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.
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Notes
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.
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).
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) ∨…].
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.
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.
I thank an anonymous referee for encouraging me to be clearer about the general objection and to provide an application to mental states.
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.
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.
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.
(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.
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.
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.
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.
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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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Hiddleston, E. Second-order properties and three varieties of functionalism. Philos Stud 153, 397–415 (2011). https://doi.org/10.1007/s11098-010-9518-z
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DOI: https://doi.org/10.1007/s11098-010-9518-z