The Liar and Related Paradoxes: Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences

The Liar and Related Paradoxes: Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences

Computation of Fuzzy Truth Values for The Liar and Related Self-Referential Systems

We study the Liar paradox and related systems of self-referential sentences. Specifically, we consider the problem of assigning consistent fuzzy truth values to systems of self-referential sentences. We show that this problem can be reduced to the solution of a system of nonlinear equations and we prove that, under certain conditions, a solution (i.e. a consistent truth value assignment) always...

On the use of fuzzy logic and learning automata optimization to resolve the Liar and related paradoxes

We show that logical paradoxes based on self-reference (of which the Liar is the best known example) are equivalent to the non-existence of solutions to a numerical system of equations, the so-called truth-value equations. Furthermore, we show that in many cases a self-referential system which does not posses a crisp (Boolean) solution can be solved by expanding the solution set to include fuzz...

Yablo’s Paradox and Kindred Infinite Liars

This is a defense and extension of Stephen Yablo’s claim that self-reference is completely inessential to the liar paradox. An infinite sequence of sentences of the form “None of these subsequent sentences are true” generates the same instability in assigning truth values. I argue Yablo’s technique of substituting infinity for self-reference applies to all so-called “self-referential” paradoxes...

Doxastic Paradoxes without Self-Reference

Certain doxastic paradoxes (paradoxes analogous to the Paradox of the Liar but involving ideal belief instead of truth) demonstrate that some formal paradoxes cannot be avoided simply by limiting the expressiveness of one's formal language in order to exclude the very possibility of self-referential thoughts and beliefs. These non-selfreferential paradoxes, moreover, should be of special intere...