The paper you shared seems to be telling a different story, or am I missing something here?

But look what Nagel says in that very book about standpoints and objectivity:

I follow up on this here:https://bsky.app/profile/mntunc.bsky.social/post/3lockwudb372r

12/ It should be emphasized that a scientific community committing to a specific alpha is exercising a form of discretion, since it can never be known with certainty how close these values are to the true optimum for long term error control. But discretion ≠ arbitrariness.

11/ Not really. As long as the specific value that these thresholds are supposed to take is defended in an epistemically principled way, there is rational disagreement, not arbitrariness. And rational disagreement in science is a feature not a bug.

10/ We admit that conventional evidential thresholds are **imperfect** solutions (or rather approximations) to an optimization problem. So, doesn't that mean the specific values are always open to debate and thus "arbitrary"?

9/ Widely shared evidential standards rooted in epistemic considerations are indispensable for collective pursuit of truth as without them there is no way to create a collectively accepted set of reference (evidential base).

..They aren’t perfect, but are deemed to be close enough to serve the long-run aim of controlling error and so converging on truth. This is also what makes it possible to learn from experiment in a piecemeal but socially organized fashion.

8/ Field conventions (like 0.05) approximate the epistemic optimum under (sometimes) conflicting epistemic aims such as discovery and justification...

7/ Alpha levels reflect an **epistemic optimization** problem. Scientists seek thresholds that maximize true positives while minimizing false ones, given sample sizes, measurement noise, and prior odds. That’s not arbitrary—that’s calibration.

6/ In fallibilist epistemology, justified belief doesn’t require certainty. So why should scientific inference require absolute thresholds? All thresholds are approximations—but that doesn’t make them unjustifiable or value-driven.

5/ There is a lesson to be learned from sorites paradox: vagueness ≠ meaninglessness. Concepts like heap are vague but still usable. “Statistical significance” is likewise vague at the boundary, but functionally essential. Fuzziness at the margins doesn’t nullify the category.

...then no amount of sand added individually, no matter how large N is, will form a heap. Similarly, no single increase in the third decimal of p-values can by itself indicate signal rather than noise.

4/ Critics claim 0.049 ≠ 0.051 is meaningless. This leads us into the **Sorites Paradox**: One grain of sand is not a heap. If we add one more sand to it, it still isn't - so if N sand is not a heap, and N+1 sand is not a heap…

3/ Yes, different fields use different thresholds (e.g., 5σ in physics, p < .05 in psych), but this isn't relativism. It's responsive adaptation to domain constraints. What’s shared is the logic of error control—not value judgments, but probability theory.

..as they are usually pre-specified, field-wide, and rooted in epistemic considerations like sample size, base rates, & discovery/accuracy trade-offs (albeit loosely or as an approximation).

2 / The meaning of arbitrariness here is ambiguous. Does it mean unfixed, inconsistent, unjustified? Standard α-levels cannot be described by any of these...

Thank you for your kind words. We would be glad to hear your takes on this.