I suppose I’ll begin to reply to my friend’s comments. His input is in italics, my comments follow.
X is dependent on Y means that Y cannot exist without X. That X causes Y is not sufficient. Multiple entities might cause Y, and hence Y would not have a dependency on any particular entity.
I did not rule out the possibility of there being several causes for Y’s existence. Indeed, I alluded to the possibility. If Y cannot exist without X then surely X is a cause of Y’s existence. If X did not exist then Y would not.
There is no inherent contradiction in an object depending on itself for it’s existence. Indeed, every object is necessarily dependent on itself for it’s existence. X cannot exist without X, trivially. The question is whether every entity must have multiple dependencies.
I disagree. I think X depending on itself to exist is inherently contradictory. To say X cannot exist without X is entirely different from saying X is dependent on X. If X cannot exist unless it already exists then it will never come into existence.
There were more comments, including a challenge to define causality. I may return to these later but I think it digresses from the main argument a bit too much for the moment.
I’d like to point out that in maths, every X must have an exactly opposite value in order to “exist” (balance the equation). The “anti-X” does not have to be a single entity, but can be multiple entities, each adding up to the opposite value of X. In this case, there is one entity which is dependent on one or more other entities for it’s existance. It seems to me that the only truly independent entity is one which is its own opposite – ie: 0
This doesn’t really generalise. The additive inverse of X does not necesarily exist. Take, for example, addition defined over the Natural Numbers ({0,1,2,…}). The only number with an additive inverse in this set is 0 (because it is it’s own additive inverse).