"Too easy an acceptance seems, frankly, sentimental, an erasure of the particular irreplaceable stuff of individuality with a vague, generalized truth".
Whereas truth negation is interpreted by a unary algebraic operation that inverts a truth order on a set of generalized truth values (see the entry on truth values), falsity negation is interpreted by an operation inverting a falsity order on generalized truth values.
The idea of negation as the inversion of arrangements of truth values, such as truth value polygons, has been developed in Varzi and Warglien 2003, see also Shramko and Wansing 2011 for negation as order-inversion in a logic of generalized truth values.
The values of generalized truth value functions can be called generalized truth values.
By employing the idea of generalized truth value functions, one can obtain a hierarchy of valuation systems starting with a certain set-theoretic representation of the valuation system for classical logic.
Some authors interpret probabilities as generalized truth values (Reichenbach 1949; Leblanc 1983).
Furthermore, there exist well-motivated theories of generalized truth values that lead far beyond Frege's classical values the True and the False.
Other logicians, such as Tarski (1936) and Adams (1998, 15), have noted that probabilities cannot be seen as generalized truth values, because probability functions are not "extensional"; for example, P cannot be expressed as a function of P and P.
If one continues the construction and applies the idea of generalized truth value functions to Belnap's four truth values, then one obtains further valuation systems which can be represented by various multilattices.
The French bishops warned against a "generalized and unjust climate of mistrust," adding, "Our society must live in truth and confidence".
