### not either, not both, and not even between.

Let ‘T’ abbreviate ‘true’;
consider:

(1) (

*x*)(T*x*v ~T*x*)
(1) says that everything is either true or not true. I say
(1) is false for an infinite number or reasons.
Here are five: it’s not true that my cat is either true or not true.
It’s not true that my nostril is either true or not true. It’s not true that a
banana is true or not true. It’s not
true that

*this italicized sentence is either true or not true*. If you’re not convinced that (1) is not true, I suggest that you consider each and every natural number*n*, and you’ll see that it’s not true that*n*is either true or not true.
But here’s
my problem. If I deny (1) by affirming

(2) ~(

*x*)(T*x*v ~T*x*)
I thereby affirm

(3) (∃

*x*)(~T*x*• T*x*)
for (2) and (3) are logically equivalent if quantifier
negation and De Morgan’s law are valid, which they are. So here’s my dilemma:
affirm (1) or affirm a contradiction. Because (1) itself will eventually lead
to a contradiction, my choice is really between affirming a contradiction now
or affirming one later. I choose never. So I say that though (1) and (2) appear
to be more than a string of symbols, they are not.

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