1,721,109 research outputs found
Book Reviews: Anita Burdman Feferman and Solomon Feferman, "Alfred Tarski: Life and Logic", Cambridge University Press, Cambridge
Full text linkBook Reviews: Anita Burdman Feferman and Solomon Feferman, "Alfred Tarski: Life and Logic", Cambridge University Press, Cambridge, UK, 2004, pp. 432
Hilbert's program then and now
Full text linkHilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial successes, and generated important advances in logical theory and metatheory, both at the time and since. The article discusses the historical background and development of Hilbert’s program, its philosophical underpinnings and consequences, and its subsequent development and influences since the 1930s
The Modal Logics of Kripke-Feferman Truth
Full text linkWe determine the modal logic of fixed-point models of truth and their axiomatizations by Solomon Feferman via Solovay-style completeness results
Indefiniteness in semi-intuitionistic set theories: On a conjecture of Feferman
Full text linkThe paper proves a conjecture of Solomon Feferman concerning the indefiniteness of the continuum hypothesis relative to a semi-intuitionistic set theory
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Predicativity
No full textWhat is predicativity? While the term suggests that there is a single idea involved, what the history will show is that there are a number of ideas of predicativity which may lead to different logical analyses, and I shall uncover these only gradually. A central question will then be what, if anything, unifies them. Though early discussions are often muddy on the concepts and their employment, in a number of important respects they set the stage for the further developments, and so I shall give them special attention. NB. Ahistorically, modern logical and set-theoretical notation will be used throughout, as long as it does not conflict with original intentions. Predicativity emerges: Russell and Poincaré To begin with, the terms predicative and non-predicative (later, impredicative) were introduced by Russell (1906) in his struggles dating from 1901 to carry out the logicist program in the face of the set-theoretical paradoxes. Russell called a propositional function ϕ(x) predicative if it defines a class, i.e., if the class {x: ϕ(x)} exists, and non-predicative otherwise. Thus, for example, th
- …
