Brains, Persons, and Society *** ABSTRACTS    Cervelli, Persone e Società ***ABSTRACTS

Vittorio Morato

Dipartimento di Filosofia, Università di Padova

Possibilia and counting questions

The legitimacy of a realm of possibilia (i.e., non actual and possible objects)

is often justified by the claim that we need such kind of objects in

order to make sense of some counting questions; this is the way in which, for

example, Timothy Williamson in [1, p. 267] justifies his ontology of “bare

possibilia”:

Merely possible members of a kind are needed to make sense of

some counting questions. [. . .] Consider two jackets J1 and J2

and two pairs of trousers T1 and T2, which actually constitute

two suits. [. . .] Intuitively, the question ‘how many possible suits

could be made from J1, J2, T1 and T2?’ has a reading on which

the answer is four, even though it is impossible for more than two

suits to be made from the set.

more generally, questions of the form “how many _s could be made from

A1 . . .An?”, where A1 . . .An are paradigmatic components of a _ and where

being a _ is an essential kind, seem to commit us, in the relevant reading, to

merely possible members of a kind.

Aim of this paper is to show that while (i) bare possibilia seem to be not

reducible to any actualistically acceptable candidates such as sets, ways or

mereological sums, nonetheless, (ii) bare possibilia are not needed to “make

sense” of counting questions like those under consideration; there are indeed

cases in which we give definite answers to those questions just because what

we are counting are not merely possible members of a kind.

Entities like sets, ways or mereological sums succumb either to what I

call “the categorical problem” or to what I call “the identity-of-artefacts

problem”.

Consider, for example, sets. One could claim that what has been counted,

in the case of suits, are those subsets of the set {J1, J2, T1, T2} formed by

exactly two elements whose components are a jacket and a pair of trousers.

While in the specific case under consideration, resorting to sets gets accidentally

the facts of counting right (there are 4 merely possible suits as there

are 4 subsets of the set {J1, J2, T1, T2} formed by exactly two elements

whose components are a jacket and a pair of trousers), this strategy is not

generalizable to other kinds of artefacts. In the case of suits, it is assumed

that there is only one way to form a suit but consider an artefact F whose

only components are an A and a B and suppose that there are different

methods C1, C2, etc., to make an F by assembling an A and a B.

Consider a specific A and a B, a and b. If a and b are actually combined

in the way C1, the result of the combination is an artefact x which is an

F; but, had a and b been combined in the way C2, the result would have

been an artefact y which would have been an F but such that it would have

been numerically distinct from x. Different methods of combining an A with

a B into an F may generate numerically distinct possible Fs. From a set

like {a, b}, then, it is possible to make more than one possible F depending

on what method of assembling is used; the alleged reduction of possible and

merely possible Fs to sets whose elements are the components parts of an F

does not work. This is the identity-of-artefacts problem.

Entities like sets succumbs also to the categorical problem. If we define

“merely possible suit made by J1, J2, T1 and T2” as an x such that it is

possible that it is a suit made from J1, J2, T1 and T2, a set cannot be the

value of such an open formula: the x that is possibly a suit is an x that is

possibly concrete while a set is an entity that is necessarily abstract.

Consider now ways. The question “how many possible routes there could

be from A to B?” seems to be successfully paraphrased by “how many ways

there are of reaching B from A?”. An ontology of ways would solve the

“identity-of-artefacts problem”. A way of combining a and b into an F by

the procedure C1 is numerically distinct from a way of combining a and b into

an F by the procedure C1. There is a way for each of the allegedly possible

Fs that could be made from a and b.

Unfortunately, qua abstract entities, ways succumb to the categorical

problem; furthermore ways are probably not as ontologically respectable as

an actualist might wish.

A last resort could be mereological sums. These entities do not succumb

to the categorical problem because mereological sums are concrete entities

(and therefore possibly concrete entities). In the case of J1, J2, T1 and T2

there are four mereological sums composed only by a jacket and a pair of

trousers. Each of them could be then the right kind of entity to be the value

of the open formula above. Unfortunately even mereological sums succumb

to the identity-of-artefacts problem because there seems to be not as many

mereological sums of a and b as there could be numerically distinct possible

Fs made from a and b.

Should we then resign ourselves to an ontology of bare possibilia?

My view is that if considerations like those suggested by the identity

of artefacts problem were really relevant in counting questions, then such

questions would rarely receive a definite answer. The case of suit, over which

Williamson generalizes, seems to be quite a peculiar one.

Define a table as an artefact composed by a wooden surface and four

legs attached to it. Consider 8 table legs a1 . . . a8 and 2 wooden surfaces

B1 and B2. The question “how many possible tables could be made from

a1 . . . a8 and B1 and B2?” may receive a definite answer, even in the special

reading under consideration, by counting all the relevant mereological sums

of a1 . . . a8 and B1 and B2 formed by 4 legs and one wooden surface. There

is a sense, however, in which it is indeterminate how many possible tables

could be formed from a1 . . . a8 and B1 and B2. Even assuming the existence

of merely possible objects thus, their great variety seems to be irrelevant for

answering the question. There are, therefore, cases where questions of the

form “How many possible Fs could be made from A1 . . .An?” may receive

a definite answer just because what we are counting are not merely possible

Fs. Counting questions should not be presented, as Williamson does, as

the privileged source of the ontological commitment to possibilia because

such entities cannot generally play the role of making the answers to such

questions determinate.

References

[1] Timothy Williamson. Bare possibilia. Erkenntnis, 48:263–281, 1998.