Argumentum a fortiori  

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The Latin phrase Template:Lang denotes "argument 'from [the] stronger [reason]'." For example, if it has been established that a person is deceased, then one can, with equal or greater certainty, argue that the person is not breathing.

Usage

In the natural sciences and in social and other human sciences where statistics plays a large role, the phrase is used to mean "even more likely" or "with even more certainty." For example, if a scientist observes certain phenomena to be present in conjunction a given percentage of the time, they may make the argument that each of the individual phenomena will a fortiori be present a greater percentage of the time (because the latter figures, but not the former, will include the occasions on which a given phenomenon is present but one or more of the others are not).

In the art of rhetoric, i.e., speaking or writing for the acknowledged primary purpose of persuasion, the a fortiori argument draws on the speaker's and/or listener's existing confidence in a proposition to argue for a second proposition that is implicit in the first, "weaker" (less controversial and more likely to be true) than the first proposition, and therefore deserving of even more confidence than the speaker and/or listener places in the first proposition. The Christian apostle Paul makes frequent use of the argument for purpose, often signaling it with the phrase "... if [A], then how much more [B]" (New International Version translation; see, e.g., 2 Corinthians 3:7–8 and 9 and Romans 5:9 and 10.)

In classical logic, truth value is binary (either absent or present, without further elaboration), as opposed to quantifiable on discrete or continuous scales as to existence and/or degree (i.e., either absent or present in some quantity that depends on the likelihood of a proposition's truth and/or the degree to which a descriptive statement applies). In classical logic, "a fortiori" is a signal indicating an attempt to justify an inferential step by claiming that the point being proven follows "from a[n even] stronger [claim]" or has been stated "by means of [an even] stronger [assertion]." That is, the phrase indicates that a) a proposition previously given or proven in the argument contains and implies a variety of "weaker" or less contentful propositions and b) the proposition being proven is only one of the propositions contained and implied.

There are two types of the a fortiori argument:

• a maiore ad minus: "from greater to smaller"
• a minore ad maius: "from smaller to greater"

Meaning

When the phrase includes the Latin or English noun, it properly denotes a proof in which one demonstrates a claim by invoking as proof an already proven, stronger claim. (Example: "When one argues that if it is forbidden to ride a bicycle with an extra passenger, it is also forbidden to ride a bike with fourteen extra passengers, one makes an argument a fortiori.)

The Latin prepositional phrase taken by itself (without "argumentum"/"argument") is adverbial. (Example: "As I've personally observed, Bob can lift a 100-pound object of size, shape, and weight distribution identical to those of this object. This object weighs only 50 pounds; a fortiori, Bob can lift it also.") So used, the phrase conveys two types of meaning, one within the sentence taken at face value and one extending beyond the sentence's face value:

• First, it adds to the sentence's propositional content by modifying a modal verb such as "is" (or the modal portion of an auxiliary verb phrase such as "can/may [main verb]"), contributing "'why' information" about the objective state of affairs described.

• Second, and less overtly, the prepositional phrase calls the listener's attention not merely to the explanatory information within the proposition but to the proposition itself in its capacity as an assertion – to the fact that it is being asserted and, indirectly, to the asserter's reasons for asserting it. In this capacity, it sheds light on the asserter's subjective mental state, providing information on subjects including why the asserter believes the weaker proposition, why the asserter's effort at persuasion features the stronger proposition, and why (in the asserter's actual or purported opinion) the person being persuaded should believe the weaker proposition. The difference between the logical and the personal appeal is expressible as the difference between "A and B; a fortiori, A" on one hand and "A and B; a fortiori, [I say] 'A'" (note "scare quotes") on the other. More fully, the personal appeal runs "I believe that [proposition X]; I am led 'by th[is] stronger [proposition]' and relevant rules of inference to believe that [proposition Y implicit in and "weaker than" X], and I hereby invoke it as justification for the assertion, which I hereby make, that ["weaker" proposition Y]. I understand you to likewise believe that [X] and to endorse these same rules of inference. Therefore, by your own logic, you have even more reason to believe that [Y] than you do to believe that [X], and you should need no external persuasion to believe that [Y]."

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 [conclusion ultimately in] question").

This argument is regularly used in Jewish Law under the name Kal V'Chomer (Easy and Hard). If one can perform a difficult action, then it follows that one can perform an action requiring strength, skill, and/or other resources similar in quality but less in quantity to those the difficult action requires; and per the argument's contrapositive, if one cannot perform an easy action, one cannot perform an action requiring greater resources of the type the easy action requires.

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).

See also

• Loss leader

References

• Grabenhorst, Thomas K.: Das Template:Lang, Verlag „Peter Lang“ 1990 ISBN 3-631-43261-5
• Schneider: Logik für Juristen, S. 158ff.