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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.
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.
The following deduction is perfectly valid: All animals live on Mars. (False) All humans are animals. (True) Therefore, all humans live on Mars. (False) The problem with the argument is that it is not sound. In order for a deductive argument to be sound, the argument must be valid and all the premises must be true. [3]
A deductive argument is sound if it is valid and all its premises are true. [36] For example, inferring the conclusion "no cats are frogs" from the premises "all frogs are amphibians" and "no cats are amphibians" is a sound argument.
Logic is the study of the forms of reasoning in arguments and the development of standards and criteria to evaluate arguments. [5] 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 ...
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 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.
An argument can be valid but nonetheless unsound if one or more premises are false; if an argument is valid and all the premises are true, then the argument is sound. For example, John might be going to work on Wednesday. In this case, the reasoning for John's going to work (because it is Wednesday) is unsound.