Beyond Toulmin vs. Carnap on ‘Probability’

In Logical Foundations of Probability, Carnap put forth the view according to which there are two fundamentally different pre-scientific concepts of probability. One is best captured by its scientific explication in terms of the logical-semantic idea of the degree of confirmation of a hypothesis with respect to the set of sentences describing the evidence (probability1). The other is best captured by its scientific explication in terms of the empirical idea of the relative frequency of an event with respect to a long sequence of instances of a mass phenomenon (probability2). Both probability1 and probability2 are viewed as legitimate scientific concepts. Thus, according to Carnap, the original, pre-scientific, distinction in meaning between these uses of probability terms was preserved and furthered in the course of the development of the scientific approach to probability. Philosophical discussions about the appropriate analysis of the meaning of probability statements are therefore pointless. In The Uses of Argument, Toulmin agrees with Carnap that it is a mistake to look for a single reference in terms of which all the uses of ‘probability’ could be accounted for. However, he also maintains that it is equally senseless to try to correct this mistake by appealing to the idea of there being two different references associated with the appropriate uses of the term rather than one. According to Toulmin, both, frequencies as well as confirmation relations, are but types of evidence one is supposed to take into account in the formulation of one’s ordinary language judgments in which the term ‘probability’ occurs. But the evidence that backs a judgment should not be confused with its meaning. Toulmin therefore claims that the term ‘probability’ does not impinge on the meaning of the statement to which it is attached; it is rather a modal modifier that modulates the force with which an agent is disposed to assert that statement. The pointlessness of the philosophical discussions Carnap talks about is real; it has a different and deeper source than the one he diagnosed though. Fifty years later, on what grounds are we to adjudicate this dispute between Toulmin and Carnap concerning the right way of characterizing our pre-scientific concepts of probability? On the one hand, the distinction Toulmin draws between the force of the modal term ‘probably’ and the criteria for its use is still illuminating. On the other hand, it is hard to accept that nothing substantial is being dealt with in the debate around the question of how best to interpret our unanalysed notion of probability. Carnap’s approach to this topic is of a kind we might term ‘transcendental-teleological’. As a matter of fact, his stride into the folk-conceptual history of the notion of probability is entirely determined by his purpose of clarifying and justifying the two concepts of scientific probability he considers there to be. The strategy followed by Toulmin to deal with this issue is to bring back the study of what non-formal probability might be to an analysis of the meaning of ordinary language sentences of probability ascription. The principle underlying the use of such a strategy seems to be the principle that, whatever a pre-scientific concept of something might amount to, our only clue to determine its content is the analysis of the way normal agents use the sentences of ordinary language carrying the term allegedly referring to it in their relevant contexts. Indeed, Toulmin ascribed to his essay “Probability” the status of a “pilot investigation” introducing ideas and distinctions that throw “a general light on the categories of rational assessment”. These words indicate that he took such a principle to be of a general scope and thus that it ought to be applied to different categories used in the rational assessment of arguments. But, even if we grant Toulmin that he is right in his analysis of the semantics of many of our ordinary language sentences of probability ascription, there are other obvious sources of information concerning the lines that mark out the categories belonging to our pre-scientific thinking that he neglects. Prominent among these is empirical psychological research. One would have to be a strenuous defender of some strong version of the Sapir-Whorf thesis in order to deny this. What I propose to do in order to adjudicate this discussion is thus to evade both transcendental-teleological reconstructions of what our pre-scientific concepts had to be, given the present outline of what our scientific concepts are, and shaky intuitions about how best to interpret our ordinary language statements, and look into some recent psychological results concerning the way subjects seem to relate pre-scientifically to contexts of perceived uncertainty, randomness or chance. Preliminary as these results are, I think that an appropriate philosophical treatment of them will allow us to identify and keep the intuitions worth preserving in Carnap’s or Toulmin’s work, on the one hand, and to leave aside what is but a direct consequence of their theoretical prejudices, on the other hand. These results seem to suggest that it is indeed possible to organize the subjects’ responses to these contexts into two distinct and clearly identifiable characterizations of them: an ‘objectivist’ one and a ‘subjectivist’ one. Therefore, if we consider the way people do seem to relate to what Toulmin calls the evidence backing our utterances of probability-statements, what we get is a revealing cleavage between two ways of conceptualizing it. On the one hand, Carnap’s claim concerning the existence of two distinct pre-scientific concepts associated with our use of probability-terms might be somehow vindicated by these results. On the other hand, however, the outlines of this division do not seem to match Carnap’s characterization of the relevant explicanda. For instance, by themselves, the data do not allow us to discriminate between Carnap’s own frequentist view of empirical-objective probability (Probability2) and other approaches, such as, e.g., the classical Laplacian view of ratios of favourable cases to the total number of cases. This is, however, presumably consistent with the fuzzy nature of folk-concepts.