Copula', Mind 111 (2002). Here is the passage (p.5):
In talking about what is true at a certain time, we
can, and we very often do, restrict our domain of discourse so as to
ignore everything located elsewhere in time. Restricted the domain in
this way, your temporal part at t_1 is deemed to be the whole of
you. So there is a good sense in which you do, after all, have *bent simpliciter*.
In other words: Terms for ordinary things are indeterminate. They don't always pick out worms. Sometimes they pick out segments, and sometimes just stages, depending on the contextually determined domain of discourse.
I think this is an improvement over the worm theory. Is it general enough? Lewis says that our terms pick out the sum of all those temporal parts of the relevant worm that are inside the domain of discourse. But don't we also attribute bent-simpliciter to the whole of me in "I'm bent now, but I wasn't bent yesterday"? Yet here the domain contains yesterday's parts as well.
Brian Weatherson now says that 'the world exists' is exactly as natural as
'there is a G', where G applies to worlds that are exactly like this one.
I agree. But this only makes things worse, because the class G denotes
seems very natural: It contains our world and all its exact intrinsic
duplicates. Is this a gruesome gerrymander? We still need a
further restriction on best theories apart from naturalness.
Intuitively, some objects are more natural than others. For example, cats
are more natural than mereological fusions of cats and elephants. I think
that ultimately, naturalness of things should be definable in terms of
naturalness of the properties the things instantiate. I'm not quite sure
how exactly this is to be done, so for now I'll stick with the intuitive
notion of naturalness. Intuitively natural things are spatiotemporally
connected, constitute a causal unity, contrast with their surroundings,
etc. The world, that is, the mereological fusion of everything that exists
at any spacetime distance from us, does fairly well here: As far as I know,
it is perfectly connected, causally united (indeed, causally closed) and
contrasts clearly with everything outside of it (such as numbers or other
worlds, if such there be). Why then does Brian Weatherson think that the
world is gruesome?
I see two ways to exclude 'the world exists' as the best theory of
everything. The first is the one I already mentioned: to state that a good
theory must imply interesting truths a priori. The second is to
stipulate that a theory must not contain individual constants. I have some
sympathy with such a stipulation, though it may stipulate away haecceitism.
It is sometimes (e.g. in David Sanford, 'Fusion Confusion', Analysis 63,
2003) said that some things are not fusions of all their parts: cats
and fusions of cat-parts for instance seem to differ in tensed and modal
properties. It may be noteworthy that on the standard definition of
'fusion', this position is outright inconsistent: X is the fusion of
Y1,Y2,... iff all of Y1,Y2,... are parts of X and no part of X is
distinct from all of Y1,Y2,.... Hence if X is not the fusion of
Y1,Y2,... then either one of Y1,Y2,... is not a part of X or some part of
X does not overlap Y1,Y2,.... So nothing can possibly fail to be the
fusion of all its parts.
In her paper 'Logical
Parts', forthcoming in the december issue of Nous, L.A. Paul presents a nice
theory of objects according to which things are mereologically composed of
their properties. Here are a couple of potential problems.
First, the theory seems to conflict with Unrestricted Composition and
incompatible properties. For suppose that P and Q are incompatible
properties, like being square and being round. By Unrestricted
Composition, there is a fusion of P and Q (or, if you prefer, of P and Q
and Paul's red cup). This fusion has both P and Q as parts, hence, on
Paul's theory, it is both P and Q. But if P and Q are incompatible, nothing
can be both P and Q.
I have the vague impression that Lewis' paper 'Things qua truthmakers', and
in particular the appendix by Lewis and Rosen, proves something important.
But I'm not sure what it is. Maybe it's that the request for truthmakers
was thoroughly misguided in the first place.
The problem is that the truthmaker principle is saisfied so eaily: Let 'w'
be a name for our world that does not apply to any qualitatively different
world, nor to anything inside any world. (That is, 'w' denotes our world
under a rather strict counterpart relation.) Let T be any qualitative
truth. Necessarily, if w exists, then T, since otherwise 'w' would be
applicable to a world in which not-T, even though T holds at our world,
contrary to the rule just stated. Hence w is a truthmaker for T, that is,
for any truth whatsoever.
Let T be any theory. If you worry about T's overabundant ontology, there is
a simple way to translate it into a theory T_i with a very sparse ontology:
For every sentence S in T introduce a new primitive predicate P that
applies to a world w iff S is true at w. Then replace S by 'the world is
P'. A more elegant method would not introduce a new primitive predicate
for every sentence, but rather use structured predicates, that are
systematically built up in the way the sentence is built up. (See Quine,
'Variables explained away', and Prior, 'Egocentric Logic'). T_i is a
theory that says the same as T with an ontology of just one individual -
the world. The price to pay for this reduction in ontology is an
overabundant ideology: Who wants all these weird predicates? Nobody.