This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{ the exact proof-theoretic ordinals of these systems are presented.

This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed. Later, we turn to least universes, strictness and name induction. Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent to Feferman's.

Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in (...) computer science such as automated theorem proving and type theory. (shrink)

The basic theory of scientific understanding presented in Sections 1–2 exploits three main ideas.First, that to understand a phenomenonP (for a given agent) is to be able to fitP into the cognitive background corpusC (of the agent).Second, that to fitP intoC is to connectP with parts ofC (via arguments in a very broad sense) such that the unification ofC increases.Third, that the cognitive changes involved in unification can be treated as sequences of shifts of phenomena inC. How the theory fits (...) typical examples of understanding and how it excludes spurious unifications is explained in detail. Section 3 gives a formal description of the structure of cognitive corpuses which contain descriptive as well as inferential components. The theory of unification is then refined in the light of so called puzzling phenomena, to enable important distinctions, such as that between consonant and dissonant understanding. In Section 4, the refined theory is applied to several examples, among them a case study of the development of the atomic model. The final part contains a classification of kinds of understanding and a discussion of the relation between understanding and explanation. (shrink)

This paper supplements an earlier one (Wassermann 1978b). Its views aim to reinforce those of Lewontin and other prominent evolutionists, but differ significantly from the opinions of some philosophers of science, notably Popper (1957) and Olding (1978). A basic distinction is made between 'laws' and 'theories of mechanisms'. The 'Theory of Evolution' is not characterized by laws, but is viewed here as a hypertheory which explains classifiable evolutionary phenomena in terms of subordinate classifiable theories of 'evolution-specific mechanisms' (ESMs), each of (...) which could apply to a host of species. Adaptations could result from ESMs that are rooted in molecular complementarities. The status of optimization theories that aim to predict best adapted states of organisms or populations is also discussed. (shrink)

The volume contains the written versions of all papers given at the workshop, divided into five chapters and followed by Alvin Goldman's replies in the sixth.

In this paper first order theories for nonmonotone inductive definitions are introduced, and a proof-theoretic analysis for such theories based on combined operator forms a la Richter with recursively inaccessible and Mahlo closure ordinals is given.

Together with its introduction, Language, Mind and Epistemology examines Davidson's unified stance towards philosophy by joining American and European authors ...

According to the paradigm of adaptive rationality, successful inference and prediction methods tend to be local and frugal. As a complement to work within this paradigm, we investigate the problem of selecting an optimal combination of prediction methods from a given toolbox of such local methods, in the context of changing environments. These selection methods are called meta-inductive strategies, if they are based on the success-records of the toolbox-methods. No absolutely optimal MI strategy exists—a fact that we call the “revenge (...) of ecological rationality”. Nevertheless one can show that a certain MI strategy exists, called “AW”, which is universally long-run optimal, with provably small short-run losses, in comparison to any set of prediction methods that it can use as input. We call this property universal access-optimality. Local and short-run improvements over AW are possible, but only at the cost of forfeiting universal access-optimality. The last part of the paper includes an empirical study of MI strategies in application to an 8-year-long data set from the Monash University Footy Tipping Competition. (shrink)

Non-classical views about important issues in logic and its philosophy are a distinctive trait of Shahid Rahman's work. This volume has been designed, on the occasion of his 50th birthday, as a gathering place for unconventional approaches, original ideas and attempts to question well-established standards. Some of the world top philosophers and logicians contributed to a brilliant collection of papers, some of which doubtlessly leave their mark on the work to come in logic and in philosophy of formal sciences. Contributors (...) are: Philippe Balbiani, Diderik Batens, Johan van Benthem, Giacomo Bonanno, Walter A. Carnielli, Newton C. A. Da Costa, Michel Crubellier, Francisco A. Doria, Dov M. Gabbay, Olivier Gasquet, Gerhard Heinzmann, Andreas Herzig, Jaakko Hintikka, Justine Jacot, Reinhard Kahle, Erik C. W. Krabbe, Decio Krause, Franck Lihoreau, Kuno Lorenz, Ilkka Niiniluoto, Graham Priest, Stephen Read, Manuel Rebuschi, Greg Restall, Gabriel Sandu, Gerhard Schurz, Francois Schwarzentruber, Yaroslav Shramko, Goran Sundholm, John Symons, Christian Thiel, Nicolas Troquard, Tero Tulenheimo, Jean Paul Van Bendegem, Daniel Vanderveken, Yde Venema, Heinrich Wansing, Jan Wolenski and John Woods. (shrink)

The paper lists all the predictions and observations of eclipses of Jupiter's satellites 1668–1678 and compares them with modern computations of the these eclipses by J. H. Lieske. We discuss Roemer's method that led to his discovery of the retardment of light and finally we shall interpret Roemer's calculations.