Predicates Rigidly Signifying the “Unnatural”
Philosophers, with few
exceptions, think they have a reasonably clear idea of what it is for indexicals and demonstratives, proper names and singular
definite descriptions to be rigid. Now in Naming and Necessity (‘N&N’
hereafter), Kripke (1980) nonetheless seems to intend
the notion to apply to expressions of different syntactic and semantic
categories, and in particular to apply, “suitably elaborated”, to predicates (N&N,
134). And, as I will illustrate, people quite often talk about predicates being
rigid and non-rigid (or flexible) in the context of discussion in philosophy of
mind, philosophy of science or metaehtics. I think
the “suitable elaboration” that underlies this common talk can be captured but
the following simple and straightforward proposal:
(*) A predicate is rigid if and only if
the property it contributes to the truth-conditions of the (simple) sentences
containing it with respect to counterfactual worlds is the same as the one it
makes to them with respect to the actual world; in short: a predicate is rigid
if and only if it signifies the same property with respect to all possible
worlds.
To
illustrate: it seems that ‘is (a drop of) water’ is intuitively rigid whereas
‘has the color Sònia likes best’ is intuitively non-rigid. Does (*) have these
desired results? It seems that it does. The property in virtue of which
sentences containing ‘is water’ are to be evaluated as true or false with
respect to any counterfactual world is, intuitively, the same as the property
in virtue of which they are to be so evaluated with respect to the actual
world. By contrast, consider a world in which this book remains the color it is
but Sònia’s taste for colors changes, due to whatever
you want to consider, so that it is no longer true that blue is the color Sònia
likes best, but rather yellow is. Now it seems that in order to evaluate the
sentence ‘this book has the color Sònia likes best’ with respect to that
counterfactual world, the relevant entity is no longer the property of being
blue but rather precisely the property of being yellow. So it seems that the
property signified by ‘has the color Sònia likes best’ with respect to that
world is a different one from that it signifies with respect to the actual world,
namely, the property of being yellow rather than the property of being blue.
Thus, it seems (*) has the intuitively right result of counting this predicate
as non-rigid.
Proposals along this line are indeed
considered and rejected in the recent literature that focuses on the topic of
the notion of rigidity for predicates. A defense of such a proposal would then
need to address at least the following three kinds of concern. First, something
like (*) assumes that the relation of signification between linguistic
expressions and entities can be coherently applied to predicates and
properties. There are several general doubts that can be raised against this
assumption, see inter alia Wright 1998.
Important as I think this issue is, I will take in this paper this assumption
for granted. Second, some have argued that, on a liberal understanding of what
properties are – like Lewisian abundant
functions from worlds to extensions – every predicate turns out to be
(trivially) rigid according to (*), see inter alia
Soames 2002. For take any (intuitively non-rigid) predicate P. The defender of
(*) thinks she can account for the intuitions regarding the non-rigidity of P
by being possibly the case that it signifies with respect to the different
worlds w’, w’’, ... the different properties Pw’,
Pw’’, ... But consider the
property P which is had by something in a world w if and only if
it has Pw in w. Now,
(vagueness aside) any (simple) predication of P would be true with respect to a
world iff the relevant object has the property P
in that world, so that the supposition that the predicate signifies this
property with respect to all worlds seems to yield the right
consequences with respect to the truth-values of the relevant (simple)
sentences containing the predicate with respect to both actual and
counterfactual worlds. But if that was the case, the proposal of (*) would make
the predicate a rigid one. This “generalization” problem could be then
stated thus: How could it be defended that the predicate P signifies with respect
to the different worlds w’, w’’, ... different properties Pw’, Pw’’, ... instead of signifying
with respect to all of them the very same property P? I have defended
elsewhere that this question can be answered. First, one could reject that
‘properties’ in (*) should be understood in such a liberal sense, so that the
claim that in general something like P is a property in the relevant
sense is blocked. But furthermore, even granting that liberal reading of
‘property,’ one can appeal to intuitive (contingent) truth of certain identity
statement involving, indirectly, the relevant predicate, via its
“canonical nominalization” (the expression that results from the predicate by
replacing the first verb it contains by its gerund form).
Even granting that the notion of
signification can be coherently applied to predicates and properties, and that
(*) does not have as a consequence that every predicate turns out (trivially)
to be rigid, there is third kind of concern that defenders of (*) should face –
and this is the focus of the present paper. This can be put in the following
terms: rigid predicates should turn out to be exactly those predicates
signifying natural properties, properties whose essences do not involve
facts about our responses in front of instantiations thereof. This is, I take
it, the content of the recent reply of Schwartz (2002) to Laporte
(2000), who defends something along the lines of (*).
Clearly there is an important difference between natural kind terms like ‘gold’ and nominal kind terms like ‘bachelor’ – and isn’t this difference based on the rigidity of the one and non-rigidity of the other? (Schwartz 2002, 266)
I want
to argue that there is such an important difference, but that it is not so
based on rigidity. That to claim the contrary, by itself, seems ungrounded may
be easily seen by considering the following line of thought. Take the case of
‘is red.’ It is a deep issue whether colors are natural properties in
the relevant sense or rather they are secondary, dispositional or response-dependent
properties. But almost all participants in this debate, on both sides, tend to
agree in that, whatever the nature of redness turns out to be, ‘is red’ rigidly
signify this property, contrary to what intuitively seems to happen with ‘has
the colors Sònia likes best.’ But if ‘is red’ could be rigid, even on the
assumption that it is a secondary property, why couldn’t ‘is a knife’ or ‘is a
philosopher’ rigidly signify the properties of being a knife and being a philosopher?
Rigidity for expressions is a question of sameness of signification across
possible worlds, i.e. sameness of the relevant entity in virtue of which
(simple) sentences containing it are to be rendered true or false when
evaluated with respect to those worlds. And on the face of it, that is something
assessable independently of (deep) issues concerning the nature of the entities
in question.
If I understand him right, Schwartz
provides the following consideration against (*). On the one hand he claims
that rigidity for singular terms play a certain role in a general argument for
the necessary if true character of identity statements involving two rigid
singular terms. I will show that the rigidity of the predicates, in the sense
of (*) plays an analogous role vis-à-vis the necessary if true character
of identity statements involving the nominalization of those predicates. But on
the other hand he seems to submit that when the predicates signify “unnatural”
properties, none of such (necessary if true) identifications would be a posteriori.
I will argue that, with possibly some independently motivated proviso dealing
with constitution vs. identity, this is in general not the case, as the case of
redness on the assumption that it is a secondary property illustrates. And I
will finally argue that even in the cases in which this is the case (as I think
they could be) that does not provide any reason for challenging the rigidity of
the predicates at stake.
References:
Kripke, Saul, 1980: Naming and
Necessity, Oxford, Basil Blackwell
LaPorte, Joseph, 2000: ‘Rigidity and Kind’,
Philosophical Studies, 97/3, 293-316
Soames, Scott 2002: Beyond
Rigidity: The Unfinished Semantic Agenda of Naming and Necessity, Oxford
University Press
Schwartz, Stephen P. 2002: ‘Kinds,
General Terms, and Rigidity: A Reply to Laporte’, Philosophical
Studies 109, 265-77
Wright, Crispin 1998: ‘Why Frege Does Not
Deserve His Grain of Salt: a Note on the Paradox of "The Concept
Horse" and the Ascription of Bedeutungen
to Predicates’, Grazer Philosophische Studien 55, New Essays on the Philosophy of Michael
Dummett , eds J.Brandl and P.Sullivan (Vienna: Rodopi), 239-63