He provides this example: "Clearly, if laws depend so heavily on public acquiescence, the case of conventions is an a fortiori [read even more compelling] one.
[5] In Islamic jurisprudence, a fortiori arguments are proved utilising the methods used in qiyas (reasoning by analogy).
Given some theorem with an additional restriction imposed upon this axiom, an "a fortiori" proof will always hold.
In logic, a maiore ad minus describes a simple and obvious inference from a claim about a stronger entity, greater quantity, or general class to one about a weaker entity, smaller quantity, or specific member of that class:[9] The reverse, less known and less frequently applicable argument is a minore ad maius, which denotes an inference from smaller to bigger.
[10] "Argumentum a maiori ad minus" (from the greater to the smaller) – works in two ways: An a fortiori argument is sometimes considered in terms of analogical reasoning – especially in its legal applications.