Hence a Paradox

As we debate one another over various things, we engage in arguments in order to prove our position to be true, or to prove the position of our opponent to be false. Within this realm of discussion, discourse and dialogue we find what are called syllogisms. Syllogisms are defined by Princeton this way: "deductive reasoning in which a conclusion is derived from two premises." Although a syllogism may be formally valid and the two premises may not contradict one another, the conclusion of a formally valid syllogism may still be false because one or both of the premises is untrue. For instance:

God has created everything that exists; Christ exists, therefore God created Christ.

I believe we can all see how the syllogism "makes formal sense" if both the premises are assumed to be true, but the conclusion is false because the first premise is false; the first premise is this, God has created everything that exists, the second premise is, Christ exists. While the second premise is true, that Christ does exist, the first premise is false, God did not create everything that exists...God exists and He did not create Himself!

Another concept we encounter as we engage others in matters of debate is that of contradictions and paradox. These two concepts are easily confused; sometimes persons think an idea or two premises are contradictory when they are actually only a paradox.

First, let's examine the two terms:

1. Contradiction - This literaly is a combination of two words, contra (which means against), and diction (which comes from the Latin word - dictio - which means words, speech, or to speak), so the word contradiction means - to speak against. The law of non contradiction states that "A" cannot be "A" and non "A" at the same time and in the same relationship. Aristotle put it this way, "one cannot say of something that it is and that it is not in the same respect and at the same time".

2. Paradox - On the other hand, a paradox (a compound word combining the idea of coming beside and speaking well of) is the combination of two or more premises which appear to be contradictory on the surface, but with further clarification (perhaps with the introduction of another premise) investigation may result in the combination's exoneration of the charge of contradiction. For further definition, this word comes from the Greek word, paradoxos which means seemingly absurd or, contrary to expectation. Below, I will use the example of a particular car and its characteristics to demonstrate the difference between a contradiction and a paradox.

And now, imagine a car, half of which is red, half of which is blue.

Premises Developed About The Car

True premises:

1. The car is blue


2. The car is red.


3. The car is blue and red.

False premises:

1. The car is not blue.


2. The car is not red.


3. The car is not blue & red.

If this was my car and it was not in view, but I attempted to describe it to you, I could state any of the 3 true premises as fact. It would be a statement of truth if I told you that my car was red. It would also be a statement of truth if I told you that my car was blue. It would also be a true statement if I told you that, my car was red; my car was blue, hence the paradox: the car is red, and the car is blue, at the same time; both statements are true and do not contradict one another because the car is painted half red and half blue. A contradiction would occur if I told you that my car was red; my car was not red, at the same time and in the same relationship.