An argument is cogent if, and only if, supposing the premises all to be true, then the conclusion is probably (but not necessarily) true. (Exactly what "probably" means is a matter of considerable debate.)
Suppose you have an argument in which the premises make the conclusion very probably true, but not necessarily true; it might still be a good argument. Such an argument we call cogent; cogency (that is the noun) is of central importance to inductive logic. Here, for example, is a cogent argument:
- There is a barrel jammed full of ordinary marbles, of different colors.
- Without looking, Jill pulled out 100 marbles from various holes in the lid; 95 of the marbles Jill pulled out were red.
- Therefore, the next marble Jill pulls out, without looking, from another hole in the lid, will be red.
Also like validity, the cogency of an argument can be assessed by examining the form of the argument. Consider, for example, the form of the above argument. We might say it follows something like this pattern:
- 95% of observed F's were G.
- Therefore, probably, the next F observed will also be G.
Just as one adds true premises to a valid argument to get soundness, you can add true premises to a cogent argument to get a strong argument. We can define strength, for arguments, as follows:
An argument is strong if, and only if, the argument is cogent and all of its premises are true.
Similar things to what one says about soundness can be said about strength. If one knows an argument is strong, then one knows that, if the premises are true, then its conclusion is probably true.
See also inductive reasoning, explanation.