The formal concept of the fallacious argument was born as the twin of logic itself. When the ancient Greeks first began to systematically examine the natural arguments people made as they sought to demonstrate the truth of propositions, they noted that certain types of arguments were vulnerable to counterexamples while others were not. The vulnerable were not true - when it was claimed that they justified a conclusion they could not rule out the alternative - and so were identified as fallacious.
Although the validity of logical arguments can be determined through logic, that doesn't particularly distinguish one fallacy from another. It is a curious fact that, despite this, some fallacies are more frequently made by human beings than others. Much more.
For example, "If P, then Q. P. Therefore, Not-Q." is just as basic and elemental an error as "If P, then Q. Q. Therefore, P." is. But the first fallacy is hardly ever found (humans being what they are, there's probably no mistake within our reach that is never made) while the second is extraordinarily common.
It is in fact generally true that we often confuse a unidirectional implication with the bidirectional. If something implies another thing, we leap to the conclusion that the second also implies the first, that the connection is equally strong each way, even though it is fairly trivial to demonstrate that this isn't necessarily the case. This error seems to be inherent to human intuition, as it occurs across contexts and subjects quite regularly, even when people are aware that it's logically invalid; only careful examination counters this tendency.
Much later, Sigmund Freud began to identify ways that people would deny assertions that they found emotionally threatening, what we now call 'psychological defense mechanisms'. The flaws in Freud's work as a whole are not directly relevant to this discussion and are beyond the scope of this site in any case. Suffice it to say that therapists and psychologists do not consider his theories to be either true or useful, that they do consider them to be unscientific and a self-reinforcing belief system, and that many of the concepts which he introduced and have been taken up into the culture at large are invalid. Not all of his work is so flawed, though - particularly his early ideas.
There is a peculiar relationship between the nature of those defense mechanisms and the intuitive fallacies.
When confronted with a contradiction in their emotionally-charged arguments, people who normally reasoned quite appropriately would suddenly begin to fall into fallacies. What's more, they would be unable to see the errors in their reasoning. Even more extraordinarily, they would often reach conclusions which were superficially related to the correct ones, but which were applied to the wrong concepts, situations, and individuals. In projection, for example, motives and traits belonging to the patients are instead asserted to belong to others or even the world itself; properties within the psyche are "projected" outward. So when a therapist demonstrated to a patient that some of their beliefs were incompatible or their arguments were contradictory, the patient might assert that the therapist was the one who had the irrational concern or obsession.
In such cases it seems clear that there is an awareness of some kind that the unpleasant conclusion must be reached, but not of where the property must be attributed. Accusing the therapist of possessing the unacceptable property seems to reduce tension of some sort - it's a relief that people actively seek out and will vehemently, even violently, defend.
Guilt, hate, fear, forbidden joys and loves - there are countless ways people will deny that they possess them. But they all tend to follow into certain predictable patterns, as the wild diversity of snowflakes still showcases repeating and similar forms.
Why is this the case? Ultimately, it took research into concept formation before psychology could really produce an answer to that question.
Next time: associational thought and the implications for rationality.
"If P, then Q. Q. Therefore, P."
I have taught this as a fallacy for the last two semesters in a propositional logic section of my course. However, given the prevalence of this fallacy, as well as the observed resistance of students to assimilating it, I would like to propose that this really isn't a fallacy but a disconnect between what we often naturally mean by "p implies q" and what it technically means in propositional logic.
I argue that what we tend to understand by the statement "p implies q" is that p is the set of things that result in q. This can be tested by the fact that if Q is known to have two causes P1 and P2, and someone says that P1 implies Q, it would be rather natural and logical for another person to "correct" them by adding that P2 also causes Q. But the word correct is too strong ... it is rather an augmentation.
I think that, like many statements in ordinary usage, "P implies Q" is a fundamentally Bayesian statement; a person means: "in my experience, P is the set of things that cause Q". The 'in my experience' means that it is possible (but not observed) that Q might not happen after P, and also that other things besides P might cause Q, but again this hasn't been observed or isn't recalled at the moment. A person is normally willing to be flexible on both points in the face of new evidence, but is taught in logic class to be absolute for a moment while considering the truth or falsity of the statement.
So finally, when an untrained person is told that "p implies q" is a true logical statement, in their efforts to be "absolute" they may think that both implied meanings are true: p always causes q AND only p causes q. It takes some training (deprogramming of what it has seemed to mean their whole natural lives) to understand that only the first is intended (p always causes q) when the statement is "True" in formal logic.