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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.
Of the many and varied argument forms that can possibly be constructed, only very few are valid argument forms. In order to evaluate these forms, statements are put into logical form . Logical form replaces any sentences or ideas with letters to remove any bias from content and allow one to evaluate the argument without any bias due to its ...
Most valid arguments are not yet known to be valid. To determine validity in non-obvious cases deductive reasoning is required. There is no deductive reasoning in an argument per se; such must come from the outside. Every argument's conclusion is a premise of other arguments. The word constituent may be used for either a premise or conclusion.
An argument is formally valid if and only if the denial of the conclusion is incompatible with accepting all the premises. In formal logic, the validity of an argument depends not on the actual truth or falsity of its premises and conclusion, but on whether the argument has a valid logical form. [citation needed] The validity of an argument is ...
For valid arguments, it is not important whether the premises are actually true but only that, if they were true, the conclusion could not be false. Valid arguments follow a rule of inference, such as modus ponens or modus tollens. Deductive reasoning plays a central role in formal logic and mathematics.
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.
More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, [2] and reductio ad ...
Whether an argument is valid only depends on its form. An important feature of formal logic is that for a valid argument, the truth of its premises ensures the truth of its conclusion, i.e. it is impossible for the premises to be true and the conclusion to be false. [18] [17] [1] [3]