[FOM] Bivalence and Law of Excluded Middle

hdeutsch@ilstu.edu hdeutsch at ilstu.edu
Wed Feb 20 09:26:46 EST 2008

Hello,  the first-degree entailment fragment (only entailments between  
truth functions) of the relevant logic that used to be known as  
"R-Mingle,"  A v -A is a zero degree theorem, but the system as a  
whole is not bivalent in that it has a four-valued characteristic  
matrix.  There must be many examples like this. hd

Quoting Joseph Vidal-Rosset <joseph.vidal-rosset at univ-nancy2.fr>:

> Hello,
> In 1989 Sayward wrote:
>> Call a statement truth definite if it or its negation is true.
>> Call a language bivalent if every statement
>> formulable in the language is truth definite. The law of
>> excluded middle holds for every bivalent language. Nobody has
>> questioned this. But does the law of excluded middle hold only for
>> bivalent languags ? Here there is controversy
>> with proponents and opponents.
> 31: 129-137, 1989)
> He argues in this paper against the view that a language à la van
> Fraassen (with super-evaluations) is able to accept the LEM without
> accepting the Bivalence.
> I would be happy to hear the opinions and the arguments of FOM
> subscribers about the question that Sayward asked in the title of this
> paper. Does the LEM require Bivalence?
> Joseph Vidal-Rosset
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