Autor: Melchin, R. Kenneth

Buch: History, Ethics and Emegent Probability

Titel: History, Ethics and Emegent Probability

Stichwort: Rekursive Schemen (schemes of recurrence): zirkulär, nicht linear; Wahrscheinlichkeit (probability) als Schlüssel zum Verständis der rek. Schemen

Kurzinhalt: ... recurring events can link together in a string or group so that the f-probable occurrence of the first event is systematically followed by the certain occurrence of the others ... The jump in the probability of recurrence of a scheme is the key ...

Textausschnitt: 4.3 Conditioned Schemes of Recurrence

16/4 The basic insight at the center of Lonergan's notion of the recurrence scheme is that of reflexivity.1 The recurrence scheme is reflexive in the sense that the functioning or operation of the scheme has the effect of curling back upon itself and fulfilling the conditions for the scheme to recur. And this reflexivity is a part of the internal structure of the scheme. Most simply a recurrence scheme is a series of events that occur in a specific pattern or order of succession. But not any pattern or order will do. For what is significant about the scheme is that the events recur over and over again in the same pattern or order of succession. And Lonergan proposes, in the reflexive character of the structure of the scheme, a possible or conceivable explanation for this recurrence of a patterned set of events. In a first type of scheme, the relationship between the events making up the scheme is such that each event in the scheme fulfills the conditions for the occurrence of the next event, and the occurrence of the last event fulfills the conditions for the recurrence of the first, thus beginning the scheme anew. In a second possible type of scheme, the events are all conjoined in an interdependent combination pattern such that once all are functioning the scheme continues to function. In any case, the point of Lonergan's notion of the recurrence scheme is that events conceivably can link together in such a way that it is not an antecedent line or string of conditioned events that accounts for the recurrence of any event but a circular or reflexive structure linking a determinate set of events into an ordered pattern. Lonergan provides a few examples of recurrence schemes. (105; Fs)

In an illustration of schemes of recurrence the reader may think of the planetary system, of the circulation of water over the surface of the earth, of the nitrogen cycle familiar to biologists, of the routines of animal life, of the repetitive, economic rhythms of production and exchange.2

17/4 The recurrence of a scheme can be ensured further by defensive circles of events such that any event which tended to upset the scheme would fulfill the conditions for a succession of further events to occur that would terminate in eliminating the intruder. Again the structure of the defensive circle is the set of links between the events in the circle. Each event fulfills the conditions for the next event (or in a circle of the second type one event conditions the occurrence of all the others). (106; Fs)

In illustration of schemes with defensive circles, one may advert to generalized equilibria. Just as a chain reaction is a cumulative series of changes terminating in an explosive difference, so a generalized equilibrium is such a combination of defensive circles that any change, within a limited range, is offset by opposite changes that tend to restore the initial situation. Thus, health in a plant or animal is a generalized equilibrium; again, the balance of various forms of plant and animal life within an environment is a generalized equilibrium; again, economic process was conceived by the older economists as a generalized equilibrium.3

18/4 The key to understanding the relevance of the notion of recurrence scheme for an account of the relationship between scientific 'levels' and strata lies in Lonergan's definition of probability. Within a particular region or environment there can be occurring a host of types of events. If these events are the outcomes of processes which exhibit an absence of recurring system, then the events will recur irregularly in accordance with a certain f-probability. For each event to occur there will be required the fulfillment of a determinate set of conditions. But because that set of conditions is, in fact, fulfilled in a coincidental convergence of laws and processes, the event occurs irregularly (in accordance with an f-probability). However, given the environmental stability of a certain set of factors or conditions, there are types or classes of events that require only the fulfillment of one or a few conditions for them to occur. And when this one or these few conditions are themselves events of another type which are already recurring within this environment (with a certain f-probable frequency) then the coincidental occurrence of the conditioning event(s) in the right time and place is systematically followed by the occurrence of the conditioned event. Given the stability of the conditions of the environment, non-systematically recurring events can link together in a string or group so that the f-probable occurrence of the first event is systematically followed by the certain occurrence of the others. (106; Fs)

19/4 When the string is extended finally to include an event which conditions the occurrence of the first in the sequence, then the string becomes a loop. In this case the mere occurrence of any one event in the loop sets off a chain that simply continues recurring until something intervenes to break the links. The complete set of conditions associated with the occurrence of any single event in the loop will certainly form a non-systematic aggregate and reach far beyond simply the occurrence of the previous events in the scheme. But given the stable fulfillment of these environmental conditions, for whatever reason in whatever chain of circumstances, it is the set of internal relations linking the events in the scheme that explains the fact that the scheme recurs once it has begun. The initial occurrence of the scheme is in accordance with the coincidental convergence of conditions. But once this occurs the recurrence of the scheme is systematic, and the system is constituted by the terms or events, and the relations linking the events into a scheme. (106f; Fs)

20/4 Lonergan expands his hypothesis to include a notion of 'emergence' that is defined in terms of the calculus of probabilities. Since probabilities - the reference throughout here is to f-probabilities - can be calculated for a succession of occurrences of events of a class, a single f-probability can be calculated for successive occurrences of a set of classes of events. This single probability for the occurrence of the whole set is the product of the individual probabilities. And since probabilities are proper fractions, the product of a set of probabilities is smaller than any of the individual probabilities. But if a set of conditions were fulfilled such that the classes of events began to function as a scheme of recurrence, then, if any one event occurred the whole scheme would occur and would continue recurring. In this case the probability of the whole set would no longer be the product of the individual probabilities. For in the case of a scheme of recurrence whose conditions are fulfilled the occurrence of any one of the events would ensure the occurrence and recurrence of all the others. The f-probability of the whole scheme would then be a new combination (a form of summation) of the individual probabilities which, because of the interlocked character of the events in a scheme, would be much higher than the original product of the events' individual f-probabilities. Lonergan concludes that there will be a leap in the probability of the combination of events, constitutive of the scheme when the prior conditions are fulfilled, and that this new probability will be the probability of the scheme's emergence.4 The jump in the probability of recurrence of a scheme is the key element in the meaning of the term 'emergence.' (107; Fs)

21/4 In addition to the probability of emergence Lonergan introduces the related notion of a probability of the survival of schemes. Insofar as all the related conditions for the operation of a scheme continue to remain fulfilled, a scheme ensures its own survival. And within limited ranges defensive circles can arise to take care of the occurrence of conditions that would otherwise interfere with a scheme. But the continued operation of a scheme depends, finally, on the non-occurrence of any condition or event that would spell the end of the scheme. (107f; Fs)

Accordingly the probability of the survival of a scheme of recurrence is the probability of the non-occurrence of any of the events that would disrupt the scheme.5

22/4 Recurrence schemes involve a conditioned series of events. But Lonergan goes on to suggest that the recurrence of schemes can constitute the fulfilling conditions for the occurrence and recurrence of further schemes. Just as the occurrence of one or more events can fulfill the remaining conditions necessary for a scheme to begin and continue, so too the functioning of that scheme can fulfill the remaining conditions for another scheme to begin and to continue. Schemes can combine such that earlier schemes can function independent of later schemes but later schemes require the functioning of earlier schemes. The result is what Lonergan calls a 'seriation,' a conditioned series of schemes which, like the scheme, continues once begun.6 (108; Fs)