Marta Sznajder (Munich Center for Mathematical Philosophy)
What exactly are the subjective and the logical interpretations of probability?
Given how often these labels are used to characterize different positions in the philosophical foundations of probability, we should have a very sharp understanding of what they mean. In my presentation, I use the example of someone whose position is taken to be fully understood and show that these two standard labels are not enough to unambiguously describe it.
From the 1940s Rudolf Carnap developed systems of inductive logic based on what he considered the logical concept of probability. According to what seems to be a leading interpretation of the development of this project, both the formal features of the systems of inductive logic and their conceptual underpinning changed significantly between 1945 and 1970.
As the popular opinion has it, Carnap's interpretation of probability had evolved from a logical towards a subjective, or Bayesian, conception. Statements to this effect have been put forward by, among others, Skyrms, Zabell, Galavotti, and Earman --- all of them leading workers in the field of probability interpretations.
However, this view of the conceptual evolution of Carnap's inductive logic is at odds with what he himself had declared. Even in the later phases, Carnap insists that his basic philosophical view of probability did not change and throughout all his probability publications he stressed the logical character of his systems and his concept of probability.
The presentation addresses this apparent clash between Carnap's self-identification and the subsequent interpretations of his work. Are the modern accounts of Carnap's evolution misguided, or was he delusional about the conceptual implications of the developments within inductive logic? Or is the real issue our lack of clarity on what our labels actually mean?
Following its original intentions, I reconstruct inductive logic as a project in explication. The picture that emerges is of a highly versatile linguistic framework, whose main function is not the discovery of objective logical relations in the object language, but the stipulation of practically useful conceptual possibilities. Within this representation, I map out the changes that the project went through and consider the way in which these changes led to a modification of the underlying concept of probability. It turns out that most of the interesting movement within the project happened on the level of the characterization of the explicandum, and not on the level of the explicated theory itself.
Seen from such an explication perspective, Carnap becomes quite hard to categorize as either a subjectivist or a logicist about probability. I go through some possible interpretations of these terms, showing how according to neither of them is the early Carnap a clear logicist and the late Carnap a clear subjectivist. The result is not only a better understanding of the original inductive logic project, but also a new impulse to rethink the conceptual basics of probability interpretations.
