55,174 research outputs found
The truth functional hypothesis does not imply the liars paradox
The truth-functional hypothesis states that indicative conditional sentences and the material implication have the same truth conditions. Haze (2011) has rejected this hypothesis. He claims that a self-referential conditional, coupled with a plausible assumption about its truth-values and the assumption that the truth-functional hypothesis is true, lead to a liar’s paradox. Given that neither the self-referential conditional nor the assumption about its truth-values are problematic, the culprit of the paradox must be the truth-functional hypothesis. Therefore, we should reject it. In this paper I argue that, contrary to what Haze thinks, the truth-functional hypothesis is not to blame. In fact, no liar’s paradox emerges when the truth-functional hypothesis is true; it emerges only if it is false
The spectrum of a vertex model and related spin one chain sitting in a genus five curve
We derive the transfer matrix eigenvalues of a three-state vertex model whose
weights are based on a -matrix not of difference form with spectral
parameters lying on a genus five curve. We have shown that the basic building
blocks for both the transfer matrix eigenvalues and Bethe equations can be
expressed in terms of meromorphic functions on an elliptic curve. We discuss
the properties of an underlying spin one chain originated from a particular
choice of the -matrix second spectral parameter. We present
numerical and analytical evidences that the respective low-energy excitations
can be gapped or massless depending on the strength of the interaction
coupling. In the massive phase we provide analytical and numerical evidences in
favor of an exact expression for the lowest energy gap. We point out that the
critical point separating these two distinct physical regimes coincides with
the one in which the weights geometry degenerate into union of genus one
curves.Comment: 22 pages, 12 figure
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