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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:
Example (invalid aae form): Premise: All colonels are officers. Premise: All officers are soldiers. Conclusion: Therefore, no colonels are soldiers. The aao-4 form is perhaps more subtle as it follows many of the rules governing valid syllogisms, except it reaches a negative conclusion from affirmative premises. Invalid aao-4 form: All A is B.
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]
A syllogism is a kind of logical argument in which one proposition (the conclusion) is inferred from two or more others (the premises) of a specific form. The classical example of a valid syllogism is: All humans are mortal. (major premise) Socrates is human. (minor premise) Therefore, Socrates is mortal. (conclusion) An example of an invalid ...
The conclusion of a valid argument is not necessarily true, it depends on whether the premises are true. If the conclusion, itself, is a necessary truth, it is without regard to the premises. Some examples: All Greeks are human and all humans are mortal; therefore, all Greeks are mortal.
An argument is sound if it is valid and the premises are true. It is possible to have a deductive argument that is logically valid but is not sound. Fallacious arguments often take that form. The following is an example of an argument that is “valid”, but not “sound”: Everyone who eats carrots is a quarterback. John eats carrots.
In logic and philosophy, a formal fallacy [a] is a pattern of reasoning rendered invalid by a flaw in its logical structure. Propositional logic, [2] for example, is concerned with the meanings of sentences and the relationships between them. It focuses on the role of logical operators, called propositional connectives, in determining whether a ...
Consider the modal account in terms of the argument given as an example above: All frogs are green. Kermit is a frog. Therefore, Kermit is green. The conclusion is a logical consequence of the premises because we can not imagine a possible world where (a) all frogs are green; (b) Kermit is a frog; and (c) Kermit is not green.