Benchmark tests are widely employed in testing for racial discrimination by police. Neil and Winship (2019) correctly point out that the use of such tests is threatened by the phenomenon of Simpson’s paradox. Nevertheless, their analysis of the paradox is inadequate, in ways that point to a more general problem with how they relate statistical quantities to discrimination hypotheses. Simpson’s paradox reveals that the statistics employed in benchmark tests will not, in general, be invariant to updating on new information. I argue that as a result of this, benchmark statistics should not by themselves be taken to provide any evidence for or against discrimination, absent additional modeling assumptions. Although Neil and Winship highlight ways in which benchmark statistics appearing to provide evidence for discrimination no longer appear to do so given additional assumptions, they lack an account of which sets of assumptions would ensure invariance. Causal models provide such an account. This motivates the use of causal models when using statistical methods as evidence for discrimination.
Nineteenth-century logic is known to have relied heavily on the background of post-Kantian philosophy to address issues such as the investigation of the conditions of thought, the characterization of abstract objects, the delimitation of objective from subjective knowledge, the systematic of scientific methodologies. The philosophical tradition of logic overlapped with the development of modern mathematical logic from the first versions of the algebra of logic in the mid nineteenth-century until inquiries into the logical foundations of mathematics from the early 1930s. This very fact strongly suggests that there might have been significant intersections between what appear now as separate disciplines, and raises the question of whether philosophical roots can be traced in the development of mathematical logic. Several studies have shed light on the philosophical background of key figures in the history of modern logic, including Richard Dedekind, Gottlob Frege, Charles Sanders Peirce. And it has been shown that even some of the main proponents of the modern conception, such as Russell and Carnap, engaged with philosophical conceptions of logic in the wake of the nineteenth-century tradition at least for part of their works. However, much remains to be investigated.
The aim of this conference is to foster further exchanges between those who are doing scholarly research on the history of logic in the nineteenth and early twentieth centuries from various perspectives, including those who focus on the philosophical tradition of the nineteenth century and its developments in neo-Kantianism and phenomenology, historians of logic and of related mathematical disciplines, as well as philosophers who are interested in the epistemological issues surrounding modern mathematical logic.