Now, if a conclusion doesn't follow from its premises, the argument is said to be invalid and no reliable judgement can be made about whether the conclusion is true, regardless of whether or not the premises are true. If the argument is valid but the premises are not true, then again the conclusion may or may not be true, but the argument can't help us decide this. Finally, if the argument is valid and the premises are true, then the argument is described as sound , and we deem the conclusion to be true. From a pragmatic point of view, we can be said to have proved something if we can find a sound argument for it. Table 1 summarises these different kinds of deductive arguments, and table 2 provides an example of each.
Fish are mammals.
Fish are warm-blooded. Mammals are warm-blooded. Mammals are cold-blooded. Humans are cold-blooded. Fish are cold-blooded.