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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.
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:
Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work". [1] Premises and conclusions express propositions or claims that can be true or false. An important ...
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. But even arguments with false premises can be deductively valid, like inferring that "no cats are frogs" from the premises "all frogs are mammals" and "no cats are mammals".
The logical form of this argument is known as modus ponens, [39] which is a classically valid form. [40] So, in classical logic, the argument is valid, although it may or may not be sound, depending on the meteorological facts in a given context. This example argument will be reused when explaining § Formalization.
The person making the argument expects that the listener will accept the provided definition, making the argument difficult to refute. [ 19 ] Divine fallacy (argument from incredulity) – arguing that, because something is so phenomenal or amazing, it must be the result of superior, divine, alien or paranormal agency.
Avoiding fallacies may help improve one's ability to produce sound arguments. [10] It can be difficult to evaluate whether an argument is fallacious, as arguments exist along a continuum of soundness and an argument that has several stages or parts might have some sound sections and some fallacious ones. [11]
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.