The reformulated standard has the same error-cost minimizing properties, but achieves them in the real world where the assumption of bivalence
does not hold and where considerable indeterminacy prevails.
We thus avoid the redundancy of the usual formalization of the excluded middle, non-contradiction, identity, bivalence
and reaffirming by double negation.
But Kahneman also offers a second rebuttal to the bivalence
objection--one that, if persuasive, would obviate the first.
It derives from the fact that the probabilist is assuming bivalence
with an excluded middle, so that one is tall or not, while the fuzzy logician is speaking of a world where one can be more or less tall.
The principle of bivalence
may not apply to the objects and events described in a joke, and the sentences may not have truth-values attached to them, but jokes clearly can have pragmatic effects on people and the world.
By abandoning bivalence
, PNL opens the door to a major revision of concepts and techniques for dealing with knowledge representation, concept definition, deduction, and question answering.
One of the rewards of Daniel Dahlstrom's Heidegger's Concept of Truth is its argument that Heidegger can illuminate such issues in the philosophy of logic as the character of propositions, the nature of bivalence
, and the concept of truth.
theory regarding technology is technorealism.
In terms of truth, the mismatch problem recounts the antagonism between bivalence
and multivalence, between the black-or-white and the gray.
The distinction between an intuitive totality (or a naive totality, one might say) and a definite one is that bivalence
with respect to quantifications over the totality in question holds for definite but not intuitive totalities.
The unsettling bivalence
of milk culminates with the extremely subtle transformation of the protective mother into the castrating mother.
Thus, by giving up bivalence
and constructing a sufficiently expressive language, Hintikka and Sandu have provided a tidy resolution to the problem of defining truth.