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If also the premises of a valid argument are proven true, this is said to be sound. [3] 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".
Another form of argument is known as modus tollens (commonly abbreviated MT). In this form, you start with the same first premise as with modus ponens. However, the second part of the premise is denied, leading to the conclusion that the first part of the premise should be denied as well. It is shown below in logical form. If A, then B Not B
An argument, more fully a premise–conclusion argument, is a two-part system composed of premises and conclusion. An argument is valid if and only if its conclusion is a consequence of its premises. Every premise set has infinitely many consequences each giving rise to a valid argument. Some consequences are obviously so, but most are not ...
An argument is sound and its conclusion logically follows (it is true) if and only if the argument is valid and its premises are true. An argument is valid if and only if it is the case that whenever the premises are all true, the conclusion must also be true. If there exists a logical interpretation where the premises are all true but the ...
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
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 not a guarantee of the truth of its conclusion. A valid argument may have false premises that render it inconclusive: the ...
An argument for psychologism is based on the idea that logic is a sub-discipline of psychology: it studies not all laws of thought, but only the subset of laws corresponding to valid reasoning. [85] Another argument focuses on the thesis that we learn about logical truths through the feeling of self-evidence, which is in turn studied by ...
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)