Q&A: The Laws of Logic as a Necessary Entity
The Laws of Logic as a Necessary Entity
Question
Hello Rabbi,
A question came up for me in a discussion with friends, in light of reading That Which Exists and That Which Does Not:
I learned that if a mathematical theory was properly constructed, and yet results were still found that seemingly refute it, then according to the dogmatic approach we could conclude that the logic underlying the derivation of conclusions from the premises describes only us and not the world (that wording is from the book).
My difficulty is this: how can one claim that there could be a logic different from ours that exists in the world, if it seems that the logic familiar to us exists necessarily?
Put differently: in order to claim that there is another way, there has to be a meaningful alternative, and anti-logical thinking is meaningless for us. Is it possible to say that there is a possibility (even if not a likely one, and even if we do not accept it) that the logic of the real world is different, and we simply are incapable of grasping it because of the way we think?
Answer
I’m not sure I understood the question. Clearly there is no other logic. I don’t know which passage in the book you meant, but perhaps the intention is that the mathematics we chose is not suitable for describing the physics in question. For example, ordinary calculation (arithmetic) is not suitable for describing the addition of forces or velocities in physics (for that you need vector calculus).
Discussion on Answer
The laws of logic are not an assumption, and in fact they are not really laws at all (that is only a borrowed term). Therefore the Holy One, blessed be He, Himself is “subject” to them (as Maimonides and Rashba and others wrote).
And note carefully that even your question presupposes the laws of logic, since you asked whether the laws of logic are an assumption or something else, and by that you assumed the law of the excluded middle. Without the laws of logic you would not be able to ask your question, and really not to speak at all.
I meant the mention of the dogmatic approach to mathematics on p. 140.
In any case, my question is whether the laws of logic are an assumption like all other assumptions (just a very strong assumption), or whether they are something else altogether (since after all, we do not really “assume” them)?