1. One or both may fail to grasp all the pertinent facts, or even the problem itself, or may assume, as true, facts or principles which are really erroneous. This should easily be ascertainable.
2. One or both may reason incorrectly even from accurate premises. This also should be discoverable.
3. One or both may see facts out of proportion—may lack a true mental balance or perspective.
4. One or both may illustrate the inherent stubbornness or imperviousness of the human mind.
Whether the student can discover the last two sources of error will depend upon his own mental characteristics. He must not forget, however, that on many matters no definite demonstrable conclusion is possible, and that the result must remain more or less a matter of opinion.
(h) REMEMBER THAT A STATEMENT IS NOT A PROOF. MANY STUDENTS THINK THEY PROVE A STATEMENT BY MERELY REPEATING IT IN DIFFERENT WORDS. YOU DO NOT UNDERSTAND A CONCLUSION UNLESS YOU CAN SEE THE STEPS IN ITS LOGICAL DEMONSTRATION.
It is quite surprising how many students commit this error. For instance, if I am asked why can I see through glass and I reply, because it is transparent, I am giving no reason at all, for transparent means what can be seen through, so I am simply saying that I can see through glass because I can see through glass. The same error often occurs in arguments or syllogisms. For instance, suppose I make the following statements:
No unsportsmanlike act should be done;
Smith's act was unsportsmanlike;
Therefore, Smith's act should not have been done.
Now, this of itself is not correct reasoning, for the reason that the word "unsportsmanlike" simply means something which no sportsman should do. The conclusion, therefore, is simply a repetition of the second statement. The real thing to be proved in this case is whether Smith's act was or was not unsportsmanlike.