UPAC Colloquium

Finitistic methods appeared in the context of Hilbert's program in the foundations of mathematics. According to Hilbert, finitism contains those elementary methods of reasoning about finite objects (integers, words, ...) that are beyond any doubt and in some sense prior to any mathematical or axiomatic reasoning. Hilbert and Bernays gave examples of finitistically acceptable principles, but never clearly delineated the extent of these methods. Over the years, there were several proposals to make them mathematically precise, most notably by Kreisel and Tait.

This is a work in progress talk in which I will discuss Georg Kreisel's approach of characterizing finitism in terms of formal systems defined by iteration of certain processes of reflection. His answer is equivalent to the association of finitistic theorems with the (forall)(exists) theorems of Peano arithmetic. However, Kreisel's approach is technically involved and is itself in need of clarification.  I will overview the ideas in Kreisel's paper and outline various associated problems.

Historically, the debate about the extent of finitism remained rather marginal; the issue can hardly ever be conclusively resolved. Nevertheless, the question is stubbornly alive, especially as a case study of the fundamental problem of how formal mathematical models of reasoning relate to contentual ones. 

Alternative explanations of the cosmic microwave background: A historical and an epistemological perspective

The tradition of a strict conceptual dichotomy between space(time) and matter originates with Democritus' atomism—everything in our universe is ultimately reducible to either atoms (matter) or void (space)—and has reigned supreme ever since Newton. It is echoed by the famous container metaphor according to which space is conceived of as a container for matter, i.e. the contained (Sklar, 1974). Importantly, this conceptual dichotomy is the shared assumption needed by the substantivalist and relationalist about spacetime to formulate their further disagreement.

Whereas this dichotomy may break down in the quantum gravity regime, I contend that reasons to worry about the breakdown of this dichotomy already appear in the context of established, experimentally well-confirmed theories, thereby following in the footsteps of Rynasiewicz (1996), Rovelli (1997) and others. This talk focuses on three case studies from cosmology and astronomy, namely dark matter, dark energy and black holes, illustrating in which sense these put pressure on a strict conceptual dichotomy between spacetime and gravity on the one hand and matter on the other, and elaborating upon the consequences of the breakdown of this distinction for philosophy and physics.

A Universe Lost to the World? On Speculative Origins; Or, Why the Universe may be running away from Cosmologists.