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:
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 follows something like this pattern:
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 royaltyexactly 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.
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.
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