This is often a good idea in mathematics. Two concepts that are equivalent in some context may no longer be equivalent once you move to a more general context; for example, familiar equivalent definitions are often no longer equivalent if you start dropping axioms from set theory or logic (e.g. the axiom of choice or excluded middle).
Outside of mathematical logic, some familiar examples include:
compactness vs. sequential compactness—generalizing from metric to topological spaces
product topology vs. box topology—generalizing from finite to infinite product spaces
finite-dimensional vs. finitely generated (and related notions, e.g. finitely cogenerated)—generalizing from vector spaces to modules
pointwise convergence vs. uniform convergence vs. norm-convergence vs. convergence in the weak topology vs....—generalizing from sequences of numbers to sequences of functions
There’s still a couple related fallacies that Bayesians can commit.
Most related to the “ludic fallacy” as you’ve described it: if you treat both epistemic (lack of knowledge) and aleatory (lack of predetermination) uncertainty with the same general probability distribution function framework, it becomes tempting to try to collapse the two together. But a PDF-over-PDFs-over-outcomes still isn’t the same thing as a PDF-over-outcomes, and if you try to compute with the latter you won’t get the right results.
Most related to the “ludic fallacy” as I inferred it from Taleb: if you perform your calculations by assigning zero priors to various models, as everybody does to make the calculations tractable, then if evidence actually points towards one of those neglected priors and you don’t recompute with it in mind, you’ll find that your posterior estimates can be grossly mistaken.
-- aristosophy
This is often a good idea in mathematics. Two concepts that are equivalent in some context may no longer be equivalent once you move to a more general context; for example, familiar equivalent definitions are often no longer equivalent if you start dropping axioms from set theory or logic (e.g. the axiom of choice or excluded middle).
Outside of mathematical logic, some familiar examples include:
compactness vs. sequential compactness—generalizing from metric to topological spaces
product topology vs. box topology—generalizing from finite to infinite product spaces
finite-dimensional vs. finitely generated (and related notions, e.g. finitely cogenerated)—generalizing from vector spaces to modules
pointwise convergence vs. uniform convergence vs. norm-convergence vs. convergence in the weak topology vs....—generalizing from sequences of numbers to sequences of functions
Arguable example: probability and uncertainty. (More or less identical in my theorizing, but some call the idea of their identity the ludic fallacy.)
There’s still a couple related fallacies that Bayesians can commit.
Most related to the “ludic fallacy” as you’ve described it: if you treat both epistemic (lack of knowledge) and aleatory (lack of predetermination) uncertainty with the same general probability distribution function framework, it becomes tempting to try to collapse the two together. But a PDF-over-PDFs-over-outcomes still isn’t the same thing as a PDF-over-outcomes, and if you try to compute with the latter you won’t get the right results.
Most related to the “ludic fallacy” as I inferred it from Taleb: if you perform your calculations by assigning zero priors to various models, as everybody does to make the calculations tractable, then if evidence actually points towards one of those neglected priors and you don’t recompute with it in mind, you’ll find that your posterior estimates can be grossly mistaken.
Oh, I read Taleb as using ‘ludic fallacy’ to mean using distributions with light tails.
However, equivalences are also the bread and butter of inference. Distinguishing more than you need to will slow you down.
Unfortunately I only have a finite amount of storage available, so I can only do that up to a certain point.