Although the theory of definability had many important antecedents—such as the descriptive set theory initiated by the French semi-intuitionists in the early 1900s—the main ideas were first laid out in precise mathematical terms by Alfred Tarski beginning in 1929. We review here the basic notions of languages, explicit definability, and grammatical complexity, and emphasize common themes in the theories of definability for four important languages underlying, respectively, descriptive set theory, recursive function theory, classical pure logic, and finite-universe logic. We review (...) the history of previous studies of the similarities and differences in the theories of definability of the first three of these four languages. A seminal role leading toward unification of the theories has been played by the separation principles introduced by Nikolai Luzin in 1927. Emphasizing analogies and driving toward further unification embracing finite-universe logic we concentrate on a simple example—the first and second separation principles for existential-universal first-order sentences . Using this as a test case for the fundamental problem of how to “finitize” arguments in classical pure logic to the finite-universe case, we are led to the analogous negative solution by using the theory of certain special graphs: a graph is - special for any positive integers m , n , p , q iff it is bipartite with m red points and n blue points and for every p -tuple of red points there is a blue point to which they are all connected . As an aside we introduce for further study a natural “Ramseyesque” increasing sequence A of positive integers, where A is the least positive integer n for which an -special graph exists. (shrink)

ABSTRACT Joseph Addison played a key role in Nicholas Phillipson's pioneering studies of eighteenth-century Scottish culture and philosophy. Post-Union Scots were in search of renewed civic purpose now political power had headed to Westminster. They found it in Addison's Spectator essays discussing virtuous living. This article pays homage to Phillipson's work by expanding the scope of the study of Addison's reception in eighteenth-century Scotland. A survey of the publishing history of Addison's works north of the border (...) indicates additional roles for the English essayist in Scotland. Addison's political works, especially his tragedy Cato, were drawn on by pro-Unionists and anti-Jacobites. His religious writings were held in high regard, while both High Flying and Moderate churchmen imitated his style. Addison was important as important within Scottish aesthetics as he was within the Humean discourse of civic morality, though, as with Hume's and Smith's treatment of Addison, Scottish aestheticists quickly superseded Addison's discussion of the ‘pleasures of the imagination’. There are, then, several additional ‘Addisons’ on top of those identified by Phillipson. (shrink)

J.W. Olson addresses the Christian doctrine of revelation by asking how theological truth claims can possibly be rooted in God’s incarnational self-communication. Engaging with the phenomenology of Martin Heidegger, Olson offers an interpretation of the Eucharist that grounds Christian knowledge in an embodied understanding of the sacrament.

The Many-Interacting-Worlds (MIW) approach to a quantum theory without wave functions proposed in [8] leads naturally to numerical integrators of the Schrödinger equation on comoving grids. As yet, little is known about concrete MIW models for more than one spatial dimension and/or more than one particle. In honour of Detlef Dürr, we report on a further development of the MIW approach to treat arbitrary degrees of freedom and provide a numerical proof of concept for ground states in 2d. The latter (...) is part of a systematic numerical study [22] that includes also 1d ground and excited states. With this step towards the treatment of higher degrees of freedom we hope to stimulate their further study. (shrink)