Compositional Realization

Over the last 40 years or so, analytic metaphysicians,

philosophers of mind, and philosophers of science have developed

a number of distinct conceptions of “realization” and “multiple

realization”. In my talk today, I want to introduce the

conceptions that Carl Gillett and I have been working with, then

indicate what seem to me to be some features of the conceptions

that should make them of interest to some of the philosophers at

this workshop. More concretely, I propose that our accounts of

realization and multiple realization reveal how multiple

realization is possible (a topic discussed by Bob Batterman in

his “XXX”). Our accounts of realization and multiple realization

complements the account of selected function realization defended

by Block, Papineau, and Rosenberg. Our accounts of realization

and multiple realization, unlike the theory of selected function

realization, is also applicable in the philosophy of chemistry.

In advancing what seem to me to be the virtues of our accounts of

realization and multiple realization, I will be venturing a bit

out of my comfort zone. I know a little bit about chemistry, but

I am by no means a philosopher of chemistry. I know a little bit

about biology, but I am by no means a philosopher of biology. I

now a little bit about physics, but I am by no means a

philosopher of physics. So, in venturing out a bit, I would be

very interested in guidance from those with more expertise in

these areas.

1.0 Some Context

Recent work by Endicott (2005, 2012) and Gillett (2010) draw

attention to that fact that distinct philosophical traditions

have develop at least three distinguishable “families” or

“clusters” of concepts of realization. There is a tradition in

analytic metaphysics deriving most notably from Tarski, 1956, and

Lewis, 1972, that conceives of realization as a satisfaction

relation that obtains between entities in the world and certain

sorts of sentences. Gillett calls this “L-realization.” There

is also a mathematical tradition, drawn upon in, for example,

Putnam, 1975, that understands realization to be an isomorphism

relation. Gillett calls this “I-Realization.” Third, there is a

tradition in the philosophy of science and philosophy of mind

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that conceives of realization as a species of determination or

generation relation wherein some properties are determined by or

generated by others. Gillett calls this “M-Realization.”

Much work on the theory of realization over the last decade

or so falls into the category of M-realization coarsely

construed. One species of M-realization is what is sometimes

called “Subset-realization.” Kim, 1998, Shoemaker, 2001, 2003,

and Wilson, 2009, among others defend this. According to this

view—very roughly and incompletely presenting the matter—one

property's realizing another is simply a matter of its forward-

looking causal features including as a subset the forward-looking

causal features of the realized property. Another species of M-

realization is what we might called “Selected Function

Realization.” Papineau, 1993, 2010, Block, 1997, and Rosenberg,

2001, among others defend this. According to this view—again

very roughly and incompletely presented—a property—a selected

function—is realized by another property that has that selected

function. So, a photoreceptor cell will have a particular light

absorption spectrum. This is a physical property. Should

natural selection confer on this cell the function of being a

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short-wavelength sensitive cone, then the cell’s light absorption

spectrum will be said to realize the function of being a short-

wavelength sensitive cone. Yet a third theory of M-realization

is what I am today calling “Compositional Realization.” This

theory, developed in Gillett, 2002, 2003, and applied in, for

example, Aizawa and Gillett, 2008, 2011a, and 2011b, is more

commonly known as the Dimensioned view of realization. According

to this view—again very roughly and incompletely presented—an

individual has a property in virtue of its parts having

properties and relations.

The accounts of realization and multiple realization that

Gillett and I have been working with are, in truth, part of a

more expansive framework that is meant to describe the

compositional concepts deployed in actual scientific theorizing.

So, in addition to the theory of realization for properties,

there are accounts of individuals and processes. So, in our

framework, there are four types of entities: individuals,

properties, processes, and powers. Individuals stand in

constitutive relations, properties stand in realization

relations, processes stand in implementation relations, and

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powers stand in comprising relations. Moreover, we maintain that

the sciences have implicit conceptions of multiple constitution,

multiple realization, multiple implementation, and multiple

comprising.

Since our accounts are meant to describe the compositional

concepts deployed in actual scientific theorizing, we take it

that our accounts are to be evaluated in terms of their adequacy

for describing actual science and scientific theorizing. And,

in fact, what I will try to do today is show some of the respects

in which I believe that our accounts of realization and multiple

realization cast light on science and scientific theorizing.

Given our aspirations for our accounts, it is probably worth

emphasizing what we think is largely irrelevant to our project.

In particular, we do not think that our accounts must be

responsive to everything that has been said about realization in

the philosophical literature. As noted above, different

philosophical traditions have developed different concepts of

realization to different ends. Nor do we think that our accounts

must be responsive to “philosophical intuitions” about what is to

count as realization and multiple realization. Indeed, we are

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sometimes concerned to show that philosophical imagination is

sometimes misguided about the character of actual scientific

theory and practice. (See, for example, Aizawa and Gillett,

2001a.) To repeat, the primary goal of our framework of

compositional relations in the sciences is to provide an

illuminating account of actual scientific theory and scientific

theorizing.

2.0 The Dimensioned View of Realization and a Theory of Multiple

Realization.

The Dimensioned view of realization maintains that

realization is a kind of compositional determination relation

wherein properties at one level determine properties at a higher

level (see, for example, (Gillett, 2002, 2003)).1 More

technically, it proposes that

Property/relation instance(s) F1-Fn realize an instance of aproperty G, in an individual s under conditions $, if and only if,under $, F1-Fn together contribute powers, to s or s’s

1 This theory of realization, thus, has affinities with theories of mechanistic explanation. See, for example, (Bechtel & Richardson, 1993), (Glennan, 1996, 2002), (Machamer, Darden, & Craver, 2000), and (Craver, 2007).It also involves a highly detailed theory of levels articulated in (Gillett, unpublished). Because the theory cannot be presented adequately in the space of even a few pages, the interested reader is encouraged to obtain a copy of Gillett’s paper.

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part(s)/constituent(s), in virtue of which s has powers thatare individuative of an instance of G, but not vice versa.

This can be a daunting formulation, but the core idea is simple:

individuals have properties in virtue of the properties of their

parts. Take a simple case. A molecule of hydrogen fluoride (HF)

has an asymmetric charge distribution, a dipole moment, of 1.82

debye (D) (Nelson, Lide, & Maryott, 1967, p. 11). It has this

property in virtue of properties of the hydrogen and fluoride

atoms (their electronegativities) and the way in which those

atoms are bonded together.

This is a theory of realization, but we also need a theory

of multiple realization. Roughly speaking, multiple realization

occurs when one set of property instances F1-Fn realizes an

instance of G and another set of property instances F*1-F*m

realizes an instance of G and the properties in the two sets are

not identical. One slight refinement is in order, however, to

take account of the fact that a neuronal realization and a

biochemical realization of pain would not constitute a case of

multiple realization. To refine the account, one can add that

the two distinct realizers that multiply realize G must be at the

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same level.2 The official formulation of multiple realization

is, therefore, that

A property G is multiply realized if and only if (i) under condition $, an individual s has an instance of property G in virtue of the powers contributed by instances of properties/relations F1-Fn to s, or s’s constituents, but not vice versa; (ii) under condition $* (which may or may not beidentical to $), an individual s* (which may or may not be identical to s) has an instance of property G in virtue of the powers contributed by instances of properties/relations F*1-F*m of s* or s*’s constituents, but not vice versa; (iii)F1-Fn ≠ F*1-F*m and (iv), under conditions $ and $*, F1-Fn of s and F*1-F*m of s* are at the same scientific level of properties.

To illustrate multiple realization we may return to the property

of having a dipole moment of 1.82 D. HF has this property in

virtue of the electronegativities of H, F, and the bond between

them, but chlorofluoromethane (CH2ClF) appears to have the same

dipole moment in virtue of the electronegativities of C, H, Cl,

and F and the bonds between them (cf., Nelson et al., 1967, p.

16). This is apparently a case of multiple realization.3

2 This is one respect in which multiple realization requires more than that there be one realized property and a diversity of realizer properties. 3 The qualifier “appears” is needed, since the dipole moments are experimentally determined values. Thus, it could be that HF and CH2ClF have the exactly same dipole moment or it could be that HF and CH2ClF have the samedipole moment to within the limits of experimental error. In the latter case, we would not have an example of multiple realization.

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3.0 How Multiple Compositional Realization is Possible

One virtue of our accounts of realization and multiple

realization is that they reveal ways in which multiple

realization is possible. In fact, there seem to be three ways in

which multiple realization arises. There is, in psychology at

least, what we might call “multiple realization through

individual differences,” “multiple realization by orthogonal

realizers,” and “multiple realization by compensatory

differences.” While there are probably many examples that could

be offered of each type of multiple realization, I will give only

one example of each. Other examples are developed in Aizawa and

Gillett, 2011a, 2011b, and Aizawa, 2013.

3.1 Multiple Realization through Individual Differences. Human vision is

trichromatic. It involves the integration of signals from three

types of cones, sometimes these are called S-, M-, and L-cones,

for short-, medium-, and long-wavelength photoreceptors.

Sometimes they are called blue, green, and red cones.

Trichromacy involves many different realizers, but present

purposes will be served by looking at properties of the cones of

the retina. A number of studies have documented the existence of

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polymorphisms in the green and red photopigments.4 For the red

photopigment, it has been estimated that roughly 44% of the

population of European descent has an amino acid chain that has

an alanine at position 180, where about 56% of the population of

European descent has an amino acid chain with a serine at

position 180. These two variants are often designated Red

(ala180) and Red (ser180), respectively. For the green

photopigment, it has been estimated that roughly 94% of the

population has an amino acid chain that has an alanine at

position 180, where about 6% of the population has an amino acid

chain with a serine at position 180.5 These variants are often

designated Green (ala180) and Green (ser180), respectively. In

addition, each of these distinct photopigment molecules will have

distinct light absorption spectra. So, for example, (Merbs &

Nathans, 1992) report that the wavelength of maximum absorption

for Red (ala180) is 552.4 nm and that for Red (ser180) is 556.7.

These differences in cone opsins lead to corresponding

differences in the photoreceptors that contain them.

4 See, for example, (M. Neitz & Neitz, 1998), (Sjoberg, Neitz, Balding, & Neitz, 1998), and (Winderickx et al., 1992). 5 This composite data is assembled in (Sharpe, Stockman, Jägle, & Nathans, 1999).

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With this configuration of properties, vision scientists

propose that trichromacy is realized (along with many other

properties) by four distinct combinations of properties:

Absorption spectrum of Red (ala180), absorption spectrum of Green (ala180),

Absorption spectrum of Red (ala180), absorption spectrum of Green (ser180),Absorption spectrum of Red (ser180), absorption spectrum of Green (ala180),Absorption spectrum of Red (ser180), absorption spectrum of Green (ser180),

Many philosophers appear to assume that this configuration will

lead vision scientists to postulate four types of trichromacy,

but they do not. Instead, vision scientists use the variations

among the lower level absorption spectra to explain individual

differences among trichromats. Vision scientists are quite

explicit about this when it comes to trichromacy. He and

Shevell, 1994, for example, write

The color matches of normal trichromatic observers show substantial and reliable individual differences. This implies the population of normal trichromats is not homogeneous, an observation that leads to the question of how one normal trichromat differs from another. … individual differences among normal trichromats are due in part to receptoral variation (He & Shevell, 1994, p. 367).6

6 Recall the claim from a footnote at the start of this section that one can rework the arguments of this section mutatis mutandis for the property of having trichromatic vision. The passage from He and Shevell supports this

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So, differences in lower level properties give rise to

differences in some higher level properties, but not others.

There is no difference in the possession of trichromatic vision.

There are, however, differences in fine color discrimination

capacities. The differences in higher level properties are

treated as individual variations in color discrimination

capacities. Moreover, the individual differences are explained

by differences among the realizers.

3.2 Multiple Realization by Compensatory Differences. Consider, now, a

second way in which multiple realization arises. The Dimensioned

theory of realization recognizes that, in many scientific cases,

a single property instance G can be realized by a set of property

instances F1-Fn.7 This “teamwork” of realizers suggests one way

that multiple realization can arise, namely, by “compensatory

differences”. The idea is that sets of properties F1-Fn and F*1-

F*m may be such that the differences between F1-Fg and F*1-F*i and

contention.7 This is a feature that Dimensioned realization shares with extant accounts of mechanistic explanation, wherein a single phenomenon or property is explained by the joint action of multiple entities. See, for example, (Machamer et al., 2000) and (Craver, 2007).

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between Fh-Fn and F*j-F*m “counterbalance” each other. Two

examples should make this clearer.

Set aside the “coarse grained” property of trichromacy in

favor of a “fine grained” property of having emmetropic vision.

This is a state in which an object at infinity is in sharp focus

with the crystalline lens in a neutral or relaxed state.

Emmetropia requires a balance between the refractive power of the

lens, on the one hand, and the axial length of the eye, on the

other. In addition, the refractive power of the lens depends on

the curvature of the front and rear surfaces of the lens and the

refractive indices of the internal components of the lens.

Throughout a normal human’s life, the crystalline lens grows

in such a way that it bulges along its central axis. This growth

is isolation leads to changes the refractive power of the lens,

which, in turn, suggests that aging will typically lead to

increasing near-sightedness. Of course, as is well known, aging

does not typically lead to increasing near-sightedness, but to

increasing far-sightedness. This is the so-called “lens

paradox.” How can it be that the aging lens typically changes in

shape to favor a decreasing focal length, which should lead to

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near-sightedness, when aging humans typically experience far-

sightedness, which implies an increasing focal length?

The most likely resolution of the paradox involves

postulating changes in the refractive indices of the internal

components of the lens in such a way as to overcompensate for the

changes in the shape of the lens.8 Our second way in which

multiple realization is possible is through compensatory

differences. In this situation, vision scientists postulate that

the lens has a single “fine grained” property of having a

particular focal length which can result from multiple distinct

combinations of lens shape and refractive indices of the internal

components.

3.3 Multiple Realization by Orthogonal Realizers. For our third way of

integrating realizers with the realized, we need to draw a

distinction between two types of realizers: Parallel realizers of

G and orthogonal realizers of G. A property F is a parallel

realizer of G if, and only if, small variations in the value of F

will lead to corresponding changes in the value of G. A property

F is an orthogonal realizer of G if, and only if, small

8 See, for example, (Moffat, Atchison, & Pope, 2002).

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variations in the value of F will not lead to corresponding

changes in the value of G.9 Let me provide an example of each

type of realizer.

Earlier we noted that the color discriminations one makes

are realized by, among other things, the absorption spectra of

cones. Take the absorption spectrum of a red cone. Slight

variations in the absorption spectrum will lead to slightly

different color discriminations among individuals with normal

color vision. Nevertheless, among those with normal human color

vision there remain differences in color discrimination

capacities. The absorption spectra of the red cones are parallel

realizers of color discrimination capacities. Moreover, these

are the kind of realizers that philosophers seem to have in mind

in their skeptical thinking about multiple realization. Slight

variations among realizers, such as cone opsin absorption

9 In truth, it can be problematic to specify what a “small” variation is.  So,for example, regarding parallel realizers, it could be that very, very tiny shifts in the absorption spectrum of the red cone opsin do not, for one reasonor another, make for differences in color discrimination capacities. In addition, regarding orthogonal realizers, at some point, sufficiently large changes in, say, the binding constant of transducin (see below), will lead to a property that is no longer a realizer property. It is unclear how this issue can be resolved, so that the account that we now have on the table is, at best, a rough approximation.

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spectra, will lead to slight variations in the realized property,

such as color discriminations, so that this will preclude the

multiple realization of a specific color discrimination capacity.

Orthogonal realizers, however, work differently. To

appreciate them, we need to look to some of the other realizers

of normal color vision, such as the properties of one component

of the mechanism of phototransduction. Upon absorption of a

photon, a single photopigment molecule will change conformation

from 11-cis- retinal to all-trans-retinal. After this

conformational change, the retinal chromophore is released into

the cytosol, while the opsin fragment remains embedded in the

cell membrane in an activated state. The activated opsin binds to

a single transducin molecule located on the inner surface of the

cell membrane. This transducin molecule, in turn, activates a

molecule of an enzyme, cGMP phosphodiesterase. There is more to

the phototransduction story, but this remainder is inessential to

the idea of orthogonal realizers.10

Notice that the properties of the transducin are among the

realizers of normal human color vision. The capacity for normal

10 For more details, see (Aizawa & Gillett, 2011) or (Kandel, Schwartz, & Jessell, 2000).

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color vision depends on the capacities of the transducin

molecules. Without the properties of transducin, there would be

no color vision. Next notice that the properties of transducins

can vary. They can vary in their binding affinities to cGMP-

phosphodiesterase. But, here is the fact that is philosophically

interesting: small changes in these binding affinities will not

change the color discriminations one makes. This means that the

binding constants for transducin molecules are orthogonal

realizers. What this means is that one can have two individuals

who are exactly alike, save for having different tranducin

binding constants, but who make exactly the same color

discriminations.

4.0 Batterman’s Treatment of the Possibility of Multiple

Realization

In “Multiple Realization and Universality,” Bob Batterman

proposes to explain how multiple realization is possible.

Nevertheless, his efforts do not map perfectly onto mine. To

make out this point, I want to greatly simplify Batterman’s

account in ways that are, I hope, illuminating, rather than

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distorting. He groups together two types of cases that I

distinguish. This is the case of pendulums and cases of

asymptotic regularity. The case of pendulums appears to work

without a notion of M-realization, where the cases of asymptotic

regularity appear to work with a notion of M-realization.

Of pendulums, Batterman, in essence, asks two questions.

First, why is it that two pendulums that are exactly alike except

differing in color can nevertheless be governed by the same

simple law of the pendulum, i.e. by the law that P = 2π√(l/g),

where P is the period, l is the length of the bob, and g is the

force of gravity. Here the answer is clear: color is irrelevant

to the period of a pendulum. Batterman’s second question is “Why

is color irrelevant to the period of a pendulum? This, however,

is a more subtle question, one for which Batterman brings in the

apparatus of renormalization group transformations.

Next notice that the first question is plausibly construed

as a question about how multiple realization is possible. Put

vaguely, how can there be sameness (of behavior) in the face of

diversity (in the properties of pendulums)? The second question,

however, is not really a question about multiple realizability.

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It is not a question about sameness in the face of diversity.

Both questions have their place in the broader scheme of

philosophy of science, but since I am focusing on multiple

realization, let me focus on Batterman’s first question.

Batterman’s question about how multiple realization is

possible is actually not the same as my question about how

multiple realization is possible. Batterman’s question does not

have a presupposition that my question does. Batterman’s

question is how it is possible that two individuals can differ

while still realizing the same property. Answer: the individuals

can differ in irrelevant properties. By contrast, recall that

Carl and I are part of the M-realization tradition. That means

that we take realization to involve the determination or

“generation” of one property by one or more other properties. We

take it that realization is a non-logical, non-causal

determination relation. So, when we ask how multiple realization

is possible, we are setting aside the irrelevant properties of

individuals. Those properties are not what we take to be

realizers. Color is not a realizer of the behavior of a

pendulum, because it does not determine the behavior of a

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pendulum. Color is not a realizer of the period of a pendulum,

because it does not determine the period of the pendulum. For

Carl and myself, the question of how multiple realization is

possible is the question of how there can be one and the same

realized property in the face of a diversity of determining

properties. And, each of our three answers to how multiple

realization is possible relies on lower level properties that

scientists take to determine a single higher level property.

Here is another way of making the point. Larry Shapiro has

repeatedly urged the point that two corkscrews that differ in

color do not count as multiple realizations of the property of

being a corkscrew. The reason is that color is irrelevant to

being a corkscrew. Color is not a property that realizes the

property of being a corkscrew. (Why color does not realize the

property of being a corkscrew is another matter.) We have

completely taken Shapiro’s point to heart. Our question is about

how a single higher level property can be determined by distinct

sets of lower level determining properties.

Of asymptotic phenomena, Batterman offers a superficially

similar explanation for the possibility of multiple realization.

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At one point, Batterman writes as if the asymptotic cases of

multiple realization get the same treatment as the pendulum case.

More interesting cases arise, as we will see, when many (if

not most) of the variables our theory requires for a

complete state description are not relevant for explaining

the behavior of interest. In fact, specifying all of the

details required for a complete state description may

actually detract from, or even block the desired

explanation. However, were one to think quasi-historically

about the development of classical mechanics, one would see

that there really is no difference between the example of

the pendulum and some of the more interesting cases we will

consider shortly. (Batterman, 2000, p. 121).

If, however, we attend closely to Batterman’s exposition of the

cases, a different picture emerges. So, Batterman writes,

Certain limit theorems of probability theory … describe

certain asymptotic regularities of mass, or collective

behavior that obtain, in effect, independently of the details

of the contributions from the individuals in the collective.

For example, let m be the number of occurrences of an event

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(e.g. heads) in n independent trials for which the

probability of the event on each trial is p where 0 < p < 1.

The De Moivre–Laplace limit theorem … describes the

collective behavior of a sequence of independent trials,

where the individual contributions to the limit become more and more

insignificant as the number of trials increases. This is an important

feature—the asymptotic regularity displayed by the normal

distribution law is in essence independent of the details of

the individual trials. (ibid.)

Then later, “So, limit theorems of the De Moivre–Laplace sort

give expression to the fact that the dominant features are

collective features and the individual values are, by and large,

irrelevant” (ibid., p. 122) and “These limit theorems describe

behavior that is largely independent of the details of the

‘interactions’ at the level of the individual components” (ibid.)

(See also comments on p. 123.)

Notice the italicized qualifications. Batterman does not

say that the contribution of single individuals or individual

trials are irrelevant simpliciter. Instead, they are “in effect” or

“by and large” irrelevant. In the limit, they “become more and

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more insignificant.” They are, in this regard, unlike the color

of the pendulum or the corkscrew. The color of the pendulum and

the corkscrew are irrelevant simpliciter. In fact, this difference

in description seems to me to mark something theoretically

important. It seems to me that, where the color of a pendulum is

not an M-realizer of the property of being a pendulum, the

individual values of some variables in some systems are sometimes

M-realizers of properties of some collectives.

I am sure that Carl and I do not want to take on board the

full range of cases that Batterman entertains. (So, for example,

our theory is that realization is a non-logical, non-

mathematical, non-causal determination relation. One of

Batterman’s examples is of the limit of a sequence of coin

tosses. Insofar as this involves a mathematical determination

relation, it is not an instance of what we mean by M-

realization.) Nevertheless, we can see some of what Batterman

describes in cases of M-realization.

Part of what Batterman apparently has in mind is that

multiple realization can arise through a kind of “swamping” of

the contributions of individual components. So, we can have this

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kind of multiple realization by having different numbers of cones

in the retina. Each cone contributes an M-realizing property

(e.g. a particular light absorption spectrum) to, say, the

trichromacy of the eye, yet each such contribution is “swamped”

by the contribution of the M-realizing properties of other cones.

This may be what is involved in multiple realization by

individual differences. In addition, Batterman seems to have

some idea of the individual contributions of the components

offsetting each other in the limit. So, the same limit might be

reached by the toss of a “head” at one point in a sequence being

offset by the toss of a “tails” at another point in the sequence.

The same temperature of a gas might be reach by the kinetic

energy of one molecule of the gas being offset by the kinetic

energy of another molecule of the gas. This may be a special

case of multiple realization by compensatory differences.

The foregoing comments are not worked out in detail. They

suppress a lot of technical detail in Batterman’s work, but also

a lot of the technical details in our theory of compositional

relations in the sciences. Still, I think one can see the value

of our theory for illuminating issues of realization and multiple

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realization and how it can illuminate the kinds of cases

Batterman examines.

5. Rosenberg’s Treatment of Selected Functions

A number of philosophers (for example, Block, Papineau, and

Rosenberg) have favored the view that so-called “selected

functions” might be multiply realized. Take an example.

Consider four photopigment molecules, the most common green

photopigment and three hybrids we may refer to as R2G3,

R3G4(Ala180), and R4G5(Ala180). All of these photopigments have

very similar absorption spectra. Each of their peak

sensitivities—their values of λmax—are within a few nm of each

other.

Photopigment λmax (nm)

Green 529.7

R2G3 529.5

R3G4(Ala18) 529.0

R4G5(Ala180) 531.6

Next assume that each of these photopigments has the selected

function of being, say, a medium-wavelength photopigment. The

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thought shared by a number of philosophers is that natural

selection confers a single selected function upon all these

photopigments because of their similar absorption spectra.

Natural selection, thus, provides an explanation of how multiple

realization is possible. Here is how the explanation goes in

Rosenberg, 2001:

Natural selection "chooses" variants by some of their

effects, those which fortuitously enhance survival and

reproduction. … As a result of random physical processes—

mutations—among such replicating and interacting molecules,

there are frequently to be found multiple physically

distinct structures with some (nearly) identical rates of

replication, … Over finite periods of time, nature can

select at most for functional similarity, not perfect

identity. Any two or more physical systems that solve a

"design problem" well enough to allow for some minimal level

of survival and reproduction rates will be selected. If

there are at least two local optima in an adaptive

landscape, and if mutation, recombination, drift, and

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selection can find them, the result will be causally

different multiple realizations. (Rosenberg, 2001, p. 366).

In short, multiple realization occurs because there are multiple

physically distinct structures with similar causal powers, hence

capable of serving the same function.

There may, or may not, be problems with a selected functions

account of multiple realization. I will not pursue those sorts

of questions here. What I do want to note is that, if you accept

the foregoing sort of account, it appears you still need

something like our theory of compositional realization and

perhaps the idea of compensatory differences that naturally

accompanies it. Getting to this point will take a few steps, so

please bear with me.

Notice, to begin with, that part of what is implicit in the

foregoing story is the availability of multiple physically

distinct structures with similar causal powers, hence similar

rates of replication. For this account of multiple realization

to work, there have to be two or more physical systems that solve

a “design problem” well enough. The point of this observation is

not to challenge it. There clearly is such variability, at least

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in the case of proteins. This is now an exceptionally well-

attested fact.

Now, many philosophers thinking about multiple realization

have dismissed this pervasive sort of variability as “not

counting” as multiple realization and imply that it is

philosophically uninteresting. Shapiro, 2008, Shapiro and

Polger, 2013, and Maley and Piccinini, 2014, seem to dismiss such

variability for no reason at all. Balari and Lorenzo, 2014, seem

to dismiss such variability because of its pervasiveness. They

write,

Discussions on the multiple realizability of a given

psychological category (say, pain or vision) cannot be based on a

raw notion of “variability,” as variation unexceptionally applies

to every single organic phenomenon. (Balari and Lorenzo, 2014,

p. 2).

But, rather than dismiss the pervasive physico-chemical

variability implied by Rosenberg’s account, one might well wonder

how and why it exists. If such variability is such a pervasive

feature of life, one might well wonder why it is such a pervasive

feature of life. Take, as a special case, the variability of

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proteins. Why are so many proteins able to solve a similar

“design problem”? (What function, if any, is served by the

capacity of proteins to solve similar “design problems”?) How is

it that so many proteins are able to solve a similar “design

problem”?

So, why are so many proteins able to solve a similar “design

problem”? What function does this serve? Here are two

speculative answers. First, this plasticity generates greater

variability in the gene pool and, second, it provides for greater

fault tolerance in the reproductive mechanisms. Evolution by

natural selection requires differential reproduction of heritable

variation. A diversity of proteins with similar physico-chemical

properties means that selection in favor of any one gene will not

be quickly eliminated from the gene pool. Diversity in the gene

pool enables natural selection to explore a range of different

possible adaptations. Second, because many proteins have similar

physico-chemical properties, it is possible for minor

malfunctions in the manufacturing of proteins from DNA to yield

functional proteins.

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So, there seem to me to be some plausible accounts of why it

would be adaptive for similar proteins—proteins with similar

primary sequences—to have similar physico-chemical properties.

Surely there are many details to be added to such a story,

provided it is on the right track. Perhaps there are other

accounts as well.

Consider, now, how it is that different proteins can share

similar physico-chemical properties. As many an introductory

textbook of biochemistry or cell biology will explain, the

properties of proteins are a function of their amino acid parts

and the way in which those parts are put together. Each protein

consists of a chain of amino acids covalently bonded together in

a sequence. The core of a protein is a polypeptide backbone to

which are attached one of 20 side chains. Proteins can, thus,

differ in the sequence and number of amino acids in their chain.

In addition, the amino acids vary in their size, whether they are

positively or negatively charged, and whether they are polar or

non-polar.

One account of why similar proteins—proteins with similar primary

structure—have similar physico-chemical properties is that

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constituent amino acids are very similar. So, for example,

aspartic acid and glutamic acid are both acidic side chains

differing only in a methyl group, hence differing primarily in

size. Asparagine and glutamine are both uncharged polar side

chains, again differing only in a methyl group, hence differing

primarily in size. Thus, two proteins that differ only in

containing aspartic acid rather than glutamic acid, or asparagine

rather than glutamine, might differ only slightly and in

proportion to the difference in the physical properties of their

amino acids. Perhaps this sort of understanding covers some

cases, but there is another possibility. This is where the idea

of compensatory differences comes in.

Presumably the differences in proteins are not (always) just

the sum of the differences in their proteins. The amino acids

interact among themselves. Sometimes the effect of an amino acid

switch is greater in one context than in another context.

Have to include error terms

Mean lamba max

R3G4(Ala180) 529.0 Difference: 4.3 nm

R3G4(Ser180) 533.3

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R4GW(Ala180) 531.6 Difference: 4.4 nm

R4G5(Ser180) 536.0

Red(Ala180) 552.4 Difference: 4.3 nm

Red(Ser180) 556.7

G2R3(Ala180) 549.6 Difference: 3.4 nm

G2R3(Ser180) 553.0

Lambda half max

R3G4(Ala18) 579.6 Difference: 1.7 nm

R3G4(Ser180) 581.3

R4GW(Ala180) 581.4 Difference: 4.1 nm

R4G5(Ser180) 585.5

Red(Ala1w) 607.3 Difference: 4.8 nm

Red(Ser180) 612.1

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G2R3(Ala18) 604.4 Difference: 4.6 nm

G2R3(Ser'1°) 609.0

Are these differences statistically significant

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