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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:
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises , meaning that it is impossible for the premises to be true and the conclusion to be false.
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 ...
Such reasoning itself, or the chain of intermediates representing it, has also been called an argument, more fully a deductive argument. In many cases, an argument can be known to be valid by means of a deduction of its conclusion from its premises but non-deductive methods such as Venn diagrams and other graphic procedures have been proposed.
Deductive reasoning is the mental process of drawing deductive inferences. Deductively valid inferences are the most reliable form of inference: it is impossible for their conclusion to be false if all the premises are true. [34] [35] This means that the truth of the premises ensures the truth of the conclusion.
A deductively valid argument is one whose premises guarantee the truth of its conclusion. [11] For instance, the argument "(1) all frogs are amphibians; (2) no cats are amphibians; (3) therefore no cats are frogs" is deductively valid. For deductive validity, it does not matter whether the premises or the conclusion are actually true.
deductive argument An argument where the conclusion necessarily follows from the premises, intended to provide conclusive proof of the conclusion. deductive consequence See syntactic consequence. [81] deductive validity 1. The property of a deductive argument where, if the premises are true, the conclusion must also be true. [82] 2.
Deductive arguments can be valid, and the valid ones can be sound: in a valid argument, premises necessitate the conclusion, even if one or more of the premises is false and the conclusion is false; in a sound argument, true premises necessitate a true conclusion.