The modal theory holds that facts (properties) are identical iff they are necessarily equivalent (coextensive). One of the most prominent arguments against the modal theory is Elliot Sober’s dual-detector argument. According to this argument, the fact that some particular thing is a triangle is distinct from the necessarily equivalent fact that it is a trilateral, since it is only the former fact that causes an output of a certain machine. I argue that the dual-detector argument fails, in part because whatever initial plausibility it has relies on the failure to take into consideration a needed relativisation to times and the failure to distinguish between two facts collectively causing a fact and their conjunction singly causing it. I also argue that variants of the argument are equally unsuccessful.
One of the most popular and well known accounts of the
identity-conditions of facts and properties is the modal theory.1 According to this theory: i) two
facts are identical iff they are necessarily equivalent to each other;
and ii) two properties are identical iff they are necessarily
coextensive to each other. That is, the modal theory holds that: i) the
fact that
A prominent argument against the modal theory is the dual-detector argument originally due to Elliot Sober.3 Briefly, according to this argument, there could be a machine that, as a result of containing detectors measuring different aspects of an input, is causally sensitive to one fact without being causally sensitive to another necessarily equivalent fact. Since, by Leibniz’s law, it follows from this that, contra the modal theory, there are distinct facts that are necessarily equivalent to each other, the argument concludes that the modal theory is false. Despite this argument’s prominence, discussions of the argument by both its proponents and opponents have been brief and cursory. This paper will provide a more sustained evaluation of the dual-detector argument and will argue that such an evaluation shows that the argument is unsuccessful.4
I will proceed as follows. In section 1, I will formulate the dual-detector argument before then arguing in section 2 that it is unsuccessful. In section 3, I will then consider two variants of the argument and I will argue that these variants, and more generally that all variants, are also unsuccessful.
Before proceeding to section 1, it will be
useful to briefly discuss another common argument against the modal
theory—the constituency argument—in order to set it aside (see, for example, Audi 2016).
Suppose (1) and (2) are
true, where ‘
(1)
(2)
According to the constituency argument, since the fact expressed by (1) has angularity as a constituent while the fact expressed by (2) doesn’t have this property as a constituent, the facts expressed by (1) and (2) are not identical to each other. Since the modal theory entails that the facts expressed by (1) and (2) are identical to each other (since they are necessarily equivalent to each other), the constituency argument concludes from this that the modal theory is false.
The constituency argument arguably begs the question against the
modal theory by in effect assuming the rival structured theory of facts.
According to this rival theory, facts are structured in the same kind of
way that sentences are structured. In particular, according to the
structured theory, facts are built up out of objects, properties,
relations, operators and quantifiers in the same way that sentences are
built up out of names, predicates, operator expressions and quantifier
expressions.5 If the structured theory holds so
that the facts expressed by (1) and (2) are built up out of objects, properties,
relations, operators and quantifiers in the same kind of way that
sentences are built up out of names, predicates and other expressions,
then it is plausible that the fact expressed by (1) has angularity as a constituent while the fact
expressed by (2) doesn’t have this constituent.
This is much less plausible, however, if the structured theory is false
and facts aren’t structured like sentences. For example, if facts are
instead structured like visual experiences or pictures, then, since it
is prima facie plausible to associate (1) and (2) with the same (type) of visual experience or
picture, it is prima facie plausible that (1) and
(2) express the same fact and hence prima facie
plausible that the facts expressed by (1) and (2) don’t differ in what constituents they have. (This
is because it is at least prima facie plausible that any picture that
represents
It is important to appreciate that the structured theory is neither self-evident nor prima facie highly plausible, and hence it cannot simply be assumed to hold in the above argument from constituency without begging the question against the modal theory. Three brief reasons for this are the following: First, prior to investigation and argument, the claim that facts are structured like sentences is no more plausible than the claim that facts have some other type of structure, such as that of visual experiences or pictures. Second, while (1) and (2) arguably differ in their cognitive significance, since a linguistically competent person arguably might endorse one of them while rejecting the other, such a difference in cognitive significance is widely thought to be able to be explained by a difference in what mode of presentation the facts expressed by (1) and (2) have when expressed by these sentences, where this explanation does not require that the facts expressed by these sentences are non-identical (see, for example, Braun 1998; McKay and Nelson 2010). Third, the structured theory conflicts with claims that are widely thought to be at least as prima facie plausible as the structured theory itself, such as the claim made by (3).
(3) ‘
(3) conflicts with the structured theory,
since, if the structured theory is true, the fact expressed by ‘
1 The Dual-Detector Argument
The dual-detector argument is not meant to rely on the cogency of the
constituency argument discussed above, nor is it meant to rely on the
truth of the structured theory of facts. Instead, the dual-detector
argument is meant to provide a separate reason for rejecting the modal
theory. The argument involves a machine
The closed straight-sided figure detector in
Sober states the dual-detector argument as follows:
Now consider a particular object—a piece of wire—which is fed into the machine, passes through both [detectors], and is then outputted by the machine. What property of the object caused it to be outputted? Given the mechanism at work here, I think that the cause was the object’s having the property of being a closed straight-sided figure having three angles (i.e., its being a triangle), and not its being a closed straight-sided figure having three sides (i.e., its being a trilateral). If this is right, and if a difference in causal efficacy is enough to insure a difference in property, it follows that being a triangle is not the same property as being a trilateral, even though “triangle” and “trilateral” are logically (mathematically) equivalent. (Sober 1982, 185, author’s emphasis)
Let ‘[
Angle. [
Side.
[
The dual-detector argument then employs Leibniz’s law to infer from
this that, since they differ in what they cause, [
(4) For any
Since these facts and properties are respectively necessarily equivalent to each other and necessarily coextensive with each other (and hence are identical to each other according to the modal theory), the dual-detector argument then concludes from the above results that the modal theory is false.7
2 Against the Dual-Detector Argument
One initial problem with the dual-detector argument is that (Angle)
is not strictly speaking true, at least if we assume as we did above
that the above described process involving
Angle. [
To see why this is the case, let us suppose that, after being fed
into
The above problem with the dual-detector argument shows that, as it
is most charitably understood, it is not (Angle) that is true
according to the argument, but is instead either (Angle
Angle
Angle
As a result of this need to relativise to either time
Side
The second version of the dual-detector argument—the
Side
As we will see, both these versions of the dual-detector argument have serious problems.9
The
Angle
Since the falsity of (Angle
I will now argue that the
To set up the needed background for the argument from causal
exclusion against (Angle
(5) [
Since [
(6) [
Since plausibly one of the causes of
(7) [
Assuming, as is plausible, that the causal transitivity principle (T)
holds in this causal situation, (5–7) then entail (Angle
T.
IF the members of
Angle
With the above background in place, it might seem like it should now
be easy to derive (Angle
Angle
However using the above background, we can now give the following
argument from causal exclusion that (Angle
(8) [at
Similarly, while [
(9) [at
Since [at
Angle
A more rigorous version of the above argument against (Angle
PCE.
In cases where there is no genuine causal overdetermination, if
In (PCE), a fact is said to occur at a certain time iff the fact only concerns how things are at that time. Genuine causal overdeterminism, on the other hand, occurs when two independent causal processes converge on the same effect, such as when a house burns down because a lit match starts a fire in the garbage at the same time as lightning strikes the house.
Since there is no genuine causal overdetermination in the case of
(10) [
If (10) is true, then [
The above argument shows that (Angle
Dep.
Suppose that
Other philosophers reject (PCE) because they hold that, in cases where there is no genuine causal overdetermination of a fact, there can still be multiple complete causal chains that converge on that fact, provided these chains are systematically related to each other in the right way. In particular, some philosophers hold that there can be multiple such causal chains provided that, for each such chain, either that chain generates all the other chains, or that chain is generated by at least one other such chain. Someone who endorses this view, for example, might endorse (Conj).13
Conj.
If
It follows from (Conj) that, contra (PCE), if there is one
causal chain leading to
In light of the above views, the argument from causal exclusion does
not by itself decisively refute the
The first attempt to justify the truth of (Angle
Angle
Let us assume that the above justification of (Angle
Side
One argument that tries to justify the falsehood of (Side
The problem with this argument for the falsity of (Side
An alternative way of trying to justify the falsehood of (Side
Conj
We can give the same kind of argument from parsimony and contingency
for the falsity of (Side
Side
Indeed, plausibly both opponents and proponents of the modal theory
should reject (Side
One problem with (Conj
A second (more serious) problem with (Conj
(11)
(12)
Such a proponent might then argue that (on its relevant causal use)
(11) is equivalent to (11
(11
(12
Assuming that these equivalences all hold, it follows that (11
A problem with this attempted justification for (Conj
(13) Jane wants to go swimming and go hiking.
(13) has a non-conjunctive reading on
which the proposition Jane is described as desiring is the proposition
that Jane goes swimming and hiking. On this reading, (13) is true iff (13
(13
(13) also has a conjunctive reading on
which (13) is true iff (13
(13
(11) is plausibly similarly ambiguous
between a non-conjunctive reading on which it is equivalent to (11
(11
(11
On its conjunctive reading, while (11) is
equivalent to ((12) (on its causal use), there
is no reason to think that (on its causal use) (11) is equivalent to (11
I will discuss one further attempt to justify both the truth of (Angle
Dep.
Suppose that
Assuming that (Dep) holds, we can derive (Angle
Angle
Assuming that (Dep) holds, then, a proponent of the
dual-detector argument can use (Dep) to justify (Angle
I have now discussed two attempts to justify the truth of (Angle
3 Variants of the Dual-Detector Argument
In the face of the failure of the original version of Sober’s
dual-detector argument, it might be thought that the argument can be
modified so that it evades the problems discussed in section 2. In particular, it might be thought that these
problems can be evaded by replacing the necessarily equivalent facts
expressed by (1
(1
(2
As far as I can see, however, this cannot be done.
To illustrate the difficulty involved in successfully modifying the
dual-detector argument in the above manner, I will briefly consider two
attempts to do this that replace the facts expressed by (1
(14)
(15)
For the first attempt, consider a machine
Curv.
[
Dist.
[
A problem with this first attempt at finding a successful variant of
the dual-detector argument is that it is no more obvious that (Curv)
holds than it is that (Angle
Angle
Instead, using transitivity reasoning, what can be uncontroversially
established in the variant case of machine
Curv
Angle
Moreover, an opponent of the modal theory who wishes to show that (Curv)
and (Dist) differ in their truth-value faces the
same challenges that a proponent of Sober’s original version of the
dual-detector argument faces in showing that (Angle
For a second attempt to show that there could be a machine that is
causally sensitive to one of the facts expressed by (14) and (15) but not
the other, consider a machine
The problem with this second variant of Sober’s version of the
dual-detector argument is that, if
Other variations of Sober’s original version of the dual-detector
argument face similar problems to those described above. Indeed, the
above two attempts to construct a successful variant of Sober’s original
version of the argument arguably illustrate a dilemma facing any such
attempt. This dilemma is the following: Suppose we have a machine whose
output is intended to be caused by the fact
Dan Marshall
https://orcid.org/0000-0002-5763-3875
Lingnan University
danmarshall@ln.edu.hk
Acknowledgements
Research in this paper was supported by an Early Career Scheme grant from the Research Grants Council of Hong Kong SAR,China (LU23607616). Thanks to Andrew Brenner, Daniel Waxman and three anonymous referees for their valuable comments on this paper.
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