Q&A: Infinity, the Perfect Being, God, Mathematics
Infinity, the Perfect Being, God, Mathematics
Question
Hello Rabbi, I wanted to ask your permission about several concepts. Unfortunately, I’m concerned that because of the limits of language and the subtlety of the topic, it will be hard to discuss, but I’ll try. (In general, the more I learn, the more I understand that I have less room to maneuver in talking about this subject without falling into nonsense.)
1. Regarding “the perfect being” (as presented in Plato), “Kabbalistic infinity” (the Zohar, the Ari, etc., in the accepted sense of course), “quantitative infinity” (the mathematical one), “metaphysical infinity” (Descartes?) and their relation to “God” (the biblical or the deistic one), I’d be glad to know whether the Rabbi can say something comprehensive on the subject, or whether there is an article I could read about it, because it feels to me that all these concepts keep getting mixed up with one another.
2. Regarding infinity, there is apparently quantitative infinity and essential-spiritual infinity. And seemingly, quantitative infinity does indeed apply to ideas (since mathematics is conceptual and one can also count things that are not physical), but it seems more connected to our material world (belonging to dimensions of time and space), whereas essential infinity is abstract at its root. Am I understanding correctly? Does spiritual infinity even have any meaning?
3. Is there any connection between quantitative infinity, which belongs to the world of mathematics, and “essential-metaphysical/spiritual” infinity? Is mathematical knowledge needed in order to understand and discuss essential spiritual infinity?
4. I saw in your book The First Existent that you do not attribute infinity (the metaphysical-spiritual kind) to God, both in Kabbalah and in philosophy; that is, infinity is something located below Him in the hierarchy. Is God outside the scale of “infinity”? Can He not be defined as infinite? Does He fall under the Platonic concept of “the perfect being”? Or is that too a concept beneath Him in the hierarchy?
5. In the chapter on the cosmological proof you brought a Greek midrash (to solve the principle of conservation of being) regarding infinity as prime matter— to which of these infinities is that connected? Since it seemingly divides and contains opposites.
6. Does the Rabbi know of an article/book that puts things in order?
(There is a book from Resling called The Thought of Infinity, but I’m not sure it will provide an answer.)
Thank you very much, and sorry for the length.
Or
Answer
Hello Or.
Unfortunately this is too heavy for a responsum answer. If you break it down into one question at a time, it may be possible to try and discuss it. Beyond that, I generally don’t deal with the meaning of terms (why something is called this or that), because that’s just semantics. The important questions are substantive, not semantic. In addition, with some of the questions I assume it would just be a matter of interpretation (whether this is talking about the same thing as that).
Discussion on Answer
Thank you, Rabbi,
I hope the Rabbi will one day write an article on the subject.
If possible, then just an answer to question 3.
I’ll ask about the others another time.
Thanks,
Or
I think infinity in its conceptual appearances usually means perfection, though not always. Mathematical knowledge can sharpen things, but it is definitely not a condition for understanding. That is, as long as you don’t want to derive specific conclusions but only to gain general understanding. In such cases, the expression “infinity” is not very important. Of course, if you want to draw conclusions (for example, that if it has no end then it also has no beginning, as in Sha’ar HaYichud; or that if it is infinite then contraction does not apply to it, and the like), then it is worthwhile to have mathematical knowledge and careful thinking. But the overwhelming majority of the sages who dealt with this also did not have the relevant knowledge, so if you want to understand what they said, you don’t need such knowledge, and it may even interfere with you. In my opinion, they also not infrequently made mistakes because of this. In general, this topic seems marginal to me.
Thank you very much.
I wasn’t able to understand how there is a connection between concrete mathematical infinity and the metaphysical-spiritual one (which is usually attributed to God). Seemingly the first speaks only about quantitative multiplicity, whereas the second speaks about something that, as stated, is simply not limited in its value/reality/quality.
I suggest not staying in the realm of general declarations. A discussion like this has to be conducted on examples. Statements that the Holy One, blessed be He, is infinite are completely quantitative. He occupies all space, He has infinite power, and so on.
How can God be quantitative if He is abstract, without space and time?
I understood “infinite” to mean in His quality, such as His influence, His value, His truth, and His existence (that is, that He stands on His own, without need of another and without limit).
I’ll just add that the expectation that a Resling book will sort out the concepts for you sounds detached from reality to me (though I don’t know this particular book).