# Are there models of causal regresses where each cause-effect pair is mapped to/from the integers?

Let's substitute the event into an integer

for example

event A is 2

"Cause B" of A is 1

cause of B is 0

Let's represent it like this

So what does an integer less than all integers mean?

the cause of all events

However, there is no integer smaller than all integers.

in other words,

Causes of all events do not exist

in other words,

If you go up to the cause of all events

That there is "no cause" at the root

Are there accounts of causal regresses where causation is discrete instead of continuous?

No.

Events are not isolated discrete things like beads on a necklace. An event is a point in space-time. It has a real number for each of its time and space dimensions, four in total. Events thus form a continuum in one time and three space dimensions.

So, for some purpose or activity, a particular event is singled out for special attention. Possibly even given a name. Real-number-close to it, in each of those dimensions, there are other events.

So we can assign integers to specific events. But these are arbitrary or convenience labels. There is a continuum of events between and on the far side of the events we might give integer designations.

Additionally, a single event by itself is not THE cause of another event. Insert here the usual discussion of causes and causality from, at least, Aristotle to Einstein to Heisenberg. Consider a trivial thing such as being warmed by a camp fire. The camp fire has physical extent and duration. You are warmed by it over some portion of that extent. And the warming itself has extent both in space and time.

In some (not all) cases we can do some ordering. This event occurred before that event. This event was west of that event.

If you are trying to get to something like a first cause, you need to work quite a bit harder.