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because for me this is a false contrast, since I say that for any property F to
exist is for laws to relate it to other such properties. However, I do take proper-
ties to be categorical in two more usual senses. First, I have just agreed with
Isaac Levi that, for any dispositional predicate F (whether F is a property or
not), a is F (at t) is a categorical statement, i.e. has a truth value, even if the
conditionals that give F its extension do not. All ascriptions of dispositions are
categorical in this semantic sense, just as all actual properties are categorical
in the ontological sense i.e. real whether they are dispositions or not.
In short, I think the war between Alexander s categorical and disposi-
tional monists is a phoney war, since all properties, including triangularity,
are both. I largely endorse Alexander s defence of the view that triangularity
is as dispositional as it is real; but I do have three comments to make about
what he says. First, even if it is trivially analytic that a figure s triangularity
is what makes counting its corners correctly give the answer 3 , its having
this property can still be what makes my counting its corners cause me to
get that answer. Second, since machines can count corners as well as people
can, triangularity is indeed independent of any power to produce effects in
human observers . Third, since I think that occurring in laws is what makes
triangularity a property, I agree in substance with Alexander s claim that its
conditional characterization [needs] appropriate generality to show it to be
genuinely dispositional , i.e. to be a real property.
However, the interesting question about a dispositional property F remains,
as Alexander says, whether it is essentially dispositional, i.e. whether nothing
could be F while lacking the conditional powers that the laws F occurs in
give it. This however is ambiguous, since properties occur in many laws, like
all those containing temperatures listed in Section 6, and each law that F
occurs in will give F-things a distinct conditional power. So something might
have been F while lacking some of these powers, if not while lacking most
or all of them. Thus, just as Alexander might have been a Labour Member
of Parliament but not perhaps a microbe, so our relativistic masses (which
232 D. H. Mellor
acceleration increases) might perhaps have been Newtonian (not increased
by acceleration) but not temperatures.
Alexander thinks, however, that some individual laws, and hence powers,
are essential to some properties, and he may be right. Indeed, a truthmaking
consideration tempts me to the even stronger claim in Stephen Mumford s
(1998: Ch. 10), that all properties necessitate all the laws they occur in. Take
the example, in Section 1 above, of truths about what is visible in a mirror.
To necessitate these we need not only the mirror, the objects it reflects and
the light by which it does so, but also the laws of reflection. Yet, as I say in
Section 7 of my (2000b),
the ontology of laws is notoriously problematic, with candidates ranging
from Humean regularities to relations between properties & It is tempting
therefore to bypass the problem & by taking the existence of factual
properties to entail the laws they occur in. For then we can dispense with
laws as truthmakers, even for law statements, which can all be made true
by the existence of the properties and relations they refer to.
However, while I feel this temptation, I have not yet succumbed to it. I
cannot yet believe, for example, that masses could not be as unaffected by
acceleration as Newton thought; and I do not despair of saying what in the
world contingent laws of nature are. But if in the end no credible account of
what laws are lets them be contingent, I may then have to follow Oscar Wilde s
advice that the only way to get rid of a temptation is to yield to it .
11 Arnold Koslow
The range of cases covered by Arnold Koslow s logic of natural possibilities
is a revelation. Its removal of the concept s common restriction to truths and
worlds is especially welcome to my reply to Tim Crane in Section 5, by making
knowing-how even more like knowing-that. For although Arnie does not give
the example, his theory shows how abilities are as much natural possibilities
for know-how as intelligible truths are for propositional knowledge.
As a logic of possibility and necessity, Arnie s theory has one obvious defect,
of which he is well aware, namely that on it necessarily x does not always
imply possibly x . Its always doing so when x is a single natural possibility (i.e.
a singleton of the power set N* of the set N of such possibilities) seems to me
not enough, since this does not cover every possibility we would naturally call
natural , such as getting an odd number (1, 3 or 5) on a throw of a die. If, how-
ever, this is (as Arnie conjectured in an email) an artefact of the construction
[he] gave for these possibilities , it should be remediable, and I hope it is.
But whether it is or not, one question that Arnie s list of kinds of possibili-
ties prompts is what distinguishes them from each other. What, in particular,
distinguishes the contingent and quantitative physical possibilities that I call
chances (Mellor 2000a), like a chance ch(H) of a coin toss landing heads? I
Real Metaphysics: replies 233
think the answer is that, being contingent, simple statements of chance like
ch(H) = 0.4 need truthmakers, which most of Arnie s other possibilities, being
necessarily possible, do not. I said in Section 1 that because P is contingent
and hence ~P is possible are necessary if true, they need no truthmakers.
Similarly for the sense in which truth and falsity are the possible truth values
of any P and ~P . Similarly again for the necessary possibility of possible
worlds, and of possible cases invoked in mathematical proofs.
Still, not all of Arnie s other possibilities are necessarily possible. Take the
possible states and transitions ascribed by theories to systems, such as the
possible orbits ascribed to planets by Newton s theory of gravity. If the theory
is contingent, so are these possible orbits. However, given whatever makes
the theory true, nothing more is needed to make just these orbits possible. It is
statements of the actual orbits of planets that need something more to make
them true. And so do statements of their chances of being actual, whether
these be 1, on a deterministic theory, or something less, on an indeterministic
theory: for no contingent P or value of p are propositions of the form ch(P)=p
complete truth-functions of P .
This is why propositions like ch(H) = 0.4 need to be made true by chances.
Or, rather, since ch(P) = 1 ch(~P) for all P, by chance distributions, in this
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