Search results
Results From The WOW.Com Content Network
The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a necessary consequence of its premises. 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:
A form of argument is valid if and only if the conclusion is true under all interpretations of that argument in which the premises are true. Since the validity of an argument depends on its form, an argument can be shown invalid by showing that its form is invalid. This can be done by a counter example of the same form of argument with premises ...
Validity is defined in classical logic as follows: An argument (consisting of premises and a conclusion) is valid if and only if there is no possible situation in which all the premises are true and the conclusion is false. For example a valid argument might run: If it is raining, water exists (1st premise) It is raining (2nd premise)
Every argument's conclusion is a premise of other arguments. The word constituent may be used for either a premise or conclusion. In the context of this article and in most classical contexts, all candidates for consideration as argument constituents fall under the category of truth-bearer : propositions, statements, sentences, judgments, etc.
A premise or premiss [a] is a proposition—a true or false declarative statement—used in an argument to prove the truth of another proposition called the conclusion. [1] Arguments consist of a set of premises and a conclusion.
For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics ), in the sense that if the premises are true (under ...
A logical fallacy where the conclusion of an argument is assumed in the premise, making the argument circular. Bew See provability predicate. BHK-interpretation The Brouwer-Heyting-Kolmogorov interpretation, a constructivist interpretation of intuitionistic logic, where the truth of a statement is equated with the existence of a proof for it. bias
However, the logical validity of an argument is a function of its internal consistency, not the truth value of its premises. For example, consider this syllogism, which involves a false premise: If the streets are wet, it has rained recently. (premise) The streets are wet. (premise) Therefore it has rained recently. (conclusion)