The concepts of omniscience can be defined as follows (using the notation of modallogic): x is omniscient =defIn words:x is omniscient =def For all propositions p: if p (is true) and p is (logically) knowable,then x knows [/can know] that p (is true)The latter definition is necessary, because there are logically true but logicallyunknowable propositions such as "Nobody knows that this sentence is true":N = "Nobody knows that N is true"If N is true, then nobody knows that N is true; and if N is false, then it is not the case thatnobody knows that N is true, which means that somebody knows that N is true. And ifsomebody knows that N is true, then N is true; therefore, N is true in any case. But if N istrue in any case, then it is logically true and nobody knows it. What is more, the logicallytrue N is not only not known to be true but also impossibly known to be true, for what islogically true is impossibly false. Sentence N is a logical counter-example to theunqualified definition of "omniscience", but it does not undermine the qualified one.ANSWERThis is an incorerct argument..according to laws of contradiction and non con-tradiction if a statement is true then itsnagation is false.If a statement is supposed such that it does imply that the laws of contrdiction and noncontradiction both are in valid then the statement is false and there is no such truestatement such that the truth of its negation does imply the truth of the given statement.now consider the statement:- N1 = "Nobody knows that N is true.................................................In the case N1 = N THERE IS A PROBLEN THAT TRUTH OF NEGATION OF NTHAT IS ~ N IMPLIES TRUTH OF N. THIS IS NOT POSSIBLE RATHER ABSURD.IF ~ IS TRUE THEN P NECESSARILY FALSE AND IF P IS TRUE THEN ~P ISNECESARILY FALSE.THERE IS NO TRUE STATEMENT SUCH THAT TRUTH OF ITS NEGATIONIMPLIES IMPLIES THE TRUTH OF IT.
SO IN THIS CASE N1 =/= "Nobody knows that N is true IS A STATEMENT.N1 = "Nobody knows that N is true , N1=/=NIS A STATEMNT.WHAT IF TRUTH OF ANY STATEMENT SAY P IMPLIES TRUTH OF ITSNEGATION OR TRUTH OF ITS NEGATION IMPLIES THE TRUTH OF THESTATEMENT.IN GENERAL IF P----> Q AND P IS TRUE AND Q IS FALSE THEN P---->Q ISFALSE. IF P IS FALSE AND Q IS TRUE THEN P---->Q IS TRUE.. IF BOTH P AND Q ARE TRUE THEN P--->Q IS TRUE AND IF BOTH ARE FALSETHEN P----------->Q IS TRUE.BUT WE KNOW THAT P=/=~Q.WHAT IF P=~QTHEN ~P---->P OR P----->~PIN THIS CASE WE CAN NOT ASSUME THE CASES BOTH P AND Q ARE TRUEAND BOTH AND Q ARE FALSE.SO IF ~P IS TRUE THEN P IS FALSE. THEN IF ~P--->P THEN ~P---->P IS FALSE.IF ~P FALSE AND P IS TRUE THEN ~P---->P IS TRUE.BUT IF IT IS SUPPOSED THAT TRUTH OF ~P IMPLIES TRUTH OF P THENTHERE IS SO SUCH STATEMENT AND IF THIS IS A TYE OF STATEMENT THENSOME NEW LAWS MAY BE MADE FOR THEM.IF ~P IMPLIES P THAT IS TRUTH OF ~P IMPLIES TRUTH OF P OR TRUTH OF PIMPLIES TRUTH OF ~P THEN BOTH P AND ~P ARE FALSE.THERE FORE THESE SENTENCES HAVE NO TRUTH VALUES AND THEY MAYBE TERMED AS STATEMENT-OIDS INSTEAD OF SENTENCES.A SENTENCE MAY BE CALLED AN STATEMENT IF IT SATISFIES THEFOLLOIWING AXIOMS.1] THE TRUTH OF NEGATION OF IT DOES NOT IMPLY THE TRUTH OF THESTATEMENT.2] THE TRUTH OF THE STATEMENT DOES NOT IMPLY THE TRUTH OF ITSNEGATION.3] IF THE STATEMENT IS TRUE THEN ITS NEGATION IS FALSE.4] IF THE NEGATION OF THE STATEMENT IS TRUE THEN THE STATEMENTIS FALSE.
THERE FORE N IS NOT A LOGICAL TRUTH SINCE IT VIOLATES THE LAWS OF NON-CONTRADICTION AND CONTRDICTION. WHAT IS A LOGICAL TRUTH ANDW HAT IS A TOTAULOGY IS A PROBLEM AND A NUMBER OF DIFFERENT DEFINATIONS MAY BE SUPPOSED. IN GENERAL A TOTAULOGY IS A LOGICAL TRUTH BUT NOT ALL LOGICAL TRUTHS ARE TOTAULOGIES . BUT THE GIVEN STATEMENT IS NOT A OGICAL TRUTH SINCE TRUTH OF ITS NEGATION DOES IMPLY THE TRUTH OF ITS AFFIRMATION AND THE CONDITION 2 IS VIOLATED. IF N1= (ﬠN) IS A STATEMENT SUCH THAT IT DOES IMPLY ~N1---à N1 THEN IT IS NOT A LOGICAL TRUTH AND HENCE NOT A TOTAULOGY. IN OTHER WORDS LET ~N1 =(ﬠX) [SUPPOSITION] ~N1 --àN ASBURD/ CONTRDICTION. THEN N1=/=(ﬠX) ONE MAY USE LOGIC OF EXCEPTION TO SHEW THE FAALCY IN THE ARGUMENT. THAT IS ‘‘ N1 = "Nobody knows that N is true EXCEPT G-D’’ AN OTHER EXAMPLE CONSIDER THE NON ATOMIC STATEMENT PΛ~P IT HAS NO TRUTH VALUE. BUT IF ~P--àP THEN IT HAS A TRUTH VALUE. THIS VIOLATES THAT TRUTH OF NEGATION OF P DOES NOT IMPLY P. A FUNDAMENTAL RULE.. Unfortunately, there are further logical examples that seem to undermine even this restricted definition, such as the following one (called "The Strengthened Divine Liar"): B = "God does not believe that B is true" If B is true, then God (or any other person) does not believe that B is true and thus doesnt
know that B is true. Therefore, if B is true, then there is a truth (viz. "B is true") whichGod doesnt know. And if B is not true (= false), then God falsely believes that B is true.But to believe the falsity that B is true is to believe the truth that B is not true. Therefore,if B is not true, then there is a truth (viz. "B is not true") which God doesnt know. So, inany case there is a truth that God does not and cannot know, for knowledge implies truebelief.While sentence N is a non-knower-relative unknowability, B is a knower-relativeunknowability, which means that our concept of omniscience apparently needs to beredefined again:RESPONSE:-THE BELEAVING IS A PROPERTY OF A HUMAN BEING AND NOT OF GOD. ITIS OMNISCIENCE THAT IS THE PROPERTY OF G-D. BUT THE STATED ABOVEARGUMRENT MAY BE USED TO REFUTHE THIS ARGUMENT AGAINSTOMNISCIENCE OF G-D AS WELL.IT IS NOT THAT THE CONCEPT OF OMNISCIENCE IS TO BE REDEFINED BUTIT DOES MEAN THAT THE CONCEPT OF A STATEMENT MUST NOT VIOLATETHE LAWS OF CONTRADICTION AND NON CONTRADICTION.LAW OF CONTRADICTION= IT IS ABSURD /IMPOSSIBLE A STATEMENT ANDITS NEGATION BOTH ARE TRUE .LAW OF NON CONTRADICTION:- IF ONE OF THE TWO CONTRADICTORIES ISTRUE THEN THE OTHER ONE IS FALSE4."MORE RESURCH SHALL BE GIVEN LATTER. INSHAA ALLAH