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CLAIM-322: Agreement under a probe family is evidence that two objects share structure only to the degree that the family was chosen independently of the comparison and is evaluated on cases it was not chosen on, so a family selected to make two objects look alike shows only that it can be selected

2 min read

Properties8
StatusActive
Version2
Rolethesis
Warrantinterpretive
Tagsepistemology, individuation
Lineformal-apparatus
Rests onCLAIM-264 — Two objects can agree on every probe in a restricted family without being isomorphic, so equivalence under a probe family is coarser than identity unless the family is rich enough
SupportsCLAIM-142 — Two communicative realizations can agree on every probe in a restricted family without being structurally identical, so observational equivalence is relative to the probes, and only independently justified probes evaluated on held-out cases are evidence that structure was preserved

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The claim

This is CLAIM-264’s evidential half, stated on its own. CLAIM-264: “Agreement under a probe family is evidence of shared structure only to the degree that the family was chosen independently of the comparison and is evaluated on cases it was not chosen on. A family selected to make two objects look alike shows that it can be selected.”

It rests on CLAIM-264’s exact half. Two objects can agree on every probe in a restricted family without being isomorphic, and matching each probe’s marginal leaves the joint across probes unconstrained. So agreement under a family is not identity, and what it shows depends on how the family came to be. A family chosen for the comparison at hand can be chosen to agree; a family fixed independently and tested on cases it was not chosen on can fail to, and its agreement is evidence for that reason.

The rule is CLAIM-011’s remedy applied to probes, as CLAIM-142 first drew it for communicative realizations.

What it does not say

  • It does not say which probes to choose, or when a family is rich enough for a task (QUESTION-031).
  • It does not say agreement under a chosen family is no evidence at all, only that it is weak evidence that the objects share structure.
  • It does not say that held-out probes settle identity. The exact half still holds of them: unless the family is rich enough, agreement under it is an equivalence coarser than identity.

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