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doubt. For example, if only one of the two women is pregnant.' the probability of cach being pregnant is 50%; however the assertion that each of them is 50% pregnant is meaningless
The Aristotelian binary logic of 'true' or 'false' (is or is not) has set foundations of Boolean Algebra, which forms the conceptual basis for all computer operations based on the binary states, 0 and 1, as intrinsic in the set theory. For a set of A and B, it can be said ‘not A is B' or 'not B is A.' This is because the universe of the A+B set is a closed universe:
i.e. if we know which one of the two women is pregnant, by implication we also know which one is not.
The usefulness of a syllogism comes from the implication. More situations develop under conditions where all the elements of a set are not defined, or their relationship is governed by nonsymmetry of implication. For example, if P implies Q, it does not necessarily mean implies P. Consider the verb 'implies' which is also used as a logical connective. For example, in the inference schema, if smoke always implicd fire, and if fire always implied smoke, it will be closed argument where fire is equivalent to smoke, and therefore there is no need for inference.. It will be self evident and redundant statement (tautology). On the other hand, consider the statement from a person who says "what I say is not true." Is it really true or false? This question has baffled Western logicians ever since Aristotle. But according to syād principle, it is obviously a contradictory statement and therefore not worth a discourse.
Genesis of doubt in an implication can best be appreciated by the following statement:
A or B implies C. If we know either A or B, we know C.
However, by knowing that C is true, one does not necessarily know A or B except for the fact that at least one of the two is true. If both A and C are true, B can be true or false resulting in the outcome of the doubtful inference. If true and false states are presented in notation, they may be symbolized in the following form:
True and false represent (1, 0) and (0, 1) respectively. Doubt and Contradiction represent (1, 1) and (0,0) respectively.
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