Amit Hagar

In the chapter “The Geometry of Visibles” in his ‘Inquiry into the Human Mind’, Thomas Reid constructs a special space, develops a special geometry for that space, and offers a natural model for this geometry. In doing so, Reid “discovers” non-Euclidean Geometry sixty years before the mathematicians. This paper examines this “discovery” and the philosophical motivations underlying it. By reviewing Reid’s ideas on visible space and confronting him with Kant and Berkeley, I hope, moreover, to resolve an alleged impasse in Reid’s philosophy concerning the contradictory characteristics of Reid’s tangible and visible space.

Hugh Everett III died of a heart attack in July 1982 at the age of 51. Almost 26 years later, a New York Times obituary for his PhD advisor, John Wheeler, mentioned him and Richard Feynman as Wheeler’s most prominent students. Everett’s PhD thesis on the relative state formulation of quantum mechanics, later known as the “Many Worlds Interpretation”, was published (in its edited form) in 1957, and later (in its original, unedited form) in 1973, and since then has given rise to one of the most radical schools of thought in the foundations of quantum theory. Several years ago two conferences held in Oxford and in the Perimeter Institute celebrated the occasion of 50 years to the first publication of Everett’s thesis. The book Many worlds? grew out from contributions to these conferences, but, as its editors emphasize, it is more than mere conference proceedings. Instead, an attempt was made to assemble an impressive collection of papers which together illustrate the promise of the many worlds interpretation and the obstacles it faces. 23 papers divided into six sections follow an introduction by Simon Saunders, one of Oxford’s fiercest Everettians. The first four sections cover two thorny issues that have been flagged by contemporary opponents to the many worlds interpretation, namely, the problem of ontology and the problem of probability, while the fifth discusses alternatives to Everett such as Bohmian mechanics and information–theoretic approaches to quantum theory. The sixth section seems to be a wild card, hosting several papers unrelated to each other, including one of the most interesting contributions to this volume on the history of Everett’s thesis and his (some may say all too) short academic career. Each section concludes with transcripts of the discussion session that took place after the talks, thus giving an additional emphasis to the points of contention. Apart from general comments on the volume, in what follows I would like to concentrate on few papers I found especially illuminating. Start with ontology..

We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the 'distance' (in terms of physical resources) from a physical state to another, and (3) the size of the set of time--complexity functions that are compatible with the physical resources required to reach a physical state from another.

We present a brief history of decoherence, from its roots in the foundations of classical statistical mechanics, to the current spin bath models in condensed matter physics. We analyze the philosophical import of the subject matter in three different foundational problems, and find that, contrary to the received view, decoherence is less instrumental to their solutions than it is commonly believed. What makes decoherence more philosophically interesting, we argue, are the methodological issues it draws attention to, and the question of the universality of quantum mechanics.

It is occasionally claimed that the important work of philosophers, physicists, and mathematicians in the nineteenth and in the early twentieth centuries made Kant’s critical philosophy of geometry look somewhat unattractive. Indeed, from the wider perspective of the discovery of non-Euclidean geometries, the replacement of Newtonian physics with Einstein’s theories of relativity, and the rise of quantificational logic, Kant’s philosophy seems “quaint at best and silly at worst”.1 While there is no doubt that Kant’s transcendental project involves his own conceptions of Newtonian physics, Euclidean geometry and Aristotelian logic, the issue at stake is whether the replacement of these conceptions collapses Kant’s philosophy into an unfortunate embarrassment.2 Thus, in evaluating the debate over the contemporary relevance of Kant’s philosophical project one is faced with the following two questions: (1) Are there any contradictions between the scientific developments of our era and Kant’s philosophy? (2) What is left from the Kantian legacy in light of our modern conceptions of logic, geometry and physics? Within this broad context, this paper aims to evaluate the Kantian project vis à vis the discovery and application of non-Euclidean geometries. Many important philosophers have evaluated Kant’s philosophy of geometry throughout the last century,3 but opinions with regard to the impact of non-Euclidean geometries on it diverge. In the beginning of the century there was a consensus that the Euclidean character of space should be considered as a consequence of the Kantian project, i.e., of the metaphysical view of space and of the synthetic a priori character of geometry. The impact of non-Euclidean geometries was then thought as undermining the Kantian project since it implied, according to positivists such..