One reason has to do with the common (natural language) reasoning involving counter-logicals, including, for example, sentences such as 'If intuitionistic logic is correct, then double negation elimination is invalid'.
Kripke [1965] provided a semantics with respect to which intuitionistic logic is correct and complete.
Moreover, logicians who disagree about which sentential logic is correct (e.g., classical or intuitionist) seem to be able to use the same language (containing ∧, →, ¬, etc).
But logical pluralism is also uncharitable in ways that logical monism is not, since it holds that the monist participants in debates over which logic is correct have been arguing based on a confusion.
Even if classical logic actually is the One True Logic, one can reason counterpossibly on what would be the case if a certain non-classical logic were the correct one (e.g., "If intuitionistic logic were correct, then the Law of Excluded Middle would fail" is true and "If intuitionistic logic were correct, then the Law of Explosion would fail" is false).
Michael Feder, Radar Logic: Spencer is correct, but there is evidence, as I've said, that those (factors he mentioned), like most elements of real estate, may depend very much on location.
Thus, if the predicted topology permits the inference of the regulatory logic it is correct in 87% ( = 13/15) of the cases.
These formulae are used as input for a supervisory control synthesis tool chain, resulting in a logic controller that is correct by design.
In a later discussion (van Inwagen 2003), van Inwagen goes farther, claiming that trinitarian doctrine is inconsistent "if the standard logic of identity is correct", and denying there is any "relation that is both universally reflexive [i.e., everything bears the relation to itself] and forces indiscernibility [i.e., things standing in the relation can't differ]" (92).
Thus we can conclude that for implicational logic (and, in fact, for implication-conjunction logic), Prawitz's completeness conjecture is correct, i.e., conjunction-implication logic is complete with respect to validity-based semantics.
The first, less controversial kind, holds that which logic is the correct one is relative to one's goal.
