Argumentum a fortiori (pron. /ˈɑː fɔːrtɪˈoʊriː/; Latin: "from a/the stronger [thing]") is a form of argumentation which draws upon existing confidence in a proposition to argue in favor of a second proposition that is held to be implicit in the first. The second proposition may be considered "weaker," and therefore the arguer utilises the former as the "stronger" proposition from which the second proposition is deduced.
If a person is dead (the stronger reason), then one can with equal or greater certainty argue a fortiori that the person is not breathing. "Being dead" trumps other arguments that might be made to show that the person is dead, such as "he is no longer breathing", therefore "he is no longer breathing" is an extrapolation from his being dead and is a derivation of this strong argument.
If driving 10 mph over the speed limit is punishable by a fine of $50, it can be inferred a fortiori that driving 20 mph over the speed limit is also punishable by a fine of at least $50.
If a teacher refuses to add 5 points to a student's grade, on the grounds that the student does not deserve an additional 5 points, it can be inferred a fortiori that the teacher will also refuse to raise the student's grade by 10 points.
Argumentum a fortiori Wikipedia
A fortiori arguments are strong arguments or premises from which all other arguments pertaining to it are derived. Therefore a good example of Argumentum a fortiori is the statement, "Mary's hair is rather well made up today" which is the a fortiori argument, and the supporting extrapolated meaning derived from the strong argument are, "she used gel, a brush, two combs, a straightener, a pair of scissors and a blow drier". In no other way is Mary's hair made up than how well it is, so the entirety of the statement can be seen as the strong argument. Mary's hair made up is greater than the sum of the parts needed to make up her hair, therefore her well made up hair is the strong argumentum a fortiori.
In the English language, the phrase a fortiori is most often used as an adverbial phrase meaning "by even greater force of logic" or "all the more so".
Bryan A. Garner has written in Garner's Modern American Usage that writers sometimes use a fortiori as an adjective, which he says is "a usage to be resisted." As an example of this he gives the sentence, "Clearly, if laws depend so heavily on public acquiescence, the case of conventions is an a fortiori [read even more compelling] one."
A fortiori arguments are regularly used in Jewish law under the name kal va-chomer, literally "mild and severe", the mild case being the one we know about, while trying to infer about the more severe case. In ancient Indian logic (nyaya), an inference derive from an a fortiori postulation is known as kaimutika or kaimutya nyaya, from the words kim uta meaning "even more so."
In Islamic jurisprudence, a fortiori arguments are proved utilising the methods used in qiyas (reasoning by analogy).