Introduction to Part II

Transcription

1 PART II PHILOSOPHY OF CAUSALITY CHAPTERS 4. THE DEFINITION OF CAUSE ANALYSIS OF THE CAUSAL PHILOSOPHY OF DAVID HUME ANALYSIS OF THE CAUSAL PHILOSOPHY OF JOHN STUART MILL Introduction to Part II The concept of causality has been analyzed in the writings of almost every important philosopher without appreciable convergence of opinion. As an indication of the fundamental nature of the controversy, note that seldom have philosophers agreed even on the definition of the word "cause"; that is, if they attempt to define it at all. Given this disagreement over the concept itself, it is not surprising that conclusions about the concept (or, actually, concepts) of causality are many and varied. The three chapters of this Part will discuss the philosophy of causality. Chapter 4 will investigate the problem of the definition of "cause". Hume's arguments and conclusions concerning causal relationships will be stated and analyzed in Chapter 5. Chapter

2 43 6 will present Mill's five Canons of [Causal] Induction and critically examines them. Certainly, no claim is made that these chapters are philosophically exhaustive, But the causal philosophies of Hume and Mill are the most insightful and influential of all the philosophers. Therefore, an analysis of the causal writings of these two great men should be quite helpful in our attempt to understand the conceptions and misconceptions about causality,

3 CHAPTER 4 THE DEFINITION OF CAUSE Sections 4.1 Introduction 4.2 Galileo's Definition of Cause Simon's Criticism of Sufficiency Conditions as a Definition of Cause Criticism of Necessary Conditions as a Definition of Cause 4.3 Cause 4.4 Hume's Mill's Definition of of Cause 4.5 Can Cause(M) Be Made Consistent with Cause(C)? Investigation of the Source of Conflict Alteration of Mill's Definition of Cause Cause(M') is still Inconsistent with Cause(C) 4.6 Construction of n Definition for Cause A Theoretical Definition is Desirable A Concept of the Causal Operation of the Universe A Theoretical Definition of Cause 4.7 Considerations Concerning an Operational D ef inition f or Cause (P) 4.1 Introduction After hundreds of years of discussion, analysis, and use--"cause" remains a word without a definition. At least, there is no appreciable agreement among philosophers and scientists upon any particular definition. Consider the following, statement made by Julian Simon in a 1970 article,

4 45...no perfect or near-perfect definition of 'cause and effect relationships' has yet been created.* *Simon, Julian L.: "The Concept of Causality in Economics", Kyklos, No.2, 1970, pp Simon goes on to say that this is not surprising due to the complex and abstract nature of the relationship. Bunge, in discussing the meaning--i.e., definition--of "cause", calls it the "thorniest of words".** **Bunge, Mario: Causality, Harvard University Press, Cambridge, Mass., 1959, p.31. In this chapter we present and analyze the definitions of cause forwarded by Galileo, Hume, and Mill. Their definitions are operational rather than theoretical (i.e. ontological) and encompass all combinations of necessary and/or sufficient conditions. Each of these definitions is shown to be inconsistant with the common usage of the term "cause", We then forward a theoretical definition of cause (called cause(p)) which is consistent with the common usage of the term. 4.2 Galileo's Definition of Cause In 1632 Galileo described the causal relationship as "a firm and constant connection".*** This

5 46 ***Galileo (1632): Dialogo sopra i due massimi sistemi del mondo, giornata 4a, in Opere, Vol. 7, p Quoted from Bunge, op. cit., p.4. is equivalent to saying that an event, A, is the cause of an event, B, if and only if A is a necessary and sufficient condition for B. Presumably this necessary and sufficient relationship must hold for any and all conditions, i.e., irrespective of the states of other events. We will denote this definition of cause by "cause(g)". Note that cause(g) is very restrictive and does not conform to the common usage of the term, "cause". Not that there is anything necessarily holy about common usages in general, but in this case the common usage of the word--denoted by "cause(c)"--is the most useful and applicable meaning of the term. No explicit definition of cause(c) is given because it is the goal of this chapter to find or formulate a definition which conveys the common usage meaning of cause. It is not necessary that cause(g) and cause(c) should be identical in every respect because cause(g) is an operational definition and cause(c) could be considered to have a theoretical definition. (This is analogous to the relationship between I.Q. and intelligence.) But a good operational definition will conform to (i.e., be consistent with) the theoritical definition, In other words, if and

6 47 only if A causes(c) B, then A should cause(g) B. In this case the face validity of cause(g) would be perfect. Cause(G) is inconsistent with cause(c) in many respects, but we will only consider two of the shortcomings here. Other sources of inconsistency, which apply to cause(g) and cause(c), will be discussed later during the analysis of Hume's and Mill's definitions. The two shortcomings considered here are not discussed later because they are not valid criticisms of either Hume's or Mill's definitions Simon's Criticism of Sufficiency Conditions as a Definition of Cause Herbert Simon* attacks the whole idea of suf- *Simon, Herbert A.: "On the Definition of the Causal Relation", The Journal of Philosophy, Vol, XLIX, No. 16, July 31, 1952, pp ficiency as a definition of cause. His comments are directed specifically toward the sufficiency definition of cause forwarded by Arthur Burks**, but they are **Burks, Arthur. W.: "The Logic of Causal Propositions", Nind, Vol LX, 1951, pp equally applicable to Galileo's definition. We will analyze the effects of Simon's criticism on sufficiency definitions of cause in general, realizing that the arguments are equally strong against necessary and sufficient definitions, namely cause(g).

7 48 Simon points out that, if A is sufficient for B, then ~B is sufficient for ~A, Therefore, under a sufficiency definition (i.e., cause(s)), whenever A causes(s) B, ~B causes(s)~a. For example, "If the rain causes [(S)] Jones to wear his raincoat, then Jones' not wearing his raincoat causes [(S)] it not to rain."* *Simon, Herbert: op,cit., p.518 It is obvious that Jones' not wearing his raincoat is not normally considered to cause(c) it not to rain. Therefore, sufficiency definitions are not consistent with cause(c); hence, cause(g) is inconsistent with cause(c), All causal(c) connections are sufficient relationships, but not all sufficient relationships are causal(c) connections. In other words, the set of all causal(c) connections is a subset of all sufficient relationships, If A causes(c) B, A is sufficient for B and ~B is sufficient for NA, But the reverse inference does not necessarily hold Criticism of Necessary Conditions as a Definition of Cause The criticism of necessary conditions as a definition of cause (denoted by cause(n)) is analogous to Simon's criticism of cause(s).

8 49 If A is necessary for B, then ~B is necessary for ~A. This can be derived as follows: If A is necessary for B, then B is sufficient for A, which implies that ~A is sufficient for ~B, which implies that ~B is necessary for ~A. If snow causes(n) Mr. Chang to wear his snow shoes, then Mr. Chang's not wearing his snow shoes causes(n) it not to snow; according to the symmetric nature of necessary conditions. This statement does not hold for cause(c). Therefore, cause(n) is inconsistent with cause(c), which implies that cause(g) is inconsistent with cause(c). 4.3 Hume's Definition of Cause David Hume--who is, by many, considered to have the ultimate insight into (or answer to) the problems associated with the concept of causality--defined a cause as:...an object precedent and contiguous* to another, and where all the objects resembling the former are placed in like relations of precedency and contiguity to all those objects that resemble the latter.** *By continuous, Hume does not mean "adjacent to", i.e., "in physical contact with". He means that the objects are connected through a chain of other objects or events or variables. **Hume: A Treatise of Human Nature, ed. L.A. Selby-Bigge, Oxford, 1880, D. 170.

9 50 Hume is saying, essentially, that an event A is the cause of an event B, if the precedent occurance of A is a necessary and sufficient condition for the later occurance of B under any and all conditions. We will denote this definition by cause(h). Hume's definition contains three questionable items. These are associated with the terms (1) "precedency", (2) "contiguity", and (3) "resemble". "Cause(H)" stipulates that the cause is (1) precedent and (2) contiguous to the effect. It, also, specifies that (3) similar causes are associated with similar effects. (1) and (2) should not be part of the definition of cause. It is logically possible that an effect could preceed its cause(c) and that a cause(c) could be non-contiguous to its effect. The assertions that the cause preceeds and is contiguous to the effect is a matter for empirical investigation and/or for assumption. Based on empirical studies we cannot prove that all causes preceed or are contiguous with their effects because we cannot observe all causes. But we can observe many cause-effect relationships and argue inductively for these conclusions. Or, what is the same, we could assume precedency and contiguity of all causes and then use empirical evidence to argue inductively that the assumptions are valid,

10 51 By putting precedency and contiguity in his definition, Hume is, in effect, assuming their universal validity. In discussing "cause(h)", we will continue to consider precedency and contiguity to be part of the definition, but one should understand and remember the true nature of these items. (3) is the problem of the lack of precision in meaning of the word "resemble", noted by Russell and others.* But, in actual fact, this is not a problem Edwards, Paul, (ed.): Encyclopedia of Philosophy, N.Y., MacMillan, 1967, p.60. concerning the definition of cause, though many philosophers have seen it to be so. If we say that events of the type A cause events of the type B, the necessary similarity of one A to another should be exactly specified in the definition of A, and the same with B. Therefore, it is not necessary that "resemble" be made precise in the definition of cause because it should be made precise--external to the causal definition--when the events, variables, or objects (A and B) are defined. The difference between cause(g) and- cause(h) is small, but important. In cause(h) the cause preceeds the effect; in cause(g) this is not necessarily the case. This is sufficient to rescue cause(h) from the two criticisms of cause(g) already discussed (in Sections and 4.2.2).'

11 52 We can see this in the following way: Let A(t) be the event A at time t. If A(t o ) is sufficient for B(t o+at), then ~B(t o +At) is sufficient for ~A(to). But in Hume's definition the cause preceeds the effect. Therefore, under Hume's definition, can not cause(h) ~A(t o ), Hence, cause(h) is not vulnerable to Simon's criticism. An analogous argument could be presented to show that cause(h) can survive a similar criticism of its necessary condition. Elsewhere*, he refers to a "cause" as a constant *Hume: "Skeptical Doubts Concerning the Operations of the Understanding, Part I", An Inquiry Concerning Human Understanding, The Library of Liberal Arts, No. l49, N.Y., conjunction (i.e., repeated association). If taken at face value this would equate Hume's and Galileo's definitions in opposition to Hume's previous statement of the definition. But we can surmise from his use of "cause", that he considered it understood in this statement that the cause preceeded the effect and, therefore, that the previous statement (cause(h)) is the definition intended by Hume. But, as with cause(g), cause(h) is inconsistent with cause(c). To illustrate the deviation of Hume's definition from common usage, consider an apple hanging from a tree. If the apple suddenly falls to the ground, the educated man on the street would

12 53 say that the gravitational field of the earth, F, caused(c) the apple to move from the tree down to the ground,d* But, if F were not present, D might *If we consider F to be positioned at its effective origin, the center of the earth, then F preceeds D by the radius of the earth divided by the velocity of gravity waves (which is equal to the velocity of light). If we consider F to be the part of the gravitational field in contact with the apple, the action of F preceeds the response of D by dt. still occur. A baseball might hit the apple at such an angle that the event D occurs; therefore F is not necessary for D, even though it can cause(c) D. This is a general problem with inserting necessary conditions into causal definitions. If F causes(n) (i.e., is necessary for) D, then F is the only cause(n) of D. But, as the example points out, D can have more than one cause(c). A collision with a baseball can cause(c) D. Also, F might be present and the apple remain on the tree, ND, because the stem prevented the apple from falling. Therefore, F is not sufficient for D under any and all conditions, even though F is sufficient for D under some conditions. Therefore, again, cause(h) is inconsistent with cause(c). One further inconsistency in cause(h) is that the definition would allow a constant, but spurious, relationship between A and B to be called a causal(h)

13 relationship. According to Hume's definition, 54 moonlight causes(h) high tides. But in common usage we would say that the moon causes(c) both high tides and moonlight and that there is no causal(c) connection between moonlight and high tides. Any one of the reasons discussed above is sufficient to imply that cause(h) is inconsistent with cause(c). 4.4 Mill's Definition of Cause John Stuart Mill forwards a definition of cause which can be considered to be either a theoretical or operational definition, depending on whether or not the scientist is able to experiment. He considers a cause of a phenomenon to be:...some antecedent, on the existence of which it [the phenomenon] is invariable and unconditionally consequent.* *Mill, John Stuart: A System of Logic, Book III, Longmans, Green and Co., 1930, p This definition is denoted by cause(m). Note that, like Hume, Mill included time precedency (anticedence) in the definition. To understand this definition, let us investigate the meanings which Mill intended for three words he used in it. Consequent can mean "following as a result of" or just "following". The first meaning would

14 55 make "cause(m)" a theoretical definition. This meaning of "consequent" indicates that the cause produces the effect. We cannot observe the act of production; we can only observe association between the cause and the effect. The second meaning of "consequent" indicates no more than observable association. In this case, cause(m) would be operational (if experimentation is possible, as we will see later). Since it was Mill's intention--due to his empiricist beliefs--to formulate an operational definition, re can conclude that he intended the second meaning for "consequent". For Mill, the word "unconditional" takes on a: very specific meaning that distinguishes it from "invariable" (which we will discuss next). We will denote Mill's specific meaning by "unconditional(m)". Mill says: Until we have done so [i.e., added the evidence of experiment to that of simple observation], we have only proved invariable antecedence within the limits of experience, but not unconditional antecedence or causation.* *Ibid., p.252 If A is unconditionally(m) antecedent to B, then A is followed by B no matter how A is brought into being, naturally or by experimental manipulation. The importance of the unconditional (Ii) antecedence of A is the following: In a non-experimental

15 50 situation, A could invariably (always) preceed B and still not be the cause(c) of B. Consider Figure 4-1. J causes(c) A with a time lag of one minute and Figure 4-1 J causes(c) B with a time lag of three minutes. Observationally, A is invariably precedent to B by two minutes but it is not unconditionally(m) precedent to B. This is because, if A is produced by an experimental manipulation, rather than by J, B will not necessarily follow. Therefore, the inclusion of "unconditional(m)" in the definition of cause(m) avoids the conclusion that A causes(m) B in situations like Figure 4-1. In other words, the unconditional(m) nature of cause(m) overcomes one of the criticisms of cause(h); it does not allow spurious relationships to be called causal(m). At this point we can show that cause(m) is an operational definition when applied to experimental,- data and a theoretical definition when confronted with non-experimental data. If we perform an experiment we can see whether or not A is an un conditional(m) antecedent of B (as we will see in Section 4.6, some relatively weak assumptions are

16 necessary to deduce this conclusion); but if no experiment is possible, we cannot determine whether or not A is unconditionally(m) connected with B. This means that cause(m) is operational for experimental situations and theoretical for observational situations. The last word to be investigated in the definition is "invariably". Mill intends invariable to mean "for any and all values of other variables". An invariable relationship is one which exists, irrespective of the situation. If A is invariably sufficient for B, A is sufficient for B, irrespective of the environmental conditions, i.e., no matter what other events occur or what values other variables take on. Mill's implicit definition of "invariable" is the same as the common usage meaning of "unconditional," which we will denote by unconditional(c). We will use this notation later. Do not confuse the common meaning with Mill's use of the term, i.e., "unconditional(n)." Now that we understand Mill's terminology, we can restate--with a slight alteration in terminology but not meaning--the definition of cause(m): The cause(m) of a phenomenon is an antecedent which is invariably and unconditionally(m) sufficient for that phenomenon.

17 How does cause(m) compare with cause(c)? Well, it is better than the previous two definitions, but cause(m) still falls short. Again, consider the apple hanging from the tree. We saw in Section 4.3 that gravity, F, could be acting and yet the apple remain attached to the tree, ~D. In other words, even though there is a causal(c) connection between F and D, it is not the case that F is invariably (i.e., unconditionally(c)) sufficient for D (i.e., sufficient for D under any and all conditions).. This shows that cause(c) conflicts with cause(m) on the principle of invariability. Does this conflict of Mill's definition with cause(c) mean that cause(m) is an unacceptable definition of cause? If the conflicts exhibited by the apple-gravity example were an isolated and atypical situation, cause(m) would still be a valuable approximation to cause(c); but this is not the case. The conflict between cause(m) and cause(c) exemplified by the relationship of F and D is not atypical. It is common. Given this conclusion, the question now becomes, "Can the definition of cause(m) he altered, in a minor way, to bring it into conformity with cause(c)?" It is the duty of the next section to first investigate the source of the conflict, second to make

18 59 minor alterations in Mill's definition (and alterations which this great philosopher might be willing to accept), and third to determine if the altered. definition is a good operational definition of cause(c), 4.5 Can Cause(M) Be Made Consistent with (2i c' ( - C ; Investigation of the Source of Conflict In Section 4.4 we found two problems with cause(m). First, the invariable or unconditional(c) nature of "cause(m)" is inconsistent with cause(c). Second, time precedence is a part of Mill's definition and it should not enter into the definition of cause (see also Section 4.3), We will investigate the possibility that unconditionally(c) sufficient conditions may be logically and/or empirically impossible. A is unconditionally(c) sufficient for B, if and only if A is sufficient for B under any and all conditions (i.e., invariably sufficient for B). Consider the following situation: If (1) A is unconditionally(c) sufficient for B and (2) C is unconditionally(c) sufficient for ^, B, what happens if (3) both events A and C occur? Does B occur or does ^wb occur? It is logically impossible--and therefore empirically impossible--for statements (1), (2), and (3) to all be true at the same time,

19 60 We know that, in general, statements of type (3) are logically and empirically possible. This leaves in question the possibility of statements (1) and (2) and ontological connections among the three statements. There are three possible solutions to the logical impossibility of the simultaneous truth of statements (1), (2), and (3). They are: (a) Laws of types (1) and/or (2) do not occur in nature, (b) The truth of a statement of type (1) rules out, by natural law, the truth of a statement of type (2) and vice versa, (c) The truth of statements of types (1) and (2) rule out, by natural law, the truth of a statement of type (3). Solution (a) can be stated as follows: Uncon ditionally(c) sufficient conditions do not exist in nature. This statement would solve the problem of unconditional(c) sufficiency in Mill's definition of cause, by eliminating invariability from the definition. Solution (b) is logically possible, but empirically it runs into trouble if the intent is to describe all or most changes in the observable universe with this solution. We know that gravity, F, is sufficient for an apple to move downward, D. But F is not unconditionally(c) sufficient for D, because a stem, S, is sufficient for ND. But, again, S is not unconditionally(c) sufficient for ND because F may be very large and overcome S.* This example

20 61 *Here again we are implicitly making some weak assumptions--which will be presented in Section 4.6--to insure the validity of experimental inference. does not imply that unconditionally(c) sufficient conditions cannot exist, but many counter examples to solution (b) could be forwarded, Therefore, we cannot broadly apply solution (b) to explain empirical phenomena. Solution (c) is again logically possible. But, as before, solution (c) cannot broadly explain the operation of the universe, Solution (a) is the only one which can be used to adequately explain all (or at least a large majority of) empirical phenomena. Therefore, we can conclude that the proper alteration of cause(m) would have to proceed in the way indicated, by solution (a). The second problem with cause(m) can be removed by omitting the time precedence condition from the definition Alteration of Mill's Definition of Cause In Section we considered solutions to the two shortcomings of Mill's definition. In this section we will alter the definition to remove these problems. The altered definition is denoted by cause(m') and it is stated as follows:

21 62 A cause(m') of a phenomenon is an event or object or variable value which is unconditionally(m) Sufficient for the phenomenon. Note that in the definition there is no reference to the conditional(c) nature of cause(m'); it simply omits the stipulation that cause is invariable (i.e., unconditional(c)). This is because environmental variables are really a separate issue from that of the definition of cause. This is not to say that environmental variables do not affect the causal(m') connection because, as we have seen, these variables may determine whether or not a causal(m') connection is operative (i.e., exists). The point is that the relationship between a causal(m') connection and its situation (i.e., its environmental variables) is a complimentary one, A complete statement about a causal(m') connection will include some reference to the important conditions for which the causal(m') connection does and does not hold (i.e., exist), but it is not the role of the definition of cause to consider these Conditions. For example, gravity will cause(m') an apple to fall, if the existant conditions are such that no one thing or combination of things is restraining the apple with a force greater than or equal to the force exerted upon the apple by gravity, Another example: a car will cause(m') digestive trouble under the condition that the car is eaten. Even these are not complete

22 63 specifications of conditions, but they convey the idea. When we make a causal statement without stipulating the conditions, we are simply using a shorthand technique. The conditions are implied in the statement and generally understood by the listener. We shall use the same shorthand notation (omitting a statement of the conditions) when the conditions are obvious or when the variables are causally(m') connected for all normal and usual conditions, The definition of cause(m) also omits any consideration of temporal ordering. This is again a matter for external specifications Cause(M') is Still Inconsistent with Cause(C) Now, we want to determine if Mill's altered definition is consistent with cause(c), The problems with Mill's original difinition were that it was invariable (i.e., unconditional(c)) and temporally ordered, Cause(M') is not invariable; it allows for the possibility (indeed, the likelihood) that the existence of a causal(?') connection may depend on the values of environmental variables (i.e., the situation in which the two connected variables are immersed). Therefore invariability is no longer a problem.

23 6 4 But the solution to the second problem leads to inconsistence of cause(m') and cause(c). Omitting the temporal precedence condition from the definition opens cause(m') to Simon's criticism (see Section 4,2.1). Therefore, we cannot remedy the problems of Mill's definition through simple alterations. We must look elsewhere for a suitable definition of cause. 4.6 Construction of a Definition for. Cause A Theoretical Definition is Desirable The previous sections have shown that necessary and/or sufficient definitions of cause are inadequate. This realization leads us to attempt the construction of our own definition of this elusive term. Probably the most important reasons that Galileo's operational definition of cause was inconsistent with cause(c) was the failure of this philosopher to first formulate a precise theoretical or ontological definition. A precisely stated theoretical definition can serve as a standard by which one can measure the face validity of a proposed operational definition. As we saw in Section 4,2, his operational definition is inconsistent with cause(c). If he had stated a theoretical definition for cause--capturing

24 65 the commonly understood meaning of the term--this inconsistence would probably have become apparent. Hume's operational definition of cause, also, suffered from the lack of a theoretical definition. But Hume's reason for not formulating a theoretical definition resulted from his empiricist philosophy. Operational definitions are observable whereas theoretical definitions are not. Since empiricism accepts only that knowledge which is observable, it would be senseless, from Hume's point of view, to consider unobservables. Therefore, Hume would not consider comparison with a theoretical definition to give any indication as to the validity of an operational definition. To Hume, a theoretical definition would be a meaningless, valueless specification. From the author's point of view, a theoretical definition is highly desirable. It is the role of a theoretical definition to convey the meaning and boundaries of a term. Any consideration as to the observability of this type of definition is misplaced. An operational definition should have two qualities: it should be observable and it should bear a one to one correspondence (or as close to that as is attainable) to the theoretical definition. In this section we will present a theoretical definition of cause, denoted by cause(p). The purpose

25 66 of cause(p) will be to serve as a standard or basis for the operational definition of cause. As will be shown in Section 4.7, the act of operationally defining cause can be approached in two different ways. An operational definition, denoted by cause(op), can be stated or we can derive a causal inquiring system based on the definition of cause(p) and a priori assumptions, A Concept of the Causal Operation of the Universe To construct a theoretical definition of cause, we need a clear understanding of our conception of the operation of the universe. This fundamental causal theory (i.e., naturalistic metaphysics) will be discussed in detail in Chapter 7, but we will summarize some of the essential points here. The universe is composed of fundamental objects or variables which are smaller than any particles yet "observed". The basic laws of the universe are causal laws acting between adjacent (i.e. touching) fundamental objects. These causal connections are called microcausal connections. A causal connection between spatially and/or temporally separated variables, say A and B, occurs via a chain of microcausal connections between A and B, like the progressive collapse of a chain of dominoes. See Figure 4-2,

26 67 Figure 4-2 The causal connection between A and B is called a macrocausal connection. Macrocausal connections are the only causal connection that we can observe, but they do not represent basic laws of the universe. Macrocausal "laws" are a construct of man and they can be broken by a rearrangement of the fundamental objects between A and B. The previously discussed definitions of Galileo, Hume, and Mill took the form of unconditional(c) definitions of macrocausal "laws". For example: A causes(m) B, if A is the antecedent of B and is unconditionally(m) and invariably sufficient for B. Any such definition is doomed to failure because of the conditional(c) nature of macrocausal "laws". For this reason it is preferable to define cause for a specific event rather than a class of events. This is the task of the next section A Theoretical Definition of Cause Based upon the considerations of Sections and 4,6.2 and others which will be discussed in this

27 68 section, we arrive at the following definitions of cause, denoted by cause(p): Definition (4-1) : X causes (7) Y, if and only if the behavior of X or. oduces a force on Y, where X and Y are specific events or behaviors. X and Y are not a generalized class of events. For example, the thrown ball caused(p) a lump on my head; not, thrown balls cause(p) lumps on the head. As defined, a causal(p) connection is a connection between two specific events or specific behaviors of variables rather than a connection between all events or all behaviors of some class. This event definition of cause does not preclude the use of the "law" definition of cause. Cause(C) is commonly used to mean both event A causes(c) event B and events of the type A cause(c) events of the type B and there is no reason why cause(p) cannot be used in the same ways. But one must understand. that there is no reason to believe that a macro causal(p) "law" will be correct in all cases--for the reasons stated in Section The causal "law" definition of cause(p) would be the same as Definition (4-1), except that X and Y represent classes of events rather than specific events. Definition (4-2): cadres (P) Y, if and only if the behavior of X produces a force on Y, where X and Y are classes of events.

28 69 Again, remember that this law definition of cause is not unconditional(c). "Behavior" has a specific, operational definition: Definition (4-3): The behavior of X is represented by the vector of the ith derivative of X with respect to time, for i equals all integers (positive, negative, and zero). The derivatives of all orders will completely describe any type of change in X. "Produce" and "force" are primitives of the system. That is to say, they are undefined in the object language; but they will be discussed by the metalanguage, English. Produce means to bring about, to give rise to. As used in Definition 0-1), force has the same meaning as it has in physics, except here force can act on any variable rather than just the acceleration of a mass. Note that the initiation of a force on a variable, say Y, does not necessarily result in a change in Y. Maybe Y was already at the value which the force would push Y toward. Or maybe the force can change Y only after it reaches a certain magnitude. This means that X may cause(p) Y even though there is no change in Y due to X; there is simply a causal(p) connection between them. In other words a causal(p) force or a causal(p) impulse may be transmitted from X to Y with no resulting change in Y.

29 70 On this point cause(c) is unclear. But the meaning we have given cause(p) is the most reasonable one. First, in defining cause from the ontological point of view, we are considering the unobservable force rather than an observable change in Y. Second, say that X forces Y to a value of 3. If we bring X to bear on Y, Y will tend to 3 irrespective of its initial value, Yo, unless Yo is 3. As already stated, any causal(p) impulse flowing from X to Y is strictly unobservable. This is obvious from the fact that if we view only X and Y, we cannot distinguish between the situation where X causes(p) Y and the situation where an unobservable variable, Z, causes(p) both X and Y, spurious correlation. We can only observe associations and make the connections in our minds, which may or may not be valid. Kant* argues that this "knowledge" of an ontological *Kant, Immanuel: Critique of Pure Reason, Translated by Norman Kemp Smith, New York, St. Martin's Press, 1965, p.55. connection is simply a Priori synthetic knowledge. In a sense we can "observe" ontological production connections indirectly, analogous to the way we observe the nucleus of an atom, through deductive inference. Say that we perform an experiment. We observe X and Y on 2000 occasions, choosing at random 1000 of these occasions, and, on them,

30 71 manipulate X. If Y behaves one way after every manipulation of X and another way after every nonmanipulation of X, we can conclude--based on two easily acceptable assumptions--that X bears an ontological production connection to Y. These assumptions are: Assumption (4-1): The results are not due to statistical sampling error, and Assumption (4-2): There is no spurious variable which is both causing(p) the experimenter to manipulate X and causing(p) Y to behave as it does. These assumptions are more easily accepted than the blatant assumption that ontological production connections exist in the natural universe, even though Assumptions (4-1) and (4-2) in combination with our sense impressions imply the existence of ontological production connections. But, unless we can be 100% certain that these two assumptions are correct, we cannot be 100% certain that the conclusion of a deductive argument, based on them, is correct. Therefore, we must conclude that we cannot be certain about the correctness of the ontological assumption contained in the definition of cause(p). But we can act as if this assumption were correct and record the number of successes and also the number of failures which can possibly be attributed to the incorrectness of the assumption. From this information we can calculate a degree of confidence

31 X 72 we can place in the usefulness of employing the assumption. Note that this confidence measure is not placed on the assumption itself. This is because it is possible for the assumption to be incorrect and yet be a pragmatic one. Let us take a practical approach along the lines just delineated. Is cause(p) a pragmatic definition? Is it useful when used to discuss the natural universe? The answer to these questions must be yes because cause(?) and cause(c) are virtually identical in meaning and all empirical sciences are based upon the common usage understanding of cause. Therefore most of our "knowledge" accepts the assumption inherent in cause(p) and our scientific knowledge is certainly useful. Hence, from a pragmatic point of view, we can accept the usefullness of the assumption inherent in the theoretical definition, cause(p). 4.7 Considerations Concerning an Onerational Definition for Cause(P) There are two equivalent approaches to the inference of causal(p) relationships: (1) From a priori assumptions and empirical observations, deduce that. causes(p) Y and (2) Define an observable or semi-observable, operational definition of cause, denoted by cause(op). From observations, determine that X causes(op) Y. And from assumptions and the knowledge that X causes(op) Y, deduce that X causes(p) Y.

32 73 In approach (1) one forwards an axiom set and assumptions. Based on these, he derives a formulation in which he can insert empirical observations to make causal(p) inferences. Approach (2) is easier: to employ, but--without a derivation of cause(op)--the assumptions upon which causal(p) inferences are based are uncertain, If the derivation is performed, approach (2) is almost identical to (1). The difference is that, at some point, the derivation is halted and a part of the formulation is designated as the operational definition of cause. To employ approach (2) it is necessary to show that the empirical observations fit the specifications of cause(op) and from that to infer-- based upon the axiom and assumption sets of the derivation--that they fit the specifications of cause(p), As was stated previously, these two approaches are in reality logically equivalent, even though they take on different forms. Since approach (1) takes on a generally accepted form that of a mathematical derivation--arid the form of approach (2) is not as well accepted or as clear to work with, we will pursue approach (1). The derivation will be Performed in Part III.