Double negative

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asked 9 years ago

Greetings to Rabbi Michael Avraham,
As part of our study of Rabbi Shmuel Almoshenino’s commentary on Rashi on the Pentateuch, we encountered the following problem that you may be able to help solve.
Regarding the verse “There are no graves in Egypt,” etc. (Exodus 14:11), Rashi says, “And because of the lack of graves,” etc. Almoshenino says:
I mean, when negation comes upon negation, Torah upon obligation, and here it is impossible for it to be interpreted that way, even though negation does not come upon negation except when the second is a herd negation, but for absolute negation it would not be done so. And the word “no” in the Holy Language is Torah for absolute negation.
In his subsequent remarks, Almoshenino explains Rashi’s commentary on the basis of the assumption that this is indeed not a double negation. We have no difficulty with these things.
The difficulty is in the paragraph I quoted above – what is the meaning of the (logical?) concepts of herd negation and absolute negation, and why can’t absolute negation be interpreted as an affirmation?

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מיכי Staff answered 9 years ago

Sorry for the delay (I just saw it now). I think he is referring to the ancient distinction between two types of negation: negative negation and positive negation. For example, the negative opposite of -1 is 0. The negative opposite of 1 is (-1). Thus the ratio between cold and heat is inverse, while the ratio between light and darkness is inverse. How do I know? Because if you add light to darkness the result will be light, so it is 0 and 1. On the other hand, heat and cold cancel each other out, so they are in a ratio of inverse negation [i.e. 1 and (-1)]. Now you can see that after performing a negative ionization on 1, you cannot return to 1 by a counter-negation (because the counter-negation of 0 is itself 0), so here a double negation is not a positive. —————————————————————————————— Asker (another): Perhaps he is referring to another ancient distinction. Double negation is possible only by removing the predicate, since if there were no openings in the gates, it would be interpreted that the gate is not blocked but open. And the formulation in the language of double negation under the predicate comes precisely to emphasize that not only does the thing itself exist but also that there is no predicate. There are three situations here: there are no openings, there are blocked openings, there are open openings, and the double negation comes to emphasize that it is the second and not the third. But in absolute negation there are only two possible situations: there is or there is not, and therefore they will not be formulated in a convoluted manner with a double negation. —————————————————————————————— Rabbi: I think what you’re saying is roughly what I said. I was talking about how when dealing with negation, one should distinguish between three states: 0, 1, and -1, and not just two. A negative negation takes me between the extremes, and a positive negation takes me from either extreme to the middle state. Therefore, the two negations do not cancel each other out. What you’re suggesting, if I understand what you’re saying, is very similar: an open opening is 1. a closed opening is -1, and no opening is 0. Isn’t that right? —————————————————————————————— Asks: Indeed, on second thought, I understand, as you say, that the content is coherent. It’s just that the explanation is not purely logical (that the negation of 0 is not -1; because there is a language in which the negation of 0 is indeed 1, as in Amos and Icha “darkness and not light”), but rather interpretive (the prolongation in a double negation expresses a different content than the positive despite the logical equivalence. The negation is negated, that is, it expresses that there is no negation). —————————————————————————————— Rabbi: It is possible

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