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The concepts of omniscience can be defined as follows (using the notation of modal logic):
x is omniscient =def
words:
niscient =def For all propositions p: if p (is true) and p is (logically) knowable, then x knows [/can know] that ue)
definition is necessary, because there are logically true but logically unknowable propositions such as nows that this sentence is true":
knows that N is true"
obody knows that N is true; and if N is false, then it is not the case that nobody knows that N is true, which ody knows that N is true. And if somebody knows that N is true, then N is true; therefore, N is true in any ue in any case, then it is logically true and nobody knows it. What is more, the logically true N is not only ue but also impossibly known to be true, for what is logically true is impossibly false. Sentence N is a logical o the unqualified definition of "omniscience", but it does not undermine the qualified one.
t argument..
of contradiction and non con-tradiction if a statement is true then its nagation is false.
upposed such that it does imply that the laws of contrdiction and non contradiction both are in valid then the and there is no such true statement such that the truth of its negation does imply the truth of the given nsider the statement:N1 = "Nobody knows that N is true .................................................
N THERE IS A PROBLEN THAT TRUTH OF NEGATION OF N THAT IS ~ N IMPLIES TRUTH OF N. SSIBLE RATHER ABSURD. IF ~ IS TRUE THEN P NECESSARILY FALSE AND IF P IS TRUE THEN LY FALSE.
RUE STATEMENT SUCH THAT TRUTH OF ITS NEGATION IMPLIES IMPLIES THE TRUTH OF IT.
E
N1 =/= "Nobody knows that N is true IS A STATEMENT.
nows that N is true , N1=/=N
H OF ANY STATEMENT SAY P IMPLIES TRUTH OF ITS NEGATION OR TRUTH OF ITS NEGATION RUTH OF THE STATEMENT.
P----> Q AND P IS TRUE AND Q IS FALSE THEN P---->Q IS FALSE. IF P IS FALSE AND Q IS TRUE TRUE. Q ARE TRUE THEN P--->Q IS TRUE AND IF BOTH ARE FALSE THEN P----------->Q IS TRUE.
THAT P=/=~Q.