The Functional Analysis of Behavior
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The Functional Analysis of Behavior: theoretical & ethical limits
8/31/09 7:18 AM
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 Functional Analysis Analysis of Behavior: Behavior: theoretical and ethical limits © 2000 Edward G. Rozycki, Ed. Ed. D.
RETURN edited 2/17/09 ARTICLE MAP:
1. Introduction: Is mathematics required? 2. The Function 3. Th Thee Function as a Set-The Set-Theo oretic Relation 4. Pro Probabilization babilization Introduces Another Variable Varia ble 5. Ski Skinner nner on Behavioral Functions Functions 6. Co Compositions mpositions of Functions 7. Defini efining ng the Beha Behavioral vioral Variable 8. What Causes What What 9. Voluntary Behavior 10. Constitutive and Mean-Ends Mean-Ends Relations 11. Partitioning Rules 12. Constructing the Behavior-Partition Behavior-Partition 13. Meta-ethica Meta-ethicall Consquences of Achieving Achieving the BP 14. Trying, Refraining and Acting
15. Defeasible Concepts 16. Conclusions 17. ENDNOTES RELATED ARTICLES: The Mathematics of Behaviorism: Behaviorism: an informal review Problems with taking too literally the idea that behavior is a function of the environment. environment. Skinner's Walden Two -- a review Critique of B.F.Skinner's personally unacknowledged philosophical philosophical commitments and a deconstruction of his utopian Walden II Skinner's Concept of Person The person as a locus of instructional instructional decision-making, decision-making, assumed assumed by the Keller approach, approach, is not theoretically compatible compatible with Skinnerian Behaviorism.
Introduction: Is mathematics required? The The mathematical mathematical concept of function plays an essential essential role in what behavioral behavioral scientists of various theoretical persuasions conceive of as science. Jum C. Nunnaly -- who is a fairly straightforward behaviorist 1 -- writes: 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 Nunnaly's philosophy as passé 3 concurs: The more complex our behavioral or neurophysiologicaI descriptions are and the more complex the hypothetical hypothetical structure structure of our theories, theories, then the more rigorous must be our logical calculi. It is a truism to say that the language language of a mature mature science must be a mathematica mathematicall one4 . http://www.newfoundations.com/EGR/FunAnBeh.html
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B. F. Skinner provides provides the most succinct statement statement of the conception conception of science that we will be concerned with. However, However, so that the arguments arguments in this essay not be restricted restricted in their scope to a critique critique of Skinner's Skinner's personal personal brand of behaviorism behaviorism,, the word external has been removed from from the following following quote, replacing replacing it with continuation dots (...) to indicate its original positions: The ... variables variables of which behavior behavior is a function function provide for what may be called a causal causal or functional functional analysis. analysis. We undertake undertake to predict and control control the behavior of the individual individual organism. organism. This is our "dependent "dependent variable -- the effect for which we are to find the cause. cause. Our "independent "independent variables variables -- the causes of behavior -- are the ... conditions conditions of which behavior is a function. function. Relations between between the two -- the "cause and effect effect relationships" relationships" in behavior behavior -- are the laws of a science. science. A synthesis of these laws expressed expressed in quantitative terms terms yields a comprehensive picture of the organism as a behaving system. 5 It will be our interest here to examine examine to what extent any functional functional analysis analysis of behavior behavior is possible. It might be said, for example, that the behavior, B, of a group or individual individual is a function function of variables X and Y. This mode of expression expression tends to replace more vulnerable vulnerable ones such as "X and Y are determining determining factors factors of influenced by X and Y." These raise immediate immediate challenges. challenges. as to what is meant by B" or "the nature of B is influenced "determining factor" or "influence." "Function" is clearer in this respect; even a casual acquaintance with mathematics mathematics exposes exposes one to its definition. definition. But while the term itself is clear, what remains remains all too often unchallenged unchallenged is the propriety of its application. Skinner remarks: The commonest objection to a thoroughgoing functional analysis is simply that it cannot be carried 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 non-existence of dragons. dragons. It is aim of this article article to show that, in certain 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 expresses rigorously one sense of our ordinary notion of relationship, as, for example, when we say that there there is a relationship relationship between between the size of a snowball snowball and length of time it takes to melt. Similarly, Similarly, one might look for a functional functional relation relation between the use one makes of one's airconditioners conditioners and the size of one's electric 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 specific kind of relation relation between sets. It is this concept concept which Nunnaly, Turner, and Skinner Skinner allude to above. For Skinner -- who accepts only external, "physical" "physical" variables variables -- - a functional functional analysis analysis of behavior 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 http://www.newfoundations.com/EGR/FunAnBeh.html
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members members of B, the set of all conceivable conceivable behavior-types. behavior-types. But there is a presumption presumption -- common common even today - that such general general classes classes as the set of all possible possible environmentalenvironmental- state-types state- types or the set of all possible behavior-types behavior-types can be coherently coherently made out.8 Imagine Imagine that we have a list of acts that John could perform, perform, e.g. 'jump', 'jump', 'talk', etc.. We will call this list "the behavior-set" behavior-set" and indicate indicate it with B. Imagine Imagine also that we have a list of environmenta environmental-statel-state-types. types. Let us call this list "the stimulus-set" stimulus-set" and indicate 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 course of the present discussion discussion which derive derive from our ignoring ignoring this sophistication. 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 particular member of S, we will see exhibited by John behavior of a particular particular type from B. Someone Someone concerned to produce a functional functional analysis analysis has both a conceptual conceptual and an empirical problem. 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, descriptions, things John might do. One might admit 'jump' but exclude exclude 'own' because jumping but not owning is something something John John might do -- - owning is not a doing. Such a decision is -- so to speak -- - "preempirical." empirical." Similarly Similarly,, one must pre-empir pre- empirically ically decide decide what is to count as an environmenta environmentall state. Only after S and B are defined defined to include all possible cases pertinent pertinent to them can one look to see what empirical empirical relationships relationships are to be found between them. In order for it to be logically possible possible that any s, whatsoever, whatsoever, in S might be found to be associated associated with any researcher to discover discover which particular particular s 's and b's are empirically b, whatsoever, in B, thus allowing the researcher related, related, we must be careful careful not only to define the s's and the b's independently independently of each other, but also to make sure the types, bi and s j, are mutually exclusive. exclusive. That means that nothing nothing which is, say, an s 1 can also be an s 2 ; nothing which which is a b4, a b17. The reason for this mutual exclusivity will be clearer after a definition definition of function function is given below. below. Let us consider consider for the moment a reason reason why S and B must be logically logically independent: independent: if talking were to be defined defined -- let us say for some research research purposes -- as speaking in the presence of a listener, then the presence presence of a listener listener could not be a stimulus stimulus for talking. talking. It would be logically, thus thus empirically, empirically, impossible impossible for someone someone to talk in the absence absence of a listener. listener. Only a restricted restricted empirical empirical relation is to be discovered discovered between talk and presence of listener, i.e. what proportion proportion of presence-of-listener-events presence-of-listener-events are also talkevents.9 The nature of the association association between between S and B is important. important. For a functional functional relation relation to obtain from S into B, that is, for behavior to be a function function of the environment, environment, each s may be associated associated with, mapped mapped into, at f(s), or b = g(s) or b = h(s), most one of the b's. (The notation for "b is a function of s" is of the form b = f(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 relation provides provides us with a set of behavioral laws, as it were. If s 3 is mapped into b5, i.e. b5 = f(s 3 ), this tells us that a subject under stimulus conditions conditions s 3 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, exclusive, we might have ended up
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with the following situation: we discover an instance of a stimulus, s ', that is of type s i and also of type s j. Suppose, however, that bk = f(s i) and b j = f( s j). s ' is mapped into both bk and b j, 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 b j - It follows that if bk and b j 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 suchand-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, (a i, b j), (a k, bm ), in the relation, if b j is different from bm , then a i is different from a k 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 http://www.newfoundations.com/EGR/FunAnBeh.html
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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- statetypes, s 1 and s 2 ; 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 (s 1, h1, b1)
(the triplet, (s1, h1, b1 ) is a simplified notation for ((s1 , h1), b 1)which shows more clearly the members of the domain and range in relation) b2 = f(s1, h2) or (s 1, h2 , b2) b3 = f(s2, h1) or (s 2, h1 , b3) b4 = f(s2, h2) or (s 2, 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 sb-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 (s 2, h2), i. e. b 3 = 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, s l, s 2; two conditioning-history types, h1, h2; and eight not necessarily different probability values, p1, p2, p3, p4 ,
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p5 , p6, p7, p8 . p1 = f(s1 , h1, b1)
P5 = f(s1, h1, b2)
p2 = f(s2 , h1, b1)
P6 = f(s2, h1, b2)
p3 = f(s1, h2, b1)
P7 = f(s1, h2, b2)
p4 = f(s2 , h2, b1))
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 (p 1, p5) = g(s 1 , h1), (p 2 , p6) = g(s 2, h1), (p 3 , p7) = g(s 1, h2 ) and (p 4, p8) = g(s 2, 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 http://www.newfoundations.com/EGR/FunAnBeh.html
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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=m 2 +y 2+z 2 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 http://www.newfoundations.com/EGR/FunAnBeh.html
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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 http://www.newfoundations.com/EGR/FunAnBeh.html
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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 welldefined 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 meansend relation' obtains is a matter of fact: X and Y must be factually42 and conceptually distinct and factually http://www.newfoundations.com/EGR/FunAnBeh.html
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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 http://www.newfoundations.com/EGR/FunAnBeh.html
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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, E 1 E2, ... , E n for which are defined a corresponding series of BP's, i.e. BP 1, BP2, ... , BP n. 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 http://www.newfoundations.com/EGR/FunAnBeh.html
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(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. 5260. 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-tobehavior-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.
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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 acttypes 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 servomechanisms 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.
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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. TO TOP
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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 Functional Analysis Analysis of Behavior: Behavior: theoretical and ethical limits © 2000 Edward G. Rozycki, Ed. Ed. D.
RETURN edited 2/17/09 ARTICLE MAP:
1. Introduction: Is mathematics required? 2. The Function 3. Th Thee Function as a Set-The Set-Theo oretic Relation 4. Pro Probabilization babilization Introduces Another Variable Varia ble 5. Ski Skinner nner on Behavioral Functions Functions 6. Co Compositions mpositions of Functions 7. Defini efining ng the Beha Behavioral vioral Variable 8. What Causes What What 9. Voluntary Behavior 10. Constitutive and Mean-Ends Mean-Ends Relations 11. Partitioning Rules 12. Constructing the Behavior-Partition Behavior-Partition 13. Meta-ethica Meta-ethicall Consquences of Achieving Achieving the BP 14. Trying, Refraining and Acting
15. Defeasible Concepts 16. Conclusions 17. ENDNOTES RELATED ARTICLES: The Mathematics of Behaviorism: Behaviorism: an informal review Problems with taking too literally the idea that behavior is a function of the environment. environment. Skinner's Walden Two -- a review Critique of B.F.Skinner's personally unacknowledged philosophical philosophical commitments and a deconstruction of his utopian Walden II Skinner's Concept of Person The person as a locus of instructional instructional decision-making, decision-making, assumed assumed by the Keller approach, approach, is not theoretically compatible compatible with Skinnerian Behaviorism.
Introduction: Is mathematics required? The The mathematical mathematical concept of function plays an essential essential role in what behavioral behavioral scientists of various theoretical persuasions conceive of as science. Jum C. Nunnaly -- who is a fairly straightforward behaviorist 1 -- writes: 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 Nunnaly's philosophy as passé 3 concurs: The more complex our behavioral or neurophysiologicaI descriptions are and the more complex the hypothetical hypothetical structure structure of our theories, theories, then the more rigorous must be our logical calculi. It is a truism to say that the language language of a mature mature science must be a mathematica mathematicall one4 . http://www.newfoundations.com/EGR/FunAnBeh.html
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B. F. Skinner provides provides the most succinct statement statement of the conception conception of science that we will be concerned with. However, However, so that the arguments arguments in this essay not be restricted restricted in their scope to a critique critique of Skinner's Skinner's personal personal brand of behaviorism behaviorism,, the word external has been removed from from the following following quote, replacing replacing it with continuation dots (...) to indicate its original positions: The ... variables variables of which behavior behavior is a function function provide for what may be called a causal causal or functional functional analysis. analysis. We undertake undertake to predict and control control the behavior of the individual individual organism. organism. This is our "dependent "dependent variable -- the effect for which we are to find the cause. cause. Our "independent "independent variables variables -- the causes of behavior -- are the ... conditions conditions of which behavior is a function. function. Relations between between the two -- the "cause and effect effect relationships" relationships" in behavior behavior -- are the laws of a science. science. A synthesis of these laws expressed expressed in quantitative terms terms yields a comprehensive picture of the organism as a behaving system. 5 It will be our interest here to examine examine to what extent any functional functional analysis analysis of behavior behavior is possible. It might be said, for example, that the behavior, B, of a group or individual individual is a function function of variables X and Y. This mode of expression expression tends to replace more vulnerable vulnerable ones such as "X and Y are determining determining factors factors of influenced by X and Y." These raise immediate immediate challenges. challenges. as to what is meant by B" or "the nature of B is influenced "determining factor" or "influence." "Function" is clearer in this respect; even a casual acquaintance with mathematics mathematics exposes exposes one to its definition. definition. But while the term itself is clear, what remains remains all too often unchallenged unchallenged is the propriety of its application. Skinner remarks: The commonest objection to a thoroughgoing functional analysis is simply that it cannot be carried 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 non-existence of dragons. dragons. It is aim of this article article to show that, in certain 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 expresses rigorously one sense of our ordinary notion of relationship, as, for example, when we say that there there is a relationship relationship between between the size of a snowball snowball and length of time it takes to melt. Similarly, Similarly, one might look for a functional functional relation relation between the use one makes of one's airconditioners conditioners and the size of one's electric 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 specific kind of relation relation between sets. It is this concept concept which Nunnaly, Turner, and Skinner Skinner allude to above. For Skinner -- who accepts only external, "physical" "physical" variables variables -- - a functional functional analysis analysis of behavior 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 http://www.newfoundations.com/EGR/FunAnBeh.html
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members members of B, the set of all conceivable conceivable behavior-types. behavior-types. But there is a presumption presumption -- common common even today - that such general general classes classes as the set of all possible possible environmentalenvironmental- state-types state- types or the set of all possible behavior-types behavior-types can be coherently coherently made out.8 Imagine Imagine that we have a list of acts that John could perform, perform, e.g. 'jump', 'jump', 'talk', etc.. We will call this list "the behavior-set" behavior-set" and indicate indicate it with B. Imagine Imagine also that we have a list of environmenta environmental-statel-state-types. types. Let us call this list "the stimulus-set" stimulus-set" and indicate 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 course of the present discussion discussion which derive derive from our ignoring ignoring this sophistication. 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 particular member of S, we will see exhibited by John behavior of a particular particular type from B. Someone Someone concerned to produce a functional functional analysis analysis has both a conceptual conceptual and an empirical problem. 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, descriptions, things John might do. One might admit 'jump' but exclude exclude 'own' because jumping but not owning is something something John John might do -- - owning is not a doing. Such a decision is -- so to speak -- - "preempirical." empirical." Similarly Similarly,, one must pre-empir pre- empirically ically decide decide what is to count as an environmenta environmentall state. Only after S and B are defined defined to include all possible cases pertinent pertinent to them can one look to see what empirical empirical relationships relationships are to be found between them. In order for it to be logically possible possible that any s, whatsoever, whatsoever, in S might be found to be associated associated with any researcher to discover discover which particular particular s 's and b's are empirically b, whatsoever, in B, thus allowing the researcher related, related, we must be careful careful not only to define the s's and the b's independently independently of each other, but also to make sure the types, bi and s j, are mutually exclusive. exclusive. That means that nothing nothing which is, say, an s 1 can also be an s 2 ; nothing which which is a b4, a b17. The reason for this mutual exclusivity will be clearer after a definition definition of function function is given below. below. Let us consider consider for the moment a reason reason why S and B must be logically logically independent: independent: if talking were to be defined defined -- let us say for some research research purposes -- as speaking in the presence of a listener, then the presence presence of a listener listener could not be a stimulus stimulus for talking. talking. It would be logically, thus thus empirically, empirically, impossible impossible for someone someone to talk in the absence absence of a listener. listener. Only a restricted restricted empirical empirical relation is to be discovered discovered between talk and presence of listener, i.e. what proportion proportion of presence-of-listener-events presence-of-listener-events are also talkevents.9 The nature of the association association between between S and B is important. important. For a functional functional relation relation to obtain from S into B, that is, for behavior to be a function function of the environment, environment, each s may be associated associated with, mapped mapped into, at f(s), or b = g(s) or b = h(s), most one of the b's. (The notation for "b is a function of s" is of the form b = f(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 relation provides provides us with a set of behavioral laws, as it were. If s 3 is mapped into b5, i.e. b5 = f(s 3 ), this tells us that a subject under stimulus conditions conditions s 3 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, exclusive, we might have ended up
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with the following situation: we discover an instance of a stimulus, s ', that is of type s i and also of type s j. Suppose, however, that bk = f(s i) and b j = f( s j). s ' is mapped into both bk and b j, 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 b j - It follows that if bk and b j 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 suchand-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, (a i, b j), (a k, bm ), in the relation, if b j is different from bm , then a i is different from a k 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 http://www.newfoundations.com/EGR/FunAnBeh.html
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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- statetypes, s 1 and s 2 ; 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 (s 1, h1, b1)
(the triplet, (s1, h1, b1 ) is a simplified notation for ((s1 , h1), b 1)which shows more clearly the members of the domain and range in relation) b2 = f(s1, h2) or (s 1, h2 , b2) b3 = f(s2, h1) or (s 2, h1 , b3) b4 = f(s2, h2) or (s 2, 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 sb-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 (s 2, h2), i. e. b 3 = 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, s l, s 2; two conditioning-history types, h1, h2; and eight not necessarily different probability values, p1, p2, p3, p4 ,
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p5 , p6, p7, p8 . p1 = f(s1 , h1, b1)
P5 = f(s1, h1, b2)
p2 = f(s2 , h1, b1)
P6 = f(s2, h1, b2)
p3 = f(s1, h2, b1)
P7 = f(s1, h2, b2)
p4 = f(s2 , h2, b1))
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 (p 1, p5) = g(s 1 , h1), (p 2 , p6) = g(s 2, h1), (p 3 , p7) = g(s 1, h2 ) and (p 4, p8) = g(s 2, 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 http://www.newfoundations.com/EGR/FunAnBeh.html
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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=m 2 +y 2+z 2 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 http://www.newfoundations.com/EGR/FunAnBeh.html
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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 http://www.newfoundations.com/EGR/FunAnBeh.html
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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 welldefined 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 meansend relation' obtains is a matter of fact: X and Y must be factually42 and conceptually distinct and factually http://www.newfoundations.com/EGR/FunAnBeh.html
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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 http://www.newfoundations.com/EGR/FunAnBeh.html
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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, E 1 E2, ... , E n for which are defined a corresponding series of BP's, i.e. BP 1, BP2, ... , BP n. 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 http://www.newfoundations.com/EGR/FunAnBeh.html
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(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. 5260. 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-tobehavior-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.
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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 acttypes 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 servomechanisms 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.
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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. TO TOP
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