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Q&A: The A Fortiori Principle in Logic

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The A Fortiori Principle in Logic

Question

Hello Rabbi,
Not long ago I was thinking about the logical status of the a fortiori principle, and when I looked through some of your books while I was at my brother’s place (which is also when I first became acquainted with you), I saw that you deal a lot with the topic of the logical status of the interpretive principles. I wanted to know what you think about what I came up with, and maybe I even landed on your view.
If we define the use of this principle in line with the approach that holds that deriving laws by a fortiori reasoning is permitted to every person, then this approach leads to complete absurdities in Jewish law. Take, for example, the prohibition of adultery. By a fortiori reasoning we could derive דווקא the opposite from it: if my wife is forbidden to you and permitted to me, then all the more so your wife, who is permitted to you, should also be permitted to me. That is a use that completely contradicts the original command, and yet both are supposed to be true. And absurd uses of this kind are possible in countless cases, thereby uprooting original commands right and left, permitting what is forbidden and forbidding what is permitted (which leads to absurdities in which things are both forbidden and permitted at once). But on the other hand, if we say that the use of this principle is only by means of tradition, then it is as though we have said that the whole essence of the principle is merely to attach scriptural support to laws, and if so, once again we would find ourselves able to permit what is forbidden and forbid what is permitted solely on the basis of laws from tradition. For example, if we take the prohibition of adultery again, and posit a law that permits adultery, we could anchor it in that very same prohibition itself (as shown above), and then it would turn out that by means of the a fortiori principle we have arrived at an absurdity once again. And if we say that according to this approach the laws that come from tradition must not contradict the laws of Scripture, then we will be forced to give up some of the laws that do in fact contradict Scripture. In any case, with this approach we run into several problems: 1. Why should we prefer the scriptural approach? After all, the authority of Scripture comes from the tradition through which we received it from the Holy One, blessed be He, and the authority of those laws likewise comes from an identical tradition. To choose to prefer the scriptural laws is, at most, a conventional decision, and has no essential basis. 2. In order to make sure there is no contradiction between those laws and Scripture (including contradiction by logical implication), we will be forced to derive halakhot logically from those very laws. But our justification for deriving from those laws is exactly what is in doubt! So how can we make use of it? 3. Why do we need to anchor the laws in Scripture at all? After all, both come from the same source: tradition.

From what I can see, only one more approach remains—a third approach. This approach would be that the use of the a fortiori principle is creative, but only so long as the law we extract does not contradict the original scriptural prohibition from which it emerged (and there is no room here for the first objection raised against the previous approach, since we are discussing a principle that creates out of Scripture, and therefore we would prefer the scriptural laws themselves as having higher status). In my opinion, this is the most logical approach to this principle. If we adopt this approach, then the a fortiori principle is a synthetic principle, since it proceeds from an existing prohibition/permission, and by definition it is not analytic; and it is also a priori, since we do not need to search in Scripture-Talmud-Jewish law for authority for this law—it follows clearly from the prohibition/permission itself. I’ll give an example: if we know that when our enemy falls we must not rejoice, then we need not go looking for a command that forbids us to rejoice when our friend falls. But the prohibition against rejoicing when our friend falls is a new prohibition, and it is not included within the prohibition of “when your enemy falls.” So we have found that the a fortiori principle is a synthetic a priori principle of Jewish law.

Answer

You should know that no interpretive principle, including a fortiori reasoning, is formal. This is not mathematics. Therefore common sense is always involved in this kind of study. The a fortiori argument you presented here has refutations against it (another man’s wife is more forbidden to him than his own wife, because she belongs to him less), and therefore it is not valid.
The question whether expounding the Torah is permitted to every person or not is unrelated to the discussion in any way. Interpretation is certainly permitted to every person, but he has to apply the interpretive principles with halakhic logic and common sense, exactly as they would do in a religious court.
Therefore this whole discussion is based on a misunderstanding of the interpretive principles. If you derive from some principle a conclusion that contradicts Scripture, it is obvious that it is void. That is indeed your conclusion, but I do not see what the other option is that you are arguing against. It goes without saying. What would be the initial assumption to say otherwise?

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