Autor: Melchin, R. Kenneth

Buch: History, Ethics and Emegent Probability

Titel: History, Ethics and Emegent Probability

Stichwort: Systematische, nicht-systematische, zufällig, unbestimmt; Münze: warum Zufall in einer Reihe von Münzenwurfen?; inverse Einsicht

Kurzinhalt: If the tossing of a coin is fully determined by the laws of physics how can there be an element of randomness in a series of tosses?

Textausschnitt: 23/3 One of the prevailing theories on statistical knowledge discussed in Randomness affirms that there exists no objective correlate in being for an inverse insight. The whole of being is systematically interrelated. Knowledge is only of 'classical' laws (laws which express a unified set of direct insights). And thus randomness, or the absence of a systematic, intelligible unity to data or to a process is merely an illusory appearance resulting from insufficient data. Hence statistical knowledge, knowledge which paradoxically grasps a sort of 'intelligibility' in randomly occurring events, is merely an imprecise substitute for complete knowledge of systematic relations.1 (69; Fs) (notabene)

24/3 McShane works towards developing a response to this challenge by introducing two examples, the movement of billiard balls on a table and the movement of a penny through a fair toss.2 I will discuss briefly this second example. When a fair coin is tossed the outcome of heads and tails from a succession of tosses would appear to be randomly or non-systematically distributed. In view of our contemporary knowledge of the laws of physics one might ask why the outcome of each toss could not be predicted successfully. But the fact remains that such prediction, under normal circumstances, is not possible. This resistance to prediction is in some way related to an absence of reason governing the processes involved in a succession of coin tosses. And this absence of reason manifests itself in the absence of system in the distributions of heads and tails in a succession of tosses. How can this be? If the tossing of a coin is fully determined by the laws of physics how can there be an element of randomness in a series of tosses? (69; Fs) (notabene)

25/3 McShane's answer involves a distinction between the terms 'non-systematic' or 'random' and 'indeterminate.'3 The toss of a coin is in no way an indeterminate process. Given enough time and enough data on
(a) the initial position of the coin,
(b) the precise motion and force imparted by the toss,
(c) all the intervening motions and operative forces, and
(d) the characteristics associated with the fall of the coin, the exact motion of the coin and thus the outcome of the toss conceivably could be accounted for. Thus the process is determinate inasmuch as it is determined by a complex of factors that can be understood in each case. (69; Fs)

26/3 But there is something queer about the way that the process is understood.4
(1) The toss consists of a succession of stages each of which involves the operation or intervention of a complex of conditions. There is no way of knowing prior to any toss (except under controlled conditions) what conditions will be operative at each stage. The very presence of any one of the conditions can be decisive for the outcome of that toss. And so no single act of understanding can grasp a generalizable pattern to the conditions operative throughout every occurrence of a succession of coin tosses. (69f; Fs)

(2) The reason why such a single act of understanding is impossible for a succession of tosses is because each condition of each toss is itself conditioned by a multiplicity of further conditions. As each condition is listed in terms of its own complex of conditions the list yields a diverging series. Each condition may be intelligible in terms of its own complex of preconditions. But the mere presence or absence of any one condition in the process is decisive for the outcome of the toss. Such presence or absence alters not simply the particular values and magnitudes in the toss but rather the entire intelligibility of that instance of the process. Each individual toss can only be understood by:
(a) performing a succession of acts of understanding of each possible condition in terms of its own complex of preconditions;
(b) judging whether and how the results of each successive act of understanding brings its respective condition to bear on the process; and
(c) grasping the resultant interaction among the particular operative conditions in that instance of the process in a subsequent act of understanding. This subsequent act of intelligence, far from grasping an intelligible unity proper to the generalized act of 'tossing a coin' grasps only the particular, unique relations among all the previous insights that were required to understand this particular toss. To understand this toss requires not only this one final act of understanding but all the previous acts which determined what conditions were operative in the toss. And the relationship among all the individual acts of understanding is not a generalizable intelligibility proper to all instances of tossing a coin.5 (70; Fs)

(3) Continued attempts to grasp an intelligible unity common to a succession of instances of coin tossing quickly brings an intelligent investigator to conclude that such attempts do not and can not lead towards a generalizable understanding of all instances of tossing a coin. There are too many conditions and pre-conditions that operate differently in each toss. And extremely small variations in each condition and pre-condition have a decisive impact on the outcome. Each toss seems to have a pattern of interrelated conditions that is for all intents and purposes unique. Consequently intelligence is led to conclude that, in any sequence of tosses there is no reason why one result should prevail recurrently over another.6 (70; Fs)

27/3 This final act of intelligence is not a failure to perform an act of intelligence. It is itself an act of intelligence. And what it grasps is an absence of a stable intelligible unity governing recurring instances of the process, and consequently an absence in intelligible reason why one or another result should regularly prevail. The process is named a non-systematic process and this final cognitional act which grasps the absence of stable, recurrent system is the devalued inverse insight. Like all acts of intelligence the content of the inverse insight goes beyond the data to affirm a generalization that is verified in instances of performance of the experiment.7 And somehow even though we admit the possibility of a long run of heads in a fair coin toss we tend to doubt whether any single intelligibility would be found to explain such an unlikely occurrence. The fact is that the continued operation of gambling casinos and lotteries never ceases to verify this particular absence of reason that is at the root of the laws of probability. (70f; Fs)

28/3 The difference, then, between the discharging of a battery as an example of a systematic process and the toss of a coin as an example of a non-systematic process rests in the difference between what can be generalized about a succession of occurrences of a class of events or processes. (71; Fs)

29/3 (A) The insight that grasps the intelligibility of any one instance of a systematic process is the same insight that grasps the intelligibility of all instances of that process. The insight is generalizable because the intelligibility governing the process is stable (invariant) under ranges of environmental conditions.
whereas
The insight that grasps the intelligibility of any one instance of the non-systematic process is different from the insights that understand each other instance of that process. The insight is non-generalizable. And a generalizable intelligibility is not to be found because the intelligibility governing the process is not stable under ranges of environmental conditions. This fact, this lack of a unified, generalizable intelligibility in all instances of the process, is what is generalized as relevant to that class of process. This grasp is the inverse insight. (71; Fs)

30/3 (B) The intelligibility that is common to all instances of the systematic process decisively relates what is particular to each instance of the process.
whereas

The intelligibility that is particular to each instance of the non-systematic process decisively interrelates what is common to all instances of the process. And so there is no generalizable intelligibility associated with the outcomes of a succession of occurrences of the process. (71; Fs)

31/3 It is interesting to observe, here, how the act of classifying events and processes and the act of understanding their intelligibility are interrelated differently in systematic and non-systematic processes. In a systematic process there is a set of insights which distinguishes this class of process from another. But there is also a set of insights which understands the systematic operation of each instance of this class of process. The classifying insights and the insights that understand the process both apply to each and every instance of the process. However, in a non-systematic process there is a set of insights which classifies the process and which applies or corresponds to every instance of the process. But there is no common set of insights which understands the outcome of each trial in terms of its conditions. And this absence of correspondence between classification and explanation in non-systematic processes will be a key element in understanding what Lonergan means by probability. (71f; Fs)