Autor: Melchin, R. Kenneth

Buch: History, Ethics and Emegent Probability

Titel: History, Ethics and Emegent Probability

Stichwort: f-probability, v-probability (Wahrscheinlichkeit); Was-Frage, Ist-Frage; Verwechslung beider Wahrscheinlichkeiten; Beispiel: Kartenspiel

Kurzinhalt: The first and basic step is to distinguish between probability as an answer to a what-question and probability as a quality of an is-answer: the former is f-probability, the latter is v-probability.

Textausschnitt: 55/3 McShane's distinction between is-questions and what-questions is based in Bernard Lonergan's account of the second and third types of cognitional operations.1 In performing the second type of operation the subject wants to understand natures and states. But the product of such a set of acts initially is nothing more than a good idea. To move beyond good ideas requires a shift in one's mental attitude. The ideas are viewed with what might be called here a 'hermeneutic of suspicion,' (to borrow a term from Ricoeur). Can the ideas be verified? Are they the case? And this new mental stance with its concern for evidence characterizes the third type of cognitional operation. (81; Fs)

56/3 The term or object of this operation is not principally the consistency of logic, the unconditional necessity of the hypothetical syllogism. Rather, the object is 'v-probable' facticity. The scientist wants to know as best he or she can what is so, in fact, and not what could conceivably be otherwise. It is this concern with facticity, with particular times and places, that distinguishes the third from the second type of cognitional operation. The second type of operation seeks intelligibility, whether of the classical or the statistical type (with its curious element of absence of intelligibility). The third type of operation seeks to go beyond the intelligibilities grasped in insights and to establish whether these insights integrate all relevant experiential data and thus correspond to the recurrent intelligibility immanent in the ongoing routines of human experience. Do the insights completely satisfy the demands of the question, and do they 'fit' with the data of experience? This is the concern of the third type of question. (81; Fs)

57/3 In the common practice of empirical science answers to is-questions include an indication of a degree of certainty, of a 'probable' certainty. But the term 'probable' here means something quite distinct from the probability that I have been discussing so far. Thus McShane coins the term 'f-probability' to denote the probability proper to statistical science and 'v-probability' for the probability of confirmation or verification in both statistical and classical science.2 (81; Fs) (notabene)

58/3 Most simply, f-probabilities and v-probabilities concern respectively what-questions and is-questions.3 (81; Fs)

The first and basic step is to distinguish between probability as an answer to a what-question and probability as a quality of an is-answer: the former is f-probability, the latter is v-probability. To distinguish them, as we shall see, is not to separate them; they are in many ways interlocked. But without the distinction, which is based on the two different mental stances, the character of their interlocking would be permanently obscured.4
59/3 F-probabilities concern distributions and patterns of distributions of frequencies of events. And the f-probability answers the question 'what is the pattern?', 'what is the ideal frequency?' V-probabilities, on the other hand, concern judgments about the correctness or truth of the answers to what-questions. And these judgments answer is-questions: 'is the law verified?', 'is the distribution normal?' In addition, f-probability does not pertain to an individual case. F-probabilities (in terms of this analysis) are ideal frequencies from which individual cases will always diverge non-systematically. And so when applied to individual cases an f-probability is only a guess.5 The inverse insight 'there is no reason why' which is at the basis of the meaning of f-probability affirms the absence of evidence relevant to individual cases. (82; Fs)

60/3 V-probability, on the other hand, affirms not the absence of evidence relevant to individual cases but the relative sufficiency of evidence available for affirming the truth or falsity of both laws and individual cases. (82; Fs)

Both a guess and a probable judgment are based on incomplete knowledge: intelligent reflection in either case shows that evidence is insufficient for certainty. In the case of the probable judgment that insufficiency is partial: there is some approximation towards sufficiency which can be grasped as such, leading to the modest commitment of a probable judgment, a judgment which is probably true, which converges in a non-statistical sense on true judgment.6

61/3 At this point two possible confusions can arise. First, some debates about the subjectivist school on probability, noted above, arise as a result of the implementation of f-probabilities in the formulation of v-probable judgments of truth. Thus the role of probabilities in statistical and classical science is doubly confusing. It is common practice to perform a succession of verification tests, both in classical and in statistical science, and to express the v-probable truth of an hypothesis in terms of the f-probable frequency of occurrence of test results that fall within a commonly accepted range. The fact that test results cluster around statistical norms bears witness to the fact that testing procedures cannot completely isolate interferences, inaccurate readings, poorly controlled tests, etc., etc. But the statistical norms in the test results are to be understood in terms of a reflective act of intelligence correlating the accepted f-probability of favourable test results with the intelligibility expressed in the insight, to pronounce a v-probable judgment of truth on the hypothesis. (82; Fs)

62/3 The second possible confusion concerns the role of f-probabilities in reasonable betting on individual cases.7 Thus the question can arise whether an f-probability can be the v-probable certainty of an individual occurrence. Clearly, given the option, it would be 'reasonable' to bet on drawing a face card from a euchre deck. And the proper fraction two-thirds that expresses the f-probability associated with the appearance of a face card in a succession of draws figures heavily in the explanation why such a bet would be 'reasonable.' Nonetheless two-thirds is not the v-probable certainty that a face card will be drawn in a single case. This is so firstly because v-probabilities (as defined here) are predicates of judgments of matters of fact. They are not relevant to predictions. We might want to use the term 'likelihood' to designate the relevance of prior evidence to predictions in statistical experiments. (82f; Fs)

63/3 Secondly, the proper fraction two-thirds does not affirm that one-third of the available evidence is missing. The fact is that this f-probability does not express the relative sufficiency of evidence bearing upon this case. The f-probability is one hundred percent of the available evidence bearing upon this case but because the event is the outcome of a non-systematic process all the available evidence still tells nothing about the outcome of this particular draw. There is no reason why any one of the twenty-four cards in the deck should prevail over any other. And it is this 'no reason why' that accounts for the fact that gamblers do not regularly lay fraud charges against casinos when improbable occurrences result in their financial destruction. Individual cases diverge non-systematically from probabilities. (83; Fs)

64/3 How then do f-probabilities figure into reasonable betting on the likelihood of outcomes in particular cases? The answer suggested here has three parts. (83; Fs)

(a) The question 'is it reasonable to bet on drawing a face card from a euchre deck?' is not properly a question of the truth of fact of an occurrence or explanation but a question for deliberation. 'Should I act in this way or not?' The question is on Lonergan's fourth level of cognitional operations.8 And while such a question for deliberation demands empirical facts, it is not answered by them. Questions for deliberation intend future prospects, goals, values, and actions that will realize such prospects. (83; Fs) (notabene)

(b) Assuming that I have decided to place one bet on drawing a face card from a euchre deck the question becomes one of anticipating the possible results of an individual outcome of a non-systematic process armed with an f-probability. 'Is it likely that I will draw a face card?' The occurrence or non-occurrence of the likely outcome will not verify or falsify the f-probability. And so there is neither an f-probability nor a v-probability applicable to the anticipation of drawing a face card. (83; Fs)

(c) But there is an imprecise but relevant meaning to the term 'likely' and this meaning is integrally related to the f-probability, two-thirds, associated with a succession of such draws. The likelihood or the reasonableness of the bet consists in the recognition that
(i) there is no knowledge available to predict individual cases,
(ii) the best available knowledge is the f-probability, two-thirds, which is the mid-point from which a large number of relative actual frequencies of drawing a face card will diverge non-systematically, and
(iii) this f-probability is to be accounted for in terms of the fact that a euchre deck has twice as many face cards as numbered cards. (83f; Fs)