The Representational Theory of Measurement (RTM), especially the canonical three volume Foundations of Measurement by Krantz et al., is a landmark accomplishment in our understanding of measurement. Despite this, it has been far from easy to pinpoint what exactly we can learn about measurement from RTM, and who the target audience for RTM’s formal results should be. In what sense does RTM provide foundations of measurement, and what is the philosophical significance of such foundations? I argue that RTM provides semantic (...) foundations of measurement, and that their philosophical significance lies in a shift towards structural representation. (shrink)

In recent work, Christopher Peacocke has argued for a kind of realism (or anti-reductionism) about magnitudes such as temperature and spatial distance. Peacocke’s argument is that magnitudes are an ineliminable commitment of scientific and everyday explanations (including high-level explanations), and that they are the natural candidates for semantic values of our ordinary magnitude talk, and for contents of our mental states. I critique these arguments, in particular focusing on whether the realist has a satisfactory account of how high-level magnitude facts (...) are grounded in lower-level facts. I argue that a less realist (i.e., more reductionist approach) is preferable, or at least viable. I also aim to substantially clarify what is at stake in the debate. (shrink)

Analog representations come in different types. One distinction is between those representations that have parts that are themselves representations and those that do not (i.e., those for which the Parts Principle is true and those for which it is not). I offer a unified account of analog representation, showing what all types have in common. This account clarifies when the Parts Principle applies and when it does not, thereby illuminating why the Parts Principle is less interesting than one might have (...) thought. Understanding analog representation instead requires understanding the kinds of magnitudes used in a particular representation, and the kinds of variation possible within a representational scheme. (shrink)

Extensive Magnitudes: Metaphysics, Representation and Epistemology.

I present an argument against the view that the additivity of mass (i.e., the property according to which a composite object’s mass is the “sum” of its parts’) is metaphysically independent of dynamical laws governing massive bodies. In particular, taking additivity to be independent of dynamics commits you to widespread unexplained correlations between the mass properties of composites and the dynamic behavior of massive bodies. The second half of the paper extends this explanatory worry, showing that the very same considerations (...) apply to aspects of mass’s quantitative structure. This gives rise to a new and powerful objection to certain influential theories about the fundamental structure of physical quantities —most notably the magnitude realism of Peacocke (2019) and the second-order absolutist accounts defended by Mundy (1987) and Eddon (2013b). (shrink)