My understanding of standardised hypothesis tests was that they serve the purposes of
avoiding calculations dependent on details of the alternative hypothesis
providing objective criteria to decide under uncertainty
There are practical reasons for both purposes. (1) is useful because the alternative hypothesis is usually more complex than the null and can have lots of parameters, thus calculating probabilities under the alternative may become impossible, especially with limited computing power. As for (2), science is a social institution—journal editors need a tool to reject publishing unfounded hypotheses without risk of being accused of having “unfair” priors, or whatever.
However I don’t understand how exactly hypothesis tests help to solve the philosophical problems with induction. Perhaps it would be helpful to list several different popular philosophical approaches to induction (not sure what are the major competing paradigms here—perhaps Bayesianism, falsificationism, “induction is impossible”?), present example of problems where the proponents of particular paradigms disagree about the conclusion, and show how a hypothesis test could resolve the disagreement?
However I don’t understand how exactly hypothesis tests help to solve the philosophical problems with induction.
I don’t think it does, in fact I’m not claiming that in my post. I’m trying to set up hypothesis testing as a way of doing induction without trying to solve the problem of induction.
I don’t think hypothesis testing would resolve disagreements among competing paradigms either—well maybe it could, but I’m not talking about that.
(I think you’re largely correct about why, in actual fact, hypothesis testing is used. There’s also some element of inertia as well)
a way of doing induction without trying to solve the problem of induction
Well, this is the thing I have problems to understand. The problem of induction is a “problem” due to the existence of incompatible philosophical approaches; there is no “problem of deduction” to solve because everybody agrees how to do that (mostly). Doing induction without solving the problem would be possible if people agreed how to do it and the disagreement was confined to inconsequential philosophical interpretations of the process. Then it would indeed be wise to do the practical stuff and ignore the philosophy.
But this is probably not the case; people seem to disagree about how to do the induction, and there are people (well represented on this site) who have reservations against frequentist hypothesis testing. I am confused.
I think Matt’s point is that under essentially all seriously proposed versions of induction currently in existence, the technique he described constitutes a valid inductive inference, therefore, in at least the cases where hypothesis testing works, we don’t have to worry about resolving the different approaches.
You’re right—we have to have some idea of how to do induction in order to do it without fully fleshing out the details, but the unresolved issues don’t have to be confined to inconsequential philosophical interpretations. For example, we could just avoid doing induction except for when what seem like plausible approaches agree. (This is probably a better approach to “robust induction” than I proposed in my post).
My understanding of standardised hypothesis tests was that they serve the purposes of
avoiding calculations dependent on details of the alternative hypothesis
providing objective criteria to decide under uncertainty
There are practical reasons for both purposes. (1) is useful because the alternative hypothesis is usually more complex than the null and can have lots of parameters, thus calculating probabilities under the alternative may become impossible, especially with limited computing power. As for (2), science is a social institution—journal editors need a tool to reject publishing unfounded hypotheses without risk of being accused of having “unfair” priors, or whatever.
However I don’t understand how exactly hypothesis tests help to solve the philosophical problems with induction. Perhaps it would be helpful to list several different popular philosophical approaches to induction (not sure what are the major competing paradigms here—perhaps Bayesianism, falsificationism, “induction is impossible”?), present example of problems where the proponents of particular paradigms disagree about the conclusion, and show how a hypothesis test could resolve the disagreement?
I don’t think it does, in fact I’m not claiming that in my post. I’m trying to set up hypothesis testing as a way of doing induction without trying to solve the problem of induction.
I don’t think hypothesis testing would resolve disagreements among competing paradigms either—well maybe it could, but I’m not talking about that.
(I think you’re largely correct about why, in actual fact, hypothesis testing is used. There’s also some element of inertia as well)
Well, this is the thing I have problems to understand. The problem of induction is a “problem” due to the existence of incompatible philosophical approaches; there is no “problem of deduction” to solve because everybody agrees how to do that (mostly). Doing induction without solving the problem would be possible if people agreed how to do it and the disagreement was confined to inconsequential philosophical interpretations of the process. Then it would indeed be wise to do the practical stuff and ignore the philosophy.
But this is probably not the case; people seem to disagree about how to do the induction, and there are people (well represented on this site) who have reservations against frequentist hypothesis testing. I am confused.
I think Matt’s point is that under essentially all seriously proposed versions of induction currently in existence, the technique he described constitutes a valid inductive inference, therefore, in at least the cases where hypothesis testing works, we don’t have to worry about resolving the different approaches.
Couldn’t this be said about any inductive method, at least in cases when the method works?
You’re right—we have to have some idea of how to do induction in order to do it without fully fleshing out the details, but the unresolved issues don’t have to be confined to inconsequential philosophical interpretations. For example, we could just avoid doing induction except for when what seem like plausible approaches agree. (This is probably a better approach to “robust induction” than I proposed in my post).