Logical Fallacy

It is standard practice to distinguish formal and informal fallacies. Formal fallacies break one or more of the rules of a system of logic and can be seen when an argument is presented in either schematic form or in a natural language. Informal fallacies, by contrast, can often only be seen when the argument is presented in natural language, since they depend often on ambiguity or some other misuse of language. Other common fallacies that do not clearly break a rule of logic are also classified as informal, even when they do not depend on misuse of language.

In traditional Aristotelian logic, a set of rules can be established for the formation of valid arguments. Because breaking any one of the rules results in an invalid argument, there is a logical fallacy corresponding to each rule. Examples of such fallacies include excluded middle, illicit major, illicit minor, etc. One important formal logical fallacy is affirming the consequent, which can be given schematically as an argument of the form "If P, then Q. Q. Therefore, P." The logic of conditional statements has been thought to be essential to the testing of scientific theories, since predictions are written in conditional form. A fact such as "Water freezes at 32° F" can be written as the conditional "If (pure) water is below 32° F, then it will freeze." However, as Karl Popper (1902–1994) emphasized, one cannot claim to prove anything if one obtains a positive result, and indeed would be committing the formal logical fallacy of affirming the consequent if this reasoning is used to support one's claim. Suppose someone had claimed that they have a magic box that freezes water, and that water always freezes when it is put into the box. One should not be impressed if this prediction comes true, not even if this experiment is repeated multiple times. What is needed is a way of isolating the different factors that may be relevant to the change of state that water undergoes—is it being in the box, or being in the dark, or being in the cold that is the crucial factor? This problem of scientific reasoning is highlighted by the fallacy of affirming the consequent. A conditional statement can properly be rejected if a negative result is obtained, but nothing can be concluded deductively from a positive result.