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 Classical Formal Fallacies
 

Most logicians recognize a category of fallacies that are considered fallacious merely because of their form. That is, even if their premisses are true, there is still a significant risk that such arguments will lead us to a false conclusion, simply because the argument is not formally valid.  The classical formal fallacies include (in propositional logic):

 

1. Affirming the Consequent
Any argument of the form, "If p then q; and q. Therefore, p."

 
2. Denying the Antecedent
Any argument of the form, "If p, then q; but not p. Therefore, not q."

 

 

In syllogistic logic there are also some classical formal fallacies, with names like Illicit Major, Illicit Minor, and Undistributed Middle. Suffice it to say that these name syllogistic forms that fail the test for deductive validity, just as the above forms fail the test of deductive validity for propositional logic.

 

Why don't I recognize the formal fallacies?
I don't recognize the "formal fallacies" as fallacies because (in my view) failing to be deductively valid is not sufficient to make an argument a fallacy.  Inductive arguments are (presumably) not deductively valid, and neither are Retroductive arguments. If failing to be deductively valid were, by itself, grounds for calling an argument fallacious, then Inductive and Retroductive arguments would all be fallacious simply by virtue of being Inductive or Retroductive rather than Deductive. Hence, if we are going to recognize forms of reasoning other than Deduction, we must not dismiss arguments as fallacious merely on the grounds that they fail to be deductively valid.

In fact, Inductive and Retroductive arguments often follow precisely the forms that are identified as formal fallacies. My explanations of Induction and Retroduction, for example, treat these forms of reasoning as syllogisms, but as syllogisms that fail to be formally valid. The name "Retroduction" actually refers to the tendency of the reasoning to move backward from consequent to antecedent. That is, Retroductive reasoning, when stated using conditional statements, usually follows the formal pattern labeled Affirming the Consequent.

Of course, just as a deductively valid argument may be fallacious (either by being circular or by having a false premiss), Inductive and Retroductive arguments may also be fallacious (either by being circular or by having false premisses). There certainly are fallacious arguments that follow the patterns described by the classical formal fallacies. However, such arguments are fallacious, not because they are bad Deductions, but because they are bad Inductions or bad Retroductions. Most of the arguments that a classical logician would label Affirming the Consequent are really Retroductions in which the causal principle to which the argument appeals is not the best explanation for the observation being explained. For example

 
  If aliens visited the earth to teach humans civilization, then we should expect civilization to spring up simultaneously in many different places. Civilization did begin in many places at about the same time. Therefore the earth was visited by aliens who taught us civilization.

 

        
The argument follows the pattern labeled Affirming the Consequent, and this argument is undeniably fallacious. However, it is fallacious because it is an Arcane Explanation (appealing to the agency of entities not generally believed to exist), not because it affirms its consequent.

 

  

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