However, it does seem the second one uses the function of the first one as “subfunction”: it needs to know the “real” answer to “2 + 2” in order to output “-4″. Therefore, the calculators are subjunctively dependent on that subfunction, even though their outputs are different. Even if the second calculator always outputs “[output of first calculator] + 1”, the calculators are still subjunctively dependent on that same function.
Why not reverse the situation? Couldn’t you just as well say that the calculator that outputs 4 is subjunctively dependent on the calculator that outputs −4, since it needs to know that the real answer to the second is −4 in order to drop the—and output 4?
Direction of causality, or even causality itself, is irrelevant to FDT. Subjunctive dependence is simply a statement that two variables are not independent across the possible worlds conditional on parameters of interest. It doesn’t say that one causes the other or that they have a common cause.
In the calculator example, the variables are the outputs of the two calculators, and the parameters of interest are inputs common to both calculators. In this case the dependence is extremely strong: there is a 1:1 relation between the outputs for any given input in all possible worlds where both calculators are functioning correctly.
For the purposes of FDT, the relevant subjunctive dependence is that between the decision process outputs and the outcomes, and the variables of interest are the inputs to the decision process. In carefully constructed scenarios such as Newcombe’s problem, the subjunctive dependence is total: Omega is a perfect predictor. When the dependence is weaker, the details matter more—but still causality is irrelevant.
In the case of weaker dependence you can get something like a direction of dependence, in that perhaps each value of variable A corresponds to a single value of variable B across possible worlds, but not vice versa. This still doesn’t indicate causality.
FDT can require that P come augmented with
information about the logical, mathematical, computational, causal, etc. structure
of the world more broadly. Given a graph G that tells us how changing a logical variable affects all other variables, we can re-use Pearl’s do operator to give a
decision procedure for FDT
FDT seems to rely heavily on this sort of assumption, but also seems to lack any sort of formalization of how the logical graphs work.
Interesting point. It seems to me that given MacAskill’s original setup of the calculators, the second one really does calculate the first one’s function and adds the -. Like, if 2 + 2 where to equal 5 tomorrow, the first calculator would output 5 and the second one −5.
Idk . MacAskill’s setup is kinda messy because it involves culture and physics and computation too, these layers introduce all sorts of complexity that makes it hard to analyze. Whereas you seem to say that causality is meaningful for logic and for mathematical functions too.
So let’s stay within math. Suppose for instance we represent functions in the common way, with f being represented as it’s graph { (x, y) where y = f(x) }. Under what conditions does one such set cause another?
Why not reverse the situation? Couldn’t you just as well say that the calculator that outputs 4 is subjunctively dependent on the calculator that outputs −4, since it needs to know that the real answer to the second is −4 in order to drop the—and output 4?
Direction of causality, or even causality itself, is irrelevant to FDT. Subjunctive dependence is simply a statement that two variables are not independent across the possible worlds conditional on parameters of interest. It doesn’t say that one causes the other or that they have a common cause.
In the calculator example, the variables are the outputs of the two calculators, and the parameters of interest are inputs common to both calculators. In this case the dependence is extremely strong: there is a 1:1 relation between the outputs for any given input in all possible worlds where both calculators are functioning correctly.
For the purposes of FDT, the relevant subjunctive dependence is that between the decision process outputs and the outcomes, and the variables of interest are the inputs to the decision process. In carefully constructed scenarios such as Newcombe’s problem, the subjunctive dependence is total: Omega is a perfect predictor. When the dependence is weaker, the details matter more—but still causality is irrelevant.
In the case of weaker dependence you can get something like a direction of dependence, in that perhaps each value of variable A corresponds to a single value of variable B across possible worlds, but not vice versa. This still doesn’t indicate causality.
What I have in mind is stuff like this:
FDT seems to rely heavily on this sort of assumption, but also seems to lack any sort of formalization of how the logical graphs work.
Interesting point. It seems to me that given MacAskill’s original setup of the calculators, the second one really does calculate the first one’s function and adds the -. Like, if 2 + 2 where to equal 5 tomorrow, the first calculator would output 5 and the second one −5.
Idk . MacAskill’s setup is kinda messy because it involves culture and physics and computation too, these layers introduce all sorts of complexity that makes it hard to analyze. Whereas you seem to say that causality is meaningful for logic and for mathematical functions too.
So let’s stay within math. Suppose for instance we represent functions in the common way, with f being represented as it’s graph { (x, y) where y = f(x) }. Under what conditions does one such set cause another?