Argumentum a fortiori
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Argumentum a fortiori (UK: /
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- 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.
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.
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A maiore ad minus
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:
- From general to particular ("What holds for all X also holds for one particular X")
- From greater to smaller ("If a door is big enough for a person two metres high, then a shorter person may also come through"; "If a canister may store ten litres of petrol, then it may also store three litres of petrol.")
- From the whole to the part ("If the law permits a testator to revoke the entirety of a bequest by destroying or altering the document expressing it, then the law also permits a testator to revoke the portion of a bequest contained in a given portion of a document by destroying or altering that portion of the document.")
- From stronger to weaker ("If one may safely use a rope to tow a truck [in the American usage], one may also use it to tow a car.")
A minore ad maius
The reverse, less known and less frequently applicable argument is a minore ad maius, which denotes an inference from smaller to bigger.
- Morwood, James (1998). A Dictionary of Latin Words and Phrases. Oxford: Oxford University Press. pp. x–xii. ISBN 978-0-19-860109-8.
- Garner, Bryan A. (2009). Garner's Modern American Usage (3rd ed.). Oxford: Oxford University Press. p. 28. ISBN 978-0-19-538275-4.
- Abramowitz, Jack. "Torah Methodology #1 – Kal v'Chomer". Orthodox Union. Retrieved 20 July 2016.
- Hallaq, Wael (2009). Sharī'a: Theory, Practice, Transformations (1st ed.). Cambridge: Cambridge University Press. p. 105. ISBN 0521678749.