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Six Birds Verified XIV: Objectivity Without Finality
When does a community of instruments settle a question? Exactly when its public tests separate what matters.
In plain words
When do public measurements settle a question about the world? This paper gives an exact answer for finite models with deterministic, noise free tests. A question is settled exactly when every pair of worlds that differ in the answer is told apart by some calibrated public test. The answer is then a unique function of the pooled readings. Agreement is not separation. A hundred calibrated instruments with separate origins can all measure x, agree perfectly, and say nothing about y. One added test that separates every relevant pair repairs the blind spot. Separation is not calibration either: relabelled reports separate the same worlds and can still fool a fixed decoder.
Instruments fail. When they fail by source groups, a question stays settled through the silent failure of any b groups exactly when every relevant pair of worlds differs in at least b plus 1 groups. Lying groups need 2b plus 1. Three instruments with separate sources reading y survive two going silent or one lying. Three that share one source fail together. Two communities can translate their readings exactly when they draw the same distinctions, and then the translation is unique. Being equally rich is not enough.
Settled is not final. A panel can settle every question put to it and still leave other questions open. The public picture can sharpen only finitely often, yet a pause proves nothing. Keeping questions settled also costs. With positive price floors, forcing a fresh test at every stage outruns every budget that grows slower than linearly, and cross validating every pair of n or more instruments at stage n outruns every linear budget. All results are formalized in Lean 4.
What it shows
- A target is identifiable exactly when every target relevant pair of worlds has a separating public test.
- Silent failure of b source groups is survivable exactly at distance b plus 1; lying needs 2b plus 1.
- Translation between communities exists exactly when their distinctions match, and is then unique.
- A panel can be sufficient for its questions without being final.
- Cost outrun results for fresh tests and pairwise cross validation.
What it does not claim
Certificates hold only within the admitted worlds and declared calibrations; whether those cover the real world is a separate question. It gives no probabilistic confidence and does not treat statistical measurement error. The cost results hold only for the declared growth models.
Cite
Tsiokos, I. (2026). Six Birds Verified XIV: Objectivity Without Finality. Zenodo. https://doi.org/10.5281/zenodo.23097945