Quod Erat Demonstrandum

[Note: This is a short piece I wrote a few years ago on the subject of proofs, as logic has long been an area of interest for me.]


These three words in Latin, which literally mean “that which was to be demonstrated,” often appear at the end of mathematical proofs. Those of us who at least pretend to be logical seek closure at the end of a discussion or an argument with these three words. However, often (and I speak from much personal experience here) our discussions with others end with neither side satisfied with the proof the other party has presented. What is the cause and what is the solution to such impasses? There are two categories of such disputes, and determining which one demands acute discernment.


Well did Jeremiah say in Jeremiah 17:9 on the limitless capacity for wickedness and deception in the human heart. There are many people, of all types, who cannot admit that they are wrong. Without just scriptural proof, they will hold on to their opinions through dishonest means, seeking to quibble constantly over word usage. Most commonly, these sort of people will seek to argue that a clear biblical directive no longer applies because events have taken place subsequently (for which no scriptural proof exists) that have nullified the original clear directive. Examples of this are almost as common as there are people, far too difficult to mention here in this limited space. Peter speaks of them in 2 Peter 3:16 when he refers to the many who have twisted Paul’s scriptures on sin and grace to their own destruction.

When faced with such self-righteous mockers, the best advice is that given by Solomon in Proverbs 26:4-5, “Do not answer a fool according to his folly, lest you also be like him. Answer a fool according to his own folly, lest he be wise in his own eyes.” In the heat of an argument it is easy for both sides to lose sight of what is true and reasonable. Even if one is right, one may present the truth to someone whose mind is not open to the truth, and all of the logic and truth will be wasted as pearls on swine, though it must sometimes be necessary anyway to correct a scorner, for the benefit of others if not for the unrepentant scorner himself.

Legitimate Confusion

There is however, another circumstance that happens more often than we may think. Often the supporting scriptures we use for a doctrine may be unclear in a given context, and thus the conclusion is in doubt. Isaiah 28:10 gives a valid, if time-consuming way, to solve some problems. Even with the study of the clear scriptures that frame the unclear ones, there may be multiple valid interpretations. Our approach to these disputes, where someone genuinely seeks to understand the scriptures but disagrees with our conclusions based on them, is vitally important in avoiding causing offense.
Hermeneutics is a large word used by theologians to define the rules of interpretation for scripture. Whether we are theologians or not, in our own scriptural defenses of our beliefs, we use such rules whether we realize it or not. One such rule is that scripture cannot be made to contradict scripture. Where an apparent contradiction exists, the true interpretation harmonizes whatever disagreement is on the surface. Another such rule is the one I mentioned above that clear scriptures explain unclear scriptures. Yet another rule is that the meaning of a given statement cannot be determined in isolation, but depends on the context. However, and this is important, God’s law is independent of cultural context. These rules of interpretation are a valuable part of our arsenal in scriptural discussions
There are cases, though, in which a scripture has multiple legitimate meanings and the various rules of interpretation allow for multiple meanings. In that case, we cannot be dogmatic that such a scripture can only have one meaning. Where the scripture is not clear, where the context is not clear, where there are few if any supporting scriptures, we cannot be rigid on the interpretation. On the other hand, if a given scripture is clear in its context, we must not hesitate the slightest in that firmness. It takes time, patience, and wisdom to rightfully divide the word of truth. We should be watch ourselves and make sure that we are not too quick to condemn. What is obvious to us may not be obvious to others, especially if they have ulterior motives.


In the end, there may be no agreement possible on a definitive answer. It is rare, after all (given the infinite capacity of the human to deceive itself), to convince other people using logic when they are not open to the true meaning of the scriptures. Sometimes it may not be known what that true meaning is, and an admission of uncertainty may be all that is necessary to amicably end the argument. Some answers we cannot know until the return of Christ. We should not let that stop us from being good brothers to those who have an honest disagreement on an unclear matter. Not all disagreement is heresy or rebelliousness. We may be satisfied with our proof of a given doctrine or position, but others may not. Some of the time this is due to willful stubbornness, sometimes due to honest disagreement. Determining between the two takes great discernment and a humble heart.


About nathanalbright

I'm a person with diverse interests who loves to read. If you want to know something about me, just ask.
This entry was posted in Christianity, Musings and tagged , , , . Bookmark the permalink.

3 Responses to Quod Erat Demonstrandum

  1. Pingback: Apologia Pro Vita Sua | Edge Induced Cohesion

  2. Pingback: The Mind Is Not A Machine | Edge Induced Cohesion

  3. Pingback: Burden Of Proof | Edge Induced Cohesion

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