# There is No Paradox of Logical Validity

@article{Cook2014ThereIN, title={There is No Paradox of Logical Validity}, author={Roy T. Cook}, journal={Logica Universalis}, year={2014}, volume={8}, pages={447-467} }

A number of authors (including Field in Saving Truth From Paradox. Oxford University Press, Oxford, 2008; Shapiro in Philos Q 61:320–342, 2010; Whittle in Analysis 64:318–326, 2004; Beall and Murzi in J Philos 110:143–165, 2013) have argued that Peano Arithmetic (PA) supplemented with a logical validity predicate is inconsistent in much the same manner as is PA supplemented with an unrestricted truth predicate. In this paper I show that, on the contrary, there is no genuine paradox of logical… Expand

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The inexpressibility of validity

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Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth;… Expand

Naïve validity

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- 2017

Beall and Murzi (J Philos 110(3):143–165, 2013) introduce an object-linguistic predicate for naïve validity, governed by intuitive principles that are inconsistent with the classical structural rules… Expand

Paradox and Logical Revision. A Short Introduction

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Logical orthodoxy has it that classical ﬁrst-order logic,orsome extension thereof, provides the right extension of thelogical consequence relation. However, together with nai¨vebut intuitive… Expand

Principles for Object-Linguistic Consequence: from Logical to Irreflexive

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- J. Philos. Log.
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Grounded validity will be shown to satisfy several desirable principles for a naïve, self-applicable notion of consequence, and is obtained by generalizing Saul Kripke’s inductive theory of truth (strong Kleene version). Expand

Validity and Truth-Preservation

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The revisionary approach to semantic paradox is commonly thought to have a somewhat uncomfortable corollary, viz. that, on pain of triviality, we cannot affirm that all valid arguments preserve truth… Expand

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It is shown that applying the distinction between-vacuous grounds allows us to give a principled solution to Kit Fine and Stephen Kramer’s paradox of (reflexive) ground, and it is argued that grounding is reflexive, contra the intuitive character of grounds. Expand

The Substitutional Analysis of Logical Consequence

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A substitutional account of logical validity for formal rst-order languages is developed and defended against competing accounts such as the model-theoretic denition of validity. Roughly, a… Expand

Towards a Non-classical Meta-theory for Substructural Approaches to Paradox

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A novel type of hybrid proof-procedure is developed, one that takes invalidities to be just as fundamental as validities, and the prospects of applying it to languages capable of expressing self-referential statements are analyzed. Expand

Faithfulness for naive validity

- Philosophy, Computer Science
- Synthese
- 2018

The paper argues, first, that the detachment principle for naive validity should be rejected, and secondly, it shows how to add a validity predicate to ST while avoiding the dilemma. Expand

Naive Modus Ponens and Failure of Transitivity

- Mathematics, Computer Science
- J. Philos. Log.
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It is argued that the meta-inference in question is independent from the logical idea of modus ponens, and that the semantic idea of the conditional as formulated by Zardini is inadequate for his purposes because it is spelled out in a vocabulary not suitable for evaluating the adequacy of the unconditional in semantics for non-transitive entailment. Expand

#### References

SHOWING 1-10 OF 19 REFERENCES

Two Flavors of Curry’s Paradox

- Philosophy
- 2013

Abstract. I believe that, for reasons elaborated elsewhere (Beall, 2009; Priest, 2006a, 2006b),
the logic LP (Asenjo, 1966; Asenjo & Tamburino, 1975; Priest, 1979) is roughly right as far as
logic… Expand

Which Modal Logic Is the Right One?

- Mathematics, Computer Science
- Notre Dame J. Formal Log.
- 1999

The question, “Which modal logic is the right one for logical necessity?,” divides into two questions, one about model-theoretic validity, the other about proof- theoretic demonstrability, and certain common objections are argued to be fallacious. Expand

Saving Truth From Paradox

- Mathematics
- 2008

Preface Introduction PART ONE: A SELECTIVE BACKGROUND 1. Chapter 1: Self-Reference and Tarski>'s Theorem 2. Validity and the Unprovability of Soundness 3. Kripke>'s Theory of Truth (Strong Kleene… Expand

Paraconsistency and dialetheism

- Computer Science, Philosophy
- The Many Valued and Nonmonotonic Turn in Logic
- 2007

This chapter discusses paraconsistent logic, in which contradictions do not entail everything. However, the roots of paraconsistency lie deep in the history of logic, its modern developments date to… Expand

Deflating Logical Consequence

- Philosophy
- 2011

Deflationists about truth seek to undermine debates about the nature of truth by arguing that the truth predicate is merely a device that allows us to express a certain kind of generality. I argue… Expand

Dialetheism, logical consequence and hierarchy

- Philosophy
- 2004

I argue that dialetheists have a problem with the concept of logical consequence. The upshot of this problem is that dialetheists must appeal to a hierarchy of concepts of logical consequence. Since… Expand

Computability and logic

- Mathematics, Computer Science
- 1974

This book discusses Computability Theory, Modal logic and provability, and its applications to first-order logic, which aims to clarify and clarify the role of language in the development of computability. Expand

PLURALISM IN LOGIC

- Computer Science, Mathematics
- The Review of Symbolic Logic
- 2009

A new form of logical pluralism is suggested which might be both interesting and true; however, the scope of the pluralism that it allows logic is extremely narrow. Expand

The Concept of Logical Consequence

- Mathematics, Philosophy
- 1986

Introduction 1. Representational semantics 2. Tarski on logical truth 3. Interpretational semantics 4. Interpreting quantifiers 5. Modality and consequence 6. The reduction principle 7. Substantive… Expand

The logic of the provability

- Mathematics, Computer Science
- 1998

This chapter is dedicated to the memory of George Boolos, the prime inspirer of the work in the logic of provability, from the start of the subject until his death on 27 May 1996. Expand