Mahmoud Jalloh

Tatiana Ehrenfest-Afanassjewa was an important physicist, mathematician, and educator in 20th century Europe. While some of her work has recently undergone reevaluation, little has been said regarding her groundbreaking work on dimensional analysis. This, in part, reflects an unfortunate dismissal of her interventions in such foundational debates by her contemporaries. In spite of this, her work on the generalized theory of homogeneous equations provides a mathematically sound foundation for dimensional analysis and has found some appreciation and development. It remains to provide a historical account of Ehrenfest-Afanassjewa's use of the theory of homogeneous functions to ground (and limit) dimensional analysis. We take as a central focus Ehrenfest-Afanassjewa's contributions to a debate on the foundations of dimensional analysis started by physicist Richard Tolman in 1914. I go on to suggest an interpretation of the more thoroughgoing intervention Ehrenfest-Afanassjewa makes in 1926 based on this earlier context, especially her limited rehabilitation of a "theory of similitude" in contradistinction to dimensional analysis. It is shown that Ehrenfest-Afanassjewa has made foundational contributions to the mathematical foundations and methodology of dimensional analysis, our conception of the relation between constants and laws, and our understanding of the quantitative nature of physics, which remain of value.

I provide an account of the physical appropriate to the task of the physicalist while remaining faithful to the usage of “physical” natural to physicists. Physicalism is the thesis that everything in the world is physical, or reducible to the physical. I presuppose that some version of this position is a live epistemic possibility. The physicalist is confronted with Hempel’s dilemma: that physicalism is either false or contentless. The proposed account of the physical avoids both horns and generalizes a recent proposal by Vicente (2011). My account defines physicalism as the thesis that there are no objects that cannot be described by physical quantities. A dimensional account of physical quantities is given: quantities are determined by measurement procedures.

People are often interested in physics due to its purported objectivity. It aims to truly be a study of nature (φύσεις) in itself. On the other hand, physics is a human construct, a language we use to describe the world as we experience it. In our quest for absolute reality, then, it seems that we must rid our description of the world of all subjectivity. This lecture concerns part of a story of such an attempt: the quest for absolute measurement. We will consider physical and philosophical aspects of the attempts of Maxwell, Peirce, and Planck to rid our language of physical measurement of undue subjectivity. This will shed some light on the possibility of knowing absolute reality—and the possibility of communication with aliens.

This paper recovers an important, century-old debate regarding the methodological and metaphysical foundations of dimensional analysis. Consideration of Richard Tolman's failed attempt to install the principle of similitude---the relativity of size---as the founding principle of dimensional analysis both clarifies the method of dimensional analysis and articulates two metaphysical positions regarding quantity dimensions. Tolman's position is quantity dimension fundamentalism. This is a commitment to dimensional realism and a set of fundamental dimensions which ground all further dimensions. The opposing position, developed primarily by Bridgman, is quantity dimension conventionalism. Conventionalism is an anti-realism regarding dimensional structure, holding our non-representational dimensional systems have basic quantity dimensions fixed only by convention. This metaphysical dispute was left somewhat unsettled. It is shown here that both of these positions face serious problems: fundamentalists are committed to surplus dimensional structure; conventionalists cannot account for empirical constraints on our dimensional systems nor the empirical success of dimensional analysis. It is shown that an alternative position is available which saves what is right in both: quantity dimension functionalism.

I argue that dimensional analysis provides an answer to a skeptical challenge to the theory of model mediated measurement. The problem arises when considering the task of calibrating a novel measurement procedure, with greater range, to the results of a prior measurement procedure. The skeptical worry is that the agreement of the novel and prior measurement procedures in their shared range may only be apparent due to the emergence of systematic error in the exclusive range of the novel measurement procedure. Alternatively: what if the two measurement procedures are not in fact measuring the same quantity? The theory of model mediated measurement can only say that we _assume_ that there is a common quantity. In contrast, I show that the satisfaction of dimensional homogeneity across the metrological extension is independent evidence for the so-called assumption. This is illustrated by the use of dimensional analysis in high pressure experiments. This results in an extension of the theory of model mediated measurement, in which a common quantity in metrological extension is no longer assumed, but hypothesized.

In this paper I present and evaluate van Inwagen’s famous Consequence Argument, as presented in An Essay on Free Will. The grounds for the incompatibility of freewill and determinism, as argued by van Inwagen, is dependent on our actions being logical consequences of events outside of our control. Particularly, his arguments depend upon, in one guise or another, the transference of the modal property of not being possibly rendered false through the logical consequence relation, i.e. the β-principle. I argue that, due to the symmetric nature of determinism, van Inwagen is exposed to what I call “reversibility arguments” in the literature. Such arguments reverse the β-principle and start from our apparent control over our own actions to our control over the initial conditions. Since van Inwagen does not endorse a particular theory of laws or logical consequence, he is open to such counterarguments. The plausibility of such reversibility arguments depends on what would be called a Wittgensteinian conception of logical consequence. In the _Remarks on the Foundation of Mathematics_, one of Wittgenstein’s main concerns is the normativity of logical inference i.e. proof. Such concerns with normativity and rule-following are generally a feature of his later philosophy. In the _Remarks_ Wittgenstein resists a conception of logical deduction which places the source of normativity outside of human practice.

Physicist Percy Bridgman has been taken by Heather Douglas to be an exemplar defender of an untenable value-free ideal for science. This picture is complicated by a detailed study of Bridgman's philosophical views of the relation between science and society. The normative autonomy of science, a version of the value-free ideal, is defended. This restriction on the provenance of permissible values in science is given a basis in Bridgman's broader philosophical commitments, most importantly, his view that science is primarily an individual commitment to a set of epistemic norms and values. Considerations of external moral or social values are not, on this view, intrinsic to scientific practice, though they have a broader pragmatic significance. What Bridgman takes as the proper relation between science and society is shown through analysis of his many writings on the topic and consideration of his rarely remarked upon involvement in the most problematic example of "Big Science" of his day: the atomic bomb. A reevaluation of Bridgman's views provides a unique characterization of what is at stake in the values in science debate: the normative autonomy of science.

I provide an account of the physical appropriate to the task of the physicalist while remaining faithful to the usage of “physical” natural to physicists. Physicalism is the thesis that everything in the world is physical, or reducible to the physical. I presuppose that some version of this position is a live epistemic possibility. The physicalist is confronted with Hempel’s dilemma: that physicalism is either false or contentless. The proposed account of the physical avoids both horns and generalizes a recent proposal by Vicente (2011). My account defines physicalism as the thesis that there are no objects that cannot be described by physical quantities. A dimensional account of physical quantities is given: quantities are determined by measurement procedures.

This dissertation draws upon historical studies of scientific practice and contemporary issues in the metaphysics and epistemology of science to account for the nature of physical quantities. My dissertation applies this integrated HPS approach to dimensional analysis—a logic for quantitative physical equations which respects the distinct dimensions of quantities (e.g. mass, length, charge). Dimensional analysis and its historical development serve both as subjects of study and as a sources for solutions to contemporary problems. The dissertation consists primarily of three related papers on: (1) the methodological and metaphysical foundations of dimensional analysis, (2) the use of dimensional analysis in determining physical symmetries, (3) the use of dimensional analysis in securing metrological extension.

In this paper a symmetry argument against quantity absolutism is amended. Rather than arguing against the fundamentality of intrinsic quantities on the basis of transformations of basic quantities, a class of symmetries defined by the Π-theorem is used. This theorem is a fundamental result of dimensional analysis and shows that all unit-invariant equations which adequately represent physical systems can be put into the form of a function of dimensionless quantities. Quantity transformations that leave those dimensionless quantities invariant are empirical and dynamical symmetries. The proposed symmetries of the original argument fail to be both dynamical and empirical symmetries and are open to counterexamples. The amendment of the original argument requires consideration of the relationships between quantity dimensions. The discussion raises a pertinent issue: what is the modal status of the constants of nature which figure in the laws? Two positions, constant necessitism and constant contingentism, are introduced and their relationships to absolutism and comparativism undergo preliminary investigation. It is argued that the absolutist can only reject the amended symmetry argument by accepting constant necessitism. I argue that the truth of an epistemically open empirical hypothesis would make the acceptance of constant necessitism costly: together they entail that the facts are nomically necessary.