If no distinct possibilities exist, the hole argument establishes formal underdetermination within a representational framework rather than genuine ontic indeterminism detectable or otherwise.

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Distinct possibilities(as used in metaphysics and modal logic): Genuinely different scenarios or ways things could actually be; options that are meaningfully different from each other, not just different descriptions of the same thing.
Formal underdetermination(as used in philosophy of science): A situation where multiple different mathematical or logical descriptions could fit the same evidence or observations, making it impossible to tell from the form or structure alone which description is correct.
Ontic indeterminism(as used in metaphysics and philosophy of science): The idea that reality itself (not just our knowledge of it) contains genuine randomness or is fundamentally indeterminate—meaning the world isn't fully determined by prior causes.
The hole argument(as used in philosophy of physics and metaphysics): A thought experiment in philosophy of physics (developed by John Earman and David Norton) that asks whether two physical situations that differ only in how we label points in spacetime are actually the same or different; it challenges whether our descriptions of reality are truly capturing what's real versus just how we're representing it.
representational framework(the background knowledge needed to understand what features matter in a watch): A system of ideas and meanings that helps us understand and talk about something—in this case, our shared understanding of what a watch is supposed to do.

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