Q&A: A Chain of Causes — as a Potential Infinity
A Chain of Causes — as a Potential Infinity
Question
Hello Rabbi,
1. I wanted to know why a chain of causes as an explanation requires a concrete infinity. Can’t the chain be presented as a potential infinity? For example, suppose there is a cyclic universe, and it is larger than anything we can describe, etc.
2. Is the understanding that a concrete infinity cannot be treated as something that exists due to the fact that one can always add yet another explanation "at the end," and is that understanding what illustrates for us why the existence of infinity is always only potential in our cognition?
3. Even if from the standpoint of our cognition we cannot properly think or define the concept of a concrete infinity (per section 2), who says it does not exist in reality? After all, we can think of a reality with no starting point whatsoever. [Maybe not understand what we are thinking, but still…]
4. Does the Rabbi accept the proof of Duties of the Heart or of Saadia Gaon regarding how we got this far if there was no starting point?
5. Why doesn’t the Rabbi mention in the second booklet the proof that a cyclic universe is in any case not an explanation (perhaps only an explanation in the sense of pushing the testimony farther away) because of the second law of thermodynamics, according to which one reaches a starting point of a universe whose time was 0 at its beginning? [Of course, all this is in any case under the assumption that one accepts a concrete infinity].
Thanks in advance! And sorry for the trouble
Answer
Hello Moshe.
Sorry for the delay (I didn’t see the question).
1. A cyclic universe is not a chain of causes. When you propose an explanation built as a chain of links, you need there to be a complete chain for there to be an explanation here. It’s like turtles all the way down.
2. Because the concept of infinity is an abstraction that, when one tries to understand it, includes contradictions within it (like Hilbert’s hotel). At face value, there is no such thing as infinity in the concrete sense, and the mathematical definitions speak of it in a potential sense.
3. If from the standpoint of our cognition we cannot properly think or define the concept of a concrete infinity (per section 2), then using it does not provide us with an explanation. When we look for an explanation, it is not enough that there be an explanation. It must be presented. It is like standing before a mystery and not being bothered by it because maybe there is an explanation that we do not understand.
4. It is an expression of the difficulty inherent in the idea of a concrete infinity.
5. A cyclic universe is not an explanation (see 1). I didn’t understand what is written here.
Discussion on Answer
That is not a simple question. One of the criticisms of Cantor’s theory of infinities was that for him infinity is concrete. But an infinite chain of explanations is really concrete, and that is an evasion of explanation, not an explanation. With Cantor, one does not assume something really positive about infinity, and therefore in my opinion it is not entirely clear that he is dealing with a concrete infinity.
Do you אולי have a reference for further elaboration?
I don’t have anything on hand. You’d need to search online.
Does the Rabbi perhaps have sources/materials on infinite regress?
No. I assume you can search online.
The Rabbi actually once gave a few links to materials on regress to someone who asked (it appears originally in the comments on the booklets). I’ll copy them here:
There is what is called the homunculus fallacy, which is also based on infinite regress:
https://he.wikipedia.org/wiki/%D7%9B%D7%A9%D7%9C_%D7%94%D7%95%D7%9E%D7%95%D7%A0%D7%A7%D7%95%D7%9C%D7%95%D7%A1
For a fuller treatment within a collection of philosophical fallacies, see this book: https://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/104/Homunculus-Fallacy
Here is one primary source: http://rationalwiki.org/wiki/Infinite_regress
And another one: http://www.informationphilosopher.com/knowledge/infinite_regress.html
And another one: http://philosophy.stackexchange.com/questions/6388/is-infinite-regress-of-causation-possible-is-infinite-regress-of-causation-nece
Is infinity as the cardinality of a set a potential infinity?