The ArgumentMany find it “notoriously difficult to see how societal context can affect in any essential way how someone solves a mathematical problem or makes a measurement.” That may be because it has been a habit of western scientists to assert their numerical schemes were untainted by any hint of anthropomorphism. Nevertheless, that Platonist penchant has always encountered obstacles in practice, primarily because the stability of any applied numerical scheme requires some alien or external warrant.This paper surveys the history of (...) measurement standards, physical dimensions and dimensionless constants as one instance of the quest to purge all anthropomorphic taint first in the metric system, then in the dimensions provided by the atom, then in physical constants intelligible to extraterrestrials, only then to end up back at overt anthropomorphism in the late 20th century. This suggests that the “naturalness” of natural numbers has always been conceptualized in locally contingent cultural terms. (shrink)

Einstein’s special theory of relativity has had a wide influence on fields far removed from physics. It has given the impression that physics has shown that there are now no absolute truths, that all beliefs are relative to the observer, and that traditional stable landmarks have been washed away. We each have our own frame of reference that is as good as any other frame, so that there are no absolute standards by which our actions may be judged. The predictions (...) of relativity theory, such as the elimination of simultaneity, the variation of mass with velocity, and the equivalence of mass and energy, are all highly counterintuitive and yet are precisely confirmed by detailed measurements. The clear rocklike mechanical physics of Newton seems to have dissolved into a swirling mist of unintelligible concepts, and familiar certainties seem to have disappeared. A detailed analysis of relativity theory shows, however, a completely different picture. Properly understood, it is a logical extension of Newtonian physics that expresses the relations of space and time in a more exact and elegant way and in the process shows forth more clearly the invariant features of the world. The apparently counterintuitive features appear as natural consequences that extend and refine our classical concepts. The traditional landmarks remain, but God’s world is more subtle than we had previously imagined. (shrink)

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. (shrink)

One of the main goals of scientific research is to provide a description of the empirical data which is as accurate and comprehensive as possible, while relying on as few and simple assumptions as possible. In this paper, I propose a definition of the notion of few and simple assumptions that is not affected by known problems. This leads to the introduction of a simple model of scientific progress that is based only on empirical accuracy and conciseness. An essential point (...) in this task is the understanding of the role played by measurability in the formulation of a scientific theory. This is the key to prevent artificially concise formulations. The model is confronted here with many possible objections and with challenging cases of real progress. Although I cannot exclude that the model might have some limitations, it includes all the cases of genuine progress examined here, and no spurious one. In this model, I stress the role of the state of the art, which is the collection of all the theories that are the only legitimate source of scientific predictions. Progress is a global upgrade of the state of the art. (shrink)