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In deductive reasoning, a sound argument is an argument that is valid and all of its premises are true (and as a consequence its conclusion is true as well). An argument is valid if, assuming its premises are true, the conclusion must be true. An example of a sound argument is the following well-known syllogism: (premises) All men are mortal.
The person making the argument expects that the listener will accept the provided definition, making the argument difficult to refute. [19] Divine fallacy (argument from incredulity) – arguing that, because something is so phenomenal or amazing, it must be the result of superior, divine, alien or paranormal agency. [20]
Deductive arguments are evaluated in terms of their validity and soundness. An argument is valid if it is impossible for its premises to be true while its conclusion is false. In other words, the conclusion must be true if the premises are true. An argument can be “valid” even if one or more of its premises are false.
[12] Thus, "fallacious arguments usually have the deceptive appearance of being good arguments, [13] because for most fallacious instances of an argument form, a similar but non-fallacious instance can be found". Evaluating an instance of an argument as fallacious is therefore often a matter of evaluating the context of the argument.
A propositional argument using modus ponens is said to be deductive. In single-conclusion sequent calculi , modus ponens is the Cut rule. The cut-elimination theorem for a calculus says that every proof involving Cut can be transformed (generally, by a constructive method) into a proof without Cut, and hence that Cut is admissible .
A fallacy is an argument, i.e. a series of premises together with a conclusion, that is unsound, i.e. not both valid and true. Fallacies are usually divided into formal and informal fallacies. Formal fallacies are unsound because of their structure, while informal fallacies are unsound because of their content.
A formal fallacy is contrasted with an informal fallacy which may have a valid logical form and yet be unsound because one or more premises are false. A formal fallacy, however, may have a true premise, but a false conclusion. The term 'logical fallacy' is sometimes used in everyday conversation, and refers to a formal fallacy.
Forms of logical reasoning can be distinguished based on how the premises support the conclusion. Deductive arguments offer the strongest possible support. Non-deductive arguments are weaker but are nonetheless correct forms of reasoning. [28] [29] The term "proof" is often used for deductive arguments or very strong non-deductive arguments. [30]