Scene I — The Dichotomy Is Introduced
Same common room. Later that morning. Fresh tea.
Blottisham (firmly):
Look, I don’t see why we’re dancing around it. Either numbers are real or they’re made up. Realism or anti-realism. Pick one.
Quillibrace (measuring sugar):
An admirable economy. Two positions, one question, no loose change.
Stray:
But I’m not sure what I’d be picking between. “Real” and “made up” feel like they belong to different conversations.
Blottisham:
They belong to this one. Are numbers out there, or are they in our heads?
Quillibrace:
Notice how obliging the universe becomes when addressed as a storage facility.
Blottisham:
Oh come on. You know what I mean.
Quillibrace:
I know how you mean. That is already most of the difficulty.
The dichotomy is placed carefully on the table, like a chessboard.
Scene II — Anti-Realism Wobbles
Early afternoon. Blottisham has not moved.
Blottisham:
Fine. Suppose they’re made up. Human inventions. Happy now?
Quillibrace:
Moderately. Let us see what follows.
Blottisham:
We invented numbers because they’re useful. End of story.
Stray:
But invented things usually admit alternatives. You can redesign a chair. You can change a traffic law. You can’t decide that seven is prime “for convenience”.
Blottisham:
That just means we invented them well.
Quillibrace:
A curious sort of invention — one whose consequences are immune to revision by the inventor.
Stray:
It feels less like making something up and more like stepping into something that tightens around you once you’re inside.
Blottisham:
So what, numbers bully us now?
Quillibrace:
Systems often do.
Anti-realism begins to sweat.
Scene III — Realism Overreaches
Later still. Sun lower. Quillibrace now standing.
Blottisham:
All right then. I’ll say they’re real. Independent. Out there. That explains the rigidity.
Quillibrace:
Does it?
Blottisham:
Yes. They don’t bend because they’re not up to us.
Stray:
But where are they real? Not on the page. Not in the stones. Not floating past the window.
Blottisham:
Abstractly real.
Quillibrace:
Ah. The most spacious cupboard of all.
Stray:
And yet their reality seems oddly dependent. No counting, no number. No measuring, no quantity. No practice, no mathematics.
Blottisham:
That’s just how we access them.
Quillibrace:
You are positing a realm that explains nothing except your discomfort with constraint arising internally.
Stray:
And if numbers were really independent objects, wouldn’t their mode of existence matter? Their relations? Their instantiations? Their failures?
Blottisham (irritated):
You’re both just allergic to the word “real”.
Quillibrace:
On the contrary. We are attending to it carefully.
Realism, now invited to do explanatory work, starts dropping plates.
Scene IV — The Dichotomy Quietly Expires
Evening. The common room thins. The clock ticks louder.
Stray:
It’s strange. The more we talk, the less the original choice seems to matter.
Blottisham:
That’s because you won’t answer the question.
Quillibrace:
Because the question presupposes that numbers must be either things or fictions.
Stray:
And they seem to be neither. They’re not imaginary in the way unicorns are. But they’re not independent in the way rocks are either.
Blottisham:
Then what are they?
Quillibrace:
Stable relational achievements.
Once certain distinctions are instituted, maintained, and recursively constrained, their consequences are no longer negotiable.
Stray:
So the force we attribute to “reality” comes from the architecture, not from an external ontology.
Blottisham (after a pause):
So realism and anti-realism were answers to the wrong kind of worry.
Quillibrace:
Yes. They reassure us that we’ve located numbers somewhere safe — either in the world or in the mind.
Stray:
When in fact they live in the ongoing success of a practice that holds together.
Blottisham:
I don’t like that.
Quillibrace (dryly):
Most collapses are unpopular with those standing on them.
The chessboard remains on the table. No one is playing anymore.
Scene V — Blottisham Relapses
Later that evening. Only the three remain. Coats nearby, but not yet claimed.
Blottisham (suddenly):
No. I’m sorry, but this still won’t do.
Stray:
Won’t do what?
Blottisham:
Won’t answer the question. You’ve talked around it, rephrased it, dissolved it — but you haven’t said whether numbers are real or not.
Quillibrace:
We have said that the demand itself is misplaced.
Blottisham:
That’s just another way of refusing. Either they’re real or they’re not. You can’t abolish the law of the excluded middle by talking softly.
Stray:
But perhaps the exclusion only applies if “real” is doing the right sort of work.
Blottisham:
There it is again. The fog.
People ask this question because they want to know whether mathematics is about something.
Quillibrace:
It is about maintaining coherence under self-imposed constraint.
Blottisham:
That sounds like psychology.
Quillibrace:
It is architecture.
Stray:
And maybe the anxiety is that if numbers aren’t “really real”, then mathematical knowledge feels… weightless.
Blottisham:
Exactly! If they’re not real, why trust them?
Quillibrace:
You trust bridges.
Blottisham:
Because they’re real.
Quillibrace:
Because they hold.
Blottisham opens his mouth, closes it, opens it again.
Blottisham:
Still sounds like evasion.
The relapse is complete. The dichotomy staggers back onstage, bruised but familiar.
Scene VI — Finch Clarifies
The door opens. Dr Finch enters, notebook already open.
Finch:
Ah. I couldn’t help overhearing. You’re debating the ontological status of numbers.
Quillibrace (mildly):
We were.
Finch:
Excellent. Then let me sharpen the issue. The question is whether numbers are ontologically fundamental or ontologically derivative. That’s the real dispute.
Stray (uneasy):
Is it?
Blottisham (relieved):
Yes! Finally. Someone making sense.
Finch:
If numbers are fundamental, they exist independently of human cognition. If derivative, they supervene on cognitive or social practices. There’s no mystery here.
Quillibrace:
You’ve replaced one binary with another.
Finch:
A more precise one.
Stray:
But it still assumes that numbers must be located somewhere — either at the base of reality or on top of us.
Finch:
Ontology requires location.
Quillibrace:
Only if you treat relations as parasitic.
Finch (scribbling):
Relations require relata.
Quillibrace:
Only if you begin with things.
Blottisham:
Now wait — that’s just metaphysics by slogan.
Finch:
Quite. Which is why we should be rigorous. The mistake here is conflating epistemology with ontology. We must keep them distinct.
Stray:
But what if that distinction is exactly what’s failing?
Finch (patiently):
Then we’ve lost our bearings entirely.
Quillibrace:
Or we’ve noticed that “bearing” was always being smuggled in.
Finch:
Without a clear ontological commitment, you cannot say what mathematics is.
Quillibrace:
We can say what it does, how it holds, and why its consequences bite.
Finch:
That is insufficient.
Stray:
Insufficient for what?
Finch:
For metaphysics.
Quillibrace (after a pause):
Then metaphysics may be asking the wrong kind of sufficiency.
Silence.
Blottisham (quietly, to Finch):
I thought you were going to clear this up.
Finch:
I have.
Stray (very softly):
No. You’ve restored the furniture.
Finch looks up, puzzled.
Coda
Later. Quillibrace and Stray alone. The lights dim.
Stray:
They keep trying to rescue the question.
Quillibrace:
Because abandoning it feels like abandoning seriousness.
Stray:
But nothing serious has been lost.
Quillibrace:
Only the illusion that ontology must come first.
They turn out the light.
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