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C00002 00002	true[w83,jmc]		Useful sentences involving the predicate true
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true[w83,jmc]		Useful sentences involving the predicate true

Does anything require true rather than merely believable?

	1. says(John,p) ⊃ true(p)

	2. says(John,p) ∧ ¬true(p) ⊃ liar(John)

	3. says(John,p) ∧ true(not p) ⊃ liar(John)

	4. ¬true(p and q) ⊃ ¬true(p) ∨ ¬true(q)

	It looks like  true  is particularly useful when we want to
use the law of the excluded middle.  Can we say that  true  satisfies
the law of the excluded middle and none of its weakenings do so?

	5. ∀p.true(p) ∨ true(not p)
is the law of the excluded middle.  When we weaken our truth axioms
in order to avoid inconsistency, we may end up weakening the law of
the excluded middle, we then may have something like

	6. ∀p. not-too-strong(p) ⊃ true(p) ∨ true(not p),

where we would like the predicate  not-too-strong  to encompass as many
sentences as possible.