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  • © 2012

Truth and Falsehood

An Inquiry into Generalized Logical Values

  • Surveys and unifies various philosophical and formal treatments of truth values
  • Discusses central issues such as the relation between truth values and consequence relations
  • Systematically develops both semantically and proof-theoretically a theory of generalized truth values as subsets of already established truth values.

Part of the book series: Trends in Logic (TREN, volume 36)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
  2. Truth Values

    • Yaroslav Shramko, Heinrich Wansing
    Pages 1-18
  3. Truth Values and the Slingshot Argument

    • Yaroslav Shramko, Heinrich Wansing
    Pages 19-40
  4. Generalized Truth Values: From FOUR 2 to SIXTEEN 3

    • Yaroslav Shramko, Heinrich Wansing
    Pages 41-62
  5. Generalized Truth Values: SIXTEEN 3 and Beyond

    • Yaroslav Shramko, Heinrich Wansing
    Pages 63-91
  6. Axiom Systems for Trilattice Logics

    • Yaroslav Shramko, Heinrich Wansing
    Pages 93-112
  7. Sequent Systems for Trilattice Logics

    • Yaroslav Shramko, Heinrich Wansing
    Pages 113-141
  8. Intuitionistic Trilattice Logics

    • Yaroslav Shramko, Heinrich Wansing
    Pages 143-170
  9. Generalized Truth Values and Many-Valued Logics: Suszko’s Thesis

    • Yaroslav Shramko, Heinrich Wansing
    Pages 189-214
  10. Further Developments

    • Yaroslav Shramko, Heinrich Wansing
    Pages 215-226
  11. Back Matter

    Pages 227-246

About this book

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi.

Reviews

"This book is an exceptional contribution to philosophical logic; no one who thinks about truth values should miss it. Taking Truth and Falsehood as objects in Frege's way, the authors serve up a compelling combination of (1) authoritative, encyclopedic, and philosophically sensitive history, (2) a careful and persuasive presentation of their beautiful and super-useful theory of sixteen (not just algebraic but really logical) truth values structured as a trilattice, and (3) a dazzling array of related conceptually motivated formal developments that bring the reader to the forefront of current research." (Prof. Nuel D. Belnap)

"Truth and Falsehood, two values. What could be simpler? We can all count to 2. Professors Shramko and Wansing in this book build on earlier work of themselves and others (including Nuel Belnap’s and my “four valued logic”) to show that 2 truth values is barely enough to get started. They consider 4 and especially 16 element truth values, and do not even stop there. Paraphrasing George Gamow, "Two Four Sixteen Infinity.” This book is thoughtful and bold, philosophical and mathematical, and very well-written." (Prof. J. Michael Dunn)

"Could something be both true and false, and neither true nor false? ‘That way,’ claimed Bob Meyer, ‘lies madness’. But if this be madness, yet there is method in’t, as Shramko and Wansing show, unearthing a rich and beautiful family of logical structures." (Prof. Graham Priest)

Authors and Affiliations

  • Dept. Philosophy, State Pedagogical University, Krivoi Rog, Ukraine

    Yaroslav Shramko

  • Inst. Philosophie, TU Dresden, Dresden, Germany

    Heinrich Wansing

Bibliographic Information

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access