2 + 2 = 4, right? If I have 2 things, and you have 2 things, we have 4 things between us. This is a logical reality that is inescapable. If we want a coherent, consistent set of rules for counting, this is the simplest and most useful, as well as what applies to the created physical (and spiritual?) reality we are in. The fact that this is the most useful, coherent and consistent system of counting is a "set in stone" fact that belongs to the Platonic world.
Question: Defining the Platonic world as Sir Roger Penrose does in "The Road to Reality"; the "mental" world of logical structures (logic, mathematics), what exactly is Hashem's relationship to it? Is it any of the following (or something else?):
1. He created the Platonic world, and designed it.
He decided that 2 + 2 = 4 in the above counting system. He could have made it so that 2 + 2 = 5, without modifying the meaning of "2" or "+" or "=" or "4" or "5" (i.e. keeping all of that exactly the same), Hashem could have still, in His omnipotence/lack-of-definition said "Let 2 plus 2 be equal to 5", and so it would have verily been and we wouldn't have been able to fathom 2 + 2 = 4 in the same way. We can't imagine how that would work, but we are compelled to believe this in light of our theology.
2. He created the Platonic world, but one does not "design" the Platonic World.
It's not possible that 2 + 2 = 5 (again, without the obvious modification of "2", or "+" or "5", or switching counting system, which is just a convention, and I am trying to be fundamental here). There's no possibility of a universe where, if you have 2 things, and I have 2 things, together we have 5 things and that makes sense. Asking Hashem to do that is as meaningless as asking Him to create a square circle. However, there was once a time when there was absolutely no such thing as squares, circles or "2" or "5" or "+", not b'po'el, not b'co'ach, not b'svara. Hashem created all that in the same way He created anything else.
3. One does not "create" the Platonic world, Hashem is also bound by its truths (ch'v)
Given that 2 + 2 = 4 and that's inevitable, then Hashem didn't create that. That's just the way it is. Hashem just "enabled" it, by creating in general, He unlocked possible, but He didn't need to do anything in terms of what's possible, that just is. 2 + 2 was always going to equal 4, and Hashem has always known that. I say chas veshalom because just expressing the idea that Hashem is "bound" by something sounds very wrong, which is why this position, while seemingly inescapable to my small, finite mind, is going to take the most work to prove.
Couple of extra points:
- I don't want to get too into the philosophy of Plato. I am just borrowing his name to quote the idea of this mental world of logical and mathematical forms in the most loose sense so we can talk about it. Anything that he said about it isn't necessarily what I am holding. E.g. we don't need to discuss here if the Platonic world is "real" or not etc. I think that's a bit much for this question and should only be addressed if absolutely necessary. My question is what do Chazal and Torah say on this, not him or any other secular philosopher (although they can be brought for context or utility!).
- I have been asking this question for a long time. I've only ever had one answer and that is (1) above. Rabbi Dovid Gottlieb told me that "yes, that's what it seems the Torah is saying, but it's very hard to understand". I've also seen it come up many times in Chabad philosophical writings, in fact it's quite a key idea behind a lot of Kabbalistic points (such as the idea that Hashem created principles, including the principle of existence itself - which is a Platonic structure)
- I don't feel qualified to "accept" an answer here but it will fall on me. I do apologise for any bias I have. I have spent most of my life believing (3) and expecting a good explanation of how it doesn't detract from Hashem's omnipotence, but lately, I think my bias is towards (1). I will look at votes, but the ideal answer will have a good explanation, go into as many details as possible (for example, if 1 is being brought, one should try to explain to some extent how it is possible that He could have made 2 + 2 = 5, and if 3 is being brought, some explanation on how we can understand Hashem being bound by anything etc), and have strong sources.