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Informal fallacies – arguments that are logically unsound for lack of well-grounded premises. [14]Argument from incredulity – when someone can't imagine something to be true, and therefore deems it false, or conversely, holds that it must be true because they can't see how it could be false.
While a logical argument is a non sequitur if, and only if, it is invalid, the term "non sequitur" typically refers to those types of invalid arguments which do not constitute formal fallacies covered by particular terms (e.g., affirming the consequent). In other words, in practice, "non sequitur" refers to an unnamed formal fallacy.
An example is a probabilistically valid instance of the formally invalid argument form of denying the antecedent or affirming the consequent. [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 ...
Deductive reasoning offers the strongest support: the premises ensure the conclusion, meaning that it is impossible for the conclusion to be false if all the premises are true. Such an argument is called a valid argument, for example: all men are mortal; Socrates is a man; therefore, Socrates is mortal. For valid arguments, it is not important ...
All men are mortal. Socrates is a man. (conclusion) Therefore, Socrates is mortal. Because of the logical necessity of the conclusion, this argument is valid; and because the argument is valid and its premises are true, the argument is sound. However, an argument can be valid without being sound. For example: All birds can fly. Penguins are birds.
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 .
An argument that is not valid is said to be "invalid". An example of a valid (and sound) argument is given by the following well-known syllogism: All men are mortal. (True) Socrates is a man. (True) Therefore, Socrates is mortal. (True) What makes this a valid argument is not that it has true premises and a true conclusion.
Being a valid argument does not necessarily mean the conclusion will be true. It is valid because if the premises are true, then the conclusion has to be true. This can be proven for any valid argument form using a truth table which shows that there is no situation in which there are all true premises and a false conclusion. [2]