A non sequitur occurs when a conclusion is drawn deductively that does not follow logically from the preceding propositions. Someone will take a fact or make a generalization or a categorization, assert than some other fact or generalization is an example of this, and then draw a conclusion. This process is called deductive reasoning.
Correct deductive reasoning can best be demonstrated using syllogisms. Let us look at perhaps the most famous of all syllogisms:
All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.
The first thing one should understand, if one is to correctly evaluate deductive reasoning, is that this is a valid deduction whether or not the initial statements "All men are mortal" and "Socrates is a man" are correct. A deduction - the last statement in the syllogism - can be judged to be valid if the structure of the syllogism is correct. This means that a conclusion can be completely wrong but the deduction can still be valid logically if the conclusion follows correctly from the initial propositions.
The truth of a proposition, as opposed to its logical validity, depends upon the truth of the information from which the proposition is deduced. In a valid syllogism, if the first two statements are true, the conclusion must be true. The presence in the syllogism of the word all is extremely important. If some men are mortal and some are not, Socrates might fall outside the set of "things that are mortal," and the syllogism would become invalid. This is precisely why the equally famous fallacious syllogism
The Virgin Mary was a virgin.
My name is Mary.
Therefore, I am a virgin.
A word here regarding inductivereasoning is in order. Inductive, as opposed to deductive, reasoning attempts to go in the reverse order. One attempts to make a generalization by examining several phenomena that seem to have something in common. One then makes the leap of faith that because all observed instances of the phenomena have this characteristic in common, therefore all instances of the phenomena, now or in the future, observed and not observed, share the characteristic.
For example, every time an object of whatever size or shape is dropped on earth, it falls down. The inductive conclusion is that the set of "things that fall down" entirely subsumes the set of "things that can he dropped" and that anything droppable will fall down if dropped.. One makes the prediction that any new object that can be dropped will head earthward if one picks it up and lets it go.
Now the deduction "since all observed instances of a certain phenomenon behave a certain way or have certain things in common, therefore all future instances of the same phenomenon will continue to behave in the same way and have the same things in common" is in all instances a non sequitur. One might come upon an exception to the rule at any time. In other words, all inductive conclusions are invalid!
Nonetheless, inductive conclusions are not necessarily unreasonable and are frequently correct. I have in my hand a pencil, which I plan to hold up and then let go. Will it fall? I predict, on the basis of inductive reasoning, that it will. Let’s see. Well, I'll be. It did it again!
The reasonableness of an inductive conclusion is evaluated not by logic but by whether enough instances of the phenomenon have been observed to make a generalization possible and by whether there are any instances that contradict the generalization. Deductive reasoning, or reasoning based on proof, would not be possible without inductive reasoning. It would be impossible to conclude that Socrates was mortal if one could not make the generalization "All men are mortal."
The determination of how many instances are required to decide whether an inductive conclusion is reasonable is a very subjective matter, because no matter how many instances there are, the next one could always be the exception. For this reason, anyone looking for mental gymnastics when someone else makes an inductive conclusion best asks the questions: Are there significant exceptions to the generalization that the first person is is making? If so, are they obvious, if only the person would look for them?
I will now describe a case in which a patient presented a therapist with a goodly number of non sequiturs. She was a single woman who came in complaining about being subjected to severely and significant repetitive sexual harassment by a co-worker. The question the therapist posed was why she had made an appointment to see a psychiatrist in the first place, since she did not seem to have any evident psychiatric problem.
As it later turned out, she did not really want to give the real answer because she was protecting her mother, from both the judgment of the therapist and from her own rage. So she gave spurious and very sublty non-rational reasons in order to throw the therapist off the track.
Her chief complaint was that she was upset - but only because someone was doing something to her about which almost anyone would be upset. People usually see a therapist because they believe there is something wrong with them or with their reactions to things. That did not seem to be the case with this woman. Why wasn’t she talking to her boss or a lawyer, the therapist wondered? Actually, she was in the process of doing both!
The therapist could not seem to get a satisfying answer from her to the central question, and knew for certain that something else was going on with her when the non sequiturs began.
She first stated that she must have done something to make the co-worker behave in this extreme fashion, because people do not hate you unless you've done something bad to them. This was a non sequitur because she had no proof that her tormenter’s behavior was based on hatred of her, and even if it were, she was quite aware that the causes of hate in the world include a great many other things. Hate can be based on prejudice, jealousy, a chip on the shoulder, or any number of things other than what someone has done to the person who hates.
The next bit of curious logic occurred when the patient told the therapist that she just could not seem to make him understand that his gossip was disturbing her. How she could possibly have thought that he was not aware of that was simply beyond comprehension. The therapist told her he thought it kind of her to wish to give him the benefit of the doubt after all he had done to her, but it seemed that she had too much evidence to the contrary to support this thesis.
The first clue about the real reason she thought she needed a psychiatrist came when the patient issued yet another non sequitur. She began to get upset with herself for being disturbed by some of the slurs verbalized by her nemesis. She stated that he was just calling her names, after all. Why should just names bother her? Sticks and stones, and all that. She should be able to ignore it, like water off a duck's back. The therapist told her she would be quite an unusual person if she had not found the barrage of insults disturbing.
When faced with a recommendation that we explore why she was so upset that the whole situation bothered her, she balked. She said that if she were to get to the reasons behind this seemingly self-defeating behavior, she might find something terrible. Well, she might, but how terrible could it be? How did she know that she would not discover something wonderful? The odds were, of course, that she might find something uncomfortable, but as Albert Ellis (the founder of cognitive psychotherapy) says, feeling that one would not be able to tolerate the discomfort is irrational, especially when the level of discomfort is already so high, and when bearing some additional discomfort could reduce it over the long run.
She correctly guessed that certain information she had related to the therapist might incline him to think that her parents' divorce when she was a pre-teen had something to do with her current reactions. She then added a non sequitur that later turned out to be the essential clue to what was really going on. She said that she was puzzled by why everyone seemed to think that a parental divorce had so traumatized her and added that she had taken the divorce in stride. It was done, and there was no reason to get upset about it. The event just did not bother her.
When she made this statement, she was trying to take what may sound like a rational position. After all, the belief that one cannot stand an unpleasant occurrence makes one suffer more than necessary. The patient was saying more than this, however. She was saying that one should not be unhappy about a traumatic experience. No disappointment. No regret. No anything. Ellis states that regret and disappointment are emotional responses that make sense. She was stating that she was unaffected entirely. Furthermore, the available evidence strongly suggested that she was more than just disappointed about what happened. She could hardly discuss the matter without breaking into tears.