Two mainstream accounts of multiple realization

Below, I would like to introduce two basic concepts of multiple realization that dominate the literature in the last decade. I won’t to argue either for or against these views. Instead of choosing between them where multiple realization becomes important in my discussion of causal exclusion, I will investigate the problem from the point of view of both theories.

1.4.3.1 A flat view of multiple realization

The first concept relies on a functional account of realization, where the higher-level function (F) of an entity (x) is realized by a lower-level causal mechanism (CM). F is multiply realized if and only if it is realizable by different kinds of underlying causal mechanisms (CM1, CM2, etc.) (see: Polger & Shapiro 2016; Shapiro 2004). A different way of putting this is to say that property F is multiply realizable if there exist at least two distinct functional analyses of F24_.

24 _{Conditions for the multiple realization of kind F in higher-level taxonomic system S1 by lower-level scientific}

taxonomic system S2 (see: Polger & Shapiro 2016:67-77):

(1) Ps and Rs are of the same kind in higher-level scientific taxonomic system S1. (higher-level sameness) (2) Ps and Rs are of different kinds in lower-level scientific taxonomic system S2. (lower-level difference) (3) The factors that lead the Ps and Rs to be differently classified by S2 are among those that lead them to be commonly classified by S1 (demands that lower-level kinds should be different in a realization relevant manner) (4) the relevant S2-variation between Ps and Rs is distinct from the S1 intra-kind variation between As and Bs. (demands that variation in the realized kind is distinct from variation between realizer kinds)

The view is called “flat” as the realized and the realizer property are attributed to the very same individual entity (see: Gillett 2003).

According to this view, multiple realization is a phenomenon distinct from mere variation. There is a lot of variation in nature and between levels of nature, but not all of that variation is relevant for our taxonomic systems. On this account, mild multiple realization points to uninteresting variability in realization. In such cases, the core realizer is always the same in terms of the lower-level taxonomy, so biconditional bridge-laws can be established as there is one unified way of explaining the higher-level property by a lower-level mechanism. However, robust multiple realization is taken seriously by this account. In such cases the core realizer of the realized kind cannot be defined in a unified manner.

Polger & Shapiro (2016:64) argue that “the question of multiple realization is a question about actual sciences, and it is always specific and contrastive”. This means, that the question concerning multiple realizability should be relativized to available levels of description. So, a mental property can be singularly realized with respect to the neurological level, but multiply realized somewhere below that level25_.

Let me show the most important features of the theory on a toy example Shapiro (2000) introduced, and that is recited by many in the literature. Consider the following kind of variation among corkscrews: (a) a waiter’s corkscrew and a winged corkscrew (see: Figure 1.4-1), (b) two waiter’s corkscrews, where one is made of aluminium and the other is made of iron, (c) two waiter’s corkscrews

25 _{There is a hot debate among theorists on whether the realization relation is transitive or not. Polger (2008)}

denies it, Gillett & Aizawa (2009) object, but this problem has no real bearing on my interests in the thesis. Figure 1.4-1

that differ only in colour. The kind corkscrew, supposing it is a real kind, is (robustly) multiply realized by waiter’s and winged corkscrews (a), because they realize the same function of removing corks by different mechanisms. The waiter’s version works by a lever mechanism, the winged version works by a rack and pinion mechanism. In case (b) there is variation between the two realizers, but they belong to the same mechanistic kind. In the terminology introduced earlier, this would be a case of mild multiple realization, as the items share core realizer features. As Shapiro (2000:645) explains, relative to the function in “a corkscrew, rigidity screens off the differences between steel and aluminum”. In the last case (c), the difference in colour is simply irrelevant for the realization of the function, so the kind corkscrew is univocally realized by the two items. To highlight the differences, in the next section, I will show how the other conceptual framework deals with the same examples.

1.4.3.2 The dimensioned view of multiple realization

The second concept of multiple realization relies on a compositional account of realization. According to this view, higher-level property F of an entity x is realized by a set of lower-level properties and relations between x’s components. F is multiply realized, when at least two, non-identical sets of property instances, {P1-Pn} and {P*1-P*n}, at the same level of composition determine another property instance of higher-level property F (see: Aizawa & Gillett 2009, Aizawa 2018)26_.

26 _{The precise definition of multiple realization according to the dimensioned view: “A property F is multiply}

realized if and only if (i) under condition $, an individual x has an instance of property F in virtue of the powers contributed by instances of properties/relations P1-Pn to x, or x ’s constituents, but not vice versa; (ii) under condition $* (which may or may not be identical to $), an individual x* (which may or may not be identical to x) has an instance of a property F in virtue of the powers contributed by instances of properties/relations P*1-P*m to x* or x*’s constituents, but not vice versa; (iii) P1-Pn ≠ P*1-P*m and (iv), under conditions $ and $*, P1-Pn and P*1-P*m are at the same scientific level of properties” (Aizawa & Gillett 2009:188, notation changed to bring it closer to my usual notations in the thesis).

The view is called dimensioned because the component parts of the whole that bears property F, the lower-level entities, their properties and relations are said to constitute and realize the whole and its properties. Gillett rejects the view according to which realized and realizer properties belong to the same subject, the kind of view he dubbed the “flat view” (Gillett 2003). This feature characterizes all present-day alternatives of the composition- based view. Along with all flat views, Gillett (2010) rejects the notion of a structural property used implicitly or explicitly by many philosophers to describe the complex lower-level state that is identified as the relevant realizer. On the composition-based view it comes out firstly,

as an unnecessary addition to the ontology of the system and secondly, as an ontological chimera that includes features of both the higher and lower-level ontology.

Gillett’s direct criticism was pointed towards a specific version of the flat view, the subset view of realization (see: Figure 1.4-3 and section 1.3.3 for a summary of the view), but the same basic insight holds for the mechanism based functionalist view as well. We simply need to replace the notion of a structural property with the notion of a lower-level mechanistic kind Shapiro (2004) prefers.

For the dimensioned view, all kinds of inter-level identities are impossible. The realization relation is an asymmetric, one-to-many composition relation between realms of qualitatively distinct properties (see: Figure 1.4-2) similarly to the case of temperature and kinetic energy as we already saw earlier (section 1.2.2). Naturally, not all constituents of the whole that bears the realized property are relevant for realization. In many cases, some constituents are parts of the core realizer, some constituents are not.

Figure 1.4-3 Figure 1.4-2

According to the dimensioned view, variation in the composition of a higher-level property provides a case for real multiple realization. Almost any level of compositional difference between realizer systems is taken to be relevant. This is because on this view ‘‘realization is a transitive relation’’ (Aizawa & Gillett 2009:194) as composition is a transitive relation27_{. Let’s take the example of mechanical hardness. On this account even the small}

differences in the metal lattice of two samples of the same original cast iron bar count as a case of multiple realization for the same hardness property, because the exact configuration of the constituent particles and the exact positions of point and line dislocations in the metal lattice are different. This is maybe the most frequently criticized aspect of the theory28_{. Here,}

I will take it as an accepted theoretical option.

Let us evaluate the example of corkscrews in the context of the Dimensioned view. For case (a) the verdict is unambiguous, waiter’s and winged corkscrews multiply realize corkscrews. However, I should highlight that in this framework the realizer is not the winged corkscrew as whole, instead, the pointed helix, the arms, and the rack, and their properties together realize a variant of corkscrew. The relevant properties of these parts are qualitatively different from the realized property (capacity for cork removal). In scenario (b) where there is a difference in the material composition of the two items, there is real multiple realization again, as the items are made of different metals, even though mechanically they are the same. On the compositional view, there is no principled difference between mild and robust cases of multiple realization or in a different parlance, between uninteresting variation and multiple

27 _{If one takes the realization relation as a species of determination relation the assumption is even more natural.} 28 _{In this view multiple realization is way more ubiquitous than on the flat view. Critics like Polger and Shapiro}

say that it is correspondingly less obvious that it is metaphysically significant as the original question by Fodor was relativized to scientific kinds at this or that level of description.

realization proper. The only case the dimensioned view dismisses is (c) where the otherwise identical items have different colours, because the variation between the realizer instances is irrelevant for the realized property in question.