Philosophical Studies

, Volume 153, Issue 3, pp 397–415

Second-order properties and three varieties of functionalism

Authors

Article

DOI: 10.1007/s11098-010-9518-z

Cite this article as:
Hiddleston, E. Philos Stud (2011) 153: 397. doi:10.1007/s11098-010-9518-z

Abstract

This paper investigates whether there is an acceptable version of Functionalism that avoids commitment to second-order properties. I argue that the answer is “no”. I consider two reductionist versions of Functionalism, and argue that both are compatible with multiple realization as such. There is a more specific type of multiple realization that poses difficulties for these views, however. The only apparent Functionalist solution is to accept second-order properties.

Keywords

ReductionFunctionalismMental propertySecond-order propertyFunctional propertyMetaphysics

This paper investigates whether there is an acceptable version of Functionalism that avoids commitment to second-order properties. I argue that the answer is “no”. I consider three varieties of Functionalism: the Functional State Identity Theory (aka “Role Functionalism”), Realizer Functionalism, and a new view I dub “Truthmaker Functionalism”. The Functional State Identity Theory holds that functional predicates express second-order, functional properties. Realizer and Truthmaker Functionalism attempt to capture what is plausible about Functionalism while embracing the reductionist view that second-order properties do not exist (or are highly “unnatural”). Multiple realization is the standard objection to reductionist versions of Functionalism, but I argue that it is compatible with all varieties. I argue that there is a more specific type of multiple realization that is problematic for the reductionist varieties, however. It appears that only the Functional State Identity Theory is able to accomodate this type.

1 Functional states versus functional descriptions

Functionalism about X is in general the view that X is “defined by what it does”. Functionalist views of the mental became prominent in the 1960s, and are widely accepted at least for intentional mental states (belief, desire). The view is plausible for many properties of the special sciences. Some even hold that all genuinely causal or explanatory properties are functional (Shoemaker 1984, 1998).

One of the main distinctions among functionalist views is whether the view is taken to apply to properties or merely to predicates. A functional property is, at a minimum, one that has some “causal powers” essentially. The idea is that an object or event is not an acid, a predator, a gene, or a belief, unless it has the potential to enter into certain causal/nomic relations. A functional predicate is one whose conditions for correctly applying to an object make reference to such causal/nomic relations.

One prominent strand among functionalist thought holds that functional predicates express nonfunctional properties, but do so by means of functional descriptions. This was the original idea of the Mind-Brain Identity Theory, especially in the versions of David Armstrong and David Lewis. Armstrong expresses the view as follows:

The concept of a mental state is primarily the concept of a state of the person apt for bringing about a certain sort of behaviour. (Armstrong 1968/1993, p. 82)

It may now be asserted that, once it be granted that the concept of a mental state is the concept of a state of a person apt for the production of certain sorts of behaviour, the identification of these states with physico-chemical states of the brain is, in the present state of knowledge, nearly as good a bet as the identification of genes with the DNA molecule. (Armstrong 1968/1993, p. 90)

Lewis sums up the view in an argument (1972, pp. 248–249):

Mental state M = the occupant of causal role R (by definition of M)

Neural state N = the occupant of causal role R (by the physiological theory)

∴ Mental state M = neural state N (by the transitivity of =)

The idea of this version of functionalism is that the predicate supplies some “causal role”, and the predicate expresses the nonfunctional property that “occupies” that role. This view is usually called “Realizer” (or “Occupant” or “Filler”) Functionalism. The usual alternative to this view takes functional predicates to express functional properties. This view is often called “Role Functionalism”, though I prefer to call it the “Functional State Identity Theory” (for reasons that will emerge).

Armstrong explains ‘causal roles’ in terms of what a state is ‘apt to cause’. Lewis uses similar terms:

The definitive causal role of an experience is given by a finite set of conditions that specify its typical causes and its typical effects under various circumstances. (1966, p. 102)

Kim uses similar terms as well (e.g., 2005, p. 24).

There is a standard objection to Realizer Functionalism and a standard response. The objection is that functional predicates correctly apply to creatures which share only a second-order, functional property (if they share anything at all). ‘Pain’ correctly applies to humans and to octopusses, Putnam suggested, and yet these creatures need share no pain-specific physiological equipment. So, ‘pain’ does not express any brain property, but only a second-order, functional one.

The standard response to this objection is to restrict the domain of objects in question. Lewis says:

We may say that some state occupies a causal role for a population… If the concept of pain is the concept of a state that occupies that role, then we may say that a state is pain for a population. Then we may say that a certain pattern of firing of neurons is pain for the population of actual Earthlings…, whereas the inflation of certain cavities in the feet is pain for the population of actual Martians… Human pain is the state that occupies the causal role for humans. Martian pain is the state that occupies that same role for Martians. (1980, p. 126)

Lewis’s idea is that on a given occasion of use, context selects a relevant population p, and ‘pain’ as used on that occasion expresses the property that occupies the pain role in p. He says that ‘pain’ is a “nonrigid designator”. On different occasions, it expresses different properties. The commonality among these uses is similar to that of an indexical: on each occasion ‘pain’ expresses the property that plays the role in the selected population. Kim also has advocated “local reductions” and species- or structure-specific identifications (1992, pp. 327–329; 1998a, pp. 110–111).1

2 A problem for realizer functionalism and a solution

Though Lewis’s response to the problem of multiple realization is widely known, it appears to have serious problems as formulated. Here I raise a problem, and reformulate the view to avoid it. The next section raises a problem for the reformulated view.

Lewis describes the “occupants” of a causal role as follows:

A state occupies a causal role for a population, and the concept of occupant of that role applies to it, if and only if, with few exceptions, whenever a member of the population is in that state, his being in that state has the sort of causes and effects given by that role. (1980, p. 126)

I will not worry about Lewis’s “few exceptions”. I also will not worry about properties (or predicates) that are defined in part by what causes them (by their “backward-looking causal powers”, as Shoemaker says).

Lewis’s characterization of occupation is puzzling in the context of the rest of his view. The claim appears to be: X occupies the role iff X has the effects specified by the role, “whenever a member of the population is in” X. Whenever a member y of population p is in a state that gives rise to some effect E, there will be a microstructural property that y has which gives rise to E. So, there would appear to be as many occupiers of this role as there are distinct microstructures in the population that give rise to E. Consider some microstructural belief-that-p realizer S. Let S’ be similar to S except that the position of an electron is altered by 1 nm. Presumably S’ will realize belief-that-p too, and give rise to whatever psychological effects S does. If positions of particles can vary continuously, then there would seem to be continuum-many nomologically possible occupiers of just about any role that has any occupiers at all. A phrase such as ‘the property that causes X in p’ will be improper, and Realizer Functionalism will have to treat the terms in question as empty.

There is an alternative way of understanding the phrase ‘the property X that typically causes E in p’. Lewis seemed to treat ‘typically’ as modifying ‘X’: it is typical among Xs in p that they give rise to E. But we could read ‘typically’ as modifying ‘E in p’ instead. On this reading, a typical cause of E in p is an X such that it is typical among Es in p that they are caused by X. It may be that there is some brain state which is common to the members of p and causes E in them whenever anything does. This would be a ‘typical cause of E in p’ on the current reading.

I will make a proposal on Lewis’s behalf that embodies this alternative understanding. Consider a functional definition of acids as proton donors. Acids are samples or substances which contribute hydronium ions (H3O+ ions) to aqueous solutions (in excess of the proportion found in pure water). Any account of acidity (or ‘acidity’) will have to make use of a conditional of the general sort: if x is dissolved in water, then x contributes hydronium ions to the resulting solution. Represent this as ‘Dx → Hx’; if x is Dissolved, then x contributes Hydronium ions. The arrow ‘→’ is a modalized conditional connective. It is stronger than the material conditional, though I hope to remain neutral on its exact interpretation.

On Lewis’s view (1970, 1972), a functional predicate ‘F’ has an associated “postulate”, “Ramsey”, and “definition” sentence. I will consider a few possibilities for Ramsey-Lewis definitions of ‘acidity’. Here is a first, using ‘A’ for acidity:

Proposal #12:
$$ (1)\ \forall {\text{x }}\left( {{\text{Ax }} \leftrightarrow \left( {{\text{Dx }} \to {\text{ Hx}}} \right)} \right)\quad \left( {\text{postulate}} \right) $$
$$(2)\ \exists {\text{P }}\forall {\text{x }}\left( {{\text{Px}} \leftrightarrow \left( {{\text{Dx}} \to {\text{Hx}}} \right)} \right)\quad \left( {\text{Ramsey sentence}} \right) $$
$$ (3)\ {\text{A}} = \iota {\text{P}}:\forall {\text{x }}\left( {{\text{Px }} \leftrightarrow \left( {{\text{Dx }} \to {\text{ Hx}}} \right)} \right)\quad \left( {\text{definition sentence}} \right) $$
The Ramsey and definition sentences involve quantification over properties, but the quantification is supposed to be logically first-order: the domain includes properties as well as individuals.3 So, the predicates that we quantify out in these sentences should be read as names, and ‘Ax’ should be read as ‘x has acidity’. The postulate says that something has acidity just in case it would contribute hydronium ions when dissolved in water; the Ramsey sentence says that there is some such property; the definition sentence says that acidity = the unique such property.

Here is a second possibility:

Proposal #2:
$$ (4)\ \forall {\text{x }}\left( {\left( {{\text{Ax }}\& {\text{ Dx}}} \right) \to {\text{Hx}}} \right)\quad \left( {\text{postulate}} \right) $$
$$ (5)\ \exists {\text{P }}\forall {\text{x }}\left( {\left( {{\text{Px }}\& {\text{ Dx}}} \right) \to {\text{Hx}}} \right)\quad \left( {\text{Ramsey sentence}} \right) $$
$$ (6)\ {\text{A }} = \, \iota {\text{P}}: \, \forall {\text{x }}\left( {\left( {{\text{Px }}\& {\text{ Dx}}} \right) \to {\text{Hx}}} \right)\quad \left( {\text{definition sentence}} \right) $$
Proposal #2’s postulate says that any object with acidity will contribute hydronium ions when dissolved; its Ramsey sentence says there is some such property; the definition sentence says that acidity is the unique property which does this.

Lewis’s own suggestion appeared to be similar to Proposal #2. The embedded condition is satisfied by far too many properties, however. Being an HCl sample, being an HCN one, and every microstructural property that gives rise to those, are all sufficient for H, given D. The definition sentence (6) is an identity with a nondenoting term on its right hand side.

Proposal #1 is a much more natural view. It is not satisfied by any realizers of acidity, however. Being an HCl sample does not satisfy it, for example: HCN samples will also lead to H in D, and so being HCl fails to satisfy ‘↔’ in the ‘←’ direction. Proposal #1’s definition sentence is satisfied by the second-order, functional property of acidity. It is uniquely satisfied, too (if such a property exists in the first place, and perhaps barring some further details about how to understand ‘D’ and ‘H’). So, Proposal #1 appears to be an adequate Ramsey–Lewis definition. It is satisfied only by a second-order, functional property, however. This proposal embodies the Functional State Identity Theory.4

Neither proposal satisfies the aims of Realizer Functionalism. In effect, Proposals #1 and #2 yield two concepts of a ‘causal role’ for a property or predicate. In the Proposal #1 sense, a ‘causal role’ for predicate ‘F’ is uniquely occupied by a second-order property; in the Proposal #2 sense, a ‘causal role’ for ‘F’ is occupied by the second-order property together with all of its realizers. Either way, a phrase such as ‘the realizer property that occupies causal role R’ is prima facie defective. In the Proposal #1 sense, the phrase is empty: no realizer plays that role. In the Proposal #2 sense, the phrase is improper: vastly many realizers play that role.5

Despite these difficulties, there may be a workable version of Realizer Functionalism to be had. Proposal #2 seems useless for purposes of constructing a definition, however, so we should try to restrict the domain of a Proposal #1 definition sentence instead. Suppose we have some acidic sample a available for individual reference. Suppose also we have a restricting relation x is chemically indistinguishable from y.6 Represent this relation: CI(x, y). Then we could potentially pick out a unique acidity-realizer by a definition sentence along the following lines:

Proposal #3:
$$ (7)\ {\text{Acidity}}_{a} = {\text{the most specific P\;such that}}: \, \left( {\text{i}} \right){\text{ P}}a,{\text{ and }}\left( {\text{ii}} \right) \, \forall {\text{x }}\left( {{\text{CI}}\left( {{\text{x}}, \, a} \right) \to \left( {{\text{Px }} \leftrightarrow \, \left( {{\text{Dx }} \to {\text{ Hx}}} \right)} \right)} \right) $$
Suppose a is a chemically pure sample of HCl. In that case, the potential satisfiers include: (a) acidity, (b) being composed of molecules which include a single halogen atom ionically bonded to a hydrogen atom (HF, HCl, HBr, etc.), (c) being composed of HCl, (d) being composed of HCl atoms in this exact momentary arrangement (the one that a has right now). Taking a domain of samples chemically indistinguishable from a rules out option (d): some members of the domain will lack the exact momentary arrangement of a. The qualification ‘most specific’ rules out options (a) and (b). So, this strategy could plausibly leave us with a unique, first-order satisfier of ‘aciditya’, namely being composed of HCl. The idea for Realizer Functionalism would be that ‘acid’, when applied to an individual sample, designates the chemical kind of that sample.

Proposal #3 embodies my alternative reading of a ‘typical cause of E in p’. Among the objects in the relevant domain, it is typical (or universal) that aciditya (=being composed of HCl molecules) is the cause of increased levels of hydronium ions when the object is dissolved in water.

Matters may not have worked out quite as intended for Realizer Functionalism, but the domain restriction response to the multiple realization problem appears prima facie workable.

3 Interdefinitions and many-many relations

In this section, I raise a further difficulty for Realizer Functionalism concerning a more specific type of multiple realization. I argue that the domain restriction response does not avoid this worry.

To get at the problem, consider how Kim sees the situation with interdefinitions. Kim (1998b, p. 105) suggests a toy Ramsey sentence for the psychological predicates ‘is in pain’, ‘is normally alert’ and ‘is in distress’. He calls this sentence ‘T’, and its Ramsey sentence ‘TR’. He says:

Suppose that the original psychology, T, is true of both humans and Martians… Then TR, too, would be true for both humans and Martians: It is only that the triple of physical states 〈H1, H2, H3〉 which realizes the three mental states 〈pain, normal alertness, distress〉 and which therefore satisfies TR, is different from the triple 〈I1, I2, I3〉, which realizes the mental triple in Martians. (Kim 1998b, p. 111)

Kim assumes that the causal role in question will be played by one triple of realizers in the case of humans, and a second, distinct triple in the case of Martians. This is one way in which triples of realizers could line up, but it is certainly not the only one. Maybe, even among humans, there are multiple properties that fit each of the three slots, and any combination of them works equally well. That is, maybe among humans there are pain realizers P1,…, P10 and alertness realizers A1,…, A10 such that any Pi and Aj will give rise to the relevant effects. The relations among the realizers could well be many-many.

It seems to me that the case of many-many relations among realizers is problematic for Realizer Functionalism. I will give a couple of more realistic examples, and use them to raise a problem.

First, the acidity-theory I mentioned earlier is only one definition of acidity (the Arhennius one). An alternative account (the Brønsted-Lowry one) does not define acids individually, but defines conjugate acidbase pairs. On this account, acids and bases are pairs where the first donates protons and the second accepts them. This account treats the usual acids as components of conjugate acid–base pairs which have H2O as the base: 〈HCl, H2O〉, 〈HCN, H2O〉, 〈H2SO4, H2O〉, etc. But there are also conjugates in which H2O is the acid, such as 〈H2O, NH3〉. And there are pairs that do not involve H2O at all.

In the case of interdefinitions, Lewis and Kim understand the relevant Ramsey and definition sentences as quantifying over n-tuples of realizer properties. I think we should see matters a bit more generally. In the case of interdefinitions, we should see the Ramsey-Lewis account as introducing a relation term. These relations are similar to sets of pairs. It may be, but need not be, that each pair of objects 〈x, y〉 in the relation are such that Px and Qy, for realizer properties P and Q. Let ‘Con(x, y)’ express that x and y stand in the conjugate acid–base relation. Let ‘Cxy’ express that x and y are chemically combined, and let ‘Dxy’ express that x donates and y accepts protons. The analogous Proposal #1 postulate, Ramsey, and definition sentences are these:
$$ (8)\ \forall {\text{x }}\forall {\text{y }}\left( {Con\left( {{\text{x}},{\text{ y}}} \right) \leftrightarrow \left( {{\text{Cxy}} \to {\text{Dxy}}} \right)} \right) $$
$$ (9)\ \exists {\text{R }}\forall {\text{x }}\forall {\text{y }}\left( {{\text{Rxy}} \leftrightarrow \left( {{\text{Cxy}} \to {\text{Dxy}}} \right)} \right) $$
$$ (10)\ Con \, = \, \iota {\text{R}}: \, \forall {\text{x }}\forall {\text{y }}\left( {{\text{Rxy}} \leftrightarrow \left( {{\text{Cxy }} \to {\text{ Dxy}}} \right)} \right) $$
The object-level quantifiers in this definition are satisfied by samples rather than substances. The relation Con holds among objects; it is similar to a set of pairs of objects. We can extend the definition to apply to substances in either of the following ways:
$$ (11)\ Con^{*}\left( {{\text{P}},{\text{Q}}} \right) \leftrightarrow \forall {\text{x }}\forall {\text{y }}\left( {\left( {{\text{Px }}\& {\text{ Qy}}} \right) \to Con\left( {{\text{x}},{\text{ y}}} \right)} \right) $$
$$ (11^{\prime})\ Con^{*} = \iota {\text{R}}: < {\text{P}},{\text{ Q}} > \in {\text{ R}} \leftrightarrow \forall {\text{x }}\forall {\text{y }}\left( {\left( {{\text{Px }}\& {\text{ Qy}}} \right) \to Con\left( {{\text{x}},{\text{ y}}} \right)} \right) $$
According to (11) and (11′), substances P and Q get to be conjugate acid–base pairs when all of their samples are. (11) and (11′) pick out a relation, which we could see as a set of pairs of properties: the 〈P, Q〉 pairs such that Ps donate protons to Qs when combined. This general type of definition could end up picking out a set of pairs of properties with a single member, a single n-tuple of properties, but it certainly need not do that. In this case, the set appears to have many members. No pair satisfies the definition of the set: for each 〈P, Q〉 it is false that (Px & Qx) is necessary for x to donate protons to y when combined. The fact that (Px & Qx) is sufficient for this potential does not by itself yield a definition of anything.

Here is a second example. Suppose we start with first-order chemical structures C1,…, Cn. Some of these structures reproduce themselves. This is an important distinction among the structures. It is a second-order feature, however. The reproducers are not ones that produce C23; the reproducers are the Cis that produce Cis. The reproducers do not reproduce in isolation, however. They reproduce only when there are adequate resources available to them, and they consume those resources in reproducing. Which resources they consume varies from one reproducer to another. So, we will have to interdefine reproducers and resources for them. The postulate would require a relation of copying among individuals. (I will have to be very sketchy about what exactly this relation is, unfortunately.) The postulate would be something roughly along the lines: x and y stand in the reproducer-resource relation iff x and y together would produce some copy z of x and consume y in the process. The definition sentence would be: the reproducer-resource relation = the R such that Rxy iff x and y together would produce some copy z of x and consume y. The property-level relation would be: the reproducer–resource* relation is the set of pairs of properties 〈P, Q〉 where any P and Q objects stand in the object-level reproducer–resource relation. We might call our reproducers ‘organisms’, and call the postulate and definition sentences “organism-theory”. Continue down this second-order road, and eventually we will find population biology, with properties (or predicates) for growth rates of populations of organisms, carrying capacities of environments, predator–prey relations, etc. In this case, too, the relations among realizers can be many-many: there can be multiple resources for a given reproducer, and the same thing can be a resource for multiple reproducers. In addition, one reproducer is often a resource for another (predation).

I will focus on this second example, even though it is more sketchy than the first. If matters work out as I think they do, the second example threatens to show that all higher-level sciences that are concerned with properties of organisms and populations of them will be unacceptable by the lights of Realizer Functionalism. The sketchiness of the example is acceptable, I hope, because the logical point I wish to make about it depends only on two features. The first feature is that ‘organism’ and ‘resource’ have to be interdefined. The second feature is that the relations among realizers are many-many: there can be multiple resources for a given organism, and multiple organisms for a given resource.

Consider the account of ‘x is an organism’. Both the Functional State Identity Theory and Realizer Functionalism see this sentence as attributing a property to x, though they differ about which property. As before in the case of Con and Con*, suppose we have two reproducer-resource relations. The first is a set of pairs of individuals; the second is a set of pairs of realizer properties. Let them be Rep and Rep*, respectively. So, both Realizer Functionalism and the Functional State Identity Theorist will give these two equivalent accounts of ‘x is an organism’:
$$ (12)\ \hbox {`}{\text{x is an organism' means that x has the property:}}\exists {\text{y }}Rep\left( {{\text{x}},{\text{ y}}} \right) $$
$$ (13)\ \hbox {`}{\text{x is an organism' means that x has the}}\,\,{\text{property:}}\exists {\text{y }}\exists {\text{P }}\exists {\text{Q }}\left( {{\text{Px }}\& {\text{ Qy }}\& \, Rep*\left( {{\text{P}},{\text{ Q}}} \right)} \right) $$
The account of (12) says that x stands in the object-level reproducer-resource relation to some object y; the account of (13) says that there are properties P, Q which stand in the property-level reproducer-resource relation, and Px and Qy, for some y.

The two versions of Functionalism differ about what relations Rep and Rep* are. The Functional State Identity Theory says that Rep* is a second-order relation. It corresponds to a set of multiple pairs; in addition, these pairs embody many-many relations among realizers. 〈P1, Q1〉 is in there, and so are ones such as 〈P1, Q2〉, 〈P1, Q3〉, and 〈P2, Q1〉. Realizer Functionalism by contrast wants to squeeze this set of pairs down to a single member 〈P, Q〉 on each occasion of use of ‘organism’, and to say that on that occasion ‘organism’ expresses P and ‘resource’ expresses Q.

It seems to me that in this case, the Realizer Functionalist has no way to pick out an individual pair of realizers 〈P, Q〉. The first pass at the Realizer Functionalist’s Rep* relation is of the form:
$$ (14)\ Rep* = \iota \langle {\text{P}},{\text{ Q}}\rangle : \, \forall {\text{x }}\forall {\text{y }}\left( {\left( {{\text{Px }}\& {\text{ Qy}}} \right) \to Rep\left( {{\text{x}},{\text{ y}}} \right)} \right) $$
By hypothesis, there is no unique 〈P, Q〉 pair as described in (14). The Realizer Functionalist must find such a pair by restricting the domain somehow. But how? Suppose we try: the relevant 〈P, Q〉 pair is the one that that thing has (pointing to some object x). But the ostended object x has a P such that Q1, Q2, etc. are all resources for Ps. Suppose we restrict the domain to microphysical duplicates of x. This does nothing to remove the problem: there can still be multiple resources for this exact microstructure. Suppose we restrict the domain to microphysical duplicates of x in environments that are microphysical duplicates of x’s current one. This is still no help: there can be multiple resources for x present here and now. Restricting the domain does not remove the problem that there is no pair that satisfies the relevant functional definition.

Suppose we tried instead to restrict the domain of pairs of realizers for (14). I do not see any acceptable way to do this. We have an organism x in an environment that includes multiple resources for x. The Functional State Identity Theorist explains ‘x is an organism’ by using phrases such as ‘there is some resource for x’. She does not know, and does not need to know, anything very specific about the resource(s) in question. Phrases such as ‘there is some resource for x’ are as yet unavailable to the Realizer Functionalist, however. Prior to settling on a specific pair of organism-resource realizers, the term ‘resource’ is undefined for her (and thus ‘organism’, too). So far there does not seem to be any way to find a specific pair, however. The only way that I can see for the Realizer Functionalist to pick out any pair at all is by making reference to a resource realizer described in lower-level terms. That is, she will have to say something to the effect ‘the reproducer-resource relation (on this occasion) = the unique pair 〈P, Q〉 such that objects indistinguishable from x have P, and Q = microphysical structure S’. This description violates a basic constraint on Realizer Functionalism, however. The first and most obvious objection to the Mind-Brain Identity Theory (“Objection 1” in Smart 1959, p. 146) was that any “illiterate peasant” knows quite a bit about mental states while knowing little about brain states. In the current case, by the lights of Realizer Functionalism, we would need knowledge of the low-level nature of some resource realizer in order even to say truly that x is an organism. That is unacceptable.

Something similar would be true in the case of mental states, if (as is usually supposed) ‘belief’ and ‘desire’ are interdefined, and if the relations among realizers are many-many. In that case, to say ‘John believes that p’ is to say that John has some state which would combine with various motivational states to produce certain actions. In terms of realizers, it is to say that John has some-or-other belief realizer which combines with some-or-other motivation realizer to produce certain actions. Suppose John does not in fact have the appropriate motivations at the time in question; and suppose that many realizers of the appropriate motivations would work in conjunction with his current belief realizer to produce the relevant action. Then again the Realizer Functionalist has no way to pick out a unique pair of belief-desire realizers to be the ones that ‘belief’ and ‘desire’ are to refer to on this occasion. Since John does not have any appropriate desire realizer, we will not be able to pick one out even by restricting the domain to John’s exact microstate here and now. In this case, Realizer Functionalism requires that we have neurological (or perhaps even microphysical) knowledge of some one of John’s possible desire realizers in order to say truly that he has a given belief. This is clearly unacceptable again.7

So, Realizer Functionalism seems unable to handle cases in which the relations among realizers are many-many. The domain restriction move seems designed for cases in which the realizers line up with each other one-to-one, and there is no a priori reason (that I can see at least) why this case should hold always (or even ever). The objection does not directly show that Realizer Functionalism is false. Instead, it shows that if Realizer Functionalism is right, some functionally defined terms lack denotation. They are similar to ‘caloric fluid’ and ‘phlogiston’.8 If my organism/resource example is correct, even in sketchy outline, then all biology from the organism-level up would be defective on this view. Sometimes Kim seems willing to accept such an error theory. He says that there are no functional properties, but mere “concepts” (Kim 1998a, pp. 110–111, 2008, pp. 111–112). Still, the error theory Kim envisions differs from the sort that Realizer Functionalism yields. Kim thinks that if psychology is multiply realized in humans, octopusses, and martians, there could still be domain restricted psychological theories that are good nonetheless: one for humans, one for octopusses, etc. This view assumes that restricting domains will leave us with a unique n-tuple of realizers. But with many-many relations among realizers, there is no apparent reason to think that there will be any good replacement theory for any domain.

So, Realizer Functionalism appears to have an adequate response to the multiple realization objection, but it does not appear to have a response to the problem of many-many relations among realizers. The Functional State Identity Theory seems highly natural by contrast. This view reads causal role definitions in the Proposal #1 way, and accepts that the properties expressed by second-order, functional predicates are themselves second-order, functional ones. Many people have metaphysical suspicions about such properties, however. Those suspicions formed the motivation for Realizer Functionalism. I will suggest a new version of Functionalism as an alternative way of capturing these metaphysical suspicions.

4 Truthmaker functionalism

In this section, I attempt to formulate a new version of functionalism, which I dub “Truthmaker Functionalism”. This view applies some ideas of John Heil (2003) and Ross Cameron (2008) to the case of functionally defined terms.

Before setting out Truthmaker Functionalism, we should distinguish metaphysical and semantic components of reductionism. At least as I see them, Realizer Functionalism and the Functional State Identity Theory are semantic views in the first instance: views about how the relevant predicates purport to express certain properties.9 But obviously enough the views are motivated by conflicting metaphysical assumptions. Realizer Functionalism is motivated by the view that second-order, functional properties are defective in some way. Kim treats functional properties as a subclass of second-order properties, and argues that the second-order ones do not exist.10 They are not properties, but mere “concepts” (Kim 1998a, pp. 110–111, 2008, pp. 111–112). Lewis says that functional properties are “excessively disjunctive”, and so cannot occupy any causal roles or serve as the denotations of functional predicates (1994, p. 307). Lewis treats properties as Carnapian intensions: functions from possible worlds to extensions. These are the “abundant” properties. Lewis then distinguishes among the “natural” and “unnatural” properties (1983). The natural properties are “sparse”; they are the ones that “carve nature at the joints”. Lewis holds that functional properties are highly unnatural.

Kim and Lewis are both willing to accept at least some properties. Setting strictly nominalist scruples aside, we at least have Lewis’s intensions to choose from. So, there does not appear to be much real difference between Kim’s view that functional properties are not properties at all but mere concepts, and Lewis’s view that they are properties but highly unnatural and disjunctive ones. So, this view looks to be the metaphysical component of reductionism:

Metaphysical Reductionism: Second-order, functional properties either do not exist, or are at best highly unnatural.

This contrasts with a semantic view:

Semantic Reductionism: Sentences containing second-order, functional predicates are true (often enough, or at least approximately), and their truth conditions make reference only to first-order, nonfunctional properties.

Semantic Reductionism embodies a sort of realism. The aim of the view is to provide truth conditions for second-order talk that are actually satisfied, and which do not require reference to any second-order entities. Realizer Functionalism attempted to do this by identifying an unexpected subject matter for second-order talk. The Truthmaker Functionalist has an alternative strategy.

Heil (2003) suggests that belief in second-order properties, and in a “layered” conception of the world more generally, derives from unreflective acceptance of a “Picture Theory” of language. According to the Picture Theory, predicates express properties (Heil’s “Principle (Φ)”, 2003, p. 26). So, in order for a sentence such as ‘Mary wants to eat a sandwich’ to be true, there must be some property of wanting to eat a sandwich. Heil rejects the Picture Theory, and second-order properties along with it. His idea is that higher-level predicates generally do not express properties; instead, applications of them have purely lower-level truthmakers. Heil does not discuss the case of functional predicates in any detail (though he does say that “the pertinent similarity dimension” involved in the case of ‘is in pain’ “includes a strong dispositional component”, p. 40, fn. 2). This seems a bit unfortunate to me: functional predicates can be seen as a nice example of his view.

To begin to spell out Truthmaker Functionalism, consider the following variant on the Proposal #1 postulate for acidity-theory:
$$ (15)\ \forall {\text{x }}\left( {{\text{Ax }} \leftrightarrow \, \exists {\text{P }}\left( {{\text{Px }}\& \, \forall {\text{y }}\left( {\left( {{\text{Py }}\& {\text{ Dy}}} \right) \, \to {\text{ Hy}}} \right)} \right)} \right) $$
(15) says that something is acidic iff it has a property that leads to hydronium ions when dissolved. (15) is very nearly equivalent to the Proposal #1 postulate suggested earlier. The only possible differences concern cases of “ungrounded” dispositions.11 (15) adds an explicit quantification over these grounds. One could potentially read the quantifier in (15) to range over first-order properties only.
The first idea of Truthmaker Functionalism is to treat a sentence such as (15) as expressing a sort of metalinguistic fact. The Ramsey-Lewis view took (15) as a description of a second-order property. Truthmaker Functionalism takes it instead as a description of a semantic role for ‘acidity’12:
$$ (16)\ \hbox{`}b{\text{ is acidic' is true iff}}{`}b\hbox{'}{\text{names some object x and }}\exists {\text{P }}\left( {{\text{Px }}\& \, \forall {\text{y }}\left( {\left( {{\text{Py }}\& {\text{ Dy}}} \right) \, \to {\text{ Hy}}} \right)} \right) $$
(16) says that an ascription of ‘acidity’ to an object is true iff the object has some property that gives rise to H in D. Truthmaker Functionalism moves the second-order quantification out of the definition of a predicate and into the truth conditions of a whole sentence. The Metaphysical Reductionist would limit the quantifier ‘∃P’ to first-order realizer properties. The aim is to make the second-order sentences come out true while the deep semantics mentions no second-order properties.
A second component of Truthmaker Functionalism is a distinction between existence and real existence (this is emphasized by Cameron 2008). The view has two sorts of existential quantifier, a “superficial” one and a “deep” one. I will use ‘∃*’ for the superficial quantifier, and ‘∃’ for the deep one. Only the deep quantifier ‘∃’ is existentially committing. The semantically realist motivations of the view require that we maintain distinctions recognized by common sense. So, ‘There exist* humans’ should turn out true, while ‘There exist* unicorns’ should turn out false, even though deep existence likely contains neither humans nor unicorns. So, the account given for ‘∃*’ will be messy, and will vary with the terms that follow it. For functional predicates, accounts will have to make reference to associated causal roles. In the case of acidity the role is (Dx → Hx), contributing hydronium ions when dissolved. So, the view can capture existential quantification over second-order properties like this. ‘Acidity exists*’ goes to ‘∃*P P = A’:
$$ (17)\ `\exists^{*}{\text{P P}} = {\text{A' is true iff }}\exists {\text{Q }}\forall {\text{y }}\left( {\left( {{\text{Qy }}\& {\text{ Dy}}} \right) \to {\text{Hy}}} \right) $$
On this reading, acidity exists superficially iff some realizer of acidity exists deeply.

I hope it is clear that Truthmaker Functionalism is immune to the general worry about multiple realization. Sentences that appear to ascribe a multiply realized property turn out true in just the cases we want. For a second-order property P, having P is equivalent to having some-or-other realizer of P. Truthmaker Functionalism tells us that sentences ascribing ‘P’ to x are true iff x has some-or-other realizer. So, those truth conditions are correct.13

Truthmaker Functionalism also avoids the worry about interdefinitions I raised for Realizer Functionalism. In the case of my sketchy “organism theory”, the property-level definition was: the reproducer-resource relation = the R such that 〈P, Q〉 ∈ R iff P and Q together produce more Ps and consume Qs. This defines a set of pairs of first-order properties. I argued that there is likely no way to restrict the domain so that ‘the R’ picks out a unique pair. Truthmaker Functionalism is completely untouched by this objection. Rather than trying to force ‘reproducer’ and ‘resource’ to denote specific Ps and Qs, this view says that objects satisfy ‘reproducer’ and ‘resource’ when they have some P and Q such that P and Q lead to more Ps and consume Qs.

Truthmaker Functionalism seems to me to be a significant improvement on Realizer Functionalism, and I recommend it to Metaphysical Reductionists. Some form of Functionalism appears to be commonly accepted for a fairly wide range of predicates. In the absence of Truthmaker Functionalism, Metaphysical Reductionism would be in serious trouble. The usual alternative to Realizer Functionalism, namely the Functional State Identity Theory, is firmly commited to second-order, functional properties. The Ramsey and definition sentences of functional definitions quantify over properties, and my objection to Realizer Functionalism was in effect that only second-order properties satisfy those quantifiers. Truthmaker Functionalism has a response: it rejects the quantifications when read to concern real existence, but accepts them when read to concern superficial existence only.

The semantics proposed by Truthmaker Functionalism is perfectly compatible with a Nonreductionist metaphysical view. Things which exist deeply also exist superficially, so the Nonreductionist will see nothing to deny in the Truthmaker Functionalist’s semantic claims. We could of course stipulate that the categories of deep and superficial existence are exclusive, but I think trivial semantic considerations rule against building this stipulation into our quantifiers ‘∃’ and ‘∃*’. It seems semantically silly to regiment the claim ‘Acidity exists’ so that it entails that acidity does not really exist. We ought to read the superficial quantifier ‘∃*’ as noncommittal, rather than as building in real nonexistence. So, the Truthmaker Functionalist’s reading of special science claims is consistent with Nonreductionism. The Nonreductionist accepts the Truthmaker Functionalist’s semantics, and then adds that second-order properties really do exist and really are natural ones. The Metaphysical Reductionist denies this further claim, and offers Truthmaker Functionalism as a way of explaining discourse.

It seems somewhat difficult to resolve this dispute. One side says certain properties exist; the other responds that they do not exist, but do exist*. As in debates about material composition, it is even tempting to think that there is something defective about the dispute: maybe the views are terminological variants of each other, or maybe they are epistemically on a par. I want to suggest a way out of this impasse. Cases of many-many relations among realizers seem problematic for the Reductionist version of Truthmaker Functionalism, too.

5 Many-many causal relations

In this section, I will raise a problem for the Reductionist version of Truthmaker Functionalism. The problem again concerns many-many relations among realizer properties.

First, I want to lay down a ground rule for the conjunction of Metaphysical Reductionism and Truthmaker Functionalism. The ground rule is that no second-order property expressions can appear in the ultimate truth conditions for any genuine truth. If such expressions did appear in the ultimate truth conditions, we would be stuck with the entities they express. There is some fundamental language, call it ‘Ontologese’, in which the ultimate truth conditions are formulated. According to the Reductionist, Ontologese contains no terms that refer to second-order properties (and none that refer to composite objects either, according to Heil (2003) and Cameron (2008)).

Suppose there are second-order properties A, B, and C, which have three exclusive realizers each: A1, A2, A3, B1,…, C3. Suppose there is a causal/nomic relation among these properties:
$$ (18)\ \forall {\text{x }}\left( {\left( {{\text{Ax }}\& {\text{ Bx}}} \right) \to {\text{Cx}}} \right) $$
A and B causally suffice for C. (If you feel inclined to deny a priori that there can be nomic relations among second-order properties, please bear with me. Feel free to treat the arrow in (18) as some sort of nomic* relation.) ‘A’, ‘B’, and ‘C’ are second-order expressions, so the Metaphysical Reductionist must find some further truth condition in terms of the realizers A1, etc. Let’s not worry about the nomic arrow ‘→’ itself. Granting ourselves the nomic arrow, what relation among realizers does (18) express?
A natural thought is that A, B, and C stand in the relation of (18) because their realizers do too. Whenever there is (apparently) an instance of (A & B) → C, there are realizers AR, BR, and CR such that (AR & BR) → CR. That is the “real” causal/nomic relation, and the second-order expression ‘(A & B) → C’ is just a sort of summary of many instances of these relations among realizers. Here is the proposed truth condition (in Ontologese) for Truthmaker Functionalism:
$$ \begin{aligned} (19)\ `\forall {\text{x }}(\left( {{\text{Ax }} \& \ {\text{ Bx}}} \right) \to {\text{Cx}})'{\text{ is true iff whenever `Ax }} \& {\text{ Bx' is satisfied by object }}a, \hfill \\ {\text{there are realizer properties A}}_{\text{R}} ,{\text{ B}}_{\text{R}} ,{\text{and C}}_{\text{R}} \, \left( {{\text{of `A'}},{\text{ `B'}},{\text{ and `C' respectively}}} \right), \hfill \\ {\text{possessed by }}a,{\text{ such that }}\forall {\text{x }}\left( {\left( {{\text{A}}_{\text{R}} {\text{x }} \& \ {\text{ B}}_{\text{R}} {\text{x}}} \right) \to {\text{C}}_{\text{R}} {\text{x}}} \right). \hfill \\ \end{aligned} $$
Sentence (19) contains no expressions that refer to second-order properties. The satisfaction of second-order predicates ‘A’, ‘B’, and ‘C’ is explained in the manner suggested before by Truthmaker Functionalism. The idea behind (19) is that the relation among second-order properties* is a superficial, nomic* relation. In reality, there are only realizer properties and nomic relations among them.
Something along the lines of (19) appears to be adopted by both Heil and Kim. Kim suggests the following account concerning mental property M and physical realizer P:

[W]hen we say “x’s having M caused E”, we should be understood as saying something like “there is a realizer P of M such that x had M on this occasion in virtue of x’s having P, and x’s having P caused E”. (Kim 2008, p. 110, fn. 15)

Heil makes a similar suggestion concerning higher-level properties H1 and H2 realized on a given occasion by physical properties P1 and P2.

What of an apparent instance of higher-level causation: H1’s causing H2? Here, the truthmaker for ‘H1 causes H2’ is just P1’s causing P2. It is true, by my lights, to say that H1 causes H2. But this truth holds, not in virtue of some higher-level causal sequence, it holds in virtue of P1’s causing P2, a ground-level sequence. (Heil 2003, p. 45)

Read generally, these two proposals appear to be similar to my suggestion (19).

The proposal (19) seems to me to embody in a somewhat different fashion than before the metaphysical assumption that the relations among realizer properties are one–one. It seems entirely possible for those relations to be many-many instead. Figures 1 and 2 illustrate two possibilities for the relation (A & B) → C.
https://static-content.springer.com/image/art%3A10.1007%2Fs11098-010-9518-z/MediaObjects/11098_2010_9518_Fig1_HTML.gif
Fig. 1

One-one causal relations among A, B, C

https://static-content.springer.com/image/art%3A10.1007%2Fs11098-010-9518-z/MediaObjects/11098_2010_9518_Fig2_HTML.gif
Fig. 2

Many-many causal relations among A, B, C

Figures 1 and 2 show two extreme cases; there are many intermediates. In Fig. 1, A1 combines with B1 to cause C1; similarly with 〈A2, B2〉 and C2, and with 〈A3, B3〉 and C3. A1 does not combine with B2 or with B3 to do anything. Since we assumed that A and B suffice for C, it must be that A1 and B2 cannot be combined––if they could be, and did not lead to C, then the assumption would be false. A1 and B1 could be some human-specific realizers of certain beliefs and desires, for example, while A2 and B2 are octopus-specific realizers. Octopus brains are not capable of having A1, and human brains are not capable of having A2. Figure 1 embodies the proposed truth condition (19).

Figure 2 represents the other extreme possibility. In it, any A-realizer combines with any B-realizer to suffice for C, but not for any specific C-realizer. This is clearly possible if indeterminism is. Suppose the A- and B-realizers are highly specific microstructural features of some acidic sample and a beaker of water in circumstances in which they are about to be combined. It could be that any (or near enough any) combination of A- and B-realizers yields a probability distribution over later states with two features: (i) every specific microstructural result has negligible probability, while (ii) all (or near enough all) resulting states share a gross feature, such as having a given concentration of hydronium ions. This is a case in which any A-realizer and any B-realizer yield C, while yielding no specific C-realizer. Some C realizer occurs in each case, but it was not necessitated by prior states. Only C was necessitated.

Figure 2 cases are apparent counterexamples to the truth condition I suggested on behalf of the Reductionist version of Truthmaker Functionalism. ‘(A & B) → C’ is true, but there are no realizers such that (AR & BR) → CR. Figure 2 represents a case in which a nomic relation obtains among second-order properties without any corresponding nomic relation obtaining among their realizers. There appear to be no statements about nomic relations among realizer properties alone that can capture ‘(A & B) → C’. It seems like the truth condition would have to be this instead:
$$ (20)\ \forall {\text{x }}\left( {\left[ {\left( {{\text{A}}_{ 1} {\text{x }} \vee {\text{ A}}_{ 2} {\text{x }} \vee {\text{ A}}_{ 3} {\text{x}}} \right)\& \left( {{\text{B}}_{ 1} {\text{x }} \vee {\text{ B}}_{ 2} {\text{x }} \vee {\text{ B}}_{ 3} {\text{x}}} \right)} \right] \, \to \left( {{\text{C}}_{ 1} {\text{x }} \vee {\text{ C}}_{ 2} {\text{x }} \vee {\text{ C}}_{ 3} {\text{x}}} \right)} \right) $$
This truth condition seems to violate the ground rule for the Reductionist version of Truthmaker Functionalism. It contains terms for second-order properties such as ‘A1 ∨ A2 ∨ A3’, and it links those expressions together with the causal/nomic arrow ‘→’. One might say that (20) involves only disjunctions of first-order properties, and not second-order ones. This response does not seem to avoid the problem, however. Metaphysical Reductionism holds that second-order properties are unnatural. They do not “carve nature at the joints”; in particular, they do not figure in any genuine causal/nomic relations. I would hope to avoid worrying about whether necessarily coextensive properties are identical, and in particular whether (A1 ∨ A2 ∨ A3)x = (A1x ∨ A2x ∨ A3x). Even if the Reductionist insists that those properties are distinct, they carve nature at exactly the same joints, across all possible worlds. So, they cannot differ in naturalness. The current truth condition invokes joint-carving entities that are at least necessarily coextensive with second-order properties. So, it requires nomic joints that correspond to second-order properties, however we choose to describe them.

In addition, we should remember that it was a simplification to suppose that A (or ‘A’) has only the three realizers A1, A2, and A3. In realistic cases, there will be infinitely many realizers at the fundamental, microstructural level. So, a finite formulation along the lines of (20) will not be possible without explicit quantification. Even in Ontologese, that quantification has to occur inside the scope of the nomic arrow, rather than outside of it. The things that are nomically related in the case (if anything is) are A, B, and C: the property of having some A-realizer, the property of having some B-realizer, and the property of having some C-realizer. Those are second-order properties. So, if Ontologese is capable of expressing truth conditions for ‘(A & B) → C’, it must include second-order property expressions, contrary to the intentions of the Reductionist.14

6 Conclusion

This paper considered three varieties of Functionalism. The Functional State Identity Theory holds that functional predicates express second-order, functional properties. Realizer and Truthmaker Functionalism attempt to capture what is plausible about Functionalism while avoiding its metaphysical baggage. Multiple realization is the standard objection to reductionist versions of Functionalism, but (I argued) all varieties are compatible with it. I raised further difficulties for the two reductionist versions of Functionalism. My objections concerned cases in which an apparently one–one relation among second-order properties corresponds to a many-many relation among their realizers. Reductionist strategies of avoiding commitment to second-order properties appeared to fail in such cases. It appears that only the Functional State Identity Theory can explain these cases.

Footnotes
1

Kim (2005, 2008) are more equivoval about these local reductions, however.

 
2

For ease of exposition, this and all subsequent formulations omit a detail which serves to rule out vacuous satisfaction by objects that could not possibly be in the conditions described by the relevant proposals. For example, an individual electron could not be dissolved in water, so it vacuously satisfies ‘(Dx → Hx)’, and thus counts having acidity by (1). The needed qualification is that x is possibly dissolved in water: ∀x (Ax ↔ ((Dx → Hx) & Possible Dx)). I will treat this qualification as understood.

 
3

Well-known triviality problems arise for Ramsey–Lewis definitions if the domain of properties includes all subsets of the domain of individuals, and if the sentences in question are purely extensional. See Melia and Saatsi (2006) for discussion. I will suppose, with Lewis I think, that the domain includes only suitably “natural” properties. In addition, my proposals make use of conditionals such as ‘Dx → Hx’ that have some modal force (which I will not attempt to specify).

 
4

One issue on which I wish to remain neutral concerns whether the Functional State Identity Theory holds that the properties in question are what I would call “fully-functional” or merely “quasi-functional”. The difference is whether the properties play the relevant causal role with metaphysical or merely nomological necessity. For example, an object x has fully-functional acidity in world w iff x satisfies (Dx → Hx) in w; an object has quasi-functional acidity in w iff it has some P such that (Px & Dx) → Hx in the actual world. The Functional State Identity Theory could be formulated either in terms of fully- or merely quasi-functional properties. In both cases, the relevant properties are similar to (possibly infinite) disjunctions of realizer properties. Fully-functional properties are similar to an infinite disjunction of the sort: [(A1 & Laws L1) ∨ A2 ∨ Laws L1) ∨…∨ (B1 & Laws L2) ∨ (B2 & Laws2) ∨…].

 
5

This is the reason, mentioned before, that I prefer the term ‘Functional State Identity Theory’ to ‘Role Functionalism’. There are multiple concepts of a causal role, and the difference between “Realizer” (or “Occupant”) Functionalism and “Role” Functionalism concerns which role is in question. Both views appeal to “occupants” of roles, but of different roles.

 
6

This relation will have to be transworld, and will also have to include times: x at t in w is chemically indistinguishable from y at t’ in w’. I suppress these complications for convenience.

 
7

I thank an anonymous referee for encouraging me to be clearer about the general objection and to provide an application to mental states.

 
8

One might object that the problem with ‘caloric fluid’ and ‘phlogiston’ is not that the terms lack denotation, but that they denote properties that are actually uninstantiated. I think the terms do lack denotation, and do in much the same way that special science terms would if Realizer Functionalism was right. At least as a rough first approximation, ‘caloric fluid’ is a descriptive name for the fluid that is responsible for heat-phenomena. There is no such thing in the actual world. There are such fluids in other worlds, with different laws. But there are multiple distinct such fluids across worlds, and we lack the resources to pick one out and say that that one is caloric fluid.

 
9

It may be that the usual understanding of these views combines semantic and metaphysical elements, but it seems best to me to distinguish these aspects. As I understand things, for example, one could accept Realizer Functionalism together with my objections to it, and conclude that terms such as ‘organism’ are denotationless. Similarly, one could accept the semantics of the Functional State Identity Theory together with the view that second-order properties do not exist, and conclude again (for different reasons) that the terms are denotationless. Both of these views end up at an error theory of the relevant special sciences. Both views are contrary to the generally realist motivations of most Functionalists, but they are possible views nonetheless. I thank an anonymous referee for raising this issue.

 
10

A bit of terminology. I understand a second-order property to be one that can be expressed in fundamental terms only by using quantification over properties: the property of having some P such that Φ(P). Functional properties by contrast are ones that have “causal powers” essentially. It is at least a philosophically open possibility that some fundamental, first-order properties are functional. And some important second-order properties are arguably not functional, such as having mean molecular kinetic energy x. This is second-order: being composed of molecules with some-or-other kinetic energy properties that average out to x. It is arguably not functional, however: the definition concerns properties of the parts rather than powers of the whole. This paper is primarily concerned with functional definitions of nonfundamental predicates. These predicates (at least appear to) express properties that are both second-order and functional.

 
11

(15) obviously implies (1). The only case in which (1) could be true while (15) is false is a case in which some object satisfies ‘D → H’, while having no property P such that Ps universally satisfy ‘D → H’. It is questionable whether such a case is possible. If the disposition in question is a fundamental property, then it would presumably be its own ground; in any case, it would fall in the range of (15)’s quantifier ‘∃P’. So, a counterexample to (1) ⇒ (15) requires a disposition that is both ungrounded in any distinct property and also not fundamental. I am inclined to doubt that is possible.

 
12

There are potential complications concerning the object in this truth condition. One aim of the Truthmaker views of Heil and Cameron is to avoid commitment to composite objects. Claims about such objects are supposed to be made true by pluralities of simples. So, some further rewriting of this truth condition will probably be required by their views.

 
13

Which more specific truth condition is correct depends upon whether functional predicates act like they express fully-functional properties or quasi-functional ones. Truthmaker Functionalism is capable of matching either truth condition.

 
14

One might hold that I have misinterpreted my model Reductionists as attempting to provide truth conditions for higher-level talk. Maybe the aim is instead only to provide truth-makers, understood as sufficient conditions for the talk to be true. And surely those sufficient conditions exist, according to the Nonreductionist, who accepts supervenience. It seems to me that the Reductionist does not even have truthmakers for the higher-level claim in my example. The Nonreductionist has principles of composition and realization that yield composite objects and second-order properties. Those entities are the immediate truthmakers of the higher-level claim. Fundamental matters, together with Nonreductionist principles, yield that the higher-claim is true. The Nonreductionist principles are crucial to that implication, however. Without them, the higher-level claim is false. So, the Reductionist does not even have truthmakers for it. She has only entities that count as truthmakers for the higher-level claim by means of principles she rejects.

 

Acknowledgements

I would like to thank Michael McKinsey, Larry Powers, Susan Vineberg, an anonymous referee, and an audience at Wayne State University for helpful comments and discussion.

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© Springer Science+Business Media B.V. 2010