Discussion 3 to Meditation 605
With logic based on contradiction, you can prove nothing.
by: Gordon Barker
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I disagree with your statement that with logic based on contradiction, you can prove anything. In reality, you can prove nothing.
In formal logic, the contradiction that interpreting the bible literally brings is A & !A.
Now if we state some absolute truth as a contradiction like John is a wise fool. (probably true at least some of the time)
Further, if we assume that God is not a penguin (also probably true unless the universe is distinctly different than the one I am familiar with)
If John is wise then it is certain that God is not a penguin, also if God is a penguin then John is wise (this is the contradiction)
But since John is a fool (our first statement), then God is a Penguin.
Actually, we haven’t proven anything because our initial absolute truth (John is a wise fool) is neither true nor false. It is the premise (axiom) from which the argument proceeds. It is an inconsistent axiom. It can be argued that the statement John is a wise fool is true sometimes and somewhat true all the time. Similarly the statement is false sometimes and somewhat false all the time. This is similar to the arguments that Socrates used on Thrasymachus in Plato’s Republic (see http://www.sacredtexts.com/cla/plato/rep/rep0108.htm for an example of this).
Once you insert a contradiction into your thought process, all results you obtain from that point further are also contradictions and faulty. A contradiction contaminates anything it touches The law of exclusion is directly violated by the presumed condition, and the entire result is null.
To put this in terms that computer people understand, we can look at an old example of contradiction in algebra
Suppose we have two variables x and y that are equal:
X = Y 

XY = Y^{2
} 
(multiply both sides by Y) 
XY = Y^{2
} 
(multiply both sides by 1) 
X^{2} – XY = X^{2} – Y^{2
} 
(Eqn 2 + Eqn 3) 
X(XY) = (X+Y)(XY) 
(factor both sides) 
X = (X+Y) 
(remove common factor) 
X = 2X 
(substitute from Eqn 1) 
1 = 2 
!!! 
The contradiction here is where (XY) is cancelled on both sides. In reality, since X=Y, you are dividing by 0. At that point the logic is contaminated and the result is null.