Non-sequitur
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The term non-sequitur literally means "it does not follow". These fallacies occur as a consequence of invalid arguments.
Affirming the Consequent
Any argument of the following form is invalid:
If A then B
B
Therefore, A
For example:
"If I am in Atlanta, then I am in Georgia. I am in Georgia, thus, I am in Atlanta."
"If my self-defense system works, then the self-confidence you present will deter others from confronting you. You have not been confronted since you began training in my system. Thus, my system works."
Denying the Antecedent
Any argument of the following form is invalid:
If A then B
Not A
Therefore, Not B
For example:
"If you get hit by a car when you are six then you will die young. But you were not hit by a car when you were six. Thus you will not die young."
"If I am in Atlanta then I am in Georgia. I am not in Atlanta, thus, I am not in Georgia."
Inconsistency
The author asserts more than one proposition such that the propositions cannot all be true. In such a case, the propositions may be contradictories or they may be contraries. For example:
"Greensboro is about 30 miles from Winston-Salem. Burlington is 10 miles from Winston-Salem. Therefore, Burlington is closer to Winston-Salem than Greensboro."
"John is taller than Jake, and Jake is taller than Fred, while Fred is taller than John."