CANADIAN JOURNAL Of PHILOSOPHY
Volume IX, Number 3, September 1979
A Goal-State Theory
of Function Attributions
FREDERICK R. ADAMS, University of Wisconsin
f
The analysis of function-ascribing statements, sIKh as "the
function of x is y", is proving to be a diffKult matter, II is diffKult
because we are only beginning to see the complexity which is
involved in ascribing functions. The process of discovery has been
slow and tedious, with each newly constructed analysis of the
meaning of fun(lional asniptions yielding insights into the strU(lure
of functional analysis and functional explanation, However, as each
analysiS is, in turn, dismantled, we seem to see our insights slip away,
fn the wake of each exchange, a new member is added to the list of
desiderata for an analysis of function-ascribing statements. Thus, the
matter of finding a proper analysis of function attributions becomes
more and more complex.
Until now the traditional method of approach to an analysis of
function allributions has been a higly intuitive one. A set of
(intuitively) ~ceptable examples of fuoction attributions are offered
and an analysis is constrlKted to meet those examples.
Counterexamples are then sought and found, and they force
amended versions of the analysis. Since the amended analyses are
modified in just those ways in which the counterexamples show
deficiencies, they are left vulnerable to new counterexamples of a
493
Frederick R. Adams
different sort. The result of this approach has led to the compleXity
which we now find in functional analyses. Throughout the entire
procedure, the putative counterexamples themselves must be
accepted or rejected on purely intuitive grounds, with no clear
agreement as to whether they should count as genuine cases of
functional relations or not. This trial and error method may indeed be
the best we can do. Nonetheless, it is appropriate to begin to search
for a new .JpproKh. We may find help by reconsidering the
foundation upon which function attributions rest, in hope of
breaking new ground. It is this approach that shall guide the present
investigation.
"
let me begin by suggesting that the essential feature of a
functional relationship is that of a means-ends relation.' For a
structure x to have a function y is, essentially, for x to do yin a system
5 and for y to lead to the fact that the system is able to output a value
O} The output value 0 will either be a goal-state of 5 or causally
contribute to S's attaining a goal-state. let uS schematically represent
the means-ends relation 01 functional relations as follows:
5
x --, y
----+-0
2 Ishould menhon ho'" lhie SQrt tlwllhere;' a ceflain transltivtly in n.~
COIl~"'S. CiYetllhal the function of x is y and lI... t y Iuds 10 I, '"' ""'Y be
wi11in110 aaeplthe anlibl/Iion thai !he n.nctiotl of x ;. I. If the flll>Cliorl of
the heart is 10 pump. and pumping leads to cin:ulalion, _ would also..,..pl
the an,;but;,;,n of thf' functiorl of ci«:ulalinl blood 10 lhe hean. The ... a...
numerous inslan«'S of this""", Just whe... th.. transilMty b ak< down is
undNr, a11houlh it "'a'!' brea.k down when _ go f,om the n......... of
funcliorl anributions at !he maaoscopic
of descriptiorl to Ill'ibutions
01 funcliorl .t !he micfOKopic level.
""'-.I
(
494
Goal-State Theory of Function Attributions
(Here, y either is 0 or is causally related to S's outputting 0.) In S. x's
doing y is the means by which 5 is able to do O. Hence x, y, and 0
stand in a means-ends nexus within the system S. If it is a function of
chlorophyll in plants to aid in photosynthesis, then aiding in
photosynthesis leads to the plant's manufacturing sugar (outputting
0, if you will) which is an end-state or goal-state for the plant.
Chlorophyll leads to the plant's being able to achieve one of its
goal-states. ]
While I am arguing for the position that functional relations are
means-ends relations, I have added the condition thaI, in the
means-ends relations which are functional relations, the end state
reached is a goal-state for the system. The last condition must be
included since not every means-ends relation is a functional relation.
There are other means-ends relations in which structures and events
stand to one other. Purely causal relations are sometimes thought of
as means-ends relations. When a variable volume of gas is heated it
expands. Its expanding is the means by which the gas maintains a
constant temperature. So, for example, if one heats a ballon
containing oxygen, it will expand. As it expands, its temperature will
lend to remain constant. Maintaining constant temperature will be an
end-state of the process of expansion; yet, we do not want to say that
it is a function (or the function, in the non-mathematical sense of
"function") of the gas'sexpanding to keep the temperature of the gas
constant. The reason that we do not is that it issimply nota goal-state
o/the volume of gas that it maintain a constant temperature. It is not
directively organized toward that end, toward that goal.' The
expansion of the gas is not causally directed toward that end, it is
merely terminated at that end-slate.
3 Ordinarilywe will say that it is the lunclion of x to do y (in Sl if doing y actually
"'ads to S's outpUlling O. Howeve,. 0 may be a goat-state lor Seven il it is
never react,.,d. Hilling the enemy ship in OUler 'pace may be a goal_state for
Ihe guided missile even if the mi"i'" misses Ihe Ship and zooms eternally
Ihrough space.
I .hould al50 poi01l oUllhat it has be,o,n argued by Achinstein [1] thaT it is
confusing to uy that if x does y and y conlribule. to S's ability to outpul 0,
that x's fUnCTion i. to conrdb<Jte to the ability of S to output a. I Ihink Ihat we
can avoid any confu'ion by casting the function attribution' In the appropriaTe condiTional form. We will say that the function of x i. Y if. under
appropriate conditions C•• would do y and ywould lead to S', outpulling 0,
4 The expansion of the volume of gas contribUTeS To its maimaining a constant
temperature. but maintaining a conSlant temperaTure is not a goal-state of
th" gas. It is nota funaion of Th" votume 0/ gas To ..xpand. nor a function of
ITS expansion to maintain constanITemperatur...
495
Frederick R. Adams
The goal-state theory of function atlributions holds that the
central feature of functional relations is not onJy that they are
means-ends relations, but also that they are means-ends relations
within or conjoined with goaJ-directed systems. In this way we can
avoid attributing functions to non-functional causaJ relations. So,
e.g.. we can avoid attributing to the moon the function of making the
tide come in and go out. Although this surely is an effect of the moon,
it simply does not warrant an ascription of function. We must have a
way to block such ascriptions, and wedding the ascription of
functions to goal-directed systems provides the means to do so.
The effect of the moon on the ebb and flow of the tides is not a
functional relation since it is not part of a goal-directed system.
Consider the contrast of the constricting action of the capillaries in
the body. We say that it is a function of capillary constriction to limit
the flow of blood to the outermost regions of the body, when the
body is cold. The body is goal.directed toward homeostasis of
temper<lture (roughly 9a.6°f) and performs cerlain activities whkh
are directed toward reaching its goal-state. Capillary constriction is
one of these activities. The greatest potential for loss of body heat
occurs when blood reaches the surface areas of the body, especially
at the outermost regions, such as hands and feet. When our body
temperature falls significantly below the optimum state (98.6°F) the
capillaries constrict and prOhibit the flow of blood to the surface
areas. Thus, the opportunity for heat loss is reduced. When the
goal-state of optimum temperature is reached, the constriction
subsides. Here, we are clearly willing to attribute to the constricting
action of the capillaries the function of limiting the flow of blood to
the surface areas of the body. limiting the flow of blood causally
contributes to the body's achieving one of its goal-states,
homeostasis of temperature. Contrast this with the tidal effects of the
moon. Although they are regul<lr effects of the moon's causal
inter<lClion with the OCe<lnS, the tides play no role in a gO<lI.directed
system. On the other hand, the constricting <Iction of the C<lpillaries
plays a functional role in attaining a goal-state of the body. Jt is the
added fe<lture of contributing to the attainment of a goal-state thai
confers the status of a functional relation upon a means-end relation
within a system.
Since the goal.state theory of function attributions closely ties the
concept of haVing a function to the concept of being goal-directed, il
is imperative that we have at least a rough characterization of what it is
to be a goal·directed system. While a complete and formaJ analysis of
goal-directedness is well beyond the scope of this paper, (in section
IV) I shall attempt to characterize the centraJ features of wh<lt il is for a
system to be goal-directed. In this way, wewill have a firm foundation
496
Goal·State Theory of Function Attributions
(
for the goal-state theory of function attributions and enough
information about the theory to assess its worth.
Before I proceed, I would like to address the nolion that to be
goal-directed is essentially mentalistic. That is, it has been argued that
the core concept of goal-directedness requires that, for a system 10
be goal-directed, it must have desires, beliefs andinlenlions.' On this
view, other systems may be said to be goal-directed, but only if they
have internal states which are analogous to mental states, and then
they are only said to be goal·directed by extension of the concept to
non-mental systems. On such a view, whether non-mental systems
(e.g., plants) are to count as goal-directed (e.g., in their tropic
responses) will be a subjective matter - subject to our finding
internal analogues to beliefs, desires, and intentions which we deem
similar enough to mental states 10 warrant calling the systems
goal·directed systems. Consequently, on this kind of goal-state
theory of function attributions, whether a structure has a function
will also be a purely subjective maller, ilthat structure occurs in a
non-mental system. Structures in those systems will be allributed
functions subject to our deciding to call the systems goal-directed.
Perhaps artifacts which contributed to the desires of their
artificers would be the only thing which could truly be said to have
functions on such a view because the artificers would be the only
systems which could truly be said to be goal directed. I believe,
however, that this view should be adopted only as a last resort. I shall
try to give an account of goal-directedness, and of something's
having a function, such 'hat whether something has a function or
whether it occurs in a goal-directed system is an objective matter of
fact. Anything less would make all talk of goal-directedness and of
functions, at least with respect to non-mental systems, purely
subjective.
I shall claim that goal-directed systems can be either mental or
non-mental systems. Beliefs, desires, and intentions are not reqUired
for a system to be goal-directed_ Consequently, the difference
between the two types of systems -when they are goal-directed - ; ,
that mental systems have beliefs, desires, and intentions as
components In the causal network which produces their
goal-directed behavior, while non-mental systems do not. In section
IV, I shall explicate being goal-directed as being a kind of cybernetic
system in which beliefs, desires, and intentions may playa causal
role, but in which they are not necessary conditions,
5
And'ew Woodlield .'gue, lor this yiew in 1l31.
497
Frederick R. Adams
Before I set out the version of the goal-state theory of function
attributions which I am defending, it will help to examine some of the
currenltheories of functional analysis.l will present them as possible
candidates for the further specification of the precise conditions
which govern the means-ends relationship of functional relations
and suggest what I find acceptable and unacceptable about them.
Then I will present an analysis of what it is for a system to be
goal.directed and of what it is for something to have a function in a
goal-directed system. finally (section Vj, I will exhibit the manner in
which this version of the view fends off putative counterexamples.
III
The view t am defending is to be distingUished from what has been
called the "good consequence view" of function attributions.· The
strongest version of that view is presented by Hempel' and by
lehman.' They require that there must be a benefit conferred upon a
system before a function can be attributed to what produced the
benefit. Further, the benefit must be one which is a necessary
condition for the system's well-functioning.' let 5 = a containing
system, X - a structure (or event) in 5, Y '" an effect of x, Y' ... an effect
of x, 0 '" a necessary condition of S's well-functioning. According to
this view, the function of x is Y if and onry if all three of the following
conditions are satisfied:
(1)
x does y (in systems of kind 51;
(2)
Y is causally relevant to the satisfaction of 0;
(3)
0 is a necessaty condition of 5's well-functioning.
Graphically, tet us represent this as follows:
6
see ""chi"'lei" 111. whe,e lie (lIar~lerize'lhe
7
see 161.
8 Ct,17).
9
498
See nole 10,
fealme. otll1i. ,ipw.
Goa/·State Theory of Function Attributions
5
--"---0
x-.~_cc--. y
-_yo
--
(The solid line indicates the causal and functional relation. while the
broken line indicates a mere effect.)
Hempel argues that we can identify functional relations by the fact
that they lead to 'the satisfaction of necessary conditions of S's
well.functioning. This allows us to exclude mere effects of x trom the
class ot x's functions. His analysis is built around the following two
statements:
I
(1)
The heartbeat in vertebrates has the function ot circulating
blood through the organism;
(2)
The heartbeat has the function of producing heart sounds
(for the heartbeat has that eHect).
Hempel wants to be able to show why (1) is acceptable while (2) is not.
(1) is acceptable because, in 5 (vertebrates). x(the heartbeat) does y
(circulates the blood) which contributes to S's doing some 0 (e.g.,
gelting nutriment to the cells and carrying away waste) which is a
necessary condition of S's well.functioning.
Although Hemple's analysis is successful at distinguishing
between (1) and (2). thereby blocking attributions 01 function to mere
effects, it is still unsuccessful as an analysis. It falls prey to other
difficulties. First, it is not clear that the conditions Hempel gives are
sufficient conditions for function attributions. His analysis cannot
handle what I shall call the problem of "fortuitous effects." Imagine
that I am a soldier in a combat area and my chaplain has given me a
small pocket version of the Bible. If I carry the Bible in my shirt
pocket, while on patrol. there is a good chance that the Bible would
stop a small caliber bullet from entering my chest. Given that this
does happen one day, during a brief exchange of fire, I may take it as
being of religious significance. That the Bible saved my life may be
interpreted by me (and by the chaplain) as a sign of God's watching
over me. Suppose I then give the Bible to a friend of mine, doubling
seriously lhal it could ever save me more than once. but thinking that
it could instill faith in my friend. Given that the enemy has expert
marksmen, they will shoot for the chest (a point ot vulnerability), with
499
Frederick R. Adams
a high degree of success. Since my friend is carrying the Bible (purely
for spiritual reasons, not for physical protection) in his shirl pocket, it
is not too unlikely that the chain of events which happened to me
could occur again. If they do, my friend may also pass the Bible on
and the chain may continue. Then Hempel's conditions are met: (1)
the Bible stops the bullets from entering the bodies of soldiers, (2)
stopping the bullets is causally relevant to keeping them from
entering the bodies of the soldiers, (3) non-entry is a necessary
condition for the well-functioning of the soldiers as soldiers - and
for the well-functioning of their bodies as numan beings. Although
the conditions are met, it is nottne or even a function of the Bible to
stop bullets. In fact, the soldiers did not carry the Bible with that
intent, but for religious reasons. The Bible produces fortuitous
effects, but it does not get ascribed the function of a bullet deflector
(shield). Therefore, Hempel's conditions may not be sufficient
conditions for attributing functions.
Second, it is doubtful that Hempel has given necessary conditions
for attributing functions; his conditions are too strong. Hempel
focuses his aUention narrowly upon vital functions and the
means-ends relationships which afe vital to the existence or
weU-function ing of a system. In an effort to loosen the restriction that
all functional relationships are vila I ones, let us try to find functional
relations which meet the following conditions:
(1)
x does y in systems of kind S;
(2)
Y is causally relevant to the satisfaction of conditions for
the output 0:
(3)
0 is a goal-state of S but is not a necessary condition of S's
well-functioning.
We are sometimes consciously goal-directed towards carrying
pens by affixing them to our pockets. We have an internal
representation of that goal-state (an idea, if you will) and we clip the
pen into place. Theclip holds the pen in place and being held in place
contributes to our goal-state of transporting the pen in our pocket.
However, it can hardly be said that carrying pens in our pockets, in
this manner, is a necessary condition of our well-functioning. After
all, some pens do not have such clips; we simply find other ways to
transport them. Having the pens fixed securely in our pockets is a
convenience and leads to a goal-state, but it is not a necessary
condition of our well-functioning. Nonetheless, it is the function of
the clips to affix the pens to our pockets.
'00
Coal·Stale Theory of Function Attributions
5inct> mOSI examples of artifacts and their functions will meet the
same conditions, Hempel's analysis is too strong to bt> taken as giving
necessary conditions for ascribing functions. Notice that it will not do
10 try 10 salvage Hempel's analysis by stipulating conditions of
well-functioning so that, say, one is not well-functioning as a
salesperson unless he hasan abundant supply of pens dipped into an
easily accessible pocket. The anillysis would then become true by
ingenuity of eXilmple or by stipulation of conditions of
well-functioning.'·
If we agree that Hempel's requirement is too strong, we may
weaken it and still hold a version of the good-consequence view. For
instance, we may say that for x to have y as a function;
(1)
x must be able to do y (in 51;
{2J
y must confer some benefit or advantage upon 5.
Various formulations of this weaker version exist. For example, y may
contribute to the well-functioning of 5 - without contributing to a
necessary condition of 5's well-functioning. Or, x's doing y may
contribute something useful to 5." X may do y and y may contribute
to an adaptive advantase of 5."
Each of these versions of the view fail. They all face the problem of
fortuitous effects, But even If we modify the view to handle that
difficulty by changing it to read as follows:
(1)
x must be able to do y (in 5);
(2)
Y must lead to 5's outputting 0 (in a non-accidental way);
OJ
0 must be a goal-state of 5;
10 We mllH ~ cIKulMi!)', In order fa< y 10 be the lunnlOfl 01 .., y must be
uusoJIy relew¥tl 10 lhe solilloOClion of a ~f)' condnion 01 S', ......
funaionins. ,""cordin, 10 H~I, When il S _l-func!ionin,fW.. ( _
soy NI, e"" 1M fUfKbOn ollhe dip is 10 .obW 1M pen 10 be affi>.t'd so a
pod..1 bK• ....., be"" SO aWl<ed is a nt'C
f)' condiltOn 01 on..', ....I..
functioning, 11_ m..tely.tipulal" Nl one is only wt'lI-IuncliotllnS when he
has a pen dipped inlO hb poc... I, w" are open 10 I"," chul" 01 eirculari!)',
11
Set' Conlield Ill.
11 This vi..... is deo<eloped b)'
It""" [101,
""
frederick R. Adams
(4)
0 must confer a good on S;
it is still not satisfactory. Once it is clear that functional relations are,
at heart, means-ends relations in goal-directed systems, then it is not
important that the goal-states be good for S. A functional relation isa
means-ends relation for achieving the goal-state; and no more.
Salmon swim upstream to spawn, after which they die. They are
goal-directed towards spawning and swimming upstream has the
function of returning the salmon to their spawning beds. Swimming
upstream contributes to their eventual spawning. Hence, conditions
(1 )-(3) are met. Yet, spawning confers no benefit upon the particular
fishes which spawn. Perhaps it contributes a benefit, at the level of
species, upon the kind of fish salmon are. But, without making this
move, it is still intuitively clear that the function 01 swimming
upstream is to get them to their spawning beds (and eventually to
spawning)." Also, people very often employ devices which have
destructive functions. Even if their conscious goal-state is one of
destruction, the structures which enter into the appropriate
means-ends relations contributing to that goal will be said to have
functions in the system. The point is that the essential feature of
functional relations is that structures or events contribute to the
goal-states via the appropriate causal route {I will argue that it must go
through the feedback loop of a cybernetic system), It is not important
that the goal-states reached be good ones - although 'he majority of
functional relations will confer benefits upon the systems in which
they occur. (In lact, in order to explain how the goal-directed systems
evolved we must assume that some adaptive advantages will occur,)
So, both versions of the good-consequence view (strong and weak)
fail. They fail because it is false that the goal-states reached by
functional relations must be good ones.
In addition to the good-consequence views of functional
relations, we should look at Nagel's version of the relation - Nagel's
was, perhaps, the first formulation of the goal-state view. Rather than
look at the role x's effect plays in S_whether or not it leads to a good
consequence - Nagel suggests that we pay specific attention to the
conditions under which an event y can come about in S. (Remember
that y may be identical with output 0.) Nagel argues that the analysis
of "the function of x is y" is the follOWing reformulation:
13 It is a very;nleresting question whether activit'e. like the ,p.owning 01 sal mon
only have a function at the level of species or whether they also have o,,1le
level of individual •. For more on this see (12). i sholl not dear further with this
question here.
502
Goal-State Theory of Function Attributions
(
y (in S);
(1)
x is necessary lor
(2)
y contributes to output 0 of S;
(3)
0 is a goal-state of S.
(Schematically, Nagel's view can be represented by the figure on p.
494 above.) The difference between Nagel's view and Hempel's is that
Nagel tries to make it possible for the presence of x to be necessary
lor y (under the conditions which actually obtain). Also, he requires
only that y contribute to a goal-state of 5, not that it is a necessary
condition of S's well.functioning. Nagel focuses special attention
upon the kind of thing x is. This is partly because he is searching for a
connection between structure and function, and partly because he
wants to be able to explain the presence of x in S. Nagel befieves that
functional explanation, if it is to explain anything, must explain the
presence of x in S. It is for this reason that he makes x a necessary
condition for y in S {condition (1»).
I shaH not rehearse past arguments for why making x a necessary
condition for y will not succeed. Hempel" and Cummins" have
adequately detailed why the D·N model for functional explanation
fails. let it suffice to say that as long as there are functional
equivalents, one cannot deduce the presence of one rather than
another of those equivalents (in 5).
Nagel notices that, in a system S, a structure x may not be logically
necessary for y; it may not even be physically necessary. He claims,
however, that given an inventory of the components 01 S which are
actually present, we will find that it is only x which can do y. Hence x
is, as a matter of lact, necessary for y. He suggests, e.g., that although
a substance other than chlorophyll may be able to aid in plant
photosynthesis, given the present genetic constitution of plants,
chlorophyll is a necessary condition for photosynthesis. I shall not
dispute the empirical facts about chlorophyll; instead I shall argue
that we could ascribe to x the function y even if x were not necessary
for y. To make this clear, let us construct the following scheme for a
goal-directed system S.
14
s~"='
lS
Cummins p......Il1. Il>i. very n",ely in lSI.
Hempel"1l.).
503
Frederick R. Adams
We will build S so that not only x but x' also does y. Whether x and x'
do y alternately, as in the case of a fall-back mechanism, or whether
they do y simultaneously is of little consequence. However, let us
suppose that they bring about y simultaneously. I want to maintain
that if we have constructed the system properly it is a function of x to
do y. I also wish to maintain that it is a function of x' todo y. Since we
will suppose that x and x' are different kinds of mechanisms, it is fal~
that x is necessary for y. It is also false that x' is necessary for y. Yet we
can ascribe to both a function to do y. If I am correct. then Nagel's
condition (1) is too strong. Even if chlorophyll were not necessary for
photosynthesis that could still be its function. It is not a necessary
condition for attributing a function to x that x be uniquely necessary
for y. There are many examples of fall-back me<:hanisms in biology
which sharpen this point. For instance. it is my understanding that it
may be a function of both the thyroid glands and of the adrenal glands
to preserve internal body temperature by the secretion of hormones
which regulate the heartbeat. constriction of the blood vessels, etc."
I am sure there are other cases to be added. Both the kidneys and the
process of sweating remove excess water from the body, and both
can operate at the same time.
II there are genuine cases which fit the scheme above - and I
have suggested that there are - then whether the cases are from
biology. or of artifacts. they force us to revise Nagel's conditions. If
we do not withhold a functional attribution to a structure in a system
simply because other structures contemporaneously have that
function. then we must weaken Nagel's condition (1). One may
attempt to block my counterexamples to Nagel's analysis by arguing
that when a structure x does y and a fall-back mechanism x' does y.
there are really two systems involved. That is, there is the system in
which x is a part and the system in which x' is a part." tn each of these
systems, it would be argued, the structure is a necessary condition for
16 These
17
504
e.am~e.
can be found in Cannon', 14], chapler 12.
In fact. Nagel come. very dose to arguing Ihis in 181. pp_
m
fl.
Goal-State Theory of Function Attributions
y, so condition (1) is salvaged. Jt seems that the mistake which belies
this type of argument is that the system in which x and x' occur is the
same. The fact that a lOlli-back system kicks in may change the relation
between the parts of 5, but it does not make 5 a different kind of
system.
In the next section I shall argue for the following formulation of
the necessary and sufficient conditions for function attributions:
(1)
In5,xdoesy;
(2)
y causally contributes to output 0 of 5 (through the
feedback loop in 5);
(3)
0 is a goal-state of 5 (where 5 is a goal-directed system).
(
IV
I shall contend that a goal-directed system _ whether mental or
non-mental - is a cybernetic system. It is a cybernetic system in the
sense that its behavior is not mere random behavior which
accidentally terminates in an end state. Rather, its behavior is
controlled or directed towards an end state or goal-state. The system
must also be able to process information about its present state (both
internal and elllernal state variables) and it must be able to compare
that information with its goal-state. The system then performs a set of
operations which minimi~e the difference between the present state
and the goal-state. In order to be able to compare information about
its present state with a goal-state, the system must have an internal
representation of the goal-state. Hence to be truly directed by a goal,
and not merely uncontrolledly approaching an end-state, a system
must have both an internal representation of a goal-state and a
feedback system which conveys information about its present state,
and its output values, back into the system as inputs. That
information is then causally efficaCious in the system's performing
successive operations which lead to its goal-state. That is, the
successive outputs of the system causally depend upon the
information about the output which is fed back as input information.
The notion of feedback is not merely that the information is
contained in the system, nor that there is a mere mathematical
one-to-one correlation of what happens at the output of the system
505
Frederick R. Adams
with what happens at the input of the system. It is crucial that there is
a causal dependence between the information about the system's
outputs and the successive adaptations in the system's performance.
Otherwise, any equilibrium system would count as a cybernetic
system, e.g., a pendulum's coming to rest, a rock's rolling down a
hill, water's reaching the lowest point, etc.
An analysis of goal-directedness which is based on a cybernetic
account maintains that a system muSI have:
(1)
an internal representation of the goal.state;
(2)
a feedback system by which information about the
system's state variables and its output values are fed back
into the system as input values;
(3)
a causal dependence between the information which is
fed back into the system and the system's performance of (
successive operations which minimize the difference between the present state of the system and its goal-state."
If any of these conditions are missing the system may behave similarly
to a goal·directed system but not be one, not be a cybernetic system
and not be a goal-directed system, according to this view.
Perhaps the simplest cybernetic system which is also a
goal-directed system is a heating system which includes a thermostat
that regulates the temperature in the home.
OS·
Heater
1:
-
Feedback loop
l~
506
There mu.t be restri<:Tions placed upon wh~t un count as a repr""enlation 0/
a goal.'tate. Not jU51 ~ny one-to-O<le <:ouelalion will do. There must be an
approp,iate etiology fo, Ihe internal Slate 10 come TO 'epresent the goal. I am
a..uming thaI thoe'e must be a c~u",1 theory 0/ ,ep,,,,,entation whkh will gi""
The exacT condition. unde' whkh an intern~1 stale will rep,,,,,,nt ~ goal·state.
See Stampe'. Pll. fo' the beginnings of such a theory.
Goal-State Theory of Function Attributions
(
The thermostat must be carefully calibrated so that the relation of its
internal structure and position accurately represents various room
temperatures. When we set the thermostat at 65', the position of the
dial becomes an internal representation of the goal-state of 65° room
temperature. As the room temperature falls below 65', the circuit to
the heater is closed and the system outputs heat. So thaI the room
temperature will not go far above 65' once the heater is activated nor
fall very far below 65° after the circuit is re-opened, the system must
be capable of monitoring the temperature in the room. If the room
reaches its goal-state the circuit opens; if it does not it remains closed
and the heater continues to output heat. In either case, the effect of
the output values on the system is monitored and fed back into the
system as input. The input information is compared with the
goal-state, as represented in the position of the thermostat, and
successive operations are performed to minimize the difference. As
long as the system is in proper working order, whether the heater
comes on, continues to run, or shuts off, depends upon the
information about the temperature of the room that is fed back as
input into the system_ It is this closed feedback loop which is the
central feature of a cybernetic system. And, it is the information
feedback system plus an internal representation of a goal-state which
are the central features of a goal-directed system.
There are many goal-directed sub-systems which operate in Jiving
systems. In complex living systems it is no doubt the central nervous
system which contains the internal representations of the goal-states
and which processes information which is fed back into the system.
For instance, the body is goal-directed toward homeostasis of
temperature. Some feature of the autonomic nervous system
contains an internal representation of the optimum body
temperature; a goal-state for the system. When the state of the
system falls below the optimum temperature, the mechanisms of
capillary constriction, secretion of adrenalin, etc., begin to function.
Their output values causally contribute to the reduction of the
difference between the present state of the system and its goal-state.
Once the goal-state is reached these mechanisms subside. Or, if the
temperature of the system exceeds the goal-state, then cooling
mechanisms begin to function, e.g., sweating etc. It is the
informational dependency between output values and input values
of the system which enable the goal-state to be reached and
maintained. Without it, it would be a lucky accident when our bodies
reached the optimum temperature for proper functioning. (Of
course, we are also conscious cybernetic systems. We know that we
must maintain a certain body temperature and we perform the
appropriate successive operations of pulling on and peeling off
507
Frederick R. Adams
layers of clothing. The same criteria for goaJ-directedness apply for
these consciously goal-directed actions.)
With this understanding of goal-directedness, let me now re-stale
the central tenet of the goal-state theory of function atlribulions. A
structure x has a function y just in case:
(1)
x does y in system 5;
(2)
Y causally contributes towards S's outputting 0 (through
the causal feedback mechanism};
(3)
0 is (or itself contributes toward) a goa/.state of $.
Since it is clear that x must be part of a cybernetic system 5 _ and 5
must also be goal-directed - we can graphically represent the
functional relation between structures and goal-states as follows.
5
x
,
y
0
Feedback loop
[The addition of the feedback loop will block attributions to effects of
structures in 5 which are merely fortuitous, and not truly functions.
The importance of this will become clear in what follows.)
Only when a system 5 is a goal-directed system can the
means-ends relation which is central to functional relations be
instantiated. It is true that we appear to attribute functions to
structures that occur in systems which are not goal-directed. To
account for this lact I will adopt the view that it is only in conjunction
with a goal-directed system that it is correct to ascribe functions 10
non-directed systems, e.g., to non-goal-directed artifacts. 50, tor
instance, it would not be a function of the clips on pens to enable
them to attach to pockets or lapels if there were no goal-directed
systems for which this was a goal.state. It would not be their function
because they would not stand in the means-ends relationship 01 the
required sort. This is not to say that the clips would not give the pens
508
Goal·State Theory of Function Attributions
(
the capacity to be affixed to pockets; they would. It is true that a
function of the clips would be to affix pens to pockets, were they to
occur in a means-ends relation to a goal-di rected system. They would
simply not actually have that function if they were not actually
associated with a goal-directed system in the appropriate way."
What I wish to capture is the intuition that, e.g., although a rock
may come to hold papers in place on a desk, it is only in virtue 01
being conjoined with a goal-directed system - Smith - that the rock
comes to acquire this function. It is not true of rocks, in general, that
one can attribute to them the function of holding papers in place,
even though they have that capacity. Further, even if the rock comes
to be associated with Smith, it must instantiate the appropriate
means-ends relation through the feedback loop to acquire a
function. Smith must have an internal representation of a goal.state
(say, an idea of holding papers in place on his desk). If this is a
consciously held goal-state, it is simply an idea or desire of Smith's.
He then performs successive operations which will tend to minimize
the difference between the present state of his desk and the
goal-state. He picks out a rock and places iton his desk. If it produces
effects which achieve the goal-state, that information will be fed back
into Smith's information processing system. That is, Smith will be
able to tell whether or not the rock makes a good paperweight. If it
does, that information will causally contribute to the rock's
successive states. For instance, if it works, Smith will continue to use
it. If it is too small, that information will be fed back and Smith will set
out in search of a new one which is a bit larger. In any event, the
system consisting of Smith plus the rock must be a goal-directed
system _ which Smith is. The rock becomes an artifactual extension
of Smith. Also, the conditions for ascribing a funClion to the rock
must be met - and they will be met if the rock makes an efficient
paperweight. It is important to note that the conditions for a system's
being goal-directed and for a structure's having a function must both
be met. Otherwise, if a rock just happened to be thrown on Smith's
desk and just happened to hold paper on his desk when a gust of
wind blew in the office, we would still not ascribe to the rock the
function of holding papers in place. The reason we would withhold
the attribution is that the rock does not, as yet, instantiate a functional
19 When I,ay"in the appropriate way" Imean through the feedback loop.AI,o,
j do not want to become embroiled ina controversy 01 whet""" in S, xha,a
function actually or only potentialfy. It seem, thaI hy reca'ting funclion
amibulion, in the ,uhjunctive, when nece,,,,ry, we will resolve thi, prob.
lem. See nole 3.
509
Frederick R, Adams
relation. II may fortuitously cause one of Smith's goal.states to be
reolched (while he was out buying a polperweight). Yel, it did not enter
into the olppropriolte meolns-ends relation in the appropriate way for it
to have <1 function. It must enter into the uusal relalions in the
feedback loop of a goal.directed system for it to attain a function. This
it Coln do when, upon returning from an unsuccessful search for a
paperweight, Smith finds that the rock will serve that role and he so
employs it. Its continuing to hold papers in the future will be causally
dependent upon its success at holding them in the past.
This view is not to be thought anthropomorphic. If a group of
cleverly constructed robots have, as goal-stales, affixing pens with
dips to their lapels, then the function of the dips can become to so
affix the pens. The robots need not be like us in any other way than
t hat they be goal.<Jirected systems and thaI they employ the pens with
the dips in the appropriate way. In fact, ",ny structure which is
conjoined with ",ny kind of goal-directed system, through the
feedback loop, can acquire a function. The goal.directed system
need nol be like uS. For instance, in the household heat lhermostat,
the function of the mercury switch is to turn the furnace off and on
with respect to the set temperature for the room. Yet, the
goal-directed system is scarcely like us in any other respect than that
it is a cybernetic system and thal it is a goal-directed system.
I have. roughly, assumed that it is possible to construct a global
theory of function attributions; a theory which covers attributions to
both natural systems and to artifacts. If I am wrong, then the
goal.state theory of function attributions may be 01 only limited
scope, i.e., apply to natural systems but not to artifacts - or vice
versa. However, at the outset, it is aworthwhileallemptto construct a
gloooitheory which applies to both.
let me summarize the reasons which move me towards the
goal-state view. Since I am arguing that the primary feature of
functional relations is their being meanS'-ends rel..tions, I w..nt to
guard ag..inst the objection that in a system (even if it is a
goal.<Jirected system) any means-ends relation establishes a
function. This view, or a similar variant. has been held by Cummins."
He claims that x has the function y when:
(1)
x does y (in S);
Q)
y contributes to some capacity of S (i.e., contributes to S's
ability to output 0, 'fyou will).
20
510
Cf. lSI.
Goal·State Theory of Function Attributions
I wish 10 block this formulalion since Hlets in too much. It makes it
possible to argue than any effect of x that we select may be one of x's
functions. One can claim that no mailer which effed of x we choose,
there must be some capacity of S to which that effect contributes regardless of how trivial or uninteresling. Thus, il is a lunction of x to
do any and all of ilSeffedS. This is surely unacceptable. Some of the
outputs 0 of Swill nol be goal-slates of S. Why should we wish to say
there there is a functional relation, a means-ends relation, between x
and 0 when 0 is not a goal-state of sr Having a liver may lead to the
capacity of 5 10 acquire cirrhosis, but surely that is not a goal-state of
S. We would, I think, not admit that the relation in which the liver
stands to cirrhosis is a functional relation." J think we should not
agree lhat it isa function 01)( in 5 to dowhatever)( can do. By adopting
the goal-state view, we have a way to block auributions to mere
effects.
We should also avoid allributing functions to Slructures which
accidentally produce fortuitous effects. We saw how to block an
attribution of function to Ihe rock which accidentally fell on Smith's
desk. I argued there that even if it is a good for a system S. that y
occur, or if y accidentally leads to a goal-state 01 5, if)( accidentally
occurs. prodUCing y, we should not automatically be willing to
attribute the function y to x. X must enter into the appropriate
means·ends relation in a goal-directed system - i.e., it must be part
of the causal chain involved in the feedback loop of lhe goal-directed
system. Even in a natural system like the body, if a brain tumor
accidentally places pressure upon the pituitary gland (which had
been malfunctioning), thereby causing it to secrele the proper
amount of hormones in the proportions required lor normal
development, we will not want to allribute to the brain tumor the
function 01 applying pressure to the pituitary gland. From the mere
fact that, in S, x produces y and y leads to some intrinsic or extrinsic
good, a benefit to S, it does not follow that it is the function of x to do
y. The brain tumor simply does not instantiate the means-ends
relation in the appropriate way in order to warrant the attribution of a
21
Lehman IT]
condi,1on 10 h~ ~Iysi>; to block ,hil mowe, bul it i.
NyJ lh~1 If"-I doins y is IUtfocienllO nuse 5 10 ..... H,me·
~dds ~
unllKC~.. ful. He
lion. l~n .....nl
Y cannot be ~ flll'l<tion of •. Ahhougtl ,hil block> 1~
funcrion of COflt,ibuling tocirrholilto lhe ~W'f, lhef~ ~~ sUll
problem•. Conllfuct,ns buildin,. wilh meW llructUffl contributes '0
C"fNCiIy of 1~ bu~dinp 10 p"" off ,adiat;"n. This does nol c~use the
building to malfunction. yef il i. ~IIO nol ~ function of the met~' "fudU,." '0
gi"" off f~d"tion. M least nol pnrru fa<~.
~nribution of ~
u...
511
Frederick R, Adams
function, The tumor would continue to apply pressure to the pituitary
gland independently of the fact that its doing so conferred a benefit
upon the body. Even if a structure or event provides a fortuitous
effect in a system, more than a good consequence is required for
something to acquire a function in a system. There must be a causal
dependency between a structure's minimizing the difference
between its goal-state and its present state (whether or not the
goal-state is agood one), and the structures continuing to perform its
operations."
v
In this section I will present putative objections to the view r am
defending and attempt to defend the view against them, In this way
we will be able both to make the view more perspicuous and, at the
same time, to examine how well it can fend off attempted
counterexamples. If the goal-state view can handle all of the
objections that other views can and not fall prey to new ones, I shall
rest fairly content with the view.
Ob;ection :#: 1. Is it not true that what confers a function upon
something is that it was selected for one or more of its propertiesr In
the case of biological organisms, it may be argued that what confers
upon x the function y is that, in 5, x has been selected for doing y
(through the processesofnaturaJ selection). With respect to artifacts,
it may be claimed that it is we who select a structure x lor its ability to
do y. In either case it is through the processes of selection that
functions are determined."
let me begin by addressing this view with regard to artilacts. It
seems that one's intentions (i.e., the fact that one selects x lor y) are
neither necessary nor sufficient for x's haVing the function y. II I build
a system 5 and include x, intending for x to do y (selecting x tory), that
is not sufficient for x's doing y. Unbeknownst to me x may not be able
21 This type of e ... mpl", shows what is wrong with ..signing ~n attribution 0/
function solely on the b~s;s of fonuitous effects. 0. Achinstein'S treatment
of the problem in 11).
23 Thi, view Can be found in several place,. Wright disr"ays the allitude on
occ..ion QH J pp. 146ft.}, and Achinsteln builds an argument lor the notion
of "design tunctions" U11 pp. 350ft.). Also d. Ruse (101.
512
(
Coa/·Stale Theory of function Attributions
I
10 do y. If I build windshieidwipersoul of <;ardboard, it is not sufficienlthat I selecled them for Iheir ability to clean windshields, that
they have that function. If they cannot enter into the means-ends
nexus in virtue of which my car outputs 0 (cleans the windshield in
the driving rain), then that is not their function. They do not actually
have that function since they <;an not actually deliver. I .... ould certainly discontinue using them when they disintegrated in the first rain
storm.
We could distinguish between the actual functions athing has and
the intended fUn<:lions it has (which it never can actually perform)."
We might think that intended functions are a category of functions
and that a thing may have intended functions in addition to what
actual functions it has. However, my own inclination is to think that
intended functions are in Ihe class of intentions, not in the class of
functions. If something is to have a function it must be able to stand in
a means-ends relationship of the required sort. It must be able to
perform that function. Merely intending that it perform the function
is not sufficient.
As for whether intentions are necessary conditions: it is a bit
harder to show that they are not. It is undeniably true that for most, if
not aU, human artifacts the intention of a designer or, at least, of the
user of the artifact, is an element in the causal chain which leads to
their acquiring functions. This is due to the fact that we are the kinds
of goal-directed systems which have desires and intentions as internal representations of goal-Slates. (We are mental systems.) II is not
clear, however, thai air goal-directed systems must be like us. Consider various animal species which employ artifacts as tools. for
instance, oilers use rocks 10 crack the shells of clams. The fact that we
can freely attribute to their use of the rocks the function of cracking
shells, without speculalingas to whether or not they hilVe intentions,
is an indication that consciously intending that x do y may not be a
necessary condition of IiC'S acquiring the function y. Goal-directed
systems may, at some stage in the biological chain, not be complex
enough to have intentions. If they still employ artifacts, then clearly
intentions would not be necessary conditions for the artifacts to
acquire functions.
I think that the same objections hold, mutatis mutandis, for
biological functions. The facllhat a structure was selecled for doing y
does not determine that doing y is ils sole function. II. structure x may
have been selected for doing y and acquire a new function y'. Con-
513
Frederick R. Adams
sider the behavioral pattern of pearlfishes. They adapted the behavior of living in the respiratory system of the sea cucumber. They
emerge at night and feed, and return to their hosts in the day. This
pattern of behavior seems to have been selected for a defense against
predators. However, it has led to the degeneration of the fishes'
mechanisms to defend against light radiation. Their eyes have reduced and their integumentary pigments, as well as other defenses,
have been lost. H It has now become a function of the behavior
pattern of the pe:arlfish to inhabit their nosts to avoid light radiation.
Although the behavior pattern was originally selected for defense
from predators, it has now acqUired another function. Hence, selec·
tion processes are not necessary conditions of function acquisition.
As long as the appropriate means-ends relation to a goal-state is
instantiated an allribution of function is warranted. (Of course, the
dependency upon the feedback information must also be satisfied.)
To see that selection processes are not sufficient for attribution of
function, think of the vestigal organs which have lost their functions
- such as the appendix.
A theory of function attributions based upon selection processes
is very close to the goal-state view. It is close since the feedback
mechanism of the goal-state theory will include both intentions and
desires in the description of the conscious design of artifacts (where
appropriate). It will also include selection processes in the description of the causal feedback loop which leads to the acquisition of
biological functions. However, a theory of function attributions
based purely on selection processes would be too restrictive and it is
this feature which I have tried to capture in the reasons which I have
cited for rejecting the theory.'·
Objection*1. Someone will no doubt object to the goal-state view in
the following way: "Surely there must be cases where x does y, in 5,
and y leads to S's OutpUlling 0, but 0 is not a goal-state for 5 and we
still attribute to x the function y." For instance, it seems perfectly all
right to attribute to the ozone layer the function of filtering radiation.
In order to handle such attributions, one must either show that there
is a go;,.l-directed system, e.g., the biosphere, for which this is a
goal-state. or claim that properly tutored intuitions would reject such
i1ttribUlions. I shaJltake the latter route. Why does it not sound odd to
attribute to the ozone layer the function of filtering radiation/It may
26
~ N~"
a'Sumenll again•• ~Ie<:tion theory as determining the I"ncrion'
of biological N.atu,es 18J.
514
Goa/·State Theory of Function Attributions
(
be that "~ find the attribution of functions to items like the ozone
layer plausible be<ause we are influenced by its effects on goal.
directed systems like ourselves. After all, the ozone layer's filtering
radiation certainly contributes to the goal-states of survival and reproduction in biologiul systems. It may be this conjunction with
goal-directed s~tems which makes function anributions of this sort
appealing. Would we. e.g., find the ascription plausible il there were
an ozone layer around Pluto and we knew that there were no goaldirected biological systems on P1utor If not. I suggest it is only due to
the connection between the ozone layer's filtering radiation. and our
reaching certain goal-states, which lends plausibility to such auribu·
tions. Since there is no causa' dependency - in a goal-directed
system _ between the filtering and our reaching certain goal.states.
we may (when intuitions are tutored) come to withhold auributions
of this kind.
Ob;ection ::#:3. In some systems there will be parts. structures, to
which we ascribe functions which do not depend on a feedback
circuit for their continuing to perform their operations. Does that not
show that to ascribe a function to a structure does not require that the
structure would not be performing its operation if it were not part of a
causal feedback loopr In a heating system the sensor which monitors
the room temperature would continue to perform its function even if
it were not in a goal·directed system, not in the feedback loop of the
heating system. That is, If its function is to monitor room temperature, it would have this function independently of occurring in a
feedback system.
In one sense. I would deny that a bimetallic strip or a container of
mercury would have the function, independently of any goaldirected system, of monitoring the room temperature. Any thermometric device only acquires its function as a thermometer by
being conjoined with a goal-directed system which employs the
device. Jt is true that the expansion and contraction 01 a container 01
mercury is not dependent upon its being conjoined with a goal.
directed system. It is false, however, that the expansion and contrac·
tion of the mercury can plilya functional role without being conjoined with a goill-directed system. So, initially. the sensor in the
heating system only ilCquires its type of function by going through the
feedback loop of the heating engineer.
After the sensor is installed in the system, the fact that it can
continue to perform its function (registering temperature) independently of a feedback circuit (that the thermometer continues to process information independently olthe output 01 the heater) requires
us to modify our analysis. Once a system acquires a function, it may
be necessary to ascribe functions to structures within that system as
515
Frederick R. Adams
acquired functions. First the system acquires its function by having at
least some of the components of the system meet the conditions of
the analysis, then other parts of the system may acquire functions
derivatively by virtue of the role they play, The mercury switch acquires the function of a sensor, derivatively, by the role it plays in the
heating system. But the crucial first step in the heating system's
acquisition of a function is that the system would nOI output heat if it
were not for the feedback loop in the control system.
Objection *4. There is a certain amount of intensionality involved
when we make lunction attributions. The goal-state view of functions
cannot capture this intensionality since if the function of x is to do y
and y leads to output 0, then when y - y', y' will lead to output 0, but
it may be false that the function of x is to do y'. II we build a paltern
recognition computer and we want the computer to detect leiters of
the alphabet (output 0) and we install a particular feature detector for
each )etler (where x is a feature detector!. then the function of the
detector x may be to detect the letter Q (which activity is y). Yet, we
know that the letter Q is the seventeenth letter of our alphabet and it
is false that the function of the feature detector is to detect the
seventeenth letter of our alphabet."
The goal·state theory must be able to explain why (1)
(1)
The function of the feature detector is to detect Qs
is true, while (2)
{2)
The function of the feature detector is to detect the
seventeenth letter of the alphabet
is a false attribution. let us assume that we build this device so that it
detects Qs by analy.<:ing their physical configurations. When this is
so, we will say that (2) is false because, although it is undeniably true
that if the device detects a Q it detects the seventeenth letter of the
alphabet, it is not in virtue of a Q's being the seventeenth letter of the
alphabet that the device detects it. Rather, it is in virtue of a Q's
having the physical configuration which it does that the device detects it. That is, we have set up the mechanism sothat it is theevent of
an item's having the physical configuration of a Q (its being a Qj that
triggers the mechanism and not the item's being the seventeenth
member of a series. It is the event of the Q's having the physical
27
516
Th;s e.ample waS suggested 10 me by Fred D,et,ke.
Goal·State Theory 01 Function Attributions
configuration it does which causes the mechanism (given its internal
configuration) to detect and output a "Q" when shown a Q.
We can show how to explicate the intensional nature 01 functional
contexts in this way without making explicit use of the fact that
function attributions are only applied to goal·directed systems, This
is clear in the above case, but let us also examine a case where we
need to appeal to the goal of a system. If (3)
(3)
The function of the heart is to circulate the blood
is true and it is also true that circulation of blood is Harvey's favorite
bodily function, it docs not follow that (4)
(4)
(
The function of the heart is to perform Harvey's favorite
bodily function
is true. (And (4) seems false even though when the heart circulates
the blood it does perform Harvey's favorite function.)
We can handle the latter case by maintaining that if the heart has
the function of circulating the blood, then circulation causally contri·
butes to an output a for which the system is directively organized.
let us suppose that output 0 is identical to the process of carrying
nutriment to the cells and removing wastes. Then, it is in virtue of
some property P, of circulation, that this process is able to be carried
out. However, that property is not the property of being Harvey's
favorite bodily function, P'. ForP' is not of the sort which could enter
into the appropriate means-ends (causal)relation with respect to out·
put O. Being Harvey's favorite bodily function is not causally relevant
to the circulation of the blood's being able to carry nutriment to the
cells and remove wastes. Thus. we cannot accept (4) as a true function
attribution. This example shows that we can account for the inten·
sionality of functional contexts where we have substitution of
codesignatlng terms for y in statement 01 the form "the function of x
is y." We can do it simply by detailing the intensionalityofthe causal
relations involved. In this way we explicate how the intensionality of
functional contexts can readily be assimilated to the intensionality of
causal contexts. Understood in this way, intensionality poses no
spedal problem for the goal-state theory of function attributions."
August 1978
28
I wish 10 Ihank Berent fnc, fred Dretske, and Elliott Sot>er for man) helpful
discussions and sugge,tion. which influenced my Irulmenl of funct;on
attribution,.
517
Frederick R. Adams
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pp.34Hi7.
[2J Braithwaite. R.B. SC",nrilic ExplilOalion. Cambridge: University Pr",•. 1955.
Chap, 10.
(3) Can/ield, J. "Teleological Explanations in Biology.'" 8riti.h Journal 01
Philo'JOphy 01 Science 14 (1'364).
[~J
Cannon, W. The Wisdom of the Body. New York: Norton. 1939, Ch.p. 12,
[SJ Cummins, Robert. "Functional Analy.i.:' Journal 01 Phllo'JOphy n (19751,
pp.741-65.
[6J Hempel, Carl. "The Logic 01 functional "'nafy<i•. " in I\s~t. of Scknrilk
bpl.nallon. New Yo"': free Pre... 1965.
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