Immanuel Can wrote: ↑Sat Jul 25, 2026 5:35 am
But we're back to the First Cause problem. Your position is that causal chains can begin without fulfilling any prerequisites -- hence, that caused things can happen without any cause.
Absolutely not. That would violate "everything either has a cause or is a "first cause" (an axiom of the relation "cause").
What do you mean by "happen" (in "things can happen"). You are sticking another meaning to the relation. Among our axioms for "cause" we have of course "there is at least one thing" << horrible things happen when you have an empty set and try to conclude something --- remember, an if X then Y statement means little if the X is not true >>
What do you mean "begin"? We are describing causal chains chains, which since the axiom "finite" have two ends, the "thing" that exists by axiom and a "first cause". If you have a physical chain, finite length, so two ends, it BEGINS where? You say that chain has one beginning?
Since determined every causal chain has a "first cause" you can just DEFINE that end "the beginning".
For reference, your axioms (I'll try to use words since you seem to have trouble with standard abstract.
1) There is at least one thing
2) Things are of two types, ordinary and first cause.
3) If x is a regular thing, then there exists a thing y which is the cause of x
4) No thing is its own cause
5) If a is a cause of y and y is a cause of z then a is a cause of z
6) The number of things is finite
Notice a few things: Using "a" instead of "the" so no implication thing has only one cause, just that it has at least one cause. Nor is specified "cause" means "immediate cause" . Axiom 6 is why you can say "no infinite regression". Not using a notion of "before" as not needed, "5" is doing that and along with "4" excluding "causal rings"
From these axioms you can indeed deduce "there exists at least one "first cause". You need to add one more to make that "first cause" unique. But feel free to try to DERIVE it from the axioms you have*. The notion "beginning" needs no axiom, you are simply NAMING the "first cause" end of the chain "the beginning". In terms of how the chain was logically generated, the other end starting from the thing known to exist, could also be thought of as "the beginning". Since the two ends different, you are just choosing names, nothing implied by that.
I know IC, that you think something like axiom 4 is unnecessary, that OF COURSE nothing is its own cause. But these axioms are specifying what sort of a relation is "cause", how it behaves. There ARE (other) relations where S(x,y) does not mean either x = y OR x not = y << both would be possible and in fact, for all x S(x,x) is true. For example, let S be the relation "same color as" -- then everything is the same color as itself and might or might not be the same color as something else >> In other words, an AXIOM is stating "causes" does not behave like "same color as" does.
BTW -- Since you are wanting to use 14th Century standards of reasoning I'd refer you to Occam himself for whether God can be deduced except I think only his text on logic is available in English and that in a translation considered questionable.
* The reason I am confident that you could not is that I can propose two alternative axioms for the seventh axiom, there exists ONLY one first cause and there exists more than one and show neither alternative is inconsistent with the six axioms.
