A fortiori argument

The Latin phrase _la. argumentum a fortiori literally means one of the following:
* "from the stronger"
* "even more so"
* "with even stronger reason"It denotes a proof of a claim by means of an already proved stronger claim. For example, if it is forbidden to ride a bike with an extra passenger, then it is also forbidden to ride a bike with two extra passengers. Or, if one can lift a 100 lb object, then it follows that one can lift a 50 lb object.

There are two types of the a fortiori argument:
* a maiore ad minus: from bigger to smaller
* a minore ad maius: from smaller to bigger

The a fortiori argument is most often used in order to reinforce a claim, though sometimes also to incorrectly justify a claim taking it as a premise (petitio principii).

This argument is regularly used in Jewish Law under the name Kal V'Chomer (Easy and Hard). If one can do the hard thing, then it follows that one can do the easy thing, and if one cannot do the easy thing then it follows that one cannot do the hard thing.

References

* Grabenhorst, Thomas K.: "Das _la. argumentum a fortiori", Verlag „Peter Lang“ 1990 ISBN-Nummer 3-631-43261-5
* Schneider: "Logik für Juristen", S. 158ff.