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SOLVING THE CIRCULARITY PROBLEM FOR FUNCTIONS

(A RESPONSE TO NANAY)

Bence Nanay1describes a circularity problem that the etiological theory of biological

functions is said to face.2The etiological theory of biological functions holds that a token

traits function depends on what traits of the relevant type were selected for. The

function of a heart is to pump blood only if traits of its type were selected for pumping

blood. Circularity sets in if we then classify traits into the relevant typesi.e., the types

relevant for the purpose of ascribing functions on the basis of their functions. That is,

if a heart is (constitutively) an organ that has the function of pumping blood and if a heart

has the function of pumping blood because (constitutively) it is a heart (and hence an

organ that has the function of pumping blood) then there is a problem of circularity.3

Nanay also holds that a good theory of functions should meet three desiderata: (1)

that a trait be allowed to have more than one function (e.g., feathers can have the function

in flight and also the function of thermoregulation), (2) that the function attributions that

we make be allowed to depend on our explanatory projects (e.g., if we are interested in

how eagles catch mice, we might be more interested in the aerodynamic function of

feathers than their function in thermoregulation) and (3) that malfunction be possible, so

that a token trait can have the function of performing F even though it cannot perform F

(e.g., a broken wing that does not enable flight can nonetheless have the function of

enabling flight).

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We agree with these desiderata,4but they are not exhaustive. Another

desideratum is that the theory gives correct function attributions. It must at least get them

approximately right, if it is to be considered in the running. There is room for some

revision but not for whole scale revision.Similarly, it is not enough to provide for the

possibility of malfunction. Our theory should entail that malfunctioning traits are

malfunctioning and that traits that are functioning normally or properly are not

malfunctioning. The usual view is that the standards for normal or proper functioning

cannot be found by peering at a token trait.

Nanay rejects the usual view in order to solve the circularity problem. He suggests

that we can avoid this problem by offering an account according to which functions

depend on facts pertaining to tokens only. This allows the analysis of functions to remain

silent on the individuation of trait types. Here we offer counterexamples to Nanays

analysis and more important, show how the etiological analysis solves the circularity

problem that it is alleged to face.

I. THE MODAL THEORY

On Nanays modal theory, the functions of token traits do not depend on what is true of

traits of the type. Instead, they depend on counterfactuals that pertain to trait tokens,

regardless of what is true of any other traits of the same type.

On Nanays modal theory, performing F is a function of an organisms (Os) trait

[token], x, at time t if and only if:

1. There is a relatively close possible world, w, where [token] x is doing F at t.

2. Doing F at t contributes to Os inclusive fitness in w.

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3. This world, w, is closer to the actual world than any of the possible worlds in

which x does F at t but this does not contribute to Os inclusive fitness.

Consider how this proposal provides for the possibility of malfunction. An

eagles broken wing is not broken in some relatively close possible world. In that world,

other things being equal, the eagle would be able to fly and its ability to fly would

contribute to its fitness. Further, a world in which this eagle can fly and flying

contributes to its fitness is closer to the actual world than one in which it can fly but this

does not contribute to its fitness. So, on Nanays analysis, this particular wing of this

individual eagle has the function of flight, even though this eagle cannot fly.

Note that, although Nanay leaves the notion of a relatively close world vague,

worlds must count as relatively close if the difference to the actual world is no greater

than any change required to avert malfunction (or else his theory cannot accommodate

actual malfunctions). This, as we will see, is a problem.

Like over half of all humans, one of us (A) is lactose intolerant. On Nanays

analysis, the mechanisms that make A lactose intolerant (unable to digest lactose as an

adult) must have the function of providing lactose tolerance (an ability to digest lactose as

an adult). Why is that, and why is it a problem?

A little human natural history makes clear why. Long ago in mammalian

evolution there was selection for turning off the lactose operon system in adults. It is

normal in mammals, including most humans, to begin producing less of the lactase

enzyme (needed for digesting lactose) after weaning. Quite recently in human evolution

circumstances made it advantageous to change this. It became advantageous to keep the

system on, allowing lactase to be produced in adults. This lactase persistence can give

adults year round access to food in certain regions (i.e., those with access to domesticated

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milk producing animals or their products). Making it advantageous of course is not the

same thing as making it happen. That would be a version of Lamarckian evolution. But

owing to improbable events at the level of the nucleotide (ones that happened twice on

chromosome 2, first about 7-9,000 years ago and again separately in the last 3000 years,

at different nucleotide sites in the region of chromosome 2 in the human genome) the

pathway that shuts down lactose digestion in adults was disabled, and the continuing

ability to digest lactose was enabled in certain (originally Balkan but later) Nordic

populations and certain sub Saharan African ones. Lactase persistence has not yet been

driven to fixation. As yet it is present in only a minority of the human population.

This succession of events confers on the mechanisms responsible for As lactose

intolerance the function of making him lactose tolerant (i.e., the function of enabling him

to digest lactose as an adult) on Nanays theory, for the mechanism satisfies all three of

Nanays modal requirements.

1. There is a possible world, w, in which A is able (as an adult) to digest lactose. It

is a world in which there was a point mutation in a cell from which A (or one of

his ancestors) developed. It is a relatively close world.

2. In w, digesting lactose contributes to As inclusive fitness.

3. World wis closer to the actual world than other worlds in which A digests

lactose but this does not contribute to As fitness.

Note that if the point mutations occurrence is an event governed by probabilistic laws,

then wdiffers from the actual world, not in any laws, nor in any initial conditions, nor

even in its history, up until the indeterministic point mutation that made A lactose

tolerant in adulthood in w. So it is a relatively close possible world. The closeness of

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worlds is notoriously hard to measure but this is about as close as possible worlds can

get.

Certainly, wis closer than a world where A is lactose tolerant in adulthood but

where that is a selectively neutral or a fitness reducing fact about A. For such worlds are

ones in which the laws are different or there are more differences in history or in our

current environment. Accordingly, if Nanay is right, the function of the mechanisms

responsible for As adult lactose intolerance is adult lactose tolerance and the relevant

mechanisms in A, in the actual world, are malfunctioning. This is not the right outcome.

It is normal for A, given his ethnicity, to have adult lactose intolerance.

For every malfunctioning token trait, Nanays theory requires that there be a

relatively close possible world in which it is not malfunctioning (e.g., a world in which

the eagle did not break its wing). At the same time, for every token trait that is

functioning normally (e.g., the shut-down of As lactose tolerance) the modal theory

requires that there be no relatively close possible world in which it is improved in some

fitness enhancing way (e.g., As lactose operon system does not shut down).

The problem is that relatively close with respect to possible worlds remains

hopelessly ill defined in Nanays theory and it is hard to see how any more precise

definition would help. One can of course deploy it in a circular fashion as follows. If the

possible world is just like ours, except that a trait that is actually malfunctioning in our

world is functioning properly in that world and all else is otherwise as similar as it can be

(consistent with this) then count that world as relatively close. But if the possible

world is just like ours, except that a trait that is functioning normally in our world is

improved upon in a fitness enhancing way and all else is otherwise as similar as it can be

(consistent with this) then count that world as too far away. However, thisis circular.

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This is a very general problem for the modal theory. Consider every beneficial

mutation that will occur in every species on Earth in the near future (in evolutionary

terms). For each such beneficial mutation, there is something beneficial, F*, that a token

trait will one day do, which traits in its lineage are presently unable to do. They can now

do F, but not F*. Many of these beneficial things that these future traits will do would be

beneficial if done now in the current environment. Many would contribute to fitness if

done now. And the possible worlds in which these traits do these beneficial things now

are relatively close possible worlds. They are as alike to our world as can be, except for

the fact that a beneficial mutation that will actually occur soon will in these worlds have

occurred sooner. These worlds are no further away than any world in which a damaging

mutation that actually occurs and that actually leads to malfunction does not occur.

Moreover, the worlds in which these improved traits do these beneficial things that

contribute to fitness is closer to the actual world than any world in which they do these

beneficial things and this does not contribute to fitness. On Nanays theory of functions,

it follows that many present day traits, which have the function to do F, also have the

function to do F*, even though no trait of the type can yet do it. By implication, on his

theory, all such traits are malfunctioning by virtue of their current inability to do F*.

Further, there is no reason to limit our concern to mutations that will soon occur.

Some beneficial mutations that could soon occur will not soon occur, and perhaps will

never occur. However, the same in principle problem applies. On Nanays theory, traits

malfunction now, by virtue of their inability to do the improved things that would be

done were such mutations to occur.

The conclusion to draw is that the functions of traits do not depend on distinctive

modal facts about token traits alone. More important, the alleged circularity problem that

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motivated this approach is one that the etiological theory can dispose of without

difficulty.

2. HOW THE ETIOLOGICAL THEORY SOLVES THE CIRCULARITY PROBLEM

Traits do not need to be typed first, prior to the identification of their functions. Instead,

trait individuation and function attributions supervene on the same underlying facts about

trait lineages and the selection pressures operating on them. They co-supervene.

Traits are located in lineages and a lineage of traits is segmented (or as we say,

parsed) both for the purpose of classifying traits andfor the purpose of ascribing

functions by changes in the selection pressures that have operated on it. No circularity is

involved. There is only a superficial appearance of circularity, as we will explain. In

what follows, we explain (1) how token traits are located in lineages, (2) how a lineage is

then parsed by changes in the selection pressures that operated on it, (3) how the

functions of trait tokens are then fixed by their locations in the lineage, and (4) how this

resolves the circularity problem.

(1) How are token traits located in lineages? The mechanisms and processes that

are responsible for inheritance link traits in ancestral and descendent relations and token

traits are located within lineages after their ancestors and before their descendants. These

are the relations that biologists attempt to trace when they trace relations of homology.5

Suppose, for example, that we are interested in a particular eagles forelimb. Its forelimb

(its wing) is located in a lineage of forelimbs, after those of its parents and before those of

its offspring, if it has any. This lineage includes ancient fish fins, ancient amphibian legs,

and the forelimbs of flightless dinosaurs, as well as the proto-wings of dinosaurs that

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could lift a little above the ground or soar some distance between the trees. More recent

are the forelimbs of ancient flying birds, more modern birds, and the wings of ancestral

eagles. Our eagles forelimbs are located in this lineage by virtue of their actual history.

(2) How is a lineage of traits parsed by changes in the selection pressures

operating on it? Suppose that we are interested in whether a particular eagle forelimb has

the function of flight. We locate the relevant lineage of vertebrate forelimbs, the one that

evolved into this eagle forelimb. Now we draw imaginary lines in this lineage whenever

selection for flight starts or stops. This segments the lineage with respect to selection for

flight. (Note that we did not assume that the forelimb had the function of flight in order

to do this. We only asked if the forelimb has the function of flight.) If a capacity for

flight evolved only once in the lineage leading to the modern eagles forelimbs, and

selection for flight did not stop once it started, there is just one line to be drawn in this

lineage in this case.

(3) How are the functions of token traits fixed? If our question is whether our

particular eagle forelimb has the function of flight, first ask to which segment of its

lineage (parsed with respect to selection for flight) it belongs. Then ask whether

selection for flight operated on ancestral homologs within that lineage. Since the answer

is affirmative, the eagles forelimb has the function of flight and it is also therefore a

wing (a forelimb that has the function of flight).6

Where lines are to be drawn in lineages will often be subject to a Sorties-like

vagueness. A capacity for flight probably evolved gradually and there can be no

selection for flight until there is flight.7But this vagueness is not a problem.

8The

vagueness of when in time there was or was not selection for flight corresponds to the

vagueness of whether certain ancestral forelimbs did or did not have the function of

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flight. In fact the vagueness of the etiological theory captures the Darwinian gradualism

of the phenomena. It is in fact vague when dinosaur forelimbs were first selected for

flight and first acquired the function of flight.

Note too how well this approach deals with the case of lactase persistence. Well

under half of all humans belong to lineages in which there has been selection for lactase

persistence. According to the etiological theory, the mechanisms that permit lactose

digestion in adulthood in this minority of people have the function of doing so. Why?

There was selection for the adult digestion of lactose operating on ancestral mechanisms

in the relevant segments of the lineages to which the mechanisms of this minority belong.

Now recall A, who is lactose intolerant. To discern the functions of the mechanism(s)

responsible for As lactose intolerance, we need to identify the lineage (or lineages)

leading to As mechanism(s). We need to parse it (or them) with respect to selection for

the adult digestion of lactose. The relevant mechanisms in A do not belong to segments

of a lineage (or segments of lineages) on which selection for the adult digestion of lactose

has operated on ancestral mechanisms. So his mechanisms are not malfunctioning in

virtue of their inability to provide for the adult digestion of lactose. On our account, one

does not need to be in the evolutionary vanguard to function properly; one need not have

all of the actually imminent or only possible improvements on our current species design

in order to function properly.9

As sketched above, this version of the etiological theory does not say that we

must type traits first and then ask what selection recently operated on that type of trait.

Instead, it tells us that token traits are located in lineages, which are parsed in accord with

stops and starts in selection for F, when it is the function to do F that is at issue. If the

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trait in question belongs to a segment of the lineage in which selection for doing F

operated on its ancestors, the token trait has the function to do F.

(4) How does this resolve the circularity problem? Function and trait typology

both depend on past selection history and on changes in selection pressures operating on

lineages. Traits are typed inascribing functions to them, not before ascribing functions to

them.10

It is important to stress that, in explaining how a particular forelimb is located in

a lineage, in explaining how the lineage is parsed with respect to selection for flight, and

in explaining how we determined on that basis if a particular forelimb has the function of

flight, we do not assume in advance that the forelimb in question had (or did not have)

the function of flight. We do not assume in advance that the eagles wing has the

function of flight.11

Rather, we ask ifit has the function of flight. Then we parse the

relevant lineage at starts and stops in selection for flight and ask if selection for flight had

operated on the relevant segment of the lineage, the one to which the token trait in

question belongs. We ask whether ancestral traits, within that segment, had been selected

for flight. In none of this do we need to know in advance whether the token trait in

question had the function of flight. We also do not need to know if it was a wing (or a

flipper, or a leg or an arm). We locate it in its lineage and go on from there.

There is only a superficial appearance of circularity on the etiological theory. The

superficial appearance of circularity derives from the common basis for both trait

typology and functions. As Neander has elsewhere remarked, Function ascriptions and

these particular kinds of trait classifications go hand-in-hand, hence the superficial

appearance of circularity. One cannot get a wife or a husband unless one marries and one

cannot get married unless one gets oneself a wife or a husband. But there is no Catch 22

here. We do them both together.12

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3. CONCLUSION

The etiological theory meets all of Nanays desiderata. Besides avoiding circularity, he

lists three. A token trait can have more than one function, our function attributions

depend on our explanatory projects, and there is the possibility of malfunction.

A token trait,x, can have more than one function. It can have the functions, F

and G. If you are interested in whether a token trait,x, has the function to F, locatexin

its lineage. Draw a line in the lineage whenever there is a stop or start in selection for

performing F. If there was selection for performing F operating on traits ancestral tox

within its segment of the lineage, then x has the function to F. Now, to see if the same

trait,x, has the function to G, again locatexin its lineage. But now draw a line in the

lineage whenever there is a stop or start in selection for performing G. If there was

selection for performing G operating on traits ancestral to x within its segment of the

lineage, thenxhas the function to G. Since there can be selection for both doing F and

doing G operating on a lineage of traits at the same time, one and the same trait can have

the function to F and to G.

The etiological theory also recognizes that function attributions depend on the

explanatory project: that is to say that the attributions we make depend on our

explanatory projects. We can ask whetherxhas the function to F, or whether it has the

function to G, depending on these explanatory projects. However, the functions

themselves are not dependent on our explanatory projects. Whetherxhas the function to

F or to G (or both) depends on history, not on which questions we ask or which questions

are relevant to our projects.

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The way this version of the etiological theory draws lines in lineages also allows

for the possibility of malfunction. A trait that cannot do F can nonetheless belong to a

segment of a lineage of traits in which selection for F-ing operated on traits ancestral tox.

A broken wing of an eagle belongs to a segment of a lineage in which selection for flight

operated on ancestral forelimbs.

The etiological theory of functions is epistemically demanding. Drawing the lines

in lineages that it employs requires a lot of phylogenetic information along with a lot of

ecological information. But the issue between Nanay and us is metaphysical: what

constitutes a function. We have expounded the metaphysical issues in terms of questions

that need to be answered so as to show that there is no circularity in the constitutive

conditions. We do not imagine that biologists will, in practice, perform these steps each

time they attribute a function to a trait, no more than we assume that we always establish

the chemical composition of water before we drink it.

KAREN NEANDER

Duke University

ALEX ROSENBERG

Duke University

1A Modal Theory of Function, THIS JOURNAL, 107 (8): 412-431.

2Others have also addressed the problem. See for instance, Paul S. Davies,Norms of

Nature(MIT: Cambridge, 2001), Paul Griffiths, In what sense does nothing in biology

make sense except in the light of evolution? inActa Biotheoretica, 57 (2009): 11-32,

and Karen Neander, How are traits typed for the purpose of ascribing functions to

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them? in Jean Gayon (ed.)La Notion de Fonction: des sciences de la vie a la

technologie (2010).

3

Nanay points out that most other theories of function potentially face a similar problem.

They all seem to need an independent function-free way to individuate trait-types or else

to abandon the idea that functions belong to tokens in virtue of their types. However, the

alternatives to typing traits by their functions do not look promising, or so Nanay argues.

For example, if we use homology as the basis for the classification of traits, the resulting

classifications are insufficiently fine-grained for many purposes (as we have previously

argued ourselves in Rosenberg and Neander, Are Homologies (Selected Effect or Causal

Role) Function Free? inPhilosophy of Science, 76, 3 (2009): 307-334). Two traits can

be homologous and yet can have very different functions and so homology does not seem

to provide the fine-grained types needed for ascribing functions to traits. For instance,

the forelimbs of vertebrates are all homologous and yet different vertebrate forelimbs

have different functions. Some have the function of assisting in flight, some in paddling

or swimming, some in grasping the branches of trees, some in walking and running and

so on. So it cannot be that we type traits for the purpose of ascribing functions to them

on the basis of homologous relations alone. But add function to the mix and oneseemsto

have a problem of circularity. The appearance is deceiving we shall argue.

4We understand (2) in such a way that biological functions do not depend on our

interests, although the attributions that we make do so depend.

5There are difficulties in providing a full treatment of historical homology and we do not

slight those difficulties but nor do we treat them here. These difficulties do not include

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the present problem of circularity and nor does Nanay seem to take issue with a notion of

historical homology.

6

A few other examples might help. Consider a modern penguins forelimb (one of its

flippers) and a modern emus forelimb (one of its vestigial wings). First, locate the

lineage of forelimbs for the penguin. Now draw imaginary lines in the lineage whenever

selection for flight starts or stops. There is thought to be at least one time when selection

for flight starts and at least one time when selection for flight stops. As long as our

penguins forelimb belongs to a segment of this lineage in which there was no selection

for flight operating on ancestral forelimbs, it does not have the function of flight. Now

consider the emus forelimb. Again, we can segment its lineage by drawing lines

whenever selection for flight stops or starts. Then we can ask whether this emus

forelimb belongs to a segment of the lineage in which ancestral forelimbs were selected

for flight. It does not. It belongs to a segment of the lineage in which there was no

selection for flight. So it is vestigial with respect to flight.

7The capacity for flight seems to have developed gradually, either from an enhancement

of an ability to soar from tree to tree in arboreal creatures or from an enhancement of an

ability to leap from the ground in ground-dwelling creatures.

8Vagueness is a problem for the modal theory of functions because, in order to apply the

theory, the vagueness of the notion of relatively close possible worlds must be resolved

in an ad hocway, after peeking at the functions of traits.

9Although it remains true on our proposal that much relevant selection is recent, relative

to a token trait, this proposal differs from the modern history version of the etiological

theory of functions that Nanay considers. In some lineages, traits can gain and lose and

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can again gain other functions fast. So it is hard to see how a non-circular answer can be

given to the question, How recent is recent enough? On our approach, we do not need

to answer that question. If selection for F-ing starts and stops in short order, there might

be more than one segment of the lineage vis a visF that is recent, in evolutionary terms.

But this does not matter for whether that trait has the function to perform F on the present

proposal. Instead, it matters only which segment the token trait belongs to and whether,

within that segment, there was selection for performing F operating on ancestral traits.

10Nanay touches on something like this strategy (see Nanay,op. cit., note 1, p. 421) but

he fails to see how it solves the circularity problem. This is presumably because Nanay

treats any appeal to what there was selection for as an appeal to function. According to

the etiological theory of functions, functions are (roughly) what traits were selected for.

So Nanay presumably thinks that, if we appeal to what there was selection for in our

proposed solution to the problem, we appeal to function and return to running around the

same old circle.

11Nor do we assume in advance that the penguins flipper or the emus vestigial wing did

not have the function of flight. See note 6.

12This is in the original English, from Neander op. cit., note 2 (p XXX), which offers an

earlier version of this solution to the circularity problem.