Logical error

A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves" in the construction of an argument. A fallacious argument may be deceptive by appearing to be better than it really is. Some fallacies are committed intentionally to manipulate or persuade by deception, while others are committed unintentionally due to carelessness or ignorance. Lawyers acknowledge that the extent to which an argument is sound or unsound depends on the context in which the argument is made.

Fallacies are commonly divided into "formal" and "informal". A formal fallacy can be expressed neatly in a standard system of logic, such as propositional logic, while an informal fallacy originates in an error in reasoning other than an improper logical form. Arguments containing informal fallacies may be formally valid, but still fallacious.

A formal fallacy is a common error of thinking that can neatly be expressed in standard system of logic. An argument that is formally fallacious is rendered invalid due to a flaw in its logical structure. Such an argument is always considered to be wrong.

The presence of a formal fallacy in a deductive argument does not imply anything about the argument's premises or its conclusion. Both may actually be true, or may even be more probable as a result of the argument; but the deductive argument is still invalid because the conclusion does not follow from the premises in the manner described. By extension, an argument can contain a formal fallacy even if the argument is not a deductive one: for instance, an inductive argument that incorrectly applies principles of probability or causality can be said to commit a formal fallacy.

Aristotle was the first to systematize logical errors into a list, as being able to refute an opponent's thesis is one way of winning an argument.Aristotle's "Sophistical Refutations" (De Sophisticis Elenchis) identifies thirteen fallacies. He divided them up into two major types Linguistic fallacies and Non-linguistic fallacies, some depending on language and others that do not depend on language. These fallacies are called verbal fallacies and material fallacies, respectively. A material fallacy is an error in what the arguer is talking about, while a verbal fallacy is an error in how the arguer is talking. Verbal fallacies are those in which a conclusion is obtained by improper or ambiguous use of words. An example of a language dependent fallacy is given as a debate as to who amongst humanity are learners: the wise or the ignorant. Language-independent fallacies may be more complex, e.g.:

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