The Unprovability Of Consistency

Author: George Boolos
Publisher: Cambridge University Press
ISBN: 9780521092975
File Size: 54,22 MB
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The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has persisted for at least thirty years between the followers of C. I. Lewis and W. V. O. Quine. The author employs semantic methods developed by Saul Kripke in his analysis of modal logical systems. The book will be of interest to advanced undergraduate and graduate students in logic, mathematics and philosophy, as well as to specialists in those fields.

Logic Logic And Logic

Author: George Boolos
Publisher: Harvard University Press
ISBN: 9780674537675
File Size: 34,77 MB
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George Boolos was one of the most prominent and influential logician-philosophers of recent times. This collection, nearly all chosen by Boolos himself shortly before his death, includes thirty papers on set theory, second-order logic, and plural quantifiers; on Frege, Dedekind, Cantor, and Russell; and on miscellaneous topics in logic and proof theory, including three papers on various aspects of the Gödel theorems. Boolos is universally recognized as the leader in the renewed interest in studies of Frege's work on logic and the philosophy of mathematics. John Burgess has provided introductions to each of the three parts of the volume, and also an afterword on Boolos's technical work in provability logic, which is beyond the scope of this volume.

Philosophical Logic

Author: George Englebretsen
Publisher: A&C Black
ISBN: 1441119116
File Size: 46,90 MB
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Introduces students to non-classical logic, syllogistic, to quantificational and modal logic. The book includes exercises throughout and a glossary of terms and symbols.

Kurt G Del

Author: Solomon Feferman
Publisher: Cambridge University Press
ISBN: 1139487752
File Size: 69,53 MB
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Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible sets.

The Logic Of Provability

Author: George Boolos
Publisher: Cambridge University Press
ISBN: 9780521483254
File Size: 25,90 MB
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Boolos, a pre-eminent philosopher of mathematics, investigates the relationship between provability and modal logic.

Set Theory And The Continuum Hypothesis

Author: Paul J. Cohen
Publisher: Courier Corporation
ISBN: 0486469212
File Size: 15,48 MB
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This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

An Introduction To G Del S Theorems

Author: Peter Smith
Publisher: Cambridge University Press
ISBN: 1107022843
File Size: 69,75 MB
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A clear and accessible treatment of Gödel's famous, intriguing, but much misunderstood incompleteness theorems, extensively revised in a second edition.

Metamagical Themas

Author: Douglas Hofstadter
Publisher: Basic Books
ISBN: 0786723866
File Size: 10,61 MB
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Hofstadter’s collection of quirky essays is unified by its primary concern: to examine the way people perceive and think.

Replacing Truth

Author: Kevin Scharp
Publisher: Oxford University Press
ISBN: 0199653852
File Size: 60,18 MB
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Kevin Scharp proposes an original theory of the nature and logic of truth on which truth is an inconsistent concept that should be replaced for certain theoretical purposes. He argues that truth is best understood as an inconsistent concept, and proposes a detailed theory of inconsistent concepts that can be applied to the case of truth. Truth also happens to be a useful concept, but its inconsistency inhibits its utility; as such, it should be replaced withconsistent concepts that can do truth's job without giving rise to paradoxes. To this end, Scharp offers a pair of replacements, which he dubs ascending truth and descending truth, along with an axiomatic theory of them and a new kind of possible-worlds semantics for this theory. He goes to developDavidson's idea that truth is best understood as the core of a measurement system for rational phenomena (e.g., belief, desire, and meaning), and offers a semantic theory that treats truth predicates as assessment-sensitive (i.e., their extension is relative to a context of assessment) and solves the problems posed by the liar and other paradoxes.

Goal Directed Proof Theory

Author: Dov M. Gabbay
Publisher: Springer Science & Business Media
ISBN: 9401717133
File Size: 62,26 MB
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Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and substructural logics. The book can also be used as an introduction to these logical systems form a procedural perspective. Readership: Computer scientists, mathematicians and philosophers, and anyone interested in the automation of reasoning based on non-classical logics. The book is suitable for self study, its only prerequisite being some elementary knowledge of logic and proof theory.