Q&A: Regarding the a fortiori inference of “a maneh is included in two hundred” in the Talmud and within the analysis of a regular a fortiori inference
Regarding the a fortiori inference of “a maneh is included in two hundred” in the Talmud and within the analysis of a regular a fortiori inference
Question
Hello Rabbi, 2 questions:
A — I’ve heard you on various occasions mention the “Belgian refutation” regarding “a maneh is included in two hundred.” Does the Talmud use such a refutation? Or is that a refutation on the logical plane but not on the Talmudic-logical plane… (and if it does use it, where?).
B — In the course of introducing the parameters alpha and beta, when you prefer “alpha and 2 alpha” over “alpha and beta,” you are making an a fortiori inference of “a maneh is included in two hundred” (“within 2 alpha there is alpha”). Seemingly one could refute it based on the Belgian refutation. For example: perhaps specifically alpha is needed in order to obligate, and if there is 2 alpha then either he would not be obligated at all (the Belgian case), or perhaps he would be liable for something more severe and I therefore can’t obligate him just like a case of alpha alone (like not imposing lashes out of concern that he may instead be liable to death).
Thank you very much, and kudos for your holy work in the field of the hermeneutical principles by which the Torah is interpreted…
Answer
Hello, and thank you.
The fact that one can find a refutation does not mean that it actually exists. I did not claim that an a fortiori inference of “a maneh is included in two hundred” is always flawed, only that it can be refuted. That is exactly like any regular a fortiori inference.
The Talmud does this as well, at least according to some opinions. For example, according to those who apply the rule “we do not derive punishments from logical inference” to an a fortiori inference of “a maneh is included in two hundred” (if one is liable for opening, then for digging all the more so). The Kesef Mishneh explains that one who passes all of his children to Molech is not punished, even though one who passes some of his children to Molech is punished. “As he plotted,” but not “as he did” (if they killed, they are not executed).
In our algorithm this kind of refutation is not relevant, because we do not identify the parameters alpha and beta. Without identifying them, it is impossible to present a refutation, even though one may perhaps be possible (that the presence of beta interferes with alpha’s operation). As long as no refutation has been presented, then of course the a fortiori inference remains standing, because the default is that this is indeed more severe. As stated, my claim is only that a refutation is possible.
Discussion on Answer
At the end of the book we comment on identifying the parameters. It definitely remains up to the learner’s judgment, but our method helps him with that.
As for “we do not derive punishments from logical inference,” one who applies that to an a fortiori inference of “a maneh is included in two hundred” assumes that there can be a refutation there too.
Hello Rabbi,
There is discussion of “a maneh is included in two hundred” in the context of deriving punishments by logical inference in rulings of Israeli courts, and you may find the subject interesting. Here is a quote from the disciplinary ruling in the matter of Judge Poznanski-Katz (link: https://www.nevo.co.il/psika_html/elyon/18002081-44.htm):
"35. There is no basis to examine the relationship between ‘removal from office’ and ‘suspension’ as the relationship between a ‘whole’ and ‘its part.’ In this context, it should be noted that in the recent past the Supreme Court discussed the question whether the rabbinical court is authorized to recommend sanctions ‘of Rabbenu Tam’ when these are not enumerated in the statute (HCJ 5185/13 Anonymous v. The Great Rabbinical Court [published in Nevo] (28.2.2017)). Justice Y. Amit held the view — consistent with the accepted position — that this authority, given to the rabbinical courts, can be derived by way of an a fortiori inference or by way of the interpretive rule ‘a maneh is included in two hundred’ or ‘the whole includes its part.’ He noted that ‘it is hard to accept that we recognize imprisonment, which infringes the fundamental right to liberty, yet do not recognize voluntary social pressure produced by the distancing measures of Rabbenu Tam’ (paragraph 6a of his opinion). In contrast, President M. Naor ruled on this point as follows:
‘On this point I disagree with my colleague, for in my view the fact that the law contains a more severe sanction does not imply that there is an implied authority to impose a less severe sanction. This is especially so where we are dealing with sanctions that infringe fundamental rights. According to the principle of legality, an authority may and is empowered to perform only those actions that the law authorized it to perform. When it comes to an act that infringes fundamental rights, the authorization for that act must be clear and explicit, whether the infringement concerns liberty or other fundamental rights… In our case, the enactments of Rabbenu Tam embody a significant infringement of protected and important fundamental rights of individuals, among them freedom of occupation and human dignity. Therefore, infringement of these rights must be by virtue of direct and explicit statutory authorization, and it cannot be derived by analogy, a fortiori inference, or any other interpretive rule.’
(HCJ 5185/13 cited above, paragraph 12)
I too believe that the fact that a law authorizes a judicial or disciplinary tribunal to impose a ‘severe’ disciplinary measure does not, in and of itself, imply that it has authority to impose any other sanction as well, even one that differs in purpose and essence, merely because ostensibly it is a less severe sanction. It should be remembered that alongside the purpose common to every punishment and every sanction, different punishments and sanctions also have distinct purposes. In addition, the comparison between a ‘severe’ sanction and a ‘less severe’ sanction is not always so simple. In other words, sometimes it is difficult for us to determine the hierarchy of severity among different sanctions, punishments, or disciplinary measures. Let us illustrate the difficulty: admittedly, everyone would agree that a sentence of ten years’ imprisonment is ‘more severe’ than a fine of 100 NIS; but it is not self-evident that a sentence of two weeks’ imprisonment is, for every person, more harmful and ‘more severe’ than a fine of 100,000 NIS. In any case, one should not view the issue from the standpoint of absolute values, as though the types of punishment were arranged on a punitive scale with a categorical and clear hierarchy of ‘severity.’ Moreover, I am prepared to recognize the existence of the rule that ‘the whole includes its part.’ But one must remember: we are dealing with an interpretive rule, nothing more. This is not a decisive rule, or in sports language a ‘tie-breaker,’ but one among various different rules. In the present case there are many interpretive reasons which, in my view — certainly when taken together — outweigh the said rule, overshadow it, and decide against it.”
Yes, a friend of mine who is a judge already sent this to me when it was written. An article of mine on this topic is even mentioned there in the ruling.
I think this is a good example of why an a fortiori inference of “a maneh is included in two hundred” can also be refuted.
Thanks for the answer. Just this: do you deal in one of the books (or in future books) with identifying the parameters, or does that remain up to the discretion of the halakhic decisor / scholar?
And specifically the rule “we do not derive punishments from logical inference” proves that because of concern for a refutation, the a fortiori inference really is undermined (or at least the obligation derived from it is undermined), no? I don’t punish because “maybe” there is a refutation…