Originally published in Philosophy of Science Vol. 29, No. 2, April 1962
( Hist-Analytic.org)

TEMPORALLY-ASYMMETRIC PRINCIPLES, PARITY BETWEEN EXPLANATION AND PREDICTION, AND MECHANISM VERSUS TELEOLOGY^*

By ADOLF GRUNBAUM^**
University of Pittsburgh

Three major ways in which temporal asymmetries enter into scientific induction are discussed as follows:

1. An account is given of the physical basis for the temporal asymmetry of recordability, which obtains in the following sense: except for humanly recorded predictions and one other class of advance indicators to be discussed, interacting systems can contain reliable indicators of only their past and not of their future interactions. To deal with the exceptional differences in the conditions requisite to the production of an indicator having retrodictive significance ("post-record"), on the one hand, and of one having predictive significance ("prerecord" or recorded prediction), on the other. Purported counter-examples to the asymmetry of spontaneous recordability are refuted.

2. It is shown how in cases of asymmetric recordability, the associated retrodiction-prediction asymmetry makes for an asymmetry of assertability as between an explanandum (or an explanans) referring to a future event and one referring to a past one. But it is argued that this epistemological asymmetry in the assertibility per se must be clearly distinguished from a logical asymmetry between the past and the future in regard to the inferability (deductive or inductive) of the explanandum from the explanans. And it is then contended that the failure to distinguish between an epistemological and a logical asymmetry vitiates the critiques that recent writers have offered of the Popper-Hempel thesis, which affirms symmetry of inferability as between predictive and post-explanatory arguments. In reply to Scriven, it is maintained that predictions based on mere indicators (rather than causes) do not establish an asymmetry in scientific understanding as between predictive arguments and post-explanatory ones.

3. As a further philosophical ramification of the retrodictive-prediction asymmetry, a set of sufficient conditions are stated for the correctness of philosophical mechanism as opposed to teleology.

^* Received June, 1961.

^** An earlier version of this paper was presented at the Conference on Induction, held at the Wesleyan Center for Advanced Studies in June, 1961. It is published here by agreement with Wesleyan University Press.

I am indebted to Professor Allen I. Janis for helpful discussions of aspects of statistical mechanics relevant to ¶2. The treatment of the barometer as an advance indicator in ¶2 benefited from a criticism which Mr. Nicholas LaPara made of an earlier formulation.

After completing this paper, I became aware that some of the objections to the Popper-Hempel thesis which are citicized in my ¶3 were also discussed independently by Professor May Brodbeck in her essay "Explanation, Prediction and 'Imperfect Knowledge'", which is to appear in H. Feigl and G. Maxwell (editors), Minnesota Studies in the Philosophy of Science, vol. III. Unfortunately, it was too late to make specific mention of Professor Brodbeck's contributions within the text.

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¶1. Introduction

In order to consider the role of temporal asymmetries in scientific induction, I wish to deal with three major questions. These are:

(i) What are the principles governing those conditions under which there is the following kind of temporal asymmetry of inferability: it is possible to infer from the state of a system at some particular time t₀ one or more states at times t prior to t₀ - this inference being called a "retrodiction" - but the same information pertaining to the time t₀ does not permit the corresponding predictive inference concerning the times t > t₀?

(ii) What is the bearing of the existence of the asymmetry between retrodiction and prediction on the following quite distinct question: Is there symmetry between the explanation of an event E on the basis of one or more antecedents of E, when E belongs to the past of the explaining scientist, on the one hand, and, on the other hand, the prediction of the same (kind of) E, when E belongs to the future of the scientist making the prediction?

(iii) What is the import of our findings in regard to the two preceding issues for the controversy between mechanism and teleology?

¶2. Conditions of Asymmetry Between Retrodictions and Predictions.

Our concern in this section is with the kind of asymmetry in which retrodiction is possible while the corresponding prediction is impossible.¹ To deal with it, we must first give an account of certain features of the physical world having the character of initial or boundary conditions within the framework of the theory of statistical mechanics. The sought-after basis of asymmetry will then emerge from principles of statistical mechanics relevant to these de facto conditions.

The universe around us exhibits striking disequilibria of temperature and other inhomogeneities. In fact, we live in virtue of the nuclear conversion of the sun's reserves of hydrogen to helium, which issues in our reception of solar radiation. As the sun dissipates its reserves of hydrogen via the emission of solar radiation, it may heat a terrestrial rock embedded in snow during the day time. At night, the rock is no longer exposed to the sun but is left with a considerably higher temperature than the snow surrounding it. Hence, at night, the warm rock and the cold snow form a quasi-isolated subsystem of either our galactic or solar system. And the relatively low entropy of that subsystem was purchased at the expense of the dissipation of the sun's reserves of hydrogen. Hence, if there is some quasi-closed system comprising the sun and the earth, the branching off of our subsystem from this wider system in a state

¹ For a discussion of the conditions under which the inverse asymmetry obtains, see A. Grunbaum, "Das Zeitproblem," Archive fur Philosophie, vol. 7, 1957. pp. 184-185. Cf. also, M. S. Watanabe, "Symmetry of Physical Laws. Part III. Prediction and Retrodiction," Reviews of Modern Physics, vol. 27, 1955, pp. 179-186.

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of low entropy at sunset involved an entropy increase in the wider system. During the night, the heat of the rock melts the snow, and thus the entropy of the rock-snow system increases. The next morning at sunrise, the rock-snow subsystems which branch off from the wider solar or galactic system, remain quasi-closed for a limited period of time, and then merge again with the wider system from which they had been separated. Following Reichenbach⁹, we shall use the term "branch system" to designate this kind of subsystem.

Branch systems are formed not only in the natural course of things, but also through human intervention: when an ice cube is placed into a glass of warm gingerale by a waiter and then covered for hygienic purposes, a subsystem has been formed. The prior freezing of the ice cube had involved an entropy increase through the dissipation of electrical energy in some larger quasi-closed system of which the electrically-run refrigerator is a part. While the ice cube melts in the covered glass subsystem, that quasi-closed system increases its entropy. But it merges again with another system when the then chilled gingerale is consumed by a person. Similarly for closed off and then heated by burning logs.

Thus, our environment abounds in branch-systems whose initial relatively low entropies are the products of their earlier coupling or interaction with outside agencies of one kind or another. This rather constant and ubiquitous formation of a branch-system in a relatively low entropy state resulting from interaction often proceeds at the expense of an entropy increase in some wider quasi-closed system from which it originated. And the de facto, nomologically contingent occurrence of these branch systems has the following fundamental consequence, at least for our region of the universe and during the current epoch: among the quasi-closed systems whose entropy is relatively low and which behave as if they might remain isolated, the vast majority have not been and will not remain permanently-closed, being branch systems instead.

Hence, upon encountering a quasi-closed system in a state of fairly low entropy, we know the following to be overwhelmingly probable: the system has not been isolated for millions and millions of years and does not just happen to be in one of the infrequent but ever-recurring low entropy states exhibited by a permanently-isolated system. Instead, our system was formed not too long ago by branching off after an interaction with an outside agency. For example, suppose that an American geologist is wandering in an isolated portion of the Sahara desert in search of an oasis and encounters a portion of the sand in the shape of "Coca Cola." He would then infer that, with overwhelming probability, a kindred person had interacted with the sand in the recent past by tracing "Coca Cola" in it. The geologist would not suppose that he was in the presence of one of those relatively low entropy configurations which are assumed by the sand particles spontaneously but very rarely, if beaten about

² Cf. H. Reichenbach, The Direction of Time. Berkeley. 1956, p. 118.

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by winds for millions upon millions of years in a state of effective isolation from the remainder of the world.

There is a further de facto property of branch systems that concerns us. For it will turn out to enter into the temporally asymmetrical statistical regularities which we shall find to be exhibited in the entropic behavior of these systems. This property consists in the following randomness obtaining as a matter of nomologically-contingent fact in the distribution of the W₁ microstates belonging to the initial macro-states of a space-ensemble of branch-systems each of which has the same initial entropy S₁=k log W₁: For each class of like branch-systems having the same initial entropy value S₁, the micro-states constituting the identical initial macro-states of entropy S₁ are random samples of the set of all W₁ micro-states yielding a macro-state of entropy S₁.³ This attribute of randomness of micro-states on the part of the initial states of the members of the space-ensemble will be recognized as the counterpart of the following attribute of the micro-states of one single, permanently-closed system: there is equi-probability of occurrence among the W₁ micro-states belonging to the time-ensemble of states of equal entropy S = k log W₁ exhibited by one single, permanently-closed system.

We can now state the statistical regularities which obtain as a consequence of the de facto properties of branch systems just set forth, when coupled with the principles of statistical mechanics. These regularities, which will be seen to yield a temporally-asymmetric behavior of the entropy of branch-systems, fall into two main groups as follows.

Group 1. In most space-ensembles of quasi-closed branch-systems each of which is initially in a state of non-equilibrium or relatively low entropy, the majority of branch-systems in the ensemble will have higher entropies after a given time t.⁴ But these branch systems simply did not exist as quasi-closed, distinct systems at a time t prior to the occurrences of their initial, branching off states. Hence, not existing then as such, the branch systems did in fact not also exhibit the same higher entropy states at the earlier times t, which they would indeed have done then had they existed as closed systems all along.

The increase after a time t in the entropy of the overwhelming majority of branch systems of initially low entropy - as confirmed abundantly by observation - can be made fully intelligble. To do so, we note the following property of the time-ensemble of entropy values belonging to a single, permanently-closed system and then affirm that property of the space-ensembles of branch systems: since large entropic downgrades or decreases are far less probable (frequent) than moderate ones, the vast majority of non-equilibrium entropy states of a permanently-closed system are located either at or in the immediate temporal vicinity of the bottom of a dip of the one-system entropy curve. In short, the vast majority of the sub-maximum entropy states are on or very near the upgrades of the one-system curve. The application of this result

³ Cf. R. C. Tolman, The Principles of Statistical Mechanics, Oxford, 1938, p. 149.

⁴ R. Furth, 'Prinzipien der Statistik," Handbuch der Physik, Vol. 4, 1929, pp. 270 and 192-193.

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to the space-ensemble of branch systems whose initial states exhibit the aforementioned de facto property of randomness then yields the following: among the initial low entropy states of these systems, the vast majority lie at or in the immediate temporal vicinity of the bottoms of the one-system entropy curve at which an upgrade begins.

Group 2. A decisive temporal asymmetry in the statistics of the temporal evolution of branch-systems arises from the further result that in most space ensembles of branch systems each of whose members is initially in a state of equilibrium or very high entropy, the vast majority of these systems in the ensemble will not have lower entropies after a finite time t, but will still be in equilibrium.⁵ For the aforementioned randomness property assures that the vast majority of those branch systems whose initial states are equilibrium states have maximum entropy values lying somewhere well within the plateau of the one-system entropy curve, rather than at the extremity of the plateau at which an entropy decrease is initiated.⁶

We see therefore that in the vast majority of branch systems, either one end of their finite entropy curves is a point of low entropy and the other a point of high entropy, or they are in equilibrium states at both ends as well as during the intervening interval. And it is likewise apparent that the statistical distribution of these entropy values on the time axis is such that the vast majority of branch systems have the same direction of entropy increase and hence also the same opposite direction of entropy decrease. Thus, the statistics of entropy increase among branch systems assure that in most space ensembles the vast majority of branch systems will increase their entropy in one of the two opposite time directions and decrease in the other. In this way the entropic behavior of branch systems confers the same statistical anisotropy on the vast majority of all those epochs of time during which the universe exhibits the requisite disequilibrium and contains branch systems satisfying initial conditions of "randomness." ⁷

⁵ ibid., p. 270.

⁶ Although the decisive asymmetry just noted was admitted by H. Mehlberg ["Physical Laws and Time's Arrow," in: Current Issues in the Philosophy of Science (ed. Feigl & Maxwell), New York, 1961, p. 129], he dismisses it as expressing "merely the factual difference between the two relevant values of probability." But an asymmetry is no less an asymmetry for depending on de facto, nomologically-contingent, boundary conditions rather than being assured by a law alone. Since our verification of laws generally has the same partial and indirect character as that of our confirmation of the existence of certain complicated de facto boundary conditions, the assertion of an asymmetry depending on de facto conditions is generally no less reliable than one wholly grounded on a law. Hence when Mehlberg [op. cit., p. 117, n. 30] urges against Schrodinger's claim of asymmetry that for every pair of branch systems which change their entropy in one direction, "there is nothing to prevent" another pair of closed subsystems from changing their entropy in the opposite direction, the reply is: Mehlberg's criticism can be upheld only by gratuitously neglecting the statistical asymmetry admitted but then dismissed by him as "merely" factual. For a more detailed cricicism of Mehlberg's denial of temporal anisotropy, see A. Grunbaum, The Philosophical Problems of Space and Time, Alfred Knopf, New York (forthcoming).

⁷ Readers familiar which Reichenbach's "hypothesis of the branch structure" as set forth in his The Direction of Time (p. 136) will note that though heavily indebted to Reichenbach, my treat-

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Let us now call the direction of entropy increase of a typical representative of these epochs the direction of "later," as indeed we have done from the outset by the mere assignment of higher time numbers in that direction without prejudice to our findings concerning the issue of the anisotropy of time. Then our results pertaining to the entropic behavior of branch systems show that the direction of "earlier than" and "later than" are not merely opposite directions bearing decreasing and increasing time coordinates respectively but are statistically anisotropic in an objective physical sense.⁸

We are now prepared to elucidate the bearing of this conclusion on the conditions under which there is asymmetry between retrodiction and prediction.

Suppose we encounter a beach whose sand forms a smooth surface except for one place where it is in the shape of a human footprint. We know from our previous considerations with high probability that instead of having evolved isolatedly from a prior state of uniform smoothness into its present uneven configuration according to the statistical entropy principle for a permanently-closed system, the beach was an open system in interaction with a stroller. And we are aware furthermore that if there is some quasi-closed wider system containing the beach and the stroller, as there often is, the beach achieved its ordered low entropy state of bearing the imprint or interaction-indicator at the expense of an at least compensatory entropy increase in that wider system comprising the stroller: the stroller increased the entropy of the wider system by scattering his energy reserves in making the footprint.

We see that the sandy footprint shape is a genuine indicator and not a randomly-achieved form resulting from the unperturbed chance concatenations of the grains of sand. The imprint thus contains information in the sense of being a veridical indicator of an interaction. Now, in all probability the entropy of the imprint-bearing beach-system increases after the interaction with the stroller through the smoothing action of the wind. And this entropy increase is parallel, in all probability, to the direction of entropy increase of the majority of branch systems. Moreover, we saw that the production of the indicator by the interaction is likely to have involved an entropy increase in some wider system of which the indicator is part. Hence, in all probability the states of the interacting systems which do contain the indicators of the interaction are the

ment of the assumptions regarding branch systems departs from Reichenbach's in several essential respects. A statement and justification of these departures is given in A. Grunbaum, "Carnap's Views on the Foundations of Geometry," footnote 97 in: P. A. Schilpp (ed.), Th Philosophy of Rudolf Carnap, Open Court Publishing Co., LaSalle, Illinois, 1962.

⁸ This is not to say that entropic changes are the sole source of the anisotropy of time. But processes which are de facto irreversible though not involving any entropy increase [Cf. K. R. Popper, "The Arrow Time," Nature 177, 538 and 178, 382 (1956); E. L. Hill and A. Grunbaum, "Popper on Irreversibility," in M. Bunge (ed.), The Critical Approach, Essays in Honor of Karl Popper, to be published by the Free Press, Glencoe, Ill.] are not of importance for the asymmetry between retrodiction and prediction, which is our guiding concern in this section.

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relatively higher entropy states of the majority of branch systems, as compared to the interaction state. Hence the indicator states are the relatively later states as compared to the states of interaction which they attest. And by being both later and indicators, these states have retrodictive significance, thereby being traces, records or memories. And due to the high degree of retroductive univocity of the low entropy states constituting the indicators, the latter are veridical to a high degree of specificity.

Confining our attention for the present to indicators whose production requires only the occurrences of the interaction which they attest, we therefore obtain the following conclusion. Apart from two classes of advance-indicators requiring very special conditions for their production and constituting exceptions, it is the case with overwhelming probability, low entropy indicator-states can exist in systems whose interactions they attest only after and not before these interactions.⁹ If this conclusion is true (assuming that there are either no cases or not enough cases of bona fide precognition to disconfirm it), then, of course, it is not an a priori truth. And it would be very shallow indeed to seek to construe it as a trivial a priori truth in the following way: calling the indicator states "traces," "records" or "memories" and noting that it then becomes tautological to assert that traces and the like have only retrodictive and no predictive significance. But this transparent verbal gambit cannot make it true a priori that - apart from the exceptions to be dealt with below - interacting systems bear indicators attesting veridically only their earlier and not their later interactions with outside agencies.

Hence, the two exceptions apart, we arrive at the fundamental asymmetry of recordability: reliable indicators in interacting systems permit only retrodictive inferences concerning the interactions for which they vouch but no predictive inferences pertaining to corresponding later interactions.

And the logical schema of these inductive inferences is roughly as follows: The premisses assert (i) the presence of a certain relatively low entropy state in the system, and (ii) a quasi-universal statistical law stating that most low entropy states are interaction-indicators and were preceded by the interactions for which they vouch. The conclusion from these premises is then the inductive retroductive one that there was an earlier interaction of a certain kind.

As already mentioned, our affirmation of the temporal asymmetry of recordability of interactions must be qualified by dealing with two exceptional cases, the first of which is the pre-recordability of those interactions which are veridically predicted by human beings (or computers). For any event which could be predicted by a scientist could also be "pre-recorded" by that scientist in various forms such as a written entry on paper asserting its occurrence at a

⁹ The two exceptions, which we shall discuss in some detail below, are constituted by the following two classes of advance indicators: (i) veridical predictions made and stored (recorded) by human (or other sentient, theory-using) beings, and physically-registered, bona fide advance indicators produced by computers, and (ii) advance indicators (e.g. suddent barometric drops) which are produced by the very cause (pressure change) that also produces the future interaction (storm) indicated by them.

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certain later time, an advance drawing, or even an advance photograph based on the pre-drawing. By the same token, artifacts like computers can pre-record events which they can predict. A comparison between the written, drawn, or photographic pre-record (i.e., recorded prediction) of, say, the crash of a plane into a house and its post-record in the form of a caved-in house, and a like comparison of the corresponding pre- and post-records of the interactions of a foot with a beach will now enable us to formulate the essential differences in the condition requisite to the respective production of pre-records and post-records as well as the usual differences in make-up between them.

The production of at least one retrodictive indicator or post-record of an interaction such as the plane's crash into the house requires only the occurrence of that interaction (as well as moderate degree of durability of the record). The retrodictive indicator states in the system which interacted with an outside agency must, of course, be distinguished from the epistemic use which human beings may make of these physical indicator states. And our assertion of the sufficiency of the interaction for the production of a post-record allows, of course, that the interpretation of actual post-records by humans as bona fide documents of the past requires their use of theory and not just the occurrence of the interaction. In contrast to the sufficiency of an interaction itself for its (at lest short-lived) post-recordability, no such sufficiency obtains in the case of the pre-recordability of an interaction: save for an overwhelmingly improbable freak occurrence, the production of even a single pre-recorded of the coupling of a system with an agency external to its requires, as a necessary condition, either (a) the use of an appropriate theory by symbol-using entities (humans, computers) having suitable information, or (b) the pre-record's being a partial effect of a cause that also produces the pre-recorded interaction, as in the barometric case to be dealt with below. And in contexts in which (a) is a necessary condition, we find the following: since pre-records are, by definition, veridical, this necessary condition cannot generally also be sufficient, unless the predictive theory employed is deterministic and the information available to the theory-using organism pertains to a closed system.

In addition to differing in regard to the conditions of their production, pre-records generally differ from post-records in the following further respect: unless the pre-record prepared by a human being (or computer) happens to be part of the interacting system to which it pertains, the pre-record will not be contained in states of the interacting system which it concerns but will be in some other system. Thus, a pre-record of the crash of a plane into a house in a heavy fog would generally not be a part of either the house or the plane, although it can happen to be. But in the case of post-recording, there will always be at least one post-record, however short-lived, in the interacting system itself to which that post-record pertains.

Our earlier example of the footprint on the beach will serve to illustrate more fully the asymmetry between the requirements for the production of a pre-record of a post-record. The pre-recording of a later incursion of the beach by a stroller would require information about the motivations

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and habits of people not now at the beach and also knowledge of the accessibility of the beach to prospective strollers. This is tantamount to knowledge of a large system which is closed, so that all relevant agencies can safely be presumed to have been included in it. For otherwise, we should be unable to guarantee, for example, that the future stroller will not be stopped enroute to the beach by some agency not included in the system, an eventuality whose occurrence would deprive our pre-record of its referent, thereby destroying its status as a veridical indicator. In short, in the case of the footprint, which is a post-record and not a pre-record of of the interaction of a human foot with the beach, the interaction itself is sufficient for its post-recording (though not for the extended durability of the record once it exists) but not for its pre-recording and prediction. Since a future interaction of a potentially open system like the beach is not itself sufficient for its pre-recordability, open systems like beaches therefore do not themselves exhibit pre-records of their own future interactions. Instead - apart from the second species of pre-recordability to be considered presently - prerecordability of interactions of potentially open systems requires the mediation of symbol and theory-using organisms or the operation of appropriate artifacts like computers. And such pre-recordability can obtain successfully only if the theory available to the pre-recording organism is deterministic and sufficiently comprehensive to include all the relevant laws and boundary conditions governing the pertinent closed systems.

The second species of exceptions to the asymmetry of recordability is exemplified by the fact that a sudden drop in the pressure reading of a barometer can be an advance-indicator or "pre-record" of a subsequent storm. To be sure, it is the immediately prior pressure change (i.e., the past interaction through pressure) which is recorded numerically by a given drop in the barometric reading, and not the pressure change that will exist at that same place at a later time: To make the changes required for a pre-recording of the pressure change will exist at a given space point at later times (i.e., of the corresponding furture interactions), comprehensive meteorological data pertaining to a large region would be essential. But it is possible in this case to base a rather reliable prediction of a future storm on the present sudden barometric drop. The latter drop, however, is, in fact, a bona fide advance indicator only because it is a partial effect of the very comprehensive cause which also produces (assures) the storm. Thus, it is the fulfillment of the necessary condition of having a causal ancestry that overlaps with that of the storm which is needed to confer the status of an advance indicator on the barometric drop. In contrast to the situation prevailing in the case of postrecordability, the existence of this necessary condition makes for the fact that the future occurrence of a storm is not sufficient for the existence of an advance indicator of that storm in the form of a sudden barometric drop at an earlier time.

An analogous account can be given of the following case, which Mr. F. Brian Skyrms has suggested to me for consideration in which human

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intentions are highly reliable advance indicators of the events envisaged by these intentions. Thus, the desire for a glass of beer, coupled with the supposed presence of the condition under which beer and a glass are obtainable produces as a partial effect the intent to get it. And, if external conditions permit (the beer is available and accessible), and, furthermore, if the required internal conditions materialize (the person desiring the beer remains able to go and get it), then the intent will issue in the obtaining and drinking of the beer. But in contrast to the situation prevailing in the case of retrodictive indicators (postrecords), the future consumption of the beer is not a sufficient condition for the existence of its probabilistic advance indicator in the form of an intention.

The consideration of some alleged counter-examples will serve to complete our statement of the temporal asymmetry of the recordability of interactions. These purported counter-examples are to the effect tht there are pre-records not depending for their production on the use of predictive theory by symbol-using organisms or on the pre-record's being a partial effect of a cause that also produces the pre-recorded interaction.

In the first place, it might be argued that there are spontaneous pre-records as exemplified in the following two kinds of scientific contexts: (1) in any essentially close dynamical system such as the solar system, a dynamical state later than one occurring at a time t₀, is a sufficient condition for the occurrence of the state at time t₀, no less than is a state prior to t₀; hence the state at time t₀ can be regarded as a pre-record of the later state no less than it can be deemed a post-record of the earlier one, and (2) a certain kind of death - say,the kind of death ensuing from leukemia - may be a sufficient condition for the existence of a pre-record of it in the form of the onset of active leukemia. But these examples violate the conditions on which our denial of spontaneous pre-recordability is predicated in the following essential respect: they involve later states which are not states of interaction with outside agencies entered into by an otherwise closed system, in the manner of our example of the beach.

In the second place, since the thesis of the temporal asymmetry of spontaneous recordability makes cases of bona fide precognition overwhelmingly improbable, it might be said that this thesis and the entropic considerations undergirding it are vulnerable to the discovery of a reasonable number of cases of genuine precognition, a discovery which is claimed by some to have already been made. To this I retort that if the purported occurrence of precognition turns out to become well authenticated, then I am, of course, prepared to envision such alterations in the body of current orthodox scientific theory as may be required.

¶3. The Bearing of the Retrodiction-Prediction Asymmetry on the Issue of Symmetry Between Explanation and Prediction

In our ¶1, we gave a preliminary demarcation of the retrodiction-prediction antithesis from the explanation-prediction distinction as understood by writers

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such as Hempel.¹⁰ We shall now complete that demarcation and will then represent the results on a diagram.

For Hempel, the particular conditions C_i (i = 1, 2, ...n) which, in conjunction with the relevant laws, account for the explanandum-event, E, may be earlier than E in both explanation and prediction Thus, a case of prediction in which the C_i would be later than E would be one in astronomy, for example, in which a future E is accounted for by reference to C_i which are still further in the future than E. These assertions hold, since Hempel's criterion for an explanation as opposed to a prediction that is that E belong to the scientist's past when he offers his account of it, and his criterion for a corresponding prediction is that E belong to the scientist's future when it is made.

On the other hand, in the retrodiction-prediction antithesis, a retrodiction is characterized by the fact that C_i are later than E, while the C_i are earlier than E in the kind of prediction which is antithetical to retrodiction but not identical with Hempelian prediction.

In the accompanying diagram, the i, k, l, m, may each range over the values 1, 2, ...n.

                     C_k may coincide                       C_k may coincide
                                   with the Now or                       with the Now
                                   or even succeed it                   or even precede it
                                            |                                             |
         prediction->   <-retrodiction                       prediction->   <-retrodiction

   *----------*---*-------------*-----|------*---------*-------*---------------*->  +t
[ C_i               E₁     E₂                  C_k ] Now     [ C_l             E₃           E₄                       C_m ]
                    G-Explanation                                            H-prediction

If we use the pre-fix "H" as an abbreviation for "Hempelian," then two consequences are apparent. Firstly, a retrodiction as well as a prediction can be an H-prediction, and a prediction as well as a retrodiction can be an H-explanation. Secondly, being an H-prediction rather than an H-explanation or conversely depends on the transient homocentric "now," but there is no such "now"-dependence in the case of being a retrodiction instead of a prediction, or conversely.

The passage in the Hempel-Oppenheim essay setting fort the symmetry thesis espoused by K. R. Popper and these authors reads as follows¹¹:

the same formal analysis, including the four necessary conditions, applies to scientific prediction as well as to explanation. The difference between the two is of a pragmatic character. If E is given, i.e. if we know that the phenomenon described by E has oc-

¹⁰ I refer here to the original paper of C. G. Hempel and P. Oppenheim "Studies in the Logic of Explanation," Philosophy of Science, 15, 135 (1948). For Hempel's most recent statement of his account of scientific explanation, see his forthcoming "Deductive Nomological vs. Statistical Explanation," Minnesota Studies in Philosophy of Science (ed. Feigl and Maxwell), vol. III, Minneapolis, 1962.

¹¹ C. G. Hempel and P. Oppenheim, op. cit. ¶3.

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curred, and a suitable set of statements C₁, C₂, ... C_k,L₁, L₂ ...,L_t is provided afterwards, we speak of an explanation of the phenomenon in question. If the latter statements are given and E is derived prior to the occurrence of the phenomenon it describes, we speak of a prediction. It may be said, therefore, that an explanation is not fully adequate unless its explanans, if taken account of in time, could have served as a basis for predicting the phenomenon under consideration.¹² - Consequently, whatever will be said in the article concerning the logical characteristics of explanation or prediction will be applicable to either, even if only one of them should be mentioned.

Hempel's thesis of symmetry or structural equality between H-explanation and H-prediction can therefore now be formulated in the following way: Any prediction which qualities logically and methodologically as an H-explanation also qualifies as an H-prediction, provided that the scientist is in possession of the information concerning the C₁ prior to the occurrence of E, and conversely. And any retrodiction which qualifies logically and methodologically as an H-explanation also qualifies as an H-prediction, provided that the information concerning the relevant C₁ is available at an appropriate time, and conversely.

Before examining critically the diverse objections which have been leveled against Hempel's thesis of symmetry in the recent literature by N. Rescher¹³, S. F. Barker¹⁴, N. R. Hanson¹⁵, and M. Scriven¹⁶, I wish to make a few remarks concerning my construal of both that thesis and of the philosophical task to whose fulfillment it pertains.

I take Hempel's affirmation of symmetry to pertain not to the assertability per se of the explanation but to the either deductive or inductive inferability of the explanandum from the explanans. The scientific relevance of dealing with predictive arguments rather than mere predictive assertions can hardly be contested by claiming with Scriven that in this context "the crucial point is that, however achieved, a prediction is what it is simply because it is produced in advance of the event it predicts; it is intrinsically nothing but a bare description of that event."¹⁷ For surely a soothsayer's unsupported prophecy that there will not be a third world war is not of scientific significance and ought not to command any scientific interest precisely because of the unreasoned manner of its achievement. Hence a scientifically warranted prediction of an event must be more than pre-assertion of the event. And in any context which is to

¹² "The logical similarity of explanation and prediction, and the fact that one is directed towards past occurrences, the other towards future ones, is a well expressed in the terms "postdictability" and "predictability" used by Reichenbach in [Quantum Mechanics], p. 13."

¹³ N. Rescher, "On Prediction and Explanation," British Journal for the Philosophy of Science, 8, 281, (1958).

¹⁴ S. F. Barker, "The Role of Simplicity in Explanation," in: Current Issues in the Philosophy of Science (ed. Feigl and Maxwell), New York, 1961, pp. 265-286 and the Comments on this paper by Salmon, Feyerabend and Rudner with Barker's Rejoinders.

¹⁵ N. R. Hanson, "On the Symmetry Between Explanation and Prediction," The Philosophical Review 68, 349 (1959).

¹⁶ M. Scriven, "Explanation and Prediction in Evolutionary Theory." Science 130, 477 (1959) and "Explanation, Predictions and Laws," in H. Feigl & G. Maxwell (eds) Minnesota Studies in the Philosophy of Science, vol. III, Minneapolis, 1962.

¹⁷ M. Scriven, "Explanation, Predictions, and Laws," op. cit. Section 3.4.

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be scientifically relevant, the following two components can be distinguished in the meaning of the term "H-predict" no less than in the meaning of of "H-explain" (or "post-explain"), and similarly for the corresponding nouns:
    (i)the mere assertion of the explanandum, which may be based on grounds other than its scientific explanans,
    (ii) the logical derivation (deductive or inductive) of the explanandum from an explanans, the character of the content of the explanans remaining unspecified until later on in this essay.

My attachment of the prefix "H" to the word "explain" (and to "explanation") and my use of "post-explain" as a synonym of "H-explain" will serve to remind us for the sake of clarity that this usage of "explain" results from a restriction to the past of one well-established usage which is temporally-neutral, viz., "explain" in the sense of providing scientific understanding (or a scientific accounting) of why something did or will occur. But, to my mind, the philosophical task before us is not the ascertainment of how the words "explain" and "predict" are used, even assuming that there is enough consistency and precision in their usage to make this lexicographic task feasible. And hence the verdict on the correctness of Hempel's symmetry thesis cannot be made to depend on whether it holds for what is taken to to be the actual or ordinary usage of these terms. Instead, in this context I conceive the philosophical task to be both the elucidation and examination of the provision of scientific understanding of an explanandum by an explanans as encountered in actual scientific theory. Accordingly, Hempel's symmetry thesis, which concerns the inferability of the explananda from a given kind of explanans and not their assertibility must be assessed on the basis of a comparison of H-predictive with H-explanatory arguments with respect to the measure of scientific understanding afforded by them. Thus, the issue of the adequacy of the symmetry thesis will revolve around whether there is temporal symmetry in regard to the degree of entailment, as it were, characterizing the logical link between the explanans and the explanandum. Specifically, we shall need to answer both of the following questions: (i) Would the type of argument which yields a prediction of a future explanandum-event not furnish precisely the same amount of scientific understanding of a corresponding past event? And (ii) Does an explanans explain an explanandum referring to a past event any more conclusively than the same kind of explanans predictively implies the explanandum pertaining to the corresponding future event?

We are now ready to turn to the appraisal of the criticisms of Hempel's symmetry thesis offered by Rescher, Barker, Hanson and Scriven. In the light of my formulation of Hempel's thesis, it becomes clear that it does not assert, as Rescher supposes, that any set of C₁ which permit a predictive inference also qualify for a corresponding retrodictive one, or that the converse is true. As Rescher notes correctly but irrelevantly, whether or not symmetry obtains between prediction and retrodiction in any given domain of empirical science is indeed not a purely logical question but depends on the content of the laws pertaining to the domain in question. We see that Hempel was

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justified in claiming¹⁸ that Rescher has confused H-explanation with retrodiction. And this confusion is also facilitated by one of Scriven's statements of the symmetry thesis, which reads¹⁹: "to predict, we need a correlation between present events and future ones - to explain, between present ones and past ones."

In agreement with Sheffler²⁰, Rescher offers a further criticism of the Hempelian assertion of symmetry: "it is inconsistent with scientific custom and usage regarding the concepts of explanation and prediction," for, among other things, "Only true statements are proper objects for explanation, but clearly not so with prediction."²¹ And in support of the latter claim of an "epistemological asymmetry," Rescher points to a large number of cases in which we have "virtually certain knowledge of the past on the basis of traces found in the present" but "merely probable knowledge of the future on the basis of knowledge of the present and/or the past."²²

The question raised by Rescher's further objection is whether this epistemological symmetry can be held to impugn the Hempelian thesis of symmetry. To deal with this question, it is fundamental to distinguish - as Rescher, Barker, Hanson, and Scriven unfortunately failed to do, much to the detriment of their theses - between the following two sets of ideas: (1) an asymmetry between H-explanation and H-prediction both in regard to the grounds on which we claim to know that the explanandum is true and correlatively in regard to the degree of our confidence in the supposed truth of the exlanandum, and (2) an asymmetry, if any, between H-explanation and H-prediction with respect to the logical relation obtaining between the explanans and the explanandum. For the sake of brevity, we shall refer to the first asymmetry as pertaining to the "assertibility" of the explanandum while speaking of the second as an asymmetry in the "inferability of "why" of the explanandum. In the light of this distinction, we shall be able to show that the existence of an epistemological asymmetry in regard to the assertibility of the explanandum cannot serve to impugn the Hempelian thesis of symmetry, which pertains to only the why of the explanandum.

If understood as pertaining to the assertibility of the expanandum, Rescher's contention of the existence of an epistemological asymmetry is indeed correct. For we saw in our ¶2 that there are highly reliable records of past interactions. And this fact has the important consequence that while we can certify the assertibility or truth of an explanandum referring to a past interaction on the basis of a record without invoking the supposed truth of any (usual) explanans therof, generally no pre-indicator but only the supposed truth of an appropriate explanans can be invoked to vouch for the assertibility or truth of the

¹⁸ Hempel, "Deductive-Nomological vs. Statistical Explanation," op. cit., Section 6.

¹⁹ Scriven, "Explanation and Prediction in Evolutionary Theory," op. cit., p. 479.

²⁰ I. Sheffler, "Explanation, Prediction and Abstraction," British J. Phil. of Science, 7, 293. (1957).

²¹ Rescher, op. cit., p. 282.

²² Ibid., p. 284.

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explanandum pertaining to a future interaction. And since the theory underlying our interpretation of records is confirmed better than are many of the theories used in an explanans, there is a very large class of cases in which an epistemological asymmetry does obtain with respect to the assertibility of the explanandum.

The entire substance of both Barker's objection to Hempelian symmetry and of Hanson's (1959) critique of it is vitiated by the following fact: these authors adduced what they failed to recognize as a temporal asymmetry in the mere assertibility of the explanandum to claim against Hempel that there is a temporal asymmetry in the why. And they did so by citing cases in which they invoke a spurious contrast between the non-assertibility of an explanandum referring to the future and the inductive inferability of an explanandum pertaining to the past. Thus we find that Barker writes: "it can be correct to speak of explanation in many cases where specific prediction is not possible. Thus, for instance, if the patient shows all the symptoms of pneumonia, sickens and dies, I can then explain his death - I kow what killed him - but I could not have definitely predicted in advance that he was going to die; for usually pneumonia fails to be fatal."²³. But this does not, of course, justify the contention that a past death, which did materialize and is reliably known from a record, can be explained by reference to earlier pneumonia any more conclusively than a future death can be inferred predictively on the basis of a present state of pneumonia. For the logical link between the explanans affirming a past state of pneumonia and the explanandum stating the recorded (known) death of a pneumonia patient is precisely the same inductive one as in the case of the corresponding avowedly probabilistic predicitive inference (H-prediction) of death on the basis of an explanans asserting a patient's present affliction with pneumonia.

It would seem that the commission of Barker's error of affirming an asymmetry in the why is facilitated by the following question-begging difference between the explanans used in his H-explanation of a death from pneumonia and the one used by him in purportedly corresponding prediction: Barker's H-explanation of the past death employs an explanans asserting the onset of pneumonia at a past time as well as the sickening at a later past time, but the further condition of sickening is omitted from the antecedents of his corresponding H-prediction. Hence the spurious asymmetry of conclusiveness between the two cases.

It is now apparent that the valid core of Barker's statement is the commonplace that in the pneumonia case, as in others, post-assertibility of the explanandum does obtain even though pre-assertibility does not. And once it is

²³ Barker, op. cit., p. 271.

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recognized that the only relevant asymmetry which does obtain in cases of the pneumonia type is one of assertibility, the philosophical challenge of this asymmetry is to specify the complex reasons for it, as I have endeavored to do in ¶2 above. But no philosophical challenge is posed for Hempel's asymmetry thesis.

An analogous confusion between the assertibility asymmetry and one in the why invalidates the paper by Hanson which Barker cites in support of his views. Suppose that a certain kind of past measurement yielded a particular ψ-function which is then used in Schrodinger's equation for the H-explanation of a later past occurrence. And suppose also that the same kind of present measurement again yields the same ψ-function for a like system and that this function is then used for the H-prediction of a correspondingly later future occurrence, which is of the same type as the past occurrence. It is patent that in quantum mechanics the logical relation between explanans (the function ψ₁ and the associated set s₁ of probability distributions at the time t₁) and explanandum (the description of a particular micro-event falling within the range of one of the s₁ probability distributions) is no less statistical (inductive) in the case of H-explanation than in the case of H-prediction. And this asymmetry in the statistical why is wholly compatible with the following asymmetry: the reliability of our knowledge that a specific kind of micro-event belonging to the range of one of the s₁ probability distributions has occurred in the past has no counterpart in our knowledge of the future occurrence of such an event, because only the results of past measurements (interactions) are available in records. Hence it was wholly amiss for Hanson to have used the latter asymmetry of recordability as a basis for drawing a pseudo-contrast between the quantum mechanical inferability of a past micro-event - this inferability being logically identical with that of a future one - and the lack of pre-assertibility of the future occurrence of the micro-event. Says he: "any single quantum phenomenon P...can be completely explained ex post facto; one can understand fully just what kind of event occurred, in terms of the well-established laws of the...quantum theory... But it is, of course, the most fundamental feature of these laws that the prediction of such a phenomenon P is, as a matter of theoretical principle, quite impossible."²⁴ Hanson overlooks that the asymmetry between pre-assertibility and post assertibility obtaining in quantum mechanics in no way makes for an asymmetry between H-explanation and H-prediction with respect to the relation of the explanandum to its quantum mechanical explanans. And the statistical character of quantum mechanics enters only in the following sense: when coupled with the recordability asymmetry of classical physics, it makes for a temporal asymmetry of the explanandum.

We see that the statistical character of the quantum mechanical account of micro-phenomena is no less compatible with the asymmetry between H-explanation and H-prediction than is the deterministic character of Newton's mechanics. And this result renders untenable what Hanson regards as the upshot of his 1959 paper on the asymmetry issue viz., "that there is a most

²⁴ Hanson, "On the Symmetry Between Explanation and Prediction," op. cit. pp. 353-354.

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intimate connection between Hempel's account of the symmetry between explanation and prediction and the logic of Newton's Principia."²⁵.

It remains to deal in some detail with Scriven's extensive critique of Hempel's thesis. Scriven argues that (i) evolutionary explanation and explanations like that of the past occurrence of paresis due to syphilis fail to meet the symmetry requirement by not allowing corresponding predictions, (ii) predictions based on mere indicators (rather than causes) such as the prediction of a storm from a sudden barometric drop are not matched by corresponding explanations, since indicators are not explanatory though they may serve to predict or, in other cases, to retrodict. And these indicator-based predictions show that the mere inferability of an explanandum does not guarantee scientific understanding of it, so that symmetry of inferability does not assure symmetry of scientific understanding between explanation and prediction.

I shall now examine several of the paradigm cases adduced by Scriven in support of these contentions.

      1. Evolutionary Theory.

He cites evolutionary theory with the aim of showing that "Satisfactory explanation of the past is possible even when prediction of the future is impossible.²⁶

Evolutionary theory does indeed afford valid examples of the epistemological asymmetry of assertibility. And this is for the following two reasons growing out of our ¶2: (1) the ubiquitous role of interactions in evolution brings the recordability of the explanandum. For in cases of H-prediction based on an explanans containing an antecedent referring to a future interaction, there is also an asymmetry of assertibility between H-prediction and H-explanation in regard to the explanans, and (2) the existence of biological properties which are emergent in the sense that even if all laws were strictly deterministic, the occurrence of these properties could not have been predicted on the basis of any and all laws which could possibly have been discovered by humans in advance of the first known occurrence of the respective properties in question. Thus, evolutionary theory makes us familiar with past biological changes which were induced by prior past interactions, the latter being post-assertible on the basis of present records. And these past interactions can serve to explain the evolutionary changes in question. But the logical relation between explanans and explanandum furnishing this explanation is completely time-symmetric. Hence this situation makes for asymmetry only the following innocuous sense: since corresponding future interactions cannot be rationally pre-asserted - there being no advance records of them - there is no corresponding pre-assertibility of those future evolutionary changes that will be effected by future interactions.

²⁵Ibid. p. 357.

²⁶M. Scriven, "Explanation and Prediction in Evolutionary Theory," op. cit., p. 477.

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In an endeavor to establish the existence of an asymmetry damaging to Hempel's thesis on the basis of the account of a case of non-survival given in evolutionary theory, Scriven writes²⁷:

there are...good grounds [of inherent unpredictability] for saying that even in principle explanation and prediction do not have the same form. Finally, it is not in general possible to list all the exceptions to a claim about, for example, the fatal effects of a a lava flow, so we have to leave it in the probability form; this has the result of eliminating th very degree of certainty from the prediction that the explanation has, when we find the fossils in the lava.

But all that the lava case entitles Scriven to conclude is that the merely probabilistic connection between the occurrence of a lava flow and the extinction of certain organisms has the result of depriving pre-assertibility of the very degree of certainty possessed by post-assertibility here. Scriven is not at all justified in supposing that predictive inferability in this case lacks even an iota of the certainty that can be ascribed to the corresponding post-explanatory inferability. For wherein does the greater degree of certainty of the post-explanation reside? I answer: only in the assertibility of the explanandum, not in the character of the logical relation between the explanans (the lava flow) and the explanandum (fatalities on the part of certain organisms). What then must be the verdict on Scriven's contention of an asymmetry in the certainty of prediction and post-explanation in this context? We see now that this contention is vitiated by a confusion between the following two radically distinct kinds of asymmetry: (i) a difference in the degree of certainty (categoricity) of our knowledge of the truth of the explanandum and of the claim of environmental unfitness made by the explanans, and (ii) a difference in the "degree of entailment," as it were, linking the explanandum to the explanans.

Very similar difficulties beset Scriven's analysis of a case of biological survival which is accounted for on the basis of environmental fitness. He says:

It is fairly obvious that no characteristics can be identified as contributing to "fitness" in all environments...we cannot predict which organisms will survive except in so far as we can predict the environmental changes. But we are very poorly equipped to do this with much precision²⁸...However, these difficulties of prediction do not mean that the idea of fitness as a factor in survival loses all its explanatory power. ...animals which happen to be able to swim are better fitted for surviving a sudden and unprecedented inundation of their arid habitat, and in some cases it is just this factor that explains their survival; let us call this a hypothetical probability prediction. But hypothetical predictions do not have any value for actual predictions except in so far as the conditions mentioned in the hypothesis are predictable...: hence there will be cases where we can explain why certain animals and plants survive even when we could not have predicted that they would.²⁹

²⁷ Ibid., p. 480.

²⁸ The environmental changes which Scriven goes on to cite are all of the nature of interactions of a potentially open system. And it is this common property of theirs which makes for their role in precluding the predictability of survival.

²⁹ Ibid. p. 478.
In a recent paper "Cause and Effect in Biology," [Science 134 (1961), p. 504] the zoologist

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There would, of course, be complete agreement with Scriven, if he had been content to point out in this context, as he does, that there are cases in which we can "explain why" but not "predict that." But he combines this correct formulation with the incorrect supposition that cases of post-explaining survival on the basis of fitness constitute grounds for an indictment of Hempel's thesis of symmetry. Let me therefore state the points of agreement and disagreement in regard to this case as follows. Once we recognize the ubiquitous role of interactions we can formulate the valid upshot of Scriven's observations by saying: insofar as future fitness and survival depend on future interactions which cannot be predicted from given information, whereas past fitness and survival depended on past interactions which can be retrodicted from that same information, there is an epistemological asymmetry between H-explanation and H-prediction in regard to the following: the assertibility both of the antecedent fitness affirmed in the explanans and the explanandum claiming survival.

This having been granted as both true and illuminating, we must go on to say at once that the following considerations - which Scriven can grant only on pain of inconsistency with his account of asymmetry in the lava case - are no less true: the scientific inferability from a cause and hence understanding of the why of survival furnished by an explanans which does contain the antecedent condition that the given animals are able to swim during a sudden, unprecedented inundation of their arid habitat is not one iota more probabilistic (i.e., less conclusive) in the case of a future inundation and survival than in the case of a past one. For if the logical nerve of intelligibility linking the explanans (fitness under specified kinds of inundational conditions) with the explanandum (survival) is only probabilistic in the future case, how could it possibly be any less probabilistic in the past case? It is evident that post-explanatory inductive inferability is entirely on par here with predictive inferability from fitness as a cause. Why then does Scriven feel entitled to speak of "probability prediction" of future survival without also speaking of "probability explanation" of past survival? It would seem that his reason is none other than the pseudo-contrast between the lack of pre-assertibility of the explanandum (which is conveyed by the term "probability" in "probability prediction") with the obtaining of post-explanatory inductive inferability of the explanandum. And this pseudo-contrast derives its plausibility from the tacit appeal to the bona fide asymmetry between the pre-assertibility and post assertibility of the explanandum, an asymmetry which cannot score against Hempel's thesis.

E. Mayr overlooks the fallacy in Scriven's statement which we are about to point out and credits Scriven with having "emphasized quite correctly that one of the most important contributions to philosophy made by the evolutionary theory is that it has demonstrated the independence of explanation from prediction." And Mayr rests this conclusion among other things on the contention that "The theory of natural selection can describe and explain phenomena with considerable precision, but it cannot make reliable predictions."

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      2. The Paresis Case

In a further endeavor to justify his repudiation of Hempel's thesis, Scriven says³⁰:

we can explain but not predict whenever we have a proposition of the form "The only cause of X is A" (I) - for example, "The only cause of paresis is syphilis." Notice that this is perfectly compatible with the statement that A is often not followed by X - in fact, very few syphilitics develop paresis (II). Hence, when A is observed, we can predict that is more likely to occur than without A, but still extremely unlikely. So, we must, on the evidence, still predict that it will not occur. But if it does, we can appeal to (I) to provide and guarantee our explanation. ...Hence an event which cannot be predicted from a certain set of well-confirmed propositions can, if it occurs, be explained by appeal to them.

In short Scriven's argument is that although a past of paresis can be explained by noting that syphilis was its cause, one cannot predict the future occurrence of paresis from syphilis as a cause. And he adds to this the following oral comment:

Suppose for the moment we include the justification of an explanation or a prediction in the explanation or prediction, as Hempel does. From a general law and antecedent conditions we are then entitled to deduce that a certain event will occur in the future. This is the deduction of a prediction. From one of the propositions of the form the only possible cause of y is x and a statement that y has occurred we are able to deduce, not only that x must have occurred, but also the proposition the cause of y in this instance was x. I take this to be a perfectly sound example of deducing and explanation. Notice, however, that what we have deduced is not all a description of the event to be explained, that is we have not got an explanandum of the kind that Hempel and Oppenheim envisage. On the contrary, we have a specific causal claim. This is a neat way of making clear one of the differences between an explanation and a prediction; by showing the different kinds of proposition that they often are. When explaining Y, we do not have to be able to deduce that Y occurs, for we typically know this already. What we have to be able to deduce (if deduction is in any way appropriate) is that Y occurred as a result of a certain X, and of course this needs a very different kind of general law from the sort of general law that is required for prediction.

I shall now show that Scriven's treatment of such cases as post-explaining paresis on the basis of syphilis suffers from the same defect as his analysis of the evolutionary cases: Insofar as there is an asymmetry, Scriven has failed to discern its precise locus, and having thus failed, he is led to suppose erroneously that Hempel's thesis is invalidated by such asymmetry as does obtain.

Given a particular case of paresis as well as the proposition that the only cause of paresis is syphilis - where a "cause" is understood here with Scriven as a "contingently necessary condition" - what can be inferred? Scriven maintains correctly that what follows is that both the paretic concerned had syphilis and that in his particular case, syphilis was the cause in the specified sense of "cause". And then Scriven goes on to maintain that his case against Hempel is established by the fact that we are able to assert that syphilis did cause paresis while not also being entitle to say that syphilis will cause paresis. But Scriven

Ibid., p. 480

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seems to have completely overlooked that our being able to make both these assertions does not at all suffice to discredit Hempel's thesis, which concerns the time-asymmetry of the inferability of the explanandum from the explanans. The inadequacy of Scriven's argument becomes evident the moment one becomes aware of the reason for not being entitled to say that syphilis "will cause" paresis though being warranted in saying that it "did cause" paresis.

The sentences containing "did cause" and "will cause" respecively each make two affirmations as follows as follows: (i) the assertion of the explanandum (paresis) per se, and (ii) the affirmation of the obtaining of a causal relation (in the sense of being a contingently necessary condition) between the explanans (syphilis) and the explanandum (paresis). Thus, for our purposes, the statement "Syphilis will cause person Z to have paresis" should be made in the form "Person Z will have paresis and it will have been caused by syphilis", and the statement "Syphilis did cause person K to have paresis" becomes "Person K has (or had) paresis and it was caused by Syphilis". And the decisive point is that in so far as a past occurrence of paresis can be inductively inferred from prior syphilis, so also a future occurrence of paresis is incontestably time-symmetric: precisely in the way and to the extent that syphilis was a necessary condition for paresis, it also will be! Hence the only bona fide asymmetry here is the record-based but innocuous one in the assertibility of the explanandum per se, but there is no asymmetry of inferability of paresis from syphilis. The former innocuous asymmetry is the one that interdicts our making the predictive assertion "will cause" while allowing us to make the corresponding post-explanatory assertion "did cause". And it is this fact which destroys the basis of Scriven's indictment of Hempel's thesis. For Hempel and Oppenheim did not maintain that an explanandum which can be post-asserted can always be pre-asserted; what they did maintain was only that the explanans never post-explains any better or more conclusively than it implies predictively, there being complete symmetry between post-explanatory inferability and predictive inferability from a given explanans. They and Popper were therefore fully justified in testing the adequacy of a proferred explanans in the social sciences on the basis of whether the post-explanatory inferability of the explanandum which was claimed for it was matched by a corresponding predictive inferability, either inductive or deductive as the case may be.

What is the force of the following comment by Scriven: in the post-explanation of of paresis we do not need to infer the explanandum from the explanans a la Hempel and Oppenheim, because we know this already from prior records (observation) of one kind or another; what we do need to infer instead is that the explanandum-event occurred as a result of the cause (necessary condition) given by the explanans, an inference which does not allow us to predict (i.e. pre-assert) the explanandum-events? This comment of Scriven's proves only that here there is record-based post-assertibility of paresis but no corresponding pre-assertibility. In short, Scriven's invocation of the paresis case, just like his citation of the

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cases from evolutionary theory, founders on the fact that he has confused an epistemological asymmetry with a logical one. To this charge, Scriven has replied irrelevantly that he has been at great pains in his writings - as for example in his discussion of the barometer case which I shall discuss below - to distinguish valid arguments based on true premises which do qualify as scientific explanations from those which do not so qualify. This reply is irrelevant, since Scriven's caveat against identifying (confusing) arguments based on true premises which are both valid and explanatory with those which are valid without being explanatory does not at all show that he made the following crucial distinction here at issue: the distinction between (1) a difference (asymmetry) in the assertibility of either a conclusion (explanandum) or a premise (explanans), and (2) a difference (asymmetry) in the inferability of the explanandum from its explanans. Although the distinction which Scriven does make cannot serve to mitigate the confusion with which I have charged him, his distinction merits examination in its own right.

To deal with it, I shall first consider examples given by him which involve non-predictive valid deductive arguments to which he denies the status of being explanatory arguments. And I shall then conclude my refutation of Scriven's critique of Hempel's thesis by discussing the paradigm case of his; the deductively valid predictive inference of a storm from a sudden barometric drop, which he adduces in an endeavor to show that such a valid deductive inference could not possibly qualify as a post-explanation of a storm.

It would be agreed on all sides, I take it, that no scientific understanding is afforded by the deduction of an explanandum from itself even though such a deduction is a species of valid inference. Hence it can surely be granted that the class of valid deductive arguments whose conclusion is an explanandum referring to some event or other is wider than the class of valid deductive arguments affording scientific understanding of the explanandum-event. But it is a quite different matter to claim, as Scriven does, that no scientific understanding is provided by those valid deductive arguments which ordinary language would not allow us to call "explanations". For example, Scriven cites the following case suggested by S. Bromberger and discussed by Hempel³¹; the height of a flagpole is deducible from the length of its shadow and a measurement of the angle of the sun taken in conjunction with the principles of geometrical optics, but the height of the flagpole could not thereby be said to have been "explained". Or take the case of a rectilinear triangle in physical space for which Euclidean geometry is presumed to hold, and let it be given that two of the angles are 37° and 59° respectively. Then it can be deductively inferred that the third angle is one of 84°, but according to Scriven, this would not constitute an explanation of the magnitude of the third angle.

Exactly what is shown by the flagpole and angle cases concerning the relation between valid deductive arguments which furnish scientific understanding and those which, according to ordinary usage, would qualify as "explanations"? I

³¹ Cf. C. G. Hempel, "Deductive-Nomological vs. Statistical Explanation," op. cit., Section 4.

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maintain that while in one respect from what usually called "explanation", the aforementioned valid deductive arguments yielding the height of the flagpole and the magnitude of the third angle provide scientific understanding no less than explanations do. And my reasons for this contention are the following.

In the flagpole case, for example, the explanandum (stating the height of the flagpole) can be deduced from two different kinds of premises: (i) an explanans of the type familiar from geometrical optics and involving laws of coexistence rather than laws of succession, antecedent events playing no role in the explanans, and (ii) an explanans involving causally antecedent events and laws of succession and referring to the temporal genesis of the flagpole as an artifact. But is this difference between the kinds of premises from which the explanandum is deducible a basis for claiming that the coexistence-law type of explanans provides less scientific understanding than does the law-of-succession type of explanans? I reply: certainly not. And I hasten to point out that the difference between pre-axiomatized and axiomatized geometry conveys the measure of the scientific understanding provided by the geometrical account given in the flagpole and angle cases on the basis of laws of coexistence. But is it not true after all that ordinary usage countenances the use of the term "explanation" only in cases employing causal antecedents and laws of succession in the explanans? To this I say: this terminological fact is as unavailing here as it is philosophical unedifying.

Finally, we turn to Scriven's citation of cases of deductively valid predictive inferences which, in his view, invalidates Hempel's thesis because they could not possibly aslo qualify as post-explanation.

      3. The Barometer Case

Scriven writes³²:

What we are trying to provide when making a prediction is simply a claim tht, at a certain time, an event or state of affairs will occur. In explanation we are looking for a cause, an event that not only occurred earlier but stands in a special relation to the other event. Roughly speaking, the prediction requires only a correlation, the explanation more. This difference has as one consequence the possibility of making predictions from indicators other than causes - for example, predicting a storm from a sudden drop in the barometric pressure. Clearly we could not say that the drop in pressure in our house caused the storm: it merely presaged it. So we can sometimes predict what we cannot explain.

Other cases of the barometric type are cases such as the presaging of mumps by its symptoms and the presaging of a weather change by rheumatic pains.

When we make a predictive inference of a storm from a sudden barometric drop, we are inferring an effect of a particular cause from another (earlier) effect of that same cause. Hence the inference to the storm is not from a cause of the storm but only from an indicator of it. And the law connecting sudden

³² M. Scriven, "Explanation and Prediction in Evolutionary Theory," op. cit. p. 480.

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barometric drops to storms is therefore a law affirming only an indicator type of connection rather than a causal connection.

The crux of the issue here is whether we have no scientific understanding of phenomena on the strength of their deductive inferability from indicator laws (in conjunction with a suitable antecedent condition), scientific understanding allegedly being provided only by an explanans making reference to one or more causes. If that were so, then Scriven could claim that although the mere inferability of particular storms from specific sudden barometric drops is admittedly time-symmetric, there is no time-symmetry in positive scientific understanding. It is clear from the discussion of the flagpole case that the terminological practice of restricting the term "explanation" though not the term "prediction" to cases in which the explanans makes reference to a partial or total cause rather than to a mere indicator cannot settle the questions at issue, which are: would the type of argument which yields a prediction of a future explanandum-event (storm) from an indicator-type of premiss furnish any scientific understanding, and, if so, does this type of argument provide the same positive amount of scientific understanding of a corresponding past event (storm)?

These questions are, of course, not answered in the negative by pointing out correctly that the law connecting the cause of the storm with the storm can serve as a reason for the weaker indicator-law. For this fact shows only that the causal law can account for both the storm and the indicator law, but it does not show that the indicator law cannot provide any scientific understanding of the occurrence of particular storms. To get at the heart of the matter, we must ask what distinguishes a causal law from an indicator law such that one might be led to claim, as Scriven does, that subsumption under indicator laws provides no scientific understanding at all, whereas subsumption under causal laws does.

Let it be noted that a causal law which is used in an explanans and is not itself derived from some wider causal law is fully as logically contingent as a mere indicator law which is likewise not derived from a causal law but is used as a premise for the deduction of an explanandum (either predictively or post-predictively). Why then prefer (predictive or post-dictive) subsumption of an explanandum under a causal law to subsumption under a mere indicator law? The justification for this preference would seem to lie not merely in the greater generality of the causal law; it also rests on the much larger number of empirical contingencies which must be ruled out in the ceteris paribus clause specifying the relevant conditions under which the indicator law holds, as compared to the number of such contingencies pertaining to the corresponding causal law. But this difference in both generality and in the number of contingencies does not show that the indicator-law provides no scientific understanding of particular phenomena subsumable under it; it shows only, so far as I can see, that one might significantly speak of degrees of scientific understanding. And this conclusion is entirely compatible with the contention required by the symmetry thesis that the barometric indicator law

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furnishes the same positive amount of scientific understanding of a past storm as of a future one predicted by it.

I believe to have shown, therefore, that with respect to the symmetry thesis, Hempel ab omni naevo vindicatus³³.

      4. The Controversy Between Mechanism and Teleology

The results of our discussion of the temporal asymmetry of recordability have a decisive bearing on the controversy between mechanism and teleology.

By mechanism we understand the philosophical thesis that all explanation must be only a tergo, i.e., that occurrences at a time t can be explained only by reference to earlier occurrences and not also by reference to later ones. And by teleology we understand a thesis which is the contrary rather than the contradictory of mechanism: all phenomena occurring at a time t (or, more narrowly, all phenomena belonging to a certain domain and occurring at a time t) are to be understood by reference to later occurrences only. We note that, thus understood, mechanism and teleology can both be false.

During our post-Newtonian epoch there is a misleading incongruity in using the term "mechanism" for the thesis of the monopoly of a tergo explanations. For in the context of the time-symmetric laws of Newton's mechanics, the given state of a closed mechanical system at a time t can be inferred from a state later than t (i.e., retrodicted) no less than the given state can be inferred from a state earlier than t (i.e., predicted). Instead of furnishing the prototype for mechanistic explanation in the philosophical sense, the phenomena described by the time-symmetric laws Newton's mechanics constitute a domain with respect to which both mechanism and teleology are false, thereby making the controversy beteen them a pseudo-issue. More generally, the controversy is a pseudo-issue with respect to any domain of phenomena constituted by the evolution of closed systems obeying time-symmetric laws, be they deterministic or statistical.

But there is indeed a wide class of phenomena with respect to which mechanism is true. And one may presume that tacit reference to this particular class of phenomena has conferred plausibility on the thesis of unrestricted validity of mechanism: traces or marks of interaction existing in a system which is essentially closed at a time t are accounted for scientifically by earlier interactions or perturbations of that system - which are called "causes" - and not by later interactions of the system.

In view of the demonstrated restricted validity of mechanism, we must therefore deem the following statement by H. Reichenbach as too strong: "We conclude: If we define direction of time in the usual sense, there is no finality, and only causality is accepted as constituting an explanation."³⁴

³³ Believing (incorrectly) to have cleaned Euclid of all blemish, G. Sachheri (1667-1733) published a book (Milan 1733) under the title Euclides ab omni naevo vindicatus.

³⁴ Reichenbach, The Direction of Time, op. cit., p. 154.

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