Situations and the Liar Paradoxes

Gene networks and liar paradoxes

Network motifs are small patterns of connections, found over-represented in gene regulatory networks. An example is the negative feedback loop (e.g. factor A represses itself). This opposes its own state so that when 'on' it tends towards 'off' - and vice versa. Here, we argue that such self-opposition, if considered dimensionlessly, is analogous to the liar paradox: 'This statement is false'. ...

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

We study self-referential sentences of the type related to the Liar paradox. In particular, we consider the problem of assigning consistent fuzzy truth values to collections of self-referential sentences. We show that the problem can be reduced to the solution of a system of nonlinear equations. Furthermore, we prove that, under mild conditions, such a system always has a solution (i.e. a consi...

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...

The Liar in Context

About twenty-five years ago, Charles Parsons published a paper that began by asking why we still discuss the Liar Paradox. Today, the question seems all the more apt. In the ensuing years we have seen not only Parsons’ work (1974), but seminal work of Saul Kripke (1975), and a huge number of other important papers. Too many to list. Surely, one of them must have solved it! In a way, most of the...