What follows is the same question in a nearby possible world, one in which Finch wins cleanly. No caricature, no incompetence — just clarity, rigour, and precisely the wrong success.
Setting: The same faculty common room. Everything is a little neater.
The clock keeps perfect time.
Arguments terminate.
Scene I — Finch Frames the Issue
Finch (calm, authoritative):
The question, “are numbers actually real?”, is straightforward once we disambiguate our terms. By “real” we mean ontologically committed. By “numbers” we mean abstract entities posited by successful mathematical theories.
Blottisham (relieved):
Thank you. At last.
Finch:
We then ask: do our best theories require such entities? If yes, we are realists. If not, we are anti‑realists. The dispute is well‑posed.
Quillibrace (tentatively):
And the role of practice?
Finch:
Epistemic. Important, but downstream.
Quillibrace makes a small note. It will not matter.
Scene II — The Decisive Argument
Finch:
Mathematics delivers indispensable explanations in physics, engineering, and economics. We cannot paraphrase away quantification over numbers without loss of explanatory power.
Blottisham:
So numbers are real.
Finch:
Yes — abstract, non‑spatiotemporal, causally inert, but indispensable.
Stray:
But doesn’t that make their reality rather thin?
Finch:
Thinness is not a defect. Ontology is not upholstery.
Blottisham (smiling):
That’s what I’ve been saying.
Finch:
The alternative is fictionalism, which cannot account for the objectivity of mathematical truth. Therefore realism wins by inference to the best explanation.
The room relaxes. The anxiety drains. The question has an answer.
Scene III — What Quietly Disappears
Stray (after a pause):
So when a child learns to count, what exactly are they doing?
Finch:
Gaining epistemic access to pre‑existing abstract entities.
Stray:
And when a new mathematical system is developed?
Finch:
Discovering further truths about that abstract domain.
Quillibrace:
And when the system changes its axioms?
Finch:
Exploring a different region of the same logical space.
Stray:
What about systems that later turn out to be inconsistent?
Finch:
They fail to refer successfully.
A small silence. No one objects.
Scene IV — The Cost Accounting
(This is where the distortions show)
Quillibrace:
Just to be clear: on this view, the source of mathematical necessity lies in the nature of abstract objects themselves.
Finch:
Correct.
Quillibrace:
Not in the internal constraints of a practice?
Finch:
Practices track necessity; they do not generate it.
Stray:
So the reason two plus two cannot equal five is…?
Finch:
Because it does not correspond to the facts about numbers.
Stray:
Facts that would remain even if no one counted.
Finch:
Precisely.
Stray nods slowly.
Scene V — The Distortions Become Visible
No one argues anymore, but several things have silently shifted:
-
Constraint is rebranded as obedienceMathematical rigour becomes submission to an external order rather than the achievement of internal coherence.
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Practice is demoted to accessLearning, invention, error, and revision are treated as epistemic noise around a fixed ontological core.
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Failure becomes metaphysicalInconsistent systems are not informative explorations; they are referentially defective.
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Stability is mystifiedThe extraordinary grip of mathematics is explained by where numbers live, not by how systems hold together.
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The question is closed too earlyInquiry ends once an ontological badge is pinned on “numbers”.
Final Moment — After the Victory
Blottisham (content):
So that’s settled.
Finch:
Yes.
Stray:
I feel as though something important has been answered… and something more important has been made unaskable.
Finch:
Metaphysics often has that effect.
Quillibrace (quietly):
We have gained an ontology and lost an explanation.
Finch:
Explanations are cheaper than ontology.
Quillibrace:
Not always.
The clock ticks. Perfectly.
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