Prevailing Circumstances of Use
A fortiori reasoning is most often adduced in order to reinforce a claim already demonstrated by other means, though the binary-logical form is occasionally invoked in order to make a previously implicit proposition explicit for the sake of convenience and clarity in further treatment. If an argument's proponent attempts to corroborate a point made earlier in an argument by comparing a stronger (more contentful) claim made later in the argument, the proponent should take care that the relevant portion of the stronger claim does not rely for justification on the earlier claim being corroborated; if it does, the effort at corroboration will not succeed, being an instance of the fallacy known as petitio principii ("begging the premise," related to but distinct from "begging the question").
This argument is regularly used in Jewish Law under the name Kal vachomer (Light and Heavy).
In ancient Indian logic (Nyaya), the a fortiori inference is known as kaimutika or kaimutya nyaya, from the words kim uta, meaning "even more so."
In Islamic jurisprudence, a fortiori arguments are among the methods used in Qiyas (reasoning by analogy).
Read more about this topic: A Fortiori Argument
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