If propositional calculus (simpler than it sounds is a good way of describing causality in the territory, I very much doubt there is a fourth option. If I’m doing logic right:
1.¬A is A’s cause(1)∨A is A’s cause (1)(By NOT-3)
2.A has a cause→ ¬A is A’s cause(1)∨A is A’s cause(1)(By THEN-1)
3.A has a cause→ ¬A is A’s cause(1)∨A is A’s cause(1)→A has a cause ∧¬A is A’s cause(1)∨A is A’s cause(1)(By AND-3)
4.A has a cause→A has a cause ∧¬A is A’s cause(1)∨ A is A’s cause(1)(Modus Ponens on 3)
¬A has a cause∨A has a cause⊢A has a cause ∧ A is A’s cause(1)∨¬A is A’s cause* (By NOT-3)
6.¬A has a cause∨A has a cause ∧ A is A’s cause(1)∨¬A is A’s cause(1)(Modus ponens on 5)
Which, translated back into English, means that something either has a cause apart from itself, is it’s own cause*,or has no cause. If you apply “has a cause apart from itself” recursively, you end up with an infinite chain of causes. Otherwise, you have to go with “is it’s own cause(1)”, which means the causal chain loops back on itself or “has no cause” which means the causal chain ends.
Nothing thus far, to my knowledge, has been found to defy the axioms of PC, and thus, if PC were wrong, it would seem not only unsatisfying but downright crazy. I believe that I could make at least a thousand claims which I believe as strongly as “If the Universe defied the principles of logic, it would seem crazy to me.” and be wrong at most once, so I assign at least a 99.9% probability to the claim that “Why is everything” has no satisfying answer if “It spontaneously sprang into being”, “Causality is cyclical.” and “an infinite chain of causes” are unsatisfying.
If propositional calculus (simpler than it sounds is a good way of describing causality in the territory, I very much doubt there is a fourth option. If I’m doing logic right:
A problem, or a strength, depending on the context, with this sort of argument is that it does not depend on the meaning of the phrase “X is caused by Y”. Logically, any binary relation forms chains that are either infinite, lead to a cycle, or stop. If the words “X is caused by Y” indeed define a binary relation, then the argument tells you this fact about that relation.
If the concept being groped for with the words is vague, ill-defined, or confused, then the argument will be working from a wrong ontology, and the precision and soundness of the argument may distract from noticing that. Hume denied causation, in favour of correlation; Pearl asserts causation as distinct but as far as I can see takes it as unproblematic enough for his purposes to leave undefined. The discussion here suggests the concept of causation is still unclear. Or if there is a clear concept, people are still unclear what it is.
As I have stated elsewhere, we would still like to know why the universe is not in a counterfactual no-infinite-chain (or loop) state. If this cannot be answered with propositional calculus, then that’s propositional calculus’ fault for containing ontological paradoxes.
Note that this applies in all situations featuring infinite chains or loops, not merely those contaning everything that exists.
If propositional calculus (simpler than it sounds is a good way of describing causality in the territory, I very much doubt there is a fourth option. If I’m doing logic right:
1.¬A is A’s cause(1)∨A is A’s cause (1)(By NOT-3)
2.A has a cause→ ¬A is A’s cause(1)∨A is A’s cause(1)(By THEN-1)
3.A has a cause→ ¬A is A’s cause(1)∨A is A’s cause(1)→A has a cause ∧¬A is A’s cause(1)∨A is A’s cause(1)(By AND-3)
4.A has a cause→A has a cause ∧¬A is A’s cause(1)∨ A is A’s cause(1)(Modus Ponens on 3)
¬A has a cause∨A has a cause⊢A has a cause ∧ A is A’s cause(1)∨¬A is A’s cause* (By NOT-3)
6.¬A has a cause∨A has a cause ∧ A is A’s cause(1)∨¬A is A’s cause(1)(Modus ponens on 5)
Which, translated back into English, means that something either has a cause apart from itself, is it’s own cause*,or has no cause. If you apply “has a cause apart from itself” recursively, you end up with an infinite chain of causes. Otherwise, you have to go with “is it’s own cause(1)”, which means the causal chain loops back on itself or “has no cause” which means the causal chain ends.
Nothing thus far, to my knowledge, has been found to defy the axioms of PC, and thus, if PC were wrong, it would seem not only unsatisfying but downright crazy. I believe that I could make at least a thousand claims which I believe as strongly as “If the Universe defied the principles of logic, it would seem crazy to me.” and be wrong at most once, so I assign at least a 99.9% probability to the claim that “Why is everything” has no satisfying answer if “It spontaneously sprang into being”, “Causality is cyclical.” and “an infinite chain of causes” are unsatisfying.
(1)Directly or indirectly
A problem, or a strength, depending on the context, with this sort of argument is that it does not depend on the meaning of the phrase “X is caused by Y”. Logically, any binary relation forms chains that are either infinite, lead to a cycle, or stop. If the words “X is caused by Y” indeed define a binary relation, then the argument tells you this fact about that relation.
If the concept being groped for with the words is vague, ill-defined, or confused, then the argument will be working from a wrong ontology, and the precision and soundness of the argument may distract from noticing that. Hume denied causation, in favour of correlation; Pearl asserts causation as distinct but as far as I can see takes it as unproblematic enough for his purposes to leave undefined. The discussion here suggests the concept of causation is still unclear. Or if there is a clear concept, people are still unclear what it is.
As I have stated elsewhere, we would still like to know why the universe is not in a counterfactual no-infinite-chain (or loop) state. If this cannot be answered with propositional calculus, then that’s propositional calculus’ fault for containing ontological paradoxes.
Note that this applies in all situations featuring infinite chains or loops, not merely those contaning everything that exists.