An earlier version of this article appeared in Educational Theory 25,3 Summer 1975, pp. 278-302 as "The Functional Analysis of Behavior."

The Functional Analysis of Behavior:
theoretical and ethical limits

© 2000  Edward G. Rozycki, Ed. D.

edited 11/19/18


1. Introduction: Is mathematics required?
2. The Function
3. The Function as a Set-Theoretic Relation
4. Probabilization Introduces Another Variable
5. Skinner on Behavioral Functions
6. Compositions of Functions
7. Defining the Behavioral Variable
8. What Causes What
9. Voluntary Behavior
10. Constitutive and Mean-Ends Relations
11. Partitioning Rules
12. Constructing the Behavior-Partition
13. Meta-ethical Consquences of Achieving the BP
14. Trying, Refraining and Acting

15. Defeasible Concepts
16. Conclusions


The Mathematics of Behaviorism: an informal review
                       Problems with taking too literally the idea that behavior is a function of the environment.

Skinner's Walden Two -- a review
                        Critique of B.F.Skinner's personally unacknowledged philosophical commitments and a deconstruction of his utopian Walden II

Skinner's Concept of Person
                        The person as a locus of instructional decision-making, assumed by the Keller approach, is not theoretically compatible with Skinnerian Behaviorism.

Introduction: Is mathematics required?

The mathematical concept of function plays an essential role in what behavioral scientists of various theoretical persuasions conceive of as science. Jum C. Nunnaly -- who is a fairly straightforward behaviorist1 -- writes:

Scientific results inevitably are reported in terms of functional relations among measured variables, and the science of psychology will progress neither slower nor faster than it becomes possible to measure important variables2
Merle B. Turner who would eschew Nunnaly's philosophy as passť3 concurs:
The more complex our behavioral or neurophysiologicaI descriptions are and the more complex the hypothetical structure of our theories, then the more rigorous must be our logical calculi. It is a truism to say that the language of a mature science must be a mathematical one4.
B. F. Skinner provides the most succinct statement of the conception of science that we will be concerned with. However, so that the arguments in this essay not be restricted in their scope to a critique of Skinner's personal brand of behaviorism, the word external has been removed from the following quote, replacing it with continuation dots (...) to indicate its original positions:
The ... variables of which behavior is a function provide for what may be called a causal or functional analysis. We undertake to predict and control the behavior of the individual organism. This is our "dependent variable -- the effect for which we are to find the cause. Our "independent variables -- the causes of behavior -- are the ... conditions of which behavior is a function. Relations between the two -- the "cause and effect relationships" in behavior -- are the laws of a science. A synthesis of these laws expressed in quantitative terms yields a comprehensive picture of the organism as a behaving system.5
It will be our interest here to examine to what extent any functional analysis of behavior is possible. It might be said, for example, that the behavior, B, of a group or individual is a function of variables X and Y. This mode of expression tends to replace more vulnerable ones such as "X and Y are determining factors of B" or "the nature of B is influenced by X and Y." These raise immediate challenges. as to what is meant by "determining factor" or "influence." "Function" is clearer in this respect; even a casual acquaintance with mathematics exposes one to its definition. But while the term itself is clear, what remains all too often unchallenged is the propriety of its application.

Skinner remarks:

The commonest objection to a thoroughgoing functional analysis is simply that it cannot be carried out, but the only evidence for this is that it has not yet been carried out.6
Skinner's demand here for evidence is inappropriate. That something cannot be the case is not shown by evidence alone but rather along with substantial theoretical argument. Evidence is hardly crucial: no number of non-dragons is evidence of the non-existence of dragons. It is aim of this article to show that, in certain important dimensions, human behavior is not subject to a functional analysis because the definitional requirements for a functional relation cannot be met.

The Function

The mathematical notion of function expresses rigorously one sense of our ordinary notion of relationship, as, for example, when we say that there is a relationship between the size of a snowball and length of time it takes to melt. Similarly, one might look for a functional relation between the use one makes of one's air-conditioners and the size of one's electric bill.

Despite the homonymity, it does not mean what we understand by function in saying, for example, that a thermostat functions to maintain a constant room temperature. This second notion is used by theorists to provide "functional" explanations of motive or analyses of institutions. Such explanations relate "outputs" via "feedback" to behavioral or structural changes.7 The mathematical notion we will be concerned with is a specific kind of relation between sets. It is this concept which Nunnaly, Turner, and Skinner allude to above. For Skinner -- who accepts only external, "physical" variables -- a functional analysis of behavior would be an empirically determined relation between two variables, S and B. S is the set all possible (conceivable) environmental-state-types (stimuli). Members of S would be associated with particular members of B, the set of all conceivable behavior-types. But there is a presumption -- common even today -- that such general classes as the set of all possible environmental- state-types or the set of all possible behavior-types can be coherently made out.8

Imagine that we have a list of acts that John could perform, e.g. 'jump', 'talk', etc.. We will call this list "the behavior-set" and indicate it with B. Imagine also that we have a list of environmental-state-types. Let us call this list "the stimulus-set" and indicate it with S. Non-behaviorists might introduce other variables, e.g. internal states, expectancies. However, let us consider Skinner's model because it is simple. It is simplified here even more because Skinner actually treats behavior as a function of two variables: immediate environment and conditioning history. We will deal with functions of many variables later; no points will be made in the course of the present discussion which derive from our ignoring this sophistication. For Skinner's functional analysis, S is the independent, B, the dependent variable. If we can obtain the right lists, we will be able to relate them so that for a particular member of S, we will see exhibited by John behavior of a particular type from B.

Someone concerned to produce a functional analysis has both a conceptual and an empirical problem. What John might or could do -- which B is to capture -- is a matter of what kinds of terms one would admit as being act descriptions, things John might do. One might admit 'jump' but exclude 'own' because jumping but not owning is something John might do -- owning is not a doing. Such a decision is -- so to speak -- "pre-empirical." Similarly, one must pre-empirically decide what is to count as an environmental state. Only after S and B are defined to include all possible cases pertinent to them can one look to see what empirical relationships are to be found between them.

In order for it to be logically possible that any s, whatsoever, in S might be found to be associated with any b, whatsoever, in B, thus allowing the researcher to discover which particular s's and b's are empirically related, we must be careful not only to define the s's and the b's independently of each other, but also to make sure the types, bi and sj, are mutually exclusive. That means that nothing which is, say, an s1 can also be an s2; nothing which is a b4, a b17. The reason for this mutual exclusivity will be clearer after a definition of function is given below.

Let us consider for the moment a reason why S and B must be logically independent: if talking were to be defined -- let us say for some research purposes -- as speaking in the presence of a listener, then the presence of a listener could not be a stimulus for talking. It would be logically, thus empirically, impossible for someone to talk in the absence of a listener. Only a restricted empirical relation is to be discovered between talk and presence of listener, i.e. what proportion of presence-of-listener-events are also talk-events.9

The nature of the association between S and B is important. For a functional relation to obtain from S into B, that is, for behavior to be a function of the environment, each s may be associated with, mapped into, at most one of the b's. (The notation for "b is a function of s" is of the form b = f(s), or b = g(s) or b = h(s), where f, g and h indicate possibly different functions.) It is possible that to a particular b are associated more than one of the s's; but not conversely.10

A functional relation provides us with a set of behavioral laws, as it were. If s3 is mapped into b5, i.e. b5 = f(s3), this tells us that a subject under stimulus conditions s3 will exhibit behavior of type b5 and of that type only. Had we not taken care to define our s's and b's to be mutually exclusive, we might have ended up with the following situation: we discover an instance of a stimulus, s', that is of type si and also of type sj. Suppose, however, that bk = f(si) and bj = f(sj). s' is mapped into both bk and bj, i.e. a functional relation does not obtain. We are faced with an ambiguous behavioral law. Similarly, suppose there is an instance of behavior, b', that belongs to both bk and bj - It follows that if bk and bj are not identical, they cannot be associated in a functional relation with any s. Unless there is mutual exclusivity among the types, logical restrictions are placed on the possibilities of functional relationship.

Actually, Skinner did not have such a simple functional relation in mind despite what he wrote about behavior as a function of the environment (and conditioning history). He says in various places11 that the probability of a certain response is a function of environment (et al.). However, it is possible for the probability of a response to be a function of other variables without its being the case that the response itself is a function of anything. And it cannot be the case that both behavior and the occurrence probabilities of behavior are in the same functional relation to the same variables.

This is to say that it is not a matter of indifference whether we speak of "behavior as a function of such-and-such" or of "the probabilities of behavior as a function of such-and- such." To see that this all is so and so as to be able to identify other a priori restrictions that Skinner has placed on the notion of function, we will have to examine a more technical definition of function. What immediately follows will seem to the mathematically unadventured reader, unfortunately, a heavy dose of didactics; the more technically proficient will risk boredom. I entreat the reader's patience, however, for if confusion would be laid bare, some rigor must be endured.

The Function as a Set-Theoretic Relation

A function is a relation between sets rather than between variables.12 Consider two sets, A and B, the members of which may themselves be sets.13 If we pair each member a of A with each member b of B, in that order, we obtain the set of ordered pairs of the form, (a,b). This set of ordered pairs is called the Cartesian product (or cross-product) of A with B and is indicated by "AXB" (read "A cross B"). Any subset of AXB is said to define a relation between A and B. A relation is a function if and only if for any two pairs, (ai, bj), (ak, bm), in the relation, if bj is different from bm, then ai is different from ak

For any function in AXB, A is called the domain, B, the range of the function. The function is said to exist between A and B or from A to B (or onto or into B depending on whether or not all the b's appear in the relation). For a function with one independent variable, the function exists between the set of values of the independent variable and the set of values of the dependent variable (see footnote 12). For example, where behavior is a function of environment, b = f(s), S happens to be the domain, B, the range of the function. However, where there are two independent variables, say, environment and conditioning history, h, the associated sets of values of which are, respectively, S and H, such that b = f(s, h), then the domain of the function is SXH, i.e. the set of pairs of the form (s, h). A function is always a binary relation between more or less complex sets. Except in the case of single variables, the domain and the range are, in general, neither variables nor their associated value-sets but are the cross-products of associated value-sets.

An equation, e.g. y = 2x2, some of the terms of which may be variables, defines relations between sets. A function is said to be defined from its domain to its range. For y = 2x2, a function is defined from the x's to the y's since for any value of x there is but one value of y that is double the square of that value of x, e.g. for x = 2, y = 8. But y = 2x2 does not define a function from the y's to the x's, since for any value of y, there are two values of x, one negative, one positive, which satisfy the equation, e.g. for y = 8, x = -2 and x = 2.

We originally considered behavior as a function of environment, b = f(s). Skinner would have it that behavior is a function of both environment and conditioning history, e.g. b = f(s, h). It is important to note that s and h need not be functionally related to each other for b to be functionally related to s and h. A simple example will illustrate: suppose, for simplicity's sake, that there are but two environmental- state-types, s1 and s2; two types of conditioning history, h1, and h2; and four behavior-types, b1, b2, b3, b4 We can define a function using either of two notations:

b1 = f(s1,, h1) or cross-product member (s1, h1, b1)

(the triplet, (s1, h1, b1) is a simplified notation for ((s1, h1), b1)which shows more clearly the members of the domain and range in relation)

b2 = f(s1, h2) or (s1, h2, b2)

b3 = f(s2, h1) or (s2, h1, b3)

b4 = f(s2, h2) or (s2, h2, b4)

Note that to each s-h-pair is mapped only one of the b's; but that each s appears with each h. Thus a functional relation exists from the s-h-pairs to the b's but neither from the s's to the h's nor from the h's to the s's. It happens that a function exists from the b's to the s-h-pairs in the example given (also from the s-b-pairs to the h's and the h-b-pairs to the s's). That this is not significant can be readily demonstrated by deleting b4 and making b3 also a function of (s2, h2), i. e. b3 = f(s2, h2)

Probabilization Introduces Another Variable

A similar example shows that if the probability of a response is a function of certain variables, then those variables themselves need not be functionally related. A probability distribution is a set of numbers the sum of which is 1 and each number of which is at least zero or no more than 1. Something is probabilizable if and only if it can be conceived as the domain of a function of which a probability distribution is the range. That the probability of a response is a function of environmental and conditioning-history variables is formulated P(b) = f(b, s, h). It is easy to overlook that b is one of the variables because it serves merely to index the particular probability-values. Certainly, the statement, "the probability of the response is a function of environmental and conditioning history variables" might give one to believe that there are only two variables involved.

Let us consider a simple example with two behavior-types, b1, b2; two environmental-state-types, sl, s2; two conditioning-history types, h1, h2; and eight not necessarily different probability values, p1, p2, p3, p4, p5, p6, p7, p8.

p1 = f(s1, h1, b1)

p2 = f(s2, h1, b1)

p3 = f(s1, h2, b1

p4 = f(s2, h2, b1))

P5 = f(s1, h1, b2)

P6 = f(s2, h1, b2)

P7 = f(s1, h2, b2)

P8 = f(s2, h2, b2)

exhibits a functional relation from the s-h-b-triples to the p's. The reader can observe that no functional relations obtain among the s's, h's and b's themselves. To reiterate an important point, even though the probabilities of behavior may be functionally related to stimulus-conditions (and as an index, the behavioral variable), the behavioral variable itself need not be functionally related to the stimulus variable.

Another way to describe the above function is to say that the probability distribution on the b's is a function of s and h, i.e. (P(B1), P(B2)) = g(s, h) so that (p1, p5) = g(s1, h1), (p2, p6) = g(s2, h1), (p3, p7) = g(s1, h2) and (p4, p8) = g(s2, h2). This comes closer to the idiomatic English formulation but is possibly misleading. Skinner confounds the mathematical terminology in speaking alternately both of behavior or of the probabilities of response as a function of environment, et al. Unfortunately, his is no concession to idiomatic usage but rather symptomatic of a more general mathematical misconception. On that has he founded a theory.

Skinner on Behavioral Functions

If we examine what Skinner has to say about behavioral functions, we discover that he has placed two restrictions on the notion: a) he seems to have in mind only one-to-one functions; and b) he confuses the distinction between a function of several variables and a composite function. These new technicalities will be explained in the course of the following exposition.

Skinner ventures a prediction:

Eventually a science of the nervous system based upon direct observation rather than inference will describe the neural states and even's which immediately precede instances of behavior. We shall know the precise neurological conditions which immediately precede, say, the response, "No, thank you." These events in turn will be found to be preceded by other neurological events, and these in turn by others. This series will lead us back to events outside the nervous system and, eventually, outside the organism.14
In theory, at least, the functional relation provides a direct connection between behavior and the external conditions which cause it:
...we have a causal chain consisting of three links: (1) an operation performed upon the organism from without-for example, water deprivation; (2) an inner condition-for example, physiological or psychic thirst; and (3) a kind of behavior-for example, drinking.15
For the present discussion it is behavior, rather than the probabilities of response that are being treated as a function of environmental variables. Skinner continues that therefore,
Unless there is a weak spot in our causal chain so that the second link is not lawfully determined by the first, or the third by the second, then the first and the third must be lawfully related.16
Here Skinner is forcing upon us the alternative that the relation between the first and second links is either a functional relation or else the second link is not lawfully determined.
If we must always go back beyond the second link for prediction and control, we may avoid tiresome and exhausting digressions by examining the third link as a function of the first.17
Skinner would "go back" from behavior to its cause. But going back through a functional relation is problematic unless the function is rather simple, say, a one-to-one function. For such a function, one can treat the range as a domain and vice versa and still preserve a functional relation. For example, if y = f(x) and y = 2x, the function is one-to-one since for every x there is but one y, doubled in value, which is associated with it; and, for every y, there is a single x, half its value, associated with it. But if y=x2 the function y = f(x) is not one-to-one, since for every y, there are two square roots, one positive, one negative, associated with it.

Suppose someone's behavior to be a function of three variables, m, y, and z, which here, for simplicity's sake, will assume only integral values. Suppose also that the equation b=m2+y2+z2 gives this relation. Now, if b = 12, there are eight different environmental states, i.e. combinations of values of m, y and z, that can be gone back to:  2,2,2;  2,2,-2;  2,-2,2;  -2,2,2; . . . etc. This would augur some practical difficulty in identifying the causes of behavior. But one may raise a much more serious point.

Skinner seems to think that nothing important can be discovered about the organism's internal states relative to its behavior and environment:

Valid information about this second link may throw light upon this relationship but can in no way alter it.18
Skinner does not even consider the possibility that behavior may be functionally related to internal-state and environmental variables which are themselves not functionally related. Skinner's notion is that behavior is a composition of functions of environmental variables. This inadvertant restriction -- it is doubtful he was aware of it -- severely biases his theory.

Compositions of Functions

For purposes of illustration, let us contrast a composition of functions with a function of, say, two variables. If b is a function of s and h, but s and h are not functionally related, then b is a function of two variables: b = f(s,h). If, however, s and h are functionally related, say, s = g(h) -- g stands for a possibly different function from f -- then b is a composition of functions of h, written b = f(g(h)). Skinner conceives of behavior as functionally related to only those internal states which are themselves functionally related to environmental states and values of the conditioning history variable, e.g. b = g(i) and i = f(s,h), thus b = g(f(s,h)). What appeared at first to be the general goal of his program, the achievement of a functional analysis of behavior, worthy of any scientific psychology, is sacrificed to his procrustean Behaviorism.

In summary: Skinner restricts the mathematical notion of function by requiring that a functional analysis of behavior (or of the probabilities of behavior) show behavior (or the probabilities of behavior) to be a composition of relatively simple functions of environmental and conditioning history variables. The functions must be relatively simple or we lose control over the behavior, not having accounted perhaps for a multiplicity of causes. The general function must be composite, lest we admit variables Skinner is not even willing to consider admissible in a scientific enquiry.

Skinner's restrictions derive from his antique belief that only efficient causation -- as philosophers are wont to call it -- is the proper object of scientific study.19 He conceives of a cause as a kind of external push and treats as "miraculous" any behavior conceived as autonomous, i.e. not functionally related to external causes.20 Skinner would treat organisms as physical systems -- he is not unique, nor necessarily mistaken in this. But he seems committed to ignoring the fact that there are many physical systems which are not models of efficient causation, in which, for example, not external variables but temporally prior states of the system are functionally related to the present behavior of the system.21

Skinner's philosophy hamstrung his science. We will not belabor the point although we will continue to examine some others of Skinner's opinions below as a focus for criticism, inasmuch as these opinion appear to guide research even today. So far, our critique has served its purpose of expounding a concept of function sufficient to our more general goal.

Defining The Behavioral Variable

We can now indicate the form of a behavioral function general enough to accommodate a wide range of theory:

P(bi) = fj(bi, x1, x2, ... , xn, f1(xh), f2(xk), ..., fn(xr), ...).

In English, this says merely that the probability of a response's being of type bi is a function of bi and of other variables or of functions of other variables. We will continue to be interested in the following: such a function can be defined only if the members of B are mutually exclusive and exhaustive of all possible behavior. If B or some subset of B can meet these two conditions of mutual exclusivity and exhaustiveness, then B or that subset will be a behavior partition -- hereafter called a BP.22

The fundamental problem in providing a functional analysis of behavior is this: how can we define a BP and retain the external validity of our behavior-types? That is, how can we simplify behavior types so that they are mathematizable and yet can be applied to behavior as it is normally identified? Skinner admonishes us in Beyond Freedom and Dignity that in order to solve the terrifying problems that face us in the world today, ". . . we need to make vast changes in human behavior." 23 Certainly, if we are to achieve a relevant "technology of behavior," the functional analysis we seek to provide must be of the behavior that we understand to be the problem, or, at least, the behavior-types in terms of which we understand the problem must be demonstrably reducible to the behavior-types which our functional analysis deals with.

Later in the same book, Skinner complains that behavior has not been treated as a subject in its own right; that theorists continually introduce "mentalistic" concepts to explain behavior.24 Elsewhere, he insists that behavior be described in "physical" terms.25 But what behavior of interest can be so identified? What might Skinner consider a physical description of behavior? He writes

When we tell an anecdote or pass along a bit of gossip, we report a single event - what someone did upon such and such an occasion: "She slammed the door and walked off without a word."26
Why is this a single event rather than two or more? How does slamming a door differ from pushing it hard in a way that physical criteria can differentiate them? What is the difference between 'walk' and 'walk off', between 'not talk' and 'refrain from talking' that can be so differentiated?

One may not shrug off such questions as philosophical quibbles, saying something like, "It doesn't matter what terms you use, but what you refer to." Such a cavalier attitude toward the common language on the part of the behavioral researcher not only begs questions of external validity but undercuts the presumption that his research is relevant to practical concerns.

Skinner writes:

A single set of facts is described by the two statements: "He eats" and "He is hungry.27
If Skinner means that the one sentence means the same as the other, he is certainly not speaking English -- any dieter could tell him the difference. On the other hand, if the description of facts is something other than given by the meaning of sentences, we must ask what exactly this "single set of facts" is and how it relates to what we understand the two sentences to mean. Skinner shares with not a few theorists the notion that behavior is something homogeneous and readily accessible to a "pretheoretical" observation. Such naivete nourishes the hope that psychology can be a natural science which might deal with phenomena in a theory-innocent manner.

What Causes What

Arthur L. Stinchcombe writes:

A science starts off with its variables defined by common sense, by the distinctions that people make in daily life. Because people, in order to live efficiently, have to take account of the causal forces at work in the world, they make distinctions which are institutionalized in the language they speak.28
Although it might be of interest, this is not the place to ask which aspiring sciences in fact started off that way and turned out successfully. A more pertinent question might be whether people are generally concerned to live "efficiently" or whether considerations of tradition and value are more likely to inform their action. More importantly, is the notion of cause or effect that seems to underlie our asking, "What makes this happen?" or "What made him do that?" the same notion as it is articulated in some of the sciences?

By way of contrast, it is clear that belief in a "naive approach" is not shared universally; Clyde H. Coombs writes:

The basic point is that our conclusions, even at the level of measurement and scaling (which seems such a firm foundation for theory building), are already a consequence of theory. A measurement or scaling model is actually a theory about behavior, admittedly on a miniature level, but nonetheless theory; so while building theory about more complex behavior it behooves us not to neglect the foundations on which the more complex theory rests .29
Our interest here is in this theory at the "miniature level" for at this level its consequences are most significant.

The reason the naive approach fails is that behavior-types in the natural language are applied according to different conventions: they can be multileveled and are not often mutually exclusive. Nor are their criteria of application normally solely physical, if physical at all, but in terms of intent, outcome and participation in social codes. Suppose, for example, that the verbs utter, say, speak, tell, warn, and surprise indicate behavior-types: I may utter something without saying anything, although in saying something I am normally also uttering, also speaking. I may say something and yet not be telling it to anyone, although in telling someone something, I -normally am saying it but perhaps not in so many words. I need not tell you something to warn you, although I may do so on occasion; nor is telling you necessarily warning you. My warning you may or may not surprise you. My surprising you might have nothing to do with my warning you.

Behavior cannot be dealt with "naively," i.e. pre-theoretically, because it takes a theory to sort out behavior-types into mutually exclusive types that will generate data. It does no good to insist that a scientist "merely reports what he sees,"30 because neither reporting nor seeing are theory-innocent activities. There is no "what-he-sees" that can be specified without recourse to some typology in terms of which it is identified; and seeing is itself not unaffected by one's expectations. It might appear that with this last contention the distinction we normally draw between theory and empirical work falls. It doesn't. The theoretical/non-theoretical contrast holds relative to specific theories or activities; there is, for behavior, just no absolutely pre-theoretical Stoff, no behavioral phenomena.

Stinchcombe would begin where one must: with the conceptions of behavior and human action that play a part in our everyday interests and problems. His mistake is in thinking that a single technical notion of cause is waiting there to be found rather than that it is something imposed from without by the theorist.

Stinchcombe's concept of cause is much the same as Skinner's: A causes B if and only if A and B are independently defined covariables such that B can be controlled by manipulating A.31 It might seem that such a notion could be "abstracted" from situations of the following common sort: one turns up the gas on the stove and the water boils more rapidly; or, one presses the door-bell button and the bell rings. But our natural language allows for other notions of cause which one ignores at the risk of undermining that presumption of relevance which one's intended research ought to have to the problems it purports to deal with.

(It is beyond the intended scope of this article to go into this at any length, so I merely offer the following as examples of explanation which are quite common yet problematic in terms of Stinchcombe's concept of cause:

a. John shouts like that because he wants to scare Mary.

b. John makes his biceps tremble by wiggling his fingers.

c. John controls the flight of his golf ball by controlling his follow-through.

d. John maintains a strong high-C by singing the note up between his eyes.

e. John learns some things more rapidly by paying attention to what he is doing.

I leave to the reader the exercise of identifying the variables and examining their relationships. These examples are unusual only in the perplexing relationship between the obvious variables. Take b. for example: John can control the wiggling of his fingers directly, but not the trembling of his biceps, directly. But clearly, from a physiological point of view, the trembling biceps are the physical cause, or a contributor thereto, of his fingers' wiggling.)

The problem in constructing a behavior-partition (BP) is this: we must begin with our everyday conceptions of behavior, the ones in terms of which we identify our problems and express our interests, without treating them prematurely as "data"; we have to simplify them to the extent it is necessary to achieve a BP, fully aware that what we do may impair the expressiveness of the natural language.

After systematizing the language, we may not even be able to formulate certain statements about human behavior; the questions that interest us most about why people do as they do may not be askable, much less answerable. To illustrate: suppose say, and assert to be behavior-types. They cannot both be in a BP, since in saying, "I am rich" under certain circumstances, one asserts that one is rich, they are not mutually exclusive-nor is one always a case of the other.

Likewise, if John scares me by grimacing, not both scare and grimace can be in the BP. Assume then, that assert and scare are not in the BP. Suppose now that we analyze "John has learned to X" as "The probability that John will X (under conditions Y) has reached p." "John has learned to tell the truth" is not expressible in our BP-terminology, since telling the truth always involves some asserting-it is not merely saying things that happen to be true-and assert is not probabilizable since it is not in the BP.

Nor can we render in our mathematizable English "John has learned to scare me, when I ignore him." In general, we might expect difficulty with a BP in dealing with two areas of interest: some descriptions of the sort "John X-es in Y-ing" - which express what I will call a constitutive relation between X and Y; and some descriptions of the sort "John X-es by Y-ing," which may indicate a means-end relationship between X and Y. These relationships are of interest because constitutive relations appear in what is called "rule-following" behavior, and means-end relations provide us with the language of purpose. Our main concern in this essay will be with self-controlled behavior. I will call this behavior "voluntary behavior" ignoring the distinction between what one does freely and what one may do under duress so long as it is the case that, disregarding the consequences, one could have acted otherwise.

At this point, it might be helpful to sketch the main argument to come: I will define below the terms "behavior" and "voluntary behavior." I will then describe the behavior of a model agent. These descriptions will enable us to obtain a set of rules for recasting statements about behavior into statements about members of the set of behavior-types with an eye to transforming this set into a BP. We will consider how this process of partitioning affects the way we can talk about the model agent. Finally, I will demonstrate that if we achieve a BP, we cannot meet the criteria for voluntary behavior; or conversely, if we maintain the criteria for voluntary behavior, we cannot achieve a BP. This argument will be followed by some extended comment on the nature of the criteria for voluntary behavior.

Voluntary Behavior

We are observing John's behavior. We will identify behavior-types by the following criterion:

B: 'X' is a behavior-type if and only if, to the question,"What is John doing?" one can answer, "John is X-ing."

By this criterion the following are not behavior-types: 'own', 'hate', 'require', 'have to and 'intend'. B is "naive" in that it is intended to capture our intuitions about what we would ordinarily think of a person as doing, without restricting such descriptions to exclude habitual or involuntary behavior as a criterion such as:

B': 'X' is a behavior-type if and only if X can be performed by John

might, since one is not normally said to be performing, or executing a performance of, a cough or, say, a twitch without implying that it is voluntary as when one is, in fact, play-acting. 'Intend' is excluded because to say that John is intending something is not normally to answer the question what he is doing.

(Also, 'intend' is to be excluded because it will be shown that it is not necessary to introduce the notion of intention per se to obtain the conclusion that voluntary behavior is not reducible to some "generic behavior language"32 of types which can be partitioned to provide a science of behavior.)

In the commentary on section 2.01 of the Model Penal Code, it is stated that:

The law cannot hope to deter involuntary movement or stimulate action that cannot physically be performed.33
Any justly intended prohibition from some type of action, say, X-ing, must presume that it is possible to refrain from X-ing. Also, to fairly require that one X must presume that X-ing is something one can try to do. In light of such considerations, I will give two characteristics of self-controlled behavior -- hereafter called "voluntary behavior." In the following formulations, B is the set of behavior-types:

Vl: 'X' is a voluntary behavior-type only if 'X' is in B and 'refrain from X' is in B.

If it is to be logically possible for someone to jump, then 'jump' must be a behavior-type. To the question, "What is John doing?" note that it is possible to answer, say, "He is refraining from talking," i.e. 'refrain from talking' is in B. (That one can so answer does not mean that another answer is not possible and this, we will see, is the whole crux of the matter.)

V2: 'X' is voluntary only if 'try to X' is in B.

This is to say that an act is voluntary only if one can try to do it. However, one may be able to try to do what one in fact cannot do -- this is why the implication only goes one way -- as when we say that someone is trying to communicate with his dead uncle.

Also, it does not follow that just because one can X and also try to X that 'X' is voluntary. For example, one might catch a ball on the fly just as it is about to strike one in the face, having seen it coming out of the corner of one's eye. Yet one may not be able to repeat the performance when trying to do so. Having caught the ball in this manner was not a voluntary act; one does not have control over the behavior in the way we will be concerned to deal with.

One might ask whether trying of any sort is a kind of behavior. There are strong prima facie grounds for accepting it as such. First -- and this is why we have chosen this criterion for behavior -- "What is John doing?" is often normally answered with a formulation of the sort, "He is trying to X." Secondly, trying-to behavior is accepted as behavior by many theorists in the belief that functional accounts of the feedback-control type mentioned early above can explain such behavior.34 Finally-and not unimportantly -- trying-to behavior can be reliably identified by different observers. Presuming the adequacy of a peripheralistic account of behavior, one might reject such trying-to types because they are not identifiable by immediately observable criteria. But there is no adequate peripheralistic account; and such a move is more than question-begging. That the criteria for trying-to behavior are not immediately observable does not disestablish the reliability of the identification of that behavior.

So as to get on with the argument, I will postpone an extended discussion of trying and refraining. Suffice it now to note that trying to X and refraining from X are voluntary acts per se; that is, there is no conceivable description of John's behavior as involuntarily trying to or involuntarily refraining from X.35 VI and V2 need not hold for trying and refraining behavior.

John -- who has served us well in previous formulae -- will be the model agent. The point here is to describe John's acts as normal human behavior but in such a manner as to be able to relate them to the set B of behavior-types. I will begin by stating all of the formulae to be given in this section. A restatement of each formula will then be given followed by pertinent comments. The formulae are all of the form A*B, where A is a true statement about John's behavior; * is a logical connective; and B, a statement about the set of behavior-types, B. The formulae are, in effect, rules which will enable us to translate some statements about John's behavior into statements about B; or, which may allow us to translate from statements about B back into statements about John's behavior. The formulae are:

1) John can X (if and) only if 'X' is in B;

1') "John is X-ing" implies " 'X' is in B";

2) John can X by Y-ing only if, for some X and some Y in B, some instance of Y is also an instance of X.

3) John can X in Y-ing only if, for some X and some Y in B, some instance of Y is also an instance of X;

4) John can refrain from X only if 'X' is in B and 'refrain from X' is in B; and finally, 5) John can try to X only if 'try to X' is in B.

The reason for the parenthesis in formula

1) John can X (if and) only if 'X' is in B

is that "John can X" normally means "John is actually able to X"; but for our purposes we need only "It is logically possible that John might X.- "Can" is ambiguous with respect to the distinction between John's actual and potential behavior, i.e. between what he is now able to do and what he is now not but might come to be able to do. If "can" is interpreted as merely indicating a logical possibility, the implication goes both ways. (Of course, since we are talking about logical possibilities, rule I admits of translation into any logically compatible language without restriction for cultural difference. This is because it makes the hardly profound statement that someone can be said to be doing only what the language allows us to say.36)

Considering rule 1, it is easy to understand a certain traditional approach to explicating learning. Skinner, for example, treats learning as "the reassortment of responses in a complex situation."37 Potential (logically possible) behavior becomes actual by having the probability of its occurrence increased.

What I here call "actual behavior" Skinner calls a "repertoire"; the repertoire is built by operant reinforcement38 and individual behavior-types may be removed from it by extinction.39 I do not think such an analysis adequate to account for many important kinds of learning,40 but it is pertinent here only to note that underlying this notion of repertoire are some important assumptions. Skinner would have it that to say that a person has learned something is to say that that response is in his repertoire. To say that he can no longer do something is to say that that response has dropped out of his repertoire. But at what point, i.e. probability value, does a response drop out of the repertoire? One may stipulate a value but that is being arbitrary. The theoretically sensible move here is to treat a response as extinct, as having been removed from the repertoire, when it is as likely to occur as a response that has not been reinforced under the specified conditions, i.e. when the response is effectively random. Any criterion for extinction other than effective randomness is theoretically arbitrary.

But here is the rub: effective randomness is a function of the size of the BP. For example, assuming, for simplicity's sake, all act-types equiprobable, if not in the repertoire, for a dichotomous BP consisting of 'X' and ,not-X', the effective-randomness criterion gives an extinction probability value .5, i.e. 1/2; for n behavior-types, it would approach 1/n. But the size of the BP is a consequence of pre-empirical decisions and Skinner protests himself innocent of such decisions. Also, he and others take an increase in the rate of response to be an indicator of an increase in the probability of response. But this presumes again a well-defined BP. That I saw two geese fly by my house on Monday and three fly by on Tuesday gives me no call to conclude that the probability of my seeing a goose is higher for Wednesday than it was for Monday, unless I know something about the size and distribution of the entire flock.

There is a corollary to 1) which deserves explicit statement:

1') "John is X-ing" implies " 'X' is in B."

Having observed John X-ing allows us to place X in B. 1' is the "empiricist corollary." The viability of our program to develop a mathernatizable set of behavior-types, a BP, presumes this corollary. So, for the purposes of exposition, we will accept it. However, it requires acceptance of a debatable philosophical theory that to describe is necessarily to name attributes characteristic of the thing described .41

Our next rule is:

2) John can X by Y-ing only if, for some X and some Y in B, some instance of Y is also an instance of X.

For example, it may be the case that John can signal me by waving his hand, or that John can warm his living room by lighting a fire in the fireplace.

3) John can X in Y-ing only if, for some X and some Y in B, some instance of Y is also an instance of X.

In snapping at me, John may express his dislike for me; in saying, "en garde," John may announce an attack on my queen. As far as the relations among members of B are concerned, 2) and 3) are much the same. A full exposition of the conventions which govern the contrastive uses of "by" and "in" is beyond the scope of this paper. However, I will briefly indicate some of the more obvious differences because they will bear on later discussion on partitioning B.

Constitutive and Means-Ends Relations

Recall from above the distinction between a constitutive relation and a means-end relation between X and Y. If, in some circumstances, Y-ing counts as X-ing, then Y is a constituent of X. This relation may obtain, for example, between waving one's hand and signalling. That something counts as something else is a conceptual rather than an empirical matter, i.e. given the appropriate circumstances, the relation holds by virtue of terminological convention rather than by additional matter of fact. On the other hand, that a means-end relation' obtains is a matter of fact: X and Y must be factually42 and conceptually distinct and factually related.43. Such a relation may obtain if 'X' = 'warm up the room' and 'Y' = 'light a fire'.

Where a constitutive relation obtains, "by" is normally used to indicate intent; "in", lack of intent. Compare

a. John signalled me by waving his hand.

b. John signalled me in waving his hand.

For b., the signalling was inadvertent. Suppose that John and I are cheating at poker. I might have occasion to say

c. John waved his hand in signalling me

if he waved his hand despite my having told him to refrain from hand movements because they were too noticeable.

d. John waved his hand by signalling me

indicates a situation of some abnormality, where John controls constituent behavior only by embedding it in a more generalized response. This sort of thing happens when we can't recite a line of poetry or sing a snatch of a melody except by doing the whole piece. d. is abnormal not only because it is strange that someone could not move his hand on request yet perform an act involving a hand motion but also because d. presumes that getting John to signal will succeed in getting him to wave his hand-as if he knew no other way to signal. (Consider the child's ploy, "I bet I can make you talk like an Indian." Any first grader knows to respond with anything but "How?")

For an X and Y which are at best contingently related, "in" indicates "in the course of" or "pursuant to," e.g.

e. In lighting the fire, John warmed the living room,

whereas "by" indicates the chosen means to the related end: compare

f. John warmed the living room by lighting the fire;

g. John lighted the fire by warming the living room.

The relevance of these considerations will become apparent when we consider below behavior that is controllable, yet not voluntary. Our next rule is a variant of Vl:

4) John can refrain from X only if 'X' is in B and 'refrain from X' is in B.

V2 gives us

5) John can try to X only if 'try to X' is in B.

In summary: By virtue of rule 1, certain behavior of our model agent John is possible; by virtue of 2 and 3, some behavior is ambiguous. However, 4 and 5 are not sufficient for some of John's behavior to be voluntary. They state conditions which are merely necessary. We will assume that some of John's behavior is voluntary.

Possible behavior is any of a type contained in B. Ambiguous behavior is any such that it may be an instance of more than one type in B. Behavior is voluntary only if it is any of a type X contained in B such that the types 'try to X' and 'refrain from X' are contained in b.

Partitioning Rules

In order to avoid logical restrictions on what may be functionally related, B must be transformed into a partitioned set, a BP. The characteristics of a BP are the mutual exclusivity of the member behavior-types and the exhaustiveness of the set vis-a-vis all types of behavior, i.e. any instance of behavior must belong to some type contained in the BP. Restricted BP'S are relatively easily defined; every research student learns to make some. It is the most general, global BP -- the philosophically important one -- that poses a problem.

If we succeed in defining a BP on B, we will have established the possibility of globally applicable behavioral variables independently of the theories in which they might be used. This is a concern of anyone, behaviorist or cognitivist or whatever, not resigned to an inevitable eclecticism in psychological theory.

Consider a tally. A tally is a function which assigns to each type of behavior a number which indicates how many instances of behavior of that type have occurred in some specific situation. For informal use or for restricted studies, we may resort to a dichotomous BP, containing X and not-X, e.g. 'jump' and 'not-jump'. Let us imagine a series of experiments, E1 E2, ... , En for which are defined a corresponding series of BP's, i.e. BP1, BP2, ... , BPn. While each particular BP serves us well enough in its particular circumstances, it does not follow that by combining the BP's (set-theoretic union), we will obtain a general BP.

This is to say that the possibility of well-defined behavior-types for specific experiments gives us no reason to presume the possibility of a general BP. That this is so can be understood by considering that we might examine the contents of a box and tally separately all the apples, fruits, shoes and useful objects it contained. But we could not tally them together for fear of multiple entry, since the same object may be an apple and a fruit as well as a useful object. This is an especially important consideration when trying to compute relative frequencies or similar measures which relate the number of occurrences of a given type to the set of types as a whole. Our concern here in attempting to define a general BP is with fixing the set of types taken as a whole.

The criterion of mutual exclusivity provides that the same instance of behavior cannot be an instance of more than one type:

Pl: If X and Y are different and both in the BP then John is X-ing only if he is not Y-ing.

The criterion of exhaustiveness would have it that not to do one thing must be to do something else:

P2: If John is not X-ing, then John is Y-ing where Y is in the BP.

It follows directly from P2 that whatever John is doing, there is some Y in the BP such that John is Y-ing. The important use of P2 is that if it is a necessary condition, for some reason that John not X, this condition can be replaced by one that it be necessary that he Y. This use will be made in an argument to follow. P1 and P2 produce what can only be called idiomatic oddities. For example, "John wants not to sing" and "John wants to not sing" are equivalent expressions and imply "John wants to X" where X is some other behavior-type.

(But, of course, "want" is not in B, so there is no problem with this oddity in particular. More pertinent to our concerns is the equivalence of "John tries not to X - with "John tries to not-X, " that is, "John tries to Y." But more on this later.)

In the previous section, five characteristics of B relating to the possibility, ambiguity and voluntariness of John's behavior were given by rules 1 through 5. We will now sieve them through P1 and P2, i.e. from the members of B, we will attempt to construct a BP.

Constructing The Behavior-Partition

1 for B is paralleled by

BP1: John can X if and only if X is in the BP.

The important difference is that X can be in a functional relation if and only if X is in the BP. "Can" indicates logical possibility.

The obvious way to meet the criterion of mutual exclusivity is to get rid of the ambiguities introduced in B by rules 2 and 3. Since by this criterion no X is also a Y unless X and Y are identical, constitutive relations are not possible among members of the BP. We can formulate

BP2: If John can X without Y-ing and Y without X-ing, then if John can X in Y-ing not both X and Y are in the BP

If X is neither a subtype of nor identical with Y, and vice versa, then a constitutive relation's obtaining between them is sufficient that they not both be in the BP. A consequence of BP2 is that only constituent behavior-types, can be in the' BP; behavior-types of which they are constituents are not. It follows therefore that either there are ultimately simple behavior-types, or there cannot be a BP. (By "ultimately simple behavior-type" I mean a behavior-type of which no behavior-type is a constituent.)

BP2 precludes the possibility that rule-following behavior can be functionally analyzed. To say, "John is following rule A" is not to name a unique behavior-type in B. Rather it is that John's X-ing or Y-ing in certain circumstances counts as following rule A. To obey a traffic signal is to stop or go or proceed with caution according to certain conventions. But to introduce the notion of convention in identifying behavior ipso facto indicates that we are dealing, not with contingent, but with conceptual relations among behavior-types.

We rid ourselve's of the ambiguities introduced by rule 3 with

BP3: If John can X without Y-ing and Y without X-ing, then if John can X by Y-ing, not both X and Y can be in the BP.

In our endeavor to construct a BP, we would compare pairs of behavior-types from B and, using BP2, reject one of any pair we might find in a constitutive relation. It appears at first glance that BP3 provides us with a similar rule of thumb for sorting out the members of B which can or cannot belong to the BP: e.g. behavior-types identified in terms of "effects" cannot be in the BP.

Consider again 'grimace' and 'frighten'. Suppose John frightens me by grimacing. It seems quite unproblematic to identify 'frighten' as an effect or result of 'grimace' and to exclude it from the BP on these grounds. It is, after all, an important descriptive convention of the natural language to identify behavior in terms of what seems to be its effects. Behavior often appears to admit of alternative description in such a way that we can sort out categories into some "cause-effect" or "input-output" relation, e.g. shoot-kill, yell-scare, kiss-excite, pull-tear, etc. But there is a rub: for many things that we do, the "input"-behavior is not voluntary and can be controlled, if at all, only through the "output"behavior, which is voluntary. If what we were dealing with were merely a case of the "same" behavior being identified by different terms according to different conventions, then the voluntariness of the behavior ought not to be affected by a mere change of description.

For example, recall John who, while playing golf, controls the flight of the ball by controlling his follow-through. The trajectory of the ball is determined by the velocity and spin of the ball. These in turn are determined by the size of the force applied to the ball by the club and by the location of the area of impact. The size and location of the applied force will vary depending upon how John swings the club. Inasmuch as the follow-through follows the swing and occurs even after the club has ceased to have contact with the ball, the follow-through can have no physical effect on the ball's trajectory.

Suppose now that we can identify different ways of swinging the club which produce a specific trajectory. Suppose also that corresponding to each type of swing there is a particular type of follow-through that John performs. Although in hitting the ball John may be able to discriminate among the types of follow-through, he may not be able to do so among the types of swing. This is indeed why concern with one's follow-through is important.

Criterion V2 has it that behavior is voluntary only if one can try to do it. But one cannot try to X in circumstances either where one does not know what X is, or where one cannot discriminate what is from what is not an X. We could not imagine, for example, what John could mean were he to say, "I don't know what I'm supposed to do but I'm trying to do it anyway." It would be similarly perplexing were he to claim, "I'm trying to control my blood pressure but I don't know how to tell when I'm doing it." (So-called " bio-feed back" devices enable us to control otherwise non-controllable behavior by providing us a means of discriminating the effects of our behavior. This does not make controlling our blood pressure a voluntary action.)

It is by no means unusual that some behavior might be controllable yet not voluntary. John controls his pre-impact swing by his follow-through. A pianist may control the duration of the individual notes he plays through his phrasing. Learning to drive a car is not equivalent to learning a complex combination of throttle-clutch-steering-wheel-positions which vary according to road conditions. Rather it is learning to keep the car properly on the road. It is the "output"-behavior through which the "inputs" -- if we can identify them at all -- are controlled. But one cannot have "inputs" and "outputs" in the same set of behavior-types and have a BP. Moreover, it is misleading -- not to say fatuous -- to borrow input-output terminology from systems analysis. Inputs and outputs are contingently related, separate variables whereas in the behavioral context these terms may not indicate separate variables.

Meta-ethical Consequences of Achieving the BP

With BP2 we lose the constitutive relation among behavior-types essential to the identification of rule-following behavior. BP3 rids us of purposive behavior as well since means and end cannot both be in the same BP. But couldn't we have more than one BP, say, BP1, which could be functionally related to other variables and contain "means "-behavior-types, and BP2, which could be functionally related to BP1 and contain the "ends"-behavior-types? There are some problems with this line of thought. One must take care not to recast our rough-hewn means-end distinction as being in fact a cause-effect relation. For someone's behavior to be purposive it is necessary that he have some notion of means and end; it is not necessary that what he takes to be a means be in fact a cause of that end: unlucky or stupid people still have purposes although through their means they may never achieve their ends. The problem with setting up BP1 and BP2 is that, without additional theory, we cannot obtain a functional relation because any means can be such to a variety of ends.44

We will now deal with voluntary behavior. Behavior is voluntary only if it can be refrained from. We can identify two conditions necessary for John to be refraining from X-ing: a) John must be in fact not X-ing; and b) John must be trying not to X. By BP2 we can replace condition b) with b') John is trying to Y, This also trivially satisfies a), since if John is trying to Y, then he is not X-ing. Thus the two conditions for refraining are satisfied by a single one that John be trying something else. This is to say that, in BP-language, John cannot fail to refrain from X-ing. If we have allowed 'fail to X' as a behavior-type, we arrive at a contradiction. On the other hand, we might not have admitted 'fail to X' as a behavior-type by B in which case we could not even express the ordinary English possibility that John might fail to refrain from X-ing.

Suppose, then, we have not admitted 'fail to X' to B. It follows from the immediately preceding considerations that for every X in the BP, there is a Y such that 'refrain from X' is identical with 'try to Y' where X and Y are different. We seem to have but two alternatives left: we surrender our intuition that refraining from sneering, for example, is not the same as trying to scratch the back of our heads, or we surrender the BP, i.e. we concede that the important difference between refraining and trying is not expressible under conditions BP1 and BP2. We might persist, however, in accepting refraining as really trying to do something different, willing to live with a truncated notion of voluntariness in order not to give up the BP. So we must consider now 'try to X' and its relationship to 'X', where 'X' is voluntary.

That both 'X' and 'try to X' are in the BP is not sufficient for 'X' to be voluntary. Let us recall an example used earlier: out of the corner of my eye I catch sight of something flying toward my face. Without thinking, I reach up and catch the object, a ball. In catching the ball, did I act voluntarily? More precisely, did I catch the ball voluntarily? I subject myself to a test. Donning adequate head protection, I have someone throw the ball at me and try to catch it a second, a third, even a fourth time. I miss every time. I can't catch the ball when it is thrown at me like that. But notice what is happening: although I am trying to X -- where X is 'catch the ball' -- since I cannot X when I am trying to X, we all conclude that my X-ing was not voluntary! The lucky catch was not an instance of a voluntary act.

Conclusion: a behavior-type, 'X', is a voluntary-behavior-type only if some instance of behavior is both an instance of 'X' and of 'try to X'. But this is to say either that if B contains voluntary behavior-types, B is not a BP or that no BP contains voluntary-behavior-types. In the next section I will discuss why it is only a necessary and not a sufficient condition for X's being voluntary that 'X' and 'try to X' have a common member. We end this section with an important result: there can be no global functional analysis of voluntary behavior.

Trying, Refraining And Acting

We have been dealing with a conception of behavior meant to be widely accommodating to different theoretical approaches. Minimal restrictions, e.g. BPI, BP2, were introduced on B for the sole purpose of defining a mathematizable set of behavior-types, a BP. In the process, we lost rule-following, purposive and voluntary behavior. Mathematics requires a set of "logical atoms," as it were. But behavior, inasmuch as it is rule-following, purposive or voluntary is essentially ambiguous. That is to say that it is incompatible with a logical atomism. Why this is so we will see upon examining more closely the concepts of trying and refraining. What we are seeking to discover may be rendered from the following: John can try -- albeit vainly -- to do the impossible. But he cannot refrain from the impossible. This is not to say that he must necessarily do the impossible, but rather that if X is not possible for John, then John can never be said to be refraining from X-ing.

Let us formulate

T1: If John is trying to X, then he believes that what he is doing will bring about X-ing.

This is clearly a necessary condition if we eschew recourse to special theories, e.g. Freudian, to explain John's behavior. The problem with TI is that we have difficulty dealing with animal and machine behavior and it has long been-part of even the academic idiom to speak of these as purposive. However, the important phrase is "if we eschew recourse to special theories," for in fact theories about drives, in the case of animals, and notions of function, in the case of machines, are exactly the special theoretical entities resorted to in order to justify the extended attribution of purpose. We need have no recourse to special theories in John's case because we have already a theory -- albeit informal -- about human behavior embedded in the logic of our natural language, for purpose cannot be seen through naive eyes.

But T1 states merely a necessary condition for John's trying to X. What is necessary to achieve sufficiency is intention. Now, intention is thought of by some45 to be an excrescence on the language of motive. The concept serves a very practical legal purpose, however. The law requires a distinction between an intentional act and an act done merely knowingly. If my purpose in giving you a certain drug is to sicken you, then my sickening you is an intentional act. If, on the other hand, my purpose in giving you the drug is to provide an antidote for another drug you've taken, then although I know a consequence of my administrations will be that you are sickened, my sickening you is not to act intentionally, but merely to act knowingly.46 It is easy to see the pragmatic value of the notion of intention but hard to see what if anything exists to correspond with it with regards to animals and robots.

Let us formulate

T2: If John is trying to X, then John intends to bring X about.

If belief and intention are jointly sufficient for trying, there is no reason why an instance of trying to X could not also be an instance of trying to Y, killing two birds with one stone, as it is said. We see here another impediment to achieving a logical atomism. Note again that the effects of John's behavior are ignored: purposive behavior need not have any particular effects, nor from the effects of behavior can we infer anything about its being purposive or not.

Unlike trying, both acting voluntarily and refraining must satisfy success conditions. Recall that two necessary conditions for John's refraining from X are

Ra) that John not X, and

Rb) that John be trying to not X.

These are paralleled by two necessary conditions for John's X-ing to be voluntary:

Va) that he be X-ing, and

Vb) that he be able to try to X.

It seems trivial to point out that if John is, in fact, not the one who is X-ing, then this X-ing is not a voluntary act of John's, despite his trying to X. If John, for example, is driving a car and we tell him to try to run over the rubber traffic cones in the middle of the road, and, if, as he approaches the cones, we, by some device, disengage his steering mechanism and cause the car to hit the cones; then, despite John's believing that hitting the cones was his voluntary act, he performed no such voluntary action.

Suppose that by stimulating John's brain in a particular manner, we can make his fight arm stretch out and his hand close about whatever object happens to be within his reach. Suppose further, that unbeknownst to John, he has been drugged so that he cannot move his right arm. We tell him now to reach out and get a certain bottle and then we stimulate his brain so that his arm extends and his hand closes around the bottle. John is mistaken if he thinks he has acted voluntarily in getting the bottle.

The presence, in both cases, hitting the traffic cones and getting the bottle, of what I shall call an independent intermediary negates the voluntariness of the act. It would seem that a necessary condition for John's X-ing to be voluntary is that, "between" John's trying to X and John's X-ing, there be no independent intermediary, be it interference of a mechanical, neurological or even a dispositional nature, e.g. a complex, or compulsion or the like.

But -- you may object -- if we are steering the car or making John's arm reach out, then it is not John who is doing it. Thus it is trivial to go on to say that he is not acting voluntarily! So far as hitting the rubber cones or getting the bottle is concerned, he is not acting at all! For John to be acting voluntarily, he must be the one who is acting. That is the necessary and trivial condition for voluntary action!

We are not necessarily disagreeing. The condition that there not be an independent intermediary implies but is not implied by the condition that John be the one who is acting. This is the problem. For some statements, "John is X-ing," e.g. "John is sitting himself up," it is unclear whether we are talking -bout an agent acting voluntarily or a body in motion. To insist that John did such-and-such does not clarify this ambiguity, necessarily, e.g. compare "John "twitched" with "John jumped." In a previous example John was sitting himself up. This could well be an effect of rigor mortis. It is the presence of an independent intermediary that makes "John is X-ing" a body-in-motion rather than a person-in-action description. (Of course some characterizations of John's behavior could never be anything but person-in-action descriptions and would be withdrawn should we discover an independent intermediary rather than modified as "involuntary," e.g. "John is constructing the proof.")

Now, it is logically necessary that there be no independent intermediary for John's X-ing to be voluntary, since "John is X-ing voluntarily" implies "There is no independent intermediary, such that .... etc." But it cannot be a pragmatic necessity that we establish that there be no independent intermediary to warrant our characterization of John's behavior as voluntary. That there is no independent intermediary seems to be an evidential question -- I do not see how to cast it non-circularly as a conceptual one. But no evidence can suffice to establish a negative universal, i.e. there is no Z, such that, in the given circumstances, Z is an independent intermediary.

The answer is, of course, that that John's behavior is voluntary is a presumption; thus we are inclined to insist that if, for example, neurological stimulation brings it about that John's arm extends, then it is really not John who is doing it. A presumption has prima facie validity as knowledge. A presumption is that which it is eminently reasonable or right or proper to assume. A presumption is that to the contrary of which a' challenger is obliged to present strong reasons. A good model for explicating the logic of presumption is H. L. A. Hart's notion of a defeasible concept.

Defeasible Concepts

A defeasible concept is one the application of which is warranted when certain conditions obtain which are pragmatically although not logically sufficient. Hart explains that the term defeasible is used of a legal interest in property which is subject to termination or "defeat" in a number of different contingencies but remains intact if no such contingencies mature.47

For example, the pragmatically necessary and sufficient conditions for the existence of a valid contract are that there be a. at least two parties, b. an offer by one, c. acceptance by the other, d. in some cases, a memorandum in writing, and e. consideration.

The contract remains valid until such a time, if ever, any -of the following challenges are made and sustained:

a'. fraudulent or innocent misrepresentation,

b'. duress or undue influence,

c'. lunacy or intoxication,

d'. contract for immoral purposes,

e'. contract unreasonably restraining freedom of trade,

V. contract perverting course of justice,

g'. changed circumstance, e.g. war, rendering contract impossible to perform, and

h'. claim barred by lapse of time.

The negations of a' through h' are logically necessary in that if a given contract is valid, it follows that none of the conditions a' through h' obtain. But these negations are not pragmatically necessary because no one is required to show that they obtain in order to justify an attempt to enforce a contract as valid.

The pragmatically sufficient conditions for someone's behavior to be properly characterized as voluntary are something like the following:

1) the actor is apparently normal,

2) the circumstances are apparently normal, and

3) the behavior being so characterized is not any of a particular type, e.g. sneezing, twitching, etc.

A person's behavior is voluntary until it is established to be not so in very much the same way that a person accused of a crime is legally innocent until proven guilty. To ask of the accused, prior to conviction, if he is "really" innocent shows either or both of two things, i.e. one does not comprehend the notion of legal innocence or one is not talking about legal innocence. To ask, in normal circumstances, if a normal person is, say, lifting his arm voluntarily, that is, "really" voluntarily, is to challenge the presumption of normalcy and to assume the burden of proof to sustain that challenge.48

(I suspect, however, that no small part of the free-will/determinism controversy derives from a simple but profound polemical impropriety: the challengers of the "normalcy theory," i.e. voluntarism, have shifted the burden of proof from themselves to the shoulders of the proponents of the theory they are challenging. "Science" is then looked to to arbitrate the dispute. But it is quite clear that science -- at least, under the conception we have been dealing with -- is not a neutral third party, but clearly committed to an anti-voluntarist position by virtue of its mathematical need for a logical atomism.)


I would very briefly like to consider two questions about the arguments of this paper that spring rather easily to mind and might seem to vitiate the force of the conclusions drawn. The first is this: the conclusion of the main argument is not that one cannot provide a functional analysis of behavior, but only that one cannot provide a functional analysis of behavior that is pre-theoretically logically unrestricted. Put another way: unless we can obtain a BP, logical restrictions are introduced on the empirical possibilities of functional relation. So what? Introduce whatever is necessary so long as we get a functional analysis.

To this I would merely answer that the restrictions introduced are rather severe and to many, I suppose, disappointing: the simplest measure function requires a BP. This is to say that voluntary acts cannot even, in general, be tallied. Thus they can neither be probabilized nor conditioned.49

Why then worry about voluntary behavior and the rest, i.e. rule-following and purposive behavior? Why sacrifice the BP and therefore the conception of science we have been dealing with just to retain these notions?

Because -- and I leave discussion for future occasions -- the meta-theoretical language of science requires concepts based on notions of voluntary, rule following and purposive behavior. To recommend a theory, to deduce a conclusion, to follow a protocol, to reject a conclusion as unwarranted is possible only given a language of voluntary action. For a theorist to argue that we ought to relinquish our language of voluntary action is as paradoxical as the Cretan's assertion, "I am now lying."


1. Behaviorism is, in the popular mind, identified with B. F. Skinner's musings; consequently, many psychologists are reluctant to be identified as behaviorists. My intent is to use the term descriptively; it is not meant derogatorily. There is ample evidence in Jum C. Nunnaly's Psychometric Theory (New York: McGraw-Hill, 1967) that he is such, e.g. he asserts that theoretical constructs (concepts) are merely heuristic devices for exploring observables, no more; that, for example, anxiety has no real counterpart in "the world of observables" (p. 97); observables themselves must be visually or otherwise "palpably" discernible (p. 21).

2. Nunnaly, op. cit., p. 5.

3. Merle B. Turner rejects "radical behaviorism" and considers himself merely a "methodological" behaviorist who accepts no a priori restrictions on theory. An upshot of the argument of this essay is that for most human behavior the distinction makes no difference.

4. Merle B. Turner, Realism and the Explanation of Behavior (New York: Appleton-CenturyCrofts, 1971), p. 22.

5. B. F. Skinner, Science and Human Behavior (New York: Free Press, 1953), p. 35. James E. McClellan in ? B. F. Skinner's Philosophy of Human Nature: A Sympathetic Criticism" in B. Paul Komisar and C. J. B. Macmillan (eds.), Psychological Concepts in Education (Chicago: Rand, McNally, 1967), pp. 224-247, writes that an underlying assumption of Skinner's theory is that man is by nature an active organism. I think McClellan is quite wrong on this point. Skinner's program to achieve a functional analysis of behavior is quite compatible with the premise that man is by nature inactive, i.e. impulsed by external forces only. Skinner need not concern himself with what causes any particular behavior because he has only to discover what is reinforcing in order to break into the causal chain. By cause Skinner means an external variable through manipulation of which specific behavior of an organism can be produced or prevented. I submit that there is little difference between Skinner's notion of cause and the hoary Efficient Cause. McClellan is oversympathetic; normally an admirable failing. However, he undermines the possibility of any seriously damaging critique of Skinner by allowing that there is such a thing as "behavior one can point to"; but lacking a philosophically significant theory for sorting out behavior-types, nothing is specified by pointing.

6. Skinner, Science and Human Behavior, p. 41.

7. See Arthur L. Stinchcombe, Constructing Social Theories (New York: Harcourt, Brace and World, 1968) on Functionalism. "Feedback"-functionalism presumes that set-theoretic-functional relations-which are our concern here-obtain between variables.

8. We are continually bathed in emanations from distant stars. Are they part of our stimulus environment? See Charles Taylor, The Explanation of Behaviour (London: Routledge & Kegan Paul, 1964) on the intensional environment in various places throughout the book; also Donald S. Blough and Richard B. Millward, "Learning: Operant Conditioning and Verbal Learning," in Paul E. Farnsworth (ed.), Annual Review of Psychology, Vo1ume 16 (Palo Alto, California: Annual Reviews, Inc., 1965) complain that operant researchers "shrug off" stimulus problems and ". . . have remained indifferent to laws that might predict what flux of energy will be a stimulus, and what manner of stimulus it will be." (p. 64)

9. Compare, for example, the empirical relations that might obtain between the class of mammals and the class of cows. Some interesting comments on this point are made by Barry F. Anderson in his book, The Psychology Experiment (Belmont, California: Brooks-Cole, 1971), Relationships between Variables, pp. 14-21.

10. See Robert G. Bartle, The Elements of Real Analysis (New York: John Wiley and Sons, 1964), p. 13, for a definition of function which expresses more compactly what I have given here and above; see also pp. 11-22 for an extended discussion on the function.

Logical operators are subsumed under the notion of function; for example, the entailment operator is a function which maps pairs of truth-values in a certain way to single truth-values: i.e. (T,T) to T; (T,F) to F; (F,T) to T; and (F,F) to T.

11. For example in Science and Human Behavior, pp. 32, 62 and 72 evidence a concern with probabilities of response as a function of conditioning history et al.

12. Anderson, op. cit., p. 11, mistakenly defines a variable as a set of mutually exclusive properties, However, a variable is a term in a statement of relation. With each variable is associated a set, members of which are called the values of the variable. A functional relation exists not between variables, but rather between their associated value-sets. What may mislead is that "Y is a function of X" may be used to assert that a function exists between the sets X and Y, if X and Y are sets. or that the pair (X,Y) is a member of a function, where X and Y are values of some variables.

13. Mathematicians regularly distinguish between a set, which is a collection of individuals; a class, which is a collection of sets; and afamily, which is a collection of classes. I don't think such niceties are necessary for our purposes. I will use the term set to indicate a collection of objects, be they individuals or sets.

14. Science and Human Behavior, p. 28 (My italics) Need psychology fear being replaced by neurophysiology? No, because ". . . we do not have and may never have this sort of neurological information at the moment it is needed in order to predict a specific instance of behavior. It is even more unlikely that we shall be able to alter the nervous system directly in order to set up the antecedent conditions of a particular instance." (p. 28) How did Skinner dare make such predictions? It should be noted that the claims quoted in this footnote are secondary to the one; given in the text to which this is a footnote: that claim is not falsifiable by evidence. If, at any particular time, one were to have challenged Skinner on it, he could have replied, "That we don't have such a science of the nervous system yet, doesn't mean we won't." Making claims which are apparently empirical but not evidentially falsifiable was the polemical device with which Skinner attempted to build strong philosophy on weak foundations.

15. Ibid., p. 34.

16. Ibid., p. 35.

17. Ibid. (My italics)

18. Ibid.

19. Skinner, Beyond Freedom and Dignity (New York: Bantam, 1972), p.

20. Ibid., p. 12.

21. Henry Margenau, "Meaning and the Scientific Status of Causality" in Arthur Danto and Sidney Morgenbesser (eds.), Philosophy of Scieace (New York: Meridian, 1960), pp. 435-449, puts it that a system of equations expresses a causal law only if the time variables can be differentiated out of them. This is to say that any process which is essentially time-dependent is importantly "autonomous" (not necessarily "miraculous" or "capricious" as Skinner would have it). Mario Bunge, Causality (Cleveland: Meridian, 1963), pp. 338-344, explains that processes the state of which at any given time depends upon a prior state are not models of efficient causation, e.g. radioactive decay, or the back EMF induced by the growing magnetic field set up by the applied EMF in an electric circuit.

22. The analysis of the BP appeared originally in my article, "Rewards, Reinforcers and Voluntary Behavior," Ethics, V. 94, No. I (October 1973), pp. 38-47, and was developed somewhat in my article, "Measurability and Educational Concerns," Educational Theory, V. 24, No. I (Winter 1974), pp. 52-60.

23. Op. cit., p. 2.

24. Ibid., pp. 18-19.

25. Science and Human Behavior, p. 36; also Beyond Freedom and Dignity, p. 12: "The task of a scientific analysis is to explain how the behavior of a person as a physical system is related to the conditions under which the human species evolved and the conditions under which the individual lives."

26. Science and Human Behavior, p. 15.

27. Ibid., p. 3 1.

28. Stinchcombe, op. cit., p. 41. (My italics)

29. Clyde H. Coombs, A Theory of Data (New York: John Wiley & Sons, 1967), p. 5.

30. Anderson, op. cit., p. 7.

31. Stinchcombe, op. cit., pp. 28-38.

32. Turner, op. cit., p. 151, "Assume that there is a generic behavior language . . . sufficient to describe both the intentional and non-intentional . . . aspects of behavior." That intentional behavior-descriptions can be reduced to non-intentional ones presumes the possibility of such an intention-neutral language.

33. The Model Penal Code (Philadelphia: The American Law Institute, 1956) in Herbert Morris (ed.), Freedom and Responsibility (Stanford: Stanford Gniv. Press, 1961), p. 112.

34. Turner, op. cit., p. 154: "Behavior is purposive, that is its distinguishing feature.... A careful functional description of a behavioral event constitutes its explanation." I am assuming that some trying-to-behavior-types are purposive-behavior-types.

35. Is some particular behavior, X, of John's voluntary? We would normally go about finding out if it were so by seeing if John could X on command or refrain from X-ing in circumstances similar to those he had X-ed in previously. This shows the difficulty with Turner's notion of a generic behavior-language. The adequacy of a language to describe voluntary behavior depends upon the possibility of formulating understandable commands in it. The generic behavior-language is supposed to be logically simpler than voluntary-behavior-language. But it is by descriptions of behavior in terms other than those of the generic behavior-language that the voluntariness or involuntariness of a particular generic behavior-type is established.

36. I importune the reader with this obvious remark only because the point of similar formulations has been severely misconstrued. Michael Schleifer in "Controlling Autonomic Processes," Ethics, V. 84, No. 4 (July 1974), pp. 349-353, attempts a critique of my article, "Rewards, Reinforcers and Voluntary Behavior." Misunderstanding criteria V1 and V2 -- given above in this article, also -- he remarks, ". . . it is far from clear how one should interpret the 'possibilities' believed open to a person at a given time in a given culture. (p. 353)

37. Science and Human Behavior, p. 65.

38. Ibid., p. 66.

39. Ibid., p. 71.

40. If, for example, learning to X means learning to Y for the proper reason Z, then the probabilistic analysis fails. We must of course distinguish between merely uttering "because Z" in the context of doing X from giving Z as a proper reason for X-ing. Uttering sounds can be contingently related to other behavior; but proper reasons are never merely contingently related to what they are proper reasons for.

41. See Stephen E. Toulmin and Kurt Baier, "On Describing," in Charles E. Caton (ed.), Philosophy and Ordinary Language (Urbana: University of Illinois Press, 1963), pp. 194-219, for a critique of this philosophical theory. Also relevant is Norman Malcolm, Problems of Mind: Descartes to Wittgenstein (New York: Harper & Row, 1971), p. 102 and preceding discussion on mental concepts. Many act-types are, so to speak, projective. "John is frightening me" does not imply anything significant about John; it does require, however, that I be seared to be true. With verbs such as "frighten," the subject may serve merely as a focus of attention, not as an agent.

42. "Venus" and "the Morning Star" are conceptually but not factually distinct.

43. Cf. C. J. B. Macmillan and James E. McClellan, Jr., "Can And Should Means-Ends Reasoning Be Used in Teaching?" Studies in Philosophy and Education, V. 5 (1967), pp. 377-408, for an explication of the means-end relation.

44. The confusion of causal with purposive notions is sufficiently widespread that one often hears of servo-mechanisms and the like described as machines with a goal or purposive mechanisms. This anthropomorphism is founded, however, on a cultivated short-sightedness: One focuses on one of many effects of the behavior of a mechanism and treats that particular effect as "the purpose for" or "the goal of' that behavior, especially if the mechanism is so constructed so as to repeat the behavior until that particular effect is produced. But neither does a purpose have to be an effect nor is an effect necessarily a purpose.

45. Cf. Turner, op. cit., p. 157: "Were it not for our mentalistic traditions in describing volitional acts, it is doubtful that the idea of intention would ever occur in the context of motivation."

46. Cf. Morris, op. cit., p. 165.

47. H. L. A. Hart, "The Ascription of Responsibility and Rights," in A. Flew (ed.), Logic and Language (New York: Anchor, 1965), p. 155.

48. Ibid., p. 158. Accepting this explication of voluntary behavior concepts does not necessarily commit one to Ascriptivism. Ascribing responsibility and describing behavior are not necessarily different activities.

49. A measure function is a function defined on a ring; a ring is a set that, among other things, is closed for set-theoretic difference. This is possible only if the elements of the ring are constructed from sets that are mutually exclusive. Cf. early sections in Sterling K. Berberian, Measure and Integration (New York: Macmillan Co., 1965).

Something is conditionable only if it is probabilizable; something is probabilizable only if some measure function can be defined on it.