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Invalid deductive arguments, which do not follow a rule of inference, are called formal fallacies. Rules of inference are definitory rules and contrast with strategic rules, which specify what inferences one needs to draw in order to arrive at an intended conclusion. Deductive reasoning contrasts with non-deductive or ampliative reasoning.
A formal fallacy, deductive fallacy, logical fallacy or non sequitur (Latin for "it does not follow") is a flaw in the structure of a deductive argument that renders the argument invalid. The flaw can be expressed in the standard system of logic. [1] Such an argument is always considered to be wrong.
Philosophy of logic is the philosophical discipline studying the scope and nature of logic. [59] It examines many presuppositions implicit in logic, like how to define its basic concepts or the metaphysical assumptions associated with them. [158]
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
In logic and philosophy, a formal fallacy [a] is a pattern of reasoning rendered invalid by a flaw in its logical structure. Propositional logic , [ 2 ] for example, is concerned with the meanings of sentences and the relationships between them.
Begging the question is not considered a formal fallacy (an argument that is defective because it uses an incorrect deductive step). Rather, it is a type of informal fallacy that is logically valid but unpersuasive, in that it fails to prove anything other than what is already assumed. [23] [24] [25]
As the study of argument is of clear importance to the reasons that we hold things to be true, logic is of essential importance to rationality. Arguments may be logical if they are "conducted or assessed according to strict principles of validity", [1] while they are rational according to the broader requirement that they are based on reason and knowledge.
In propositional logic, modus tollens (/ ˈ m oʊ d ə s ˈ t ɒ l ɛ n z /) (MT), also known as modus tollendo tollens (Latin for "method of removing by taking away") [2] and denying the consequent, [3] is a deductive argument form and a rule of inference. Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q ...