Can causality be translated into logical formalism to analyze it via mathematical logic?

Question

An observation about causality:

It produces state change. It happens via some thing operating on another thing changing it into the effect. A thing happens that's not an invariant.

Furthermore, it implements the rules of classical logic:

By taking a state and transforming it over, it passess along the truthhood of what held about the state and distributes it to the effect, yiedling a true statement.

It thus entails an implication.

By states being distinguishable, only assuming LEM, truth-falsehood and implication implement implicational propositional calculus which is equivalent to classical logic.

Now with causality lifted into formal logic, here's what I thought:

By doing so, it can help answer questions in philosophy of religion:

First a direct formalization of naturalism follows, since lifting into a formal system yields behaviors all reducible to (certain, nonconstructive) axioms and rules of inferrence, thus these account for all information there can possibly be, without exterior independent axioms.

The existence of possible/contingent things is necessary itself as the axioms need to correspond to something, which falsifies classical theism that attributes necessity solely to one thing alone.

However, the important question here is: Is this a justified line of thought?

Mapping a causal process into a statement mapping that into a formal system... any objections to that?

Answer 1

Non liquet but ...

both logic and causality are understood/framed as this follows - (non) sequitur and post (hoc ergo propter hoc) - from that.

Answer 2

A implies B - If A is true at time t, then B is true at time t.

A causes B - If A had not been true at t₁, then B wouldn't have been true at t₂ = t₁ + Δt (Δt > 0).

The human mind only has one logic. If it didn't, we would all do absurd things all the time, and we don't.

So, causality has the same logic, but it is about something else, just as counterfactual scenarios have the same logic but about something else again, namely, alternative scenarios.

Answer 3

Causality is an influence by which one event, process, state, or object (a cause) contributes to the production of another event, process, state, or object (an effect) where the cause is partly responsible for the effect, and the effect is partly dependent on the cause.

By suggesting that :

causality implements the rules of classical logic

you are taking a big step, that needs to be justified. Some people generally assume that causality is like a chain of events/states in such a way that if the x never existed, then the x+1 wouldn't exist too, or would exist in an another form. I will not expand to this now.

Now, from another perspective, going by the definition, do you see how "a seed becoming a tree" cannot be grounded to classical logic? Surely a chain of events lead the seed to become a tree, but is that all? We all knew that the seed would (probably) become a tree from the beginning! How would you formalize this?