Every sentence (or rather, proposition) is both true and false, since "false" is defined here to mean having a true negation (and all negations are established as being true.) So for P to be both true and false would be for both P and ~P to be true, or, deflatively, for it to obtain that P and ~P.
If (alternatively) neither P nor ~P - as might sometimes be the case according to intuitionists - we would say that P is neither true nor false.
Every sentence (or rather, proposition) is both true and false, since "false" is defined here to mean having a true negation (and all negations are established as being true.)
If false is defined as the property of having a true negation, than under trivialism there's no real semantic distinction between true and false, since there's no property that can distinguish between the set of true and false propositions. This is of course to be expected, but I was curious if trivialism could be interpreted as a system that poses significant distinction...
Straight from Wikipedia.
I just had to stare at this a while. We can have papers published about this, we really ought to be able to get papers published about Friendly AI subproblems.
My favorite part is at the very end.
Trivialism is the theory that every proposition is true. A consequence of trivialism is that all statements, including all contradictions of the form "p and not p" (that something both 'is' and 'isn't' at the same time), are true.[1]
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