A Parallel Common Room (The Realist Victory Scenario)

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:

1. Constraint is rebranded as obedience
   Mathematical rigour becomes submission to an external order rather than the achievement of internal coherence.

2. Practice is demoted to access
   Learning, invention, error, and revision are treated as epistemic noise around a fixed ontological core.

3. Failure becomes metaphysical
   Inconsistent systems are not informative explorations; they are referentially defective.

4. Stability is mystified
   The extraordinary grip of mathematics is explained by where numbers live, not by how systems hold together.

5. The question is closed too early
   Inquiry 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.

The Ontological Status of Numbers (A Faculty Dialogue)

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.

Are Numbers Actually Real? (A Faculty Dialogue)

Setting: Faculty common room, late morning.

A clock ticks with unnecessary authority.

Professor Quillibrace sits with a notebook, diagram half-drawn.

Mr Blottisham stands, arms folded, already dissatisfied.

Miss Elowen Stray perches on the edge of a chair, listening.

---

Blottisham (briskly):

Honestly, I don’t see the difficulty. The question is simple: are numbers actually real? Either they exist or they don’t. We can stop there.

Quillibrace (without looking up):

One could stop there, certainly. One would simply not have begun.

Blottisham:

That’s evasive. Mathematics works. You can’t deny that.

Quillibrace:

I have no intention of denying it. I am merely interested in what is working, where, and under what relations. The question you’ve asked collapses all three.

Stray (softly):

It’s the word “actually” that catches me. It feels as though the question is reaching for something beneath the practice, as if the practice were a kind of disguise.

Blottisham (impatient):

Or as if we’re just asking whether numbers are inventions or discoveries. That’s hardly exotic.

Quillibrace (turning the notebook slightly):

Notice what you’ve done there. You’ve already arranged the architecture: invention on one side, discovery on the other. Two rooms, one corridor, no windows.

Blottisham:

Because those are the options.

Quillibrace:

They are the options if numbers are the kind of thing that could be waiting to be found or merely fabricated. The question assumes its own answer space.

Stray:

So the problem isn’t whether numbers are real, but that the question treats “number” as a kind of object, rather than… something that happens?

Quillibrace (pleased, but minimally):

Something that holds, rather than something that sits.

A pattern of constraint, not an item of inventory.

Blottisham:

Constraint or not, two plus two still equals four. You can’t hand-wave that away.

Quillibrace:

I wouldn’t dream of it. But ask yourself why it cannot be otherwise.

Not because four is hovering in metaphysical space, but because once the relations are fixed, deviation is incoherent.

Stray:

So the certainty comes from the tightness of the system, not from the independence of its elements.

Quillibrace:

Precisely.

Blottisham (snorting):

That sounds like saying numbers are real “in some sense” — which is just academic fog.

Quillibrace:

On the contrary. It is saying they are real as relations, not as things.

The fog enters when we insist on asking about their “actual” reality, as though relation were a lesser mode of being.

Stray (after a pause):

Then the question fails because it asks for an answer at the wrong level. It wants an ontological verdict where a structural description is required.

Quillibrace:

Exactly. It demands a metaphysical passport for something that already functions by virtue of its internal coherence.

Blottisham:

So what — we’re not allowed to ask whether things are real anymore?

Quillibrace (dryly):

You are always allowed. You are not always entitled to an answer that respects the question as asked.

Stray (smiling faintly):

Perhaps the real issue is that “real” sounds like praise. And we’re worried numbers won’t survive without it.

Quillibrace:

Numbers survive perfectly well without our compliments.