The Liar's Non-Paradox: Why Liar Sentences Present No Problems for the Concept of Truth

By John S. Pletz

The Liar's Non-Paradox explains why the Liar's Paradox is not a paradox of all because the Liar sentence does not have truth potential and cannot be confirmed. Its superficially convincing contradiction ("If 'This sentence is false' is true, then it is false, but if it is false, then it is true") depends completely upon hypothetical premises which cannot support the conclusion that our ordinary concept of truth is deficient because it does not extend to all assertions. The author sets out in detail why that position is invalid and why the proper conclusion is that the Liar sentence is neither true nor false. He then goes on to explain why the back-up arguments of Liar proponents, such as the Strengthened Liar and the Revenge Liar, do not salvage their contentions about the existence of serious problems for the concept of truth due to a Liar. Because the Liar's Paradox does not present a meaningful contradiction, it creates no paradox. Therefore, the numerous efforts which have been made to curtail or mitigate the supposed problems stemming from this faux paradox have been unnecessary.

• Language: English
• Publisher: John S. Pletz
• Release date: Jul 23, 2015
• ISBN: 9781310699238

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The Liar’s Non-Paradox:

Why Liar Sentences Present No Problems for the Concept of Truth

John S. Pletz

Second Edition

Copyright 2016 John S. Pletz

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Table of Contents

Introduction

1. The Lack of Truth Potential in the Liar’s Paradox

2. The Unconfirmability of the Liar’s Sentence

3. Failed Attempts to Salvage a Paradox

A. The Strengthened Liar

B. The Revenge Liar

C. Other Liar Variants

Conclusion

About the Author

Introduction

The Liar’s Paradox (This sentence is false) is said to necessarily lead to a contradiction: If it is true, then it is false, but if it is false, then it is true. Negative conclusions are then drawn about the concept of truth from this supposed contradiction–that truth is not a potential characteristic of all assertions and that its definition and application must therefore be relative or otherwise tenuous.

Those conclusions are so unwelcome that they have generated a number of different types of efforts to avoid or curtail them. Alfred Tarski believed that the Liar’s Paradox revealed a defect in the common definitions of truth, and he thought that it was necessary to resort to metalanguages in order to achieve an understanding of truth. His solution, however, not only is quite confusing to most people but also concedes an inadequacy in our grasp of truth which is unnecessary if the Liar’s Paradox does not present a problematic contradiction or paradox. Others have focused on the fact that the Liar’s Paradox is a self-referential sentence and suggested that whenever we discuss these issues, we could avoid those unpleasant consequences by relegating all self-referential sentences to an isolated box where they would be excluded from discussions about truth, so that they would not infect the truth that is wanted and needed in ordinary life. Of course, that approach creates one limitation on the extension of truth in order to try to avoid another one, thus making the cure as bad as the disease.

No such efforts to minimize damage to truth from the Liar’s Paradox need to be made, however, if the Liar’s Paradox is in error. I believe that to be the case and that the solution to the problem posed for the nature of truth by the supposed paradox lies in the recognition of its fallacious reasoning. The Liar’s Paradox produces neither a problematic contradiction nor a real paradox because: (1) the sentence lacks truth potential, and (2) it would be unconfirmable even if it had truth potential.

1. The Lack of Truth Potential in the Liar’s Paradox

Turning first to its lack of truth potential, the Liar’s Paradox only appears to make sense in referring to itself, but in reality it does not effectively do that because of the nature and requirements of its particular predicate. We use the two words, is false, to assert that some disagreement exists between an idea or a representation that has been made and the underlying reality that the idea or representation describes. The nature of truth is such that when the concept about the correctness of a sentence (in either its positive or negative form) is used in a predicate, it can be meaningfully applied only to a complete assertion which alleges that some fact exists.¹ Only then can a predicate about the truth value of a sentence be meaningful, thereby contending that the assertion under consideration is in agreement or in disagreement with the asserted fact. That is the sole way in which we can arrive, for example, at A sentence is true if and only if what it says is so (Aristotle),² or For a statement to be true is for things to be as they are stated to be (Mackie),³ or Meaning matching fact is truth (Quine).⁴ Similarly, to say that something is false because the fact to which it refers is not (Moore)⁵ or because of the disagreement between our ideas and reality (James),⁶ we need some statement that is asserted about a fact or reality that