Mutually contradictory, but both true!
Here is an example from Mathematics which shows that what appears to be two contradicxtory statements may both be true in their own setting, provided the hypothesis of that setting is granted. Look at the following statement where you are not immediately being told where it is coming from:

(*)
5 plus 3 = 1 = 5 times 3
Obviously this is a wrong statement. This is the conclusion we would arrive at if we were not told anything else. Our reason for taking this to be an untrue statement is the fact that it contradicts what we know ordinarily to be true, namely,
(**)
5 plus 3 = 8 ; 5 times 3 is 15 ; 8 is not equal to 15
This contradiction would be resolved if we know under what hypothesis
we made the statement (*).
It was made under the hypothesis that
every number would be treated as equivalent to
the remainder it produces after a division by 7.
Once this hypothesis is made
we see that
8 is equivalent to 1 and 15 is also equivalent to 1.

Click here
to see that it is not as if this is a bizarre or unsound hypothesis)
So (*) is a true statement under the hypothesis made.
It certainly contradicts the other 'natural' statement (**) ,
but the two 'contrary' statements are both 'true'
in their respective worlds that follow from the hypothesis made for them.
Question: Are you not giving bizarre meanings to the ordinary numbers 5 and 3 to get your statement (*) ? Give them the ordinary meanings; then would you get the contradiction?
 
February 1, 1999
Copyright V. Krishnamurthy
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