by Scott F. Aikin and Robert B. Talisse
Why We Argue (And How We Should) is centrally concerned to elucidate the concept of a dialectical fallacy. This concept deserves comment. “Fallacy” is the name given to especially common and attractive failures of reasoning. Works in logic and critical thinking typically distinguish between formal and informal fallacies.
Formal fallacies are pervasive errors of formal inferences. Consider the argument:
If Bill is a carpenter, then Bill is handy.
Bill is handy.
Therefore, Bill is a carpenter.
This argument fails because the truth of the premises does not guarantee the truth of the conclusion: the first premise states that being a carpenter is sufficient for being handy; it does not claim that all and only handy people are carpenters. After all, Bill could be a handy car mechanic who has never cut a piece of wood. We call this error the fallacy of affirming the consequent. This error gets its own name because we are especially prone to this kind of mistake. Once one is trained to spot it, one will find that this fallacy is committed frequently.
By contrast, informal fallacies are pervasive errors in informalinferences. Informal inferences differ from formal ones in that the latter propose to demonstrate the truth of their conclusions whereas the former aspire only to show that their conclusions are most likely true. A familiar informal fallacy is the ad populum fallacy. Consider:
Most people think that Joe is guilty.
Therefore, Joe is guilty.
This argument fails because it appeals simply to what “most people” think, without any regard for questions concerning the level to which “most people” are informed of the relevant facts of Joe's case. The mere fact that “most people” agree about some claim is no evidence at all for its truth.
The important thing about fallacies is that they are attractive and so pervasive errors of reasoning. Part of what accounts for their popularity is the way in which they mimic or ride piggyback on proper inferences. The fallacy of affirming the consequent is a mimic of the obviously successful inference known as modus ponens:
If Bill is a carpenter, then Bill is handy.
Bill is a carpenter.
Therefore, Bill is handy.
