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MugaSofer comments on Wrong Questions - Less Wrong
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Comments (126)
Or there could be a fourth explanation neither of us has thought of.
"There could be an (n+1)th explanation neither of us has thought of" is a fully general counterargument to any argument by cases.
It's valid too. Which is one reason not to put p=1.0 on anything.
Most fully general counterarguments are valid, taken at face value. This does not mean they're worth giving much weight. For example, someone could answer any argument I post on LW with "but satt, it's always possible you are wrong about that!" Which would be correct but rarely helpful.
Similarly, although I'm sympathetic to the idea of never assigning p=0 or p=1 to anything, any well-specified model I make is going to leave something out. So for me to make any inferences at all, I have to implicitly assign p=0 or p=1 to something. If I started throwing out models on that basis I'd have nothing left.
Why yes, yes it is. Arguing that someone else is wrong, therefore you are right is a well-known cheap debating trick.
Would you care to explain why I'm wrong, rather than sorting my argument into a low-status category?
When I was complaining about the "but satt, it's always possible you are wrong about that!" argument, I wasn't complaining about all arguments that have "you are wrong, satt, therefore I am right" as a conclusion. I'm only taking issue with people mumbling "well, have you ever considered you might be wrong?" without elaborating. There's nothing wrong with someone arguing I might be wrong about something. But they should at least give a hint as to why I'd be wrong.
In this case, "there could be a fourth explanation neither of us has thought of" amounts to saying "there could be a fourth possible terminal state for a causal chain". Well, sure, it's always possible. But why should I assign that possibility any substantial probability?
Causal chains are pretty basic, abstract objects — directed graphs. I'm not talking about a set of concrete objects, where a fourth example could be hiding somewhere in the physical world where no one can see it. I'm not talking about some abstruse mathematical object that's liable to have weird properties I'm not even aware of. I'm talking about boxes connected by arrows. If there were some fourth terminal state I could arrange them to have I'd expect to know about it.
What I've just said might be mistaken. But you haven't given any specifics as to where or how it goes wrong, so your comment is just another form of "but satt, it's always possible you are wrong about that!", which doesn't help me.
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)
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.