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.
This appears to be a cogent argument. That means that if the two premises are true, then probably the conclusion is true; for all we know, the next marble might not be red, but it probably will be. Notice this: maybe there is no barrel, or maybe all of the marbles were blue; in that case, both premises of the above argument would be false. But that would not matter to the claim that this argument is cogent. If the argument is cogent, then supposing the premises to be true, the conclusion is probably true. Like validity, cogency is a conditional property.
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 basically follows something like this pattern:
- 95% of observed F's were G.
- Therefore, probably, the next F observed will also be G.
Nearly any argument that follows the above will be cogent. There are some complications that we are ignoring here; for example, suppose we were working with a deck containing 100 cards, and we know in advance that five of them are special cards called "jesters." All the other cards are called "royalty." Then, suppose it is true that 95% of drawn cards were royalty; in that case, the five cards that are left are jesters. In that case, the premise would lead one conclude that the next observed card will not be royalty--exactly the opposite of what the argument form would explain. Exactly what sort of complications are necessary are studied by inductive logic. We would need to mention background assumptions, random sample, having a large enough sample size, and so forth. So bear in mind that the argument form above is a simplification for purposes of illustration.
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.