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adam_strandberg comments on Stuff That Makes Stuff Happen - Less Wrong
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I can construct examples where for this to be true requires us to treat mathematical truths as causes. Of course, this causes problems for the Bayesian definition of "cause".
Can you provide an example? I would claim that for any model in which you have a mathematical truth as a node in a causal graph, you can replace that node by whatever series of physical events caused you to believe that mathematical truth.
I add 387+875 to get 1262, from this I can conclude that anyone else doing the same computation will get the same answer despite never having interacted with them.
You can't conclude that unless you are aware of the contingent fact that they are capable of getting the answer right.
"The same computation" doesn't cover that?
Why would you want a mathematical truth on a causal graph? Are the transation probabilities ever going to be less than 1.0?
The transition probabilities from the mathematical truth on something non-mathematical will certainly be less than 1.0.
And the transition probabilities to a truth will be 1.0. So why write it in? It would be like sprinkiling a circuit diagram with zero ohm resistors.
Because otherwise the statement I quoted in the great-great-grandparent becomes false.
Inasmuch as you have stipulated that "performing the same calculation" means "perforing the same calculation correcly", rahter than something like "launching the same algorithm but possibly crashing", your statement is tautologous. In fact, it isa special case of the general statement that anyone succesfully performing a calculation will get the same result as everyone else. But why woud you want to use a causal diagrtam to represent a tuatlotlogy? The two have different properties. Causal diagrams have <1.0 transition probabilities, which tautologies don't. Tautologies have concpetually intelligible relationships between their parts, which causal diagrams don't.
Observe that your two objections cancel each other out. If someone performs the same calculation, there is a significant (but <1.0) chance that it will be done correctly.
What has that to do with mathemmatica truth? You might as well say that if someone follows the same recipe there e is a significant chance that the same dish will be produced. Inasmuch as you are takling about someting that can haphazardly fail, you are not talking about mathematical truth.
I can predict what someone else will conclude, without any causal relationship, in the conventional sense, between us.