Veronica J. Vieland

Statistical analysis is often used to evaluate the strength of evidence for or against scientific hypotheses. Here we consider evidence measurement from the point of view of representational measurement theory, focusing in particular on the 0-points of measurement scales. We argue that a properly calibrated evidence measure will need to count up from absolute 0, in a sense to be defined, and that this 0-point is likely to be something other than what one might have expected. This suggests the need for a new theory of statistical evidence in the context of which calibrated evidence measurement becomes tractable.

Hacking’s Law of Likelihood says – paraphrasing– that data support hypothesis H1 over hypothesis H2 whenever the likelihood ratio for H1 over H2 exceeds 1. But Hacking noted a seemingly fatal flaw in the LR itself: it cannot be interpreted as the degree of “evidential significance” across applications. I agree with Hacking about the problem, but I don’t believe the condition is incurable. I argue here that the LR can be properly calibrated with respect to the underlying evidence, and I sketch the rudiments of a methodology for so doing.

The dissertation develops a research program for the investigation of certain philosophically interesting features of scientific theories through the analysis of scientific language. The starting point is Rudolf Carnap's The Logical Syntax of Language. In Chapter One, Carnap's program is considered, with particular attention given to the connection between Carnap's conception of the language of science and his employment of certain formal logical systems for the purposes of explicating the logical syntax of that language. The suggestion is made that insofar as Carnap's investigations failed to achieve the strength of meta-theoretic results with respect to the natural sciences which the same techniques offered with respect to mathematical theories, the problems can in large measure be ascribed to the nature of the formal logics employed. In Chapter Two, the task of formalization is considered more broadly. The argument is made that while formalization may indeed be interesting and feasible for some of natural science, the formal systems of meta-mathematics are not necessarily vital nor even adequate to the task. A formal theory of natural language structure is presented, based on the work of Zellig Harris, which suggests a methodology for a more direct logical investigation of scientific language. Chapter Three develops a strategy for applying the formal linguistic techniques to a scientific sublanguage, by presenting the formal analysis of causatives in a corpus of research articles drawn from cellular immunology. Chapter Four considers the question of whether or not the analysis yielded in Chapter Three suffices for formalization of the causatives in any interesting sense. The results are mixed: while the causatives do not yield an interesting formalism, the reasons for this failure are of interest, and in part confirm the efficacy of the methods. They indicate as well possible fruitful lines of research for future applications

In this paper we consider the problem of how to measure the strength of statistical evidence from the perspective of evidence amalgamation operations. We begin with a fundamental measurement amalgamation principle : for any measurement, the inputs and outputs of an amalgamation procedure must be on the same scale, and this scale must have a meaningful interpretation vis a vis the object of measurement. Using the p value as a candidate evidence measure, we examine various commonly used approaches to amalgamation of evidence across similar studies, including standard forms of meta-analysis. We show that none of these methods satisfies MAP. Thus an underlying measurement problem remains. We argue that a successful approach to evidence amalgamation necessitates a solution to the problem of evidence measurement, and we suggest some lines of reasoning that might guide further work towards this end.

Hacking’s Law of Likelihood says—paraphrasing—that data support hypothesis H1 over hypothesis H2 whenever the likelihood ratio for H1 over H2 exceeds 1. But Hacking later noted a seemingly fatal flaw in the LR itself: it cannot be interpreted as the degree of “evidential significance” across applications. I agree with Hacking about the problem, but I do not believe the condition is incurable. I argue here that the LR can be properly calibrated with respect to the underlying evidence, and I sketch the rudiments of a methodology for so doing.