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Eugine_Nier comments on Stuff That Makes Stuff Happen - Less Wrong
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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.
Your prediction is a prediction of what someone else will conclude, given a set of initial conditions (the mathematical problem) and a set of rules to apply to these conditions. The conclusion that you arrive at is a causal descendant of the problem and the rules of mathematics; the conclusion that the other person arrives at is a causal descendant of the same initial problem and the same rules.
That's the causal link.
That's my point. Specifically, that one should have nodes in one's causal diagram for mathematical truths, what you called "rules of mathematics".
Surely the node should be "person X was taught basic mathematics", and not mathematics itself?
The point of having the node is to have a common cause of person X's beliefs about mathematics and person Y's beliefs about mathematics that explains why these two beliefs are correlated even if both discovered said mathematics interdependently.
What has that to do with any causal powers of mathematical truth?
If you what your causal graph to have the property I quoted here, you need to add nodes for mathematical truths.
Two people can arrive at the same solution to a crossword, but that does not mean there is a Cruciverbial Truth that has causal powers.
Yes it does. In this case said truth even has a physical manifestation, i.e., as the crossword-writer's solution as it exists in some combination of his head and his notes which is causal to the form of the crossword the solver sees.
It only has a physical manifestation. Cruciverbial Truth only summarises what could have been arrived at by a massively fine-grained examinination of the crossword-solver's neurology. It doesn't have causal powers of its own. Its redundant in relation to physics.