Re: The logic of atheism

Paul Holbach <paulholbachDELETETHENAME@xxxxxxxxxx> wrote:
Paul Holbach wrote:
Paul Holbach wrote:

The following definition of "omniscience" appears consistently
defensible:

x is omniscient =def Ap((p & <>Kp) -> Kxp)

x is omniscient
=def
For all propositions p: if p and p is (logically) knowable, then x knows that p

Remark:
This definition also covers possible cases in which "p" is neither true
nor false or both true and false:

Of course, classical logicians, who adhere to the law of excluded
middle, consider such cases impossible.

Actually, that's not the law of excluded middle. From

http://en.wikipedia.org/wiki/Principle_of_bivalence

"In logic, the principle of bivalence states that for any proposition P,
either P is true or P is false.

This is not to be confused with the law of excluded middle and the law of
noncontradiction. See bivalence and related laws for a summary of the
differences.

In classical logic, the principle of bivalence is equivalent to the result
that there are no propositions that are neither true nor false. A
proposition P that is neither true nor false is undecidable. In
intuitionistic logic, sometimes the truth-value of a proposition P cannot be
determined (i.e. P cannot be proved nor disproved). In such a case, P simply
does not have a truth-value. Other logics, e.g. multi-valued logic, may
assign P an indeterminate truth-value."

--
Mike

-------------------------------
"Our enemies are innovative and resourceful, and so are we. They never stop
thinking about new ways to harm our country and our people, and neither do
we," George W. "Shrub" Bush Aug 5, 2004
.

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