Author: John JonesJohn Jones Date: Aug 30, 2008 10:26
The laws of bivalence, excluded middle, and non-contradiction are alike
in that as "laws" they act upon objects.
We can say, in that case, that an application of these laws introduces
objects where objects would otherwise have not been up for consideration.
Let's work with the example "Socrates is mortal". This says no more or
less than that Socrates is mortal. However, if we enforce the unargued
for mandate of the general form of a law which is "laws must be applied"
we immediately introduce other objects which, inavriably, are only
vaguely intimated at.
Thus, applying the law of excluded middle to "Socrates is mortal" , we
have the proposition "Either Socrates is mortal or Socrates is not mortal."
This proposition introduces another object or domain of objects where
Socrates, either as he is in himself, or as he appears in a domain of
veiled objects, is not mortal.
It makes no difference whether we apply an intuitionist logic and
announce that there is an alternative to laws of disjunction. If the law
of excluded middle is not applied, and we apply a law of included middle
instead, we still introduce another object. Note please that while
objects may be regarded as disjunctively related, laws cannot.
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