Results 1 
7 of
7
Advice on Abductive Logic
 Logic Journal of the IGPL
"... The action of thought is excited by the initiation of doubt and ceases when belief is attained; so that the production of belief is the sole function of thought. ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
The action of thought is excited by the initiation of doubt and ceases when belief is attained; so that the production of belief is the sole function of thought.
Turing Oracle Machines, Online Computing, and Three Displacements in Computability Theory
, 2009
"... ..."
Transfer Principles in Set Theory
, 1997
"... CONTENTS PART A. HIGHLIGHTS. Introduction. A1. Two basic examples of transfer principles. A2. Some formal conjectures. A3. Sketch of some proofs. A4. Ramsey Cardinals. A5. Towards a new view of set theory. PART B. FULL LIST OF CLAIMS. (Based on 5/1996 abstract) 1. Transfer principles from N to On. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
CONTENTS PART A. HIGHLIGHTS. Introduction. A1. Two basic examples of transfer principles. A2. Some formal conjectures. A3. Sketch of some proofs. A4. Ramsey Cardinals. A5. Towards a new view of set theory. PART B. FULL LIST OF CLAIMS. (Based on 5/1996 abstract) 1. Transfer principles from N to On. A. Mahlo cardinals. B. Weakly compact cardinals. C. Ineffable cardinals. D. Ramsey cardinals. E. Ineffably Ramsey cardinals. F. Subtle cardinals. G. From N to <On. H. Converses. 2. Transfer principles for general functions. A. Equivalence with Mahloness. B. Equivalence with weak compactness. C. Equivalence with ineffability. D. Equivalence with Ramseyness. E. Equivalence with ineffable Ramseyness. F. From N to <On. G. Converses. H. Some necessary conditions. 3. Transfer principles with arbitrary alternations of quantifiers. 4. Decidability of statements on N. 5. Decidability of statements on <On and On. NOTE: Talks are based on Part A only 2 PART A. HIGHLI
Economic Dynamics and Computation Resurrecting the Icarus Tradition ∗
, 2003
"... "The [hydraulic] mechanism just described is the physical analogue of the ideal economic market. The elements which contribute to the determination of prices are represented each with its appropriate rôle and open to the scrutiny of the eye. We are thus enabled ..."
Abstract
 Add to MetaCart
"The [hydraulic] mechanism just described is the physical analogue of the ideal economic market. The elements which contribute to the determination of prices are represented each with its appropriate rôle and open to the scrutiny of the eye. We are thus enabled
Independence and Large Cardinals
, 2010
"... The independence results in arithmetic and set theory led to a proliferation of mathematical systems. One very general way to investigate the space of possible mathematical systems is under the relation of interpretability. Under this relation the space of possible mathematical systems forms an intr ..."
Abstract
 Add to MetaCart
The independence results in arithmetic and set theory led to a proliferation of mathematical systems. One very general way to investigate the space of possible mathematical systems is under the relation of interpretability. Under this relation the space of possible mathematical systems forms an intricate hierarchy of increasingly strong systems. Large cardinal axioms provide a canonical means of climbing this hierarchy and they play a central role in comparing systems from conceptually distinct domains. This article is an introduction to independence, interpretability, large cardinals and their interrelations. Section 1 surveys the classic independence results in arithmetic and set theory. Section 2 introduces the interpretability hierarchy and describes some of its basic features. Section 3 introduces the notion of a large cardinal axiom and discusses some of the central examples. Section 4 brings together the previous themes by discussing the manner in which large cardinal axioms provide a canonical means for climbing the hierarchy of interpretability and serve as an intermediary in the comparison
4. The Second Incompleteness Theorem. 5. Lengths of Proofs.
, 2007
"... Gödel's legacy is still very much in evidence. We will not attempt to properly discuss the full impact of his work and all of the ongoing important research programs that it suggests. This would require a book length manuscript. Indeed, there are several books discussing the Gödel legacy from many p ..."
Abstract
 Add to MetaCart
Gödel's legacy is still very much in evidence. We will not attempt to properly discuss the full impact of his work and all of the ongoing important research programs that it suggests. This would require a book length manuscript. Indeed, there are several books discussing the Gödel legacy from many points of view, including, for example, [Wa87], [Wa96], [Da05], and the historically comprehensive five volume set [Go,8603]. In sections 27 we briefly discuss some research projects that are suggested by some of his most famous contributions. In sections 811 we discuss some highlights of a main recurrent theme in our own research, which amounts to an expansion of the Gödel incompleteness phenomenon in a critical direction.
MATHEMATICAL LOGIC: WHAT HAS IT DONE FOR THE PHILOSOPHY OF MATHEMATICS?
"... to discuss some claims concerning the relationship between mathematical logic and the philosophy of mathematics that repeatedly occur in his writings. Although I do not know to what extent they are representative of his present position, they correspond to widespread views of the logical community a ..."
Abstract
 Add to MetaCart
to discuss some claims concerning the relationship between mathematical logic and the philosophy of mathematics that repeatedly occur in his writings. Although I do not know to what extent they are representative of his present position, they correspond to widespread views of the logical community and so seem worth discussing anyhow. Such claims will be used as reference to make some remarks about the present state of relations between mathematical logic and the philosophy of mathematics. Kreisel’sviewsgreatlyinfluencedmeintheSixtiesandthe Seventies. His critical remarks on the foundational programs taught me that one could and should have an approach to the subject of mathematical logic less dogmatic, corporative and even thoughtless than the one the logical community sometimes used to have. This is even more true today when the professionalization of mathematical logic generates a flood of results but few new ideas and the lack of ideas leads to the sheer byzantinism of most current production in mathematical logic. In the past few years,however,IhavecometotheconclusionthatKreisel’scriticism hasnot been radical enough: his main worry seems to have been to preserve as much as possible to save the savable of the tradition of mathematical logic. His critical remarks have focused on the defects of the foundational schools, thus drawing attention away from the intrinsic defects of mathematical logic itself