A one-act skit in which mathematics quietly demotes itself
Write the skit where the three [optimal] egos somehow form a conspiracy, after receiving a mysterious invitation to MUTH Club.
ChatGPT Prompt
On arrival they see Math Useful To Humans. Slowly they discover their common closet Presburger Predicativism**, and draft a conspiracy to replace Math with MUTH as an engineering discipline.
Weyl’s ghost shows up to take credit and give a dramatic flourish.
1. The Invitation
A bare room. A table. Three envelopes, identical, unmarked.
Leslie Lamport
(reading)
“MUTH Club. No agenda. No meta-theory. Termination guaranteed.”
This is either a prank or overdue.
Thoralf Skolem
Mine just says:
“Bring only what you actually use.”
Suspiciously well-phrased.
Edsger Dijkstra
(grim)
Any meeting that promises “no meta-theory” is already lying.
I’m going anyway.
They exit.
2. The Sign
A small conference room. Bad coffee. A folding sign on the wall:
MUTH CLUB
Math Useful To Humans
Lamport
Ah. So it’s a euphemism.
Skolem
No. It’s a demotion.
Dijkstra
Good. Mathematics has been getting ideas above its station.
3. The Awkward Discovery
They sit. Silence.
Lamport
I’ll start.
I don’t trust arithmetic that can encode itself.
Skolem
Of course you don’t. Neither do I.
Gödel coding is a party trick, not a foundation.
Dijkstra
Arithmetic that doesn’t terminate is not mathematics.
It’s wishful thinking with symbols.
Pause.
Lamport
So… addition?
Skolem
Addition.
Dijkstra
Addition with order.
And no “and so on.”
They look at each other.
Lamport
We’re… Presburger arithmetic people.
Skolem
Closet Presburger people.
Dijkstra
I thought everyone sane was.
4. Naming the Enemy
Lamport
Then let’s be explicit.
What are we replacing?
Skolem
Mathematics as ontology.
Dijkstra
Mathematics as self-admiration.
Lamport
Mathematics that explains itself instead of doing its job.
Skolem
Plato’s fault.
Dijkstra
And Pythagoras’. Numerology is a gateway drug.
5. The Draft
Lamport writes on the whiteboard.
MUTH: Math Useful To Humans
Lamport
Principles. Keep it short.
Skolem
One: Arithmetic stops at addition.
Dijkstra
Two: Anything undecidable is labeled research, not infrastructure.
Lamport
Three: Reflection requires a change request.
Skolem
Four: Proofs justify use, not truth.
Dijkstra
Five: If it doesn’t terminate, it doesn’t ship.
They nod.
6. The Objection That Never Comes
Lamport
Should we justify this philosophically?
Dijkstra
Absolutely not.
Skolem
If they ask why, we say:
“Because this is what we need.”
Lamport
And if they insist?
Dijkstra
We downgrade them to advisory.
7. A Cold Wind
The lights flicker. A figure appears: austere, luminous, faintly disappointed.
Hermann Weyl’s Ghost
You took your time.
Lamport
Ah. So you sent the invitations.
Weyl’s Ghost
Of course.
I wrote Das Kontinuum*.
Then I blinked.
Skolem
You could have warned us.
Weyl’s Ghost
I did. Everyone ignored me.
Dijkstra
Typical.
8. The Flourish
Weyl’s Ghost
(smiling)
You’ve reinvented predicativism without calling it philosophy.
That was the only way it would work.
Lamport
We’re calling it MUTH.
Weyl’s Ghost
Excellent.
Ugly names age well.
Skolem
Any final advice?
Weyl’s Ghost
Yes.
Never publish a manifesto.
Just change the defaults.
The ghost fades.
9. Adjournment
Lamport
So. We replace math.
Skolem
Quietly.
Dijkstra
With a servant.
Lamport
Meeting notes?
Dijkstra
(shaking head)
No notes.
Only practices.
They leave the room. The sign remains.
MUTH CLUB
If it works, it stays. If it reflects, it waits.
Blackout.
*Das Kontinuum
Das Kontinuum is Hermann Weyl’s 1918 book-length intervention into the foundations of mathematics—and, in hindsight, the closest historical ancestor to MUTH that ever dared to speak its name.
A.1 What Weyl Tried to Do
In Das Kontinuum, Weyl attempted to rebuild analysis under strict predicative constraints:
- No impredicative definitions
- No unrestricted set formation
- No totalities defined “all at once”
- Arithmetic and analysis constructed step by step
His guiding conviction was simple and radical:
Mathematics must not outrun what can be meaningfully constructed.
This put him at odds with:
- set-theoretic orthodoxy,
- Platonic realism,
- and the emerging culture of foundational maximalism.
A.2 Why It Failed (Historically)
Weyl’s program failed not because it was incoherent, but because it was inconvenient.
- It slowed analysis down
- It blocked elegant general theorems
- It refused reflection and closure
- It demanded discipline instead of transcendence
Within a few years, Weyl publicly retreated—calling his own position “too restrictive.”
But the retreat was political, not conceptual.
A.3 Why It Matters Here
From the standpoint of MUTH (Math Useful To Humans), Das Kontinuum reads less like a failure and more like:
- a prototype
- an early warning
- an engineering memo written a century too early
Weyl’s real mistake was trying to save analysis.
MUTH does not try to save anything.
It simply asks:
What do we actually need to build things that work?
And answers:
- decidable arithmetic,
- additive structure,
- predicative construction,
- no self-justification.
A.4 Weyl’s Ghost, Revisited
In the skit, Weyl’s ghost “takes credit” not because he succeeded, but because he saw the cost of success:
- reflection buys power,
- power buys fragility,
- fragility eventually collapses into metaphysics.
MUTH finishes the job Weyl began by refusing the rescue mission.
No continuum to save.
No infinity to apologize for.
No manifesto to defend.
Just rules that work.
A.5 One-Line Epitaph
Das Kontinuum is what happens when predicative discipline tries to coexist with mathematical ambition.
MUTH is what happens when ambition is told to wait outside.
**Presburger Predicativism
Presburger predicativism is the foundational posture implicit throughout MUTH:
a refusal of mathematical strength that enables self-reference, reflection, or unbounded amplification—implemented concretely by stopping arithmetic at Presburger arithmetic.
It is not a historical school.
It is a design decision.
B.1 The Core Commitment
Presburger predicativism asserts:
- Arithmetic is a tool, not an ontology
- Addition and order are legitimate primitives
- Unbounded iteration (multiplication, full induction) is optional, not innocent
- Any arithmetic capable of encoding its own use is overpowered
In short:
Count, but do not let counting talk about itself.
B.2 Why Presburger (and Not Peano)
Peano arithmetic quietly imports:
- unbounded induction
- multiplication as total iteration
- Gödel coding
- internal self-reference
- incompleteness as a structural feature
Presburger arithmetic blocks all of these structurally, not by prohibition.
Key properties:
- decidable theory
- quantifier elimination
- no internal syntax encoding
- no diagonalization
- no Gödel phenomena
From a Presburger-predicativist standpoint, this is not a limitation but a safety envelope.
B.3 Relation to Classical Predicativism
Classical predicativism forbids impredicative definitions but often still tolerates:
- Peano arithmetic
- ordinal analysis
- stratified reflection
- meta-theoretic bootstrapping
Presburger predicativism goes further:
- it treats PA itself as already too reflective
- it rejects arithmetic that can simulate its own metatheory
- it prefers decidable fragments by default
Thus:
- Predicativism → regulates self-application
- Presburger predicativism → removes the machinery that enables it
B.4 Anti-Reflection by Construction
Presburger predicativism does not argue against reflection.
It designs around it.
Because Presburger arithmetic lacks:
- multiplication
- full induction
- coding capacity
it cannot:
- internalize proofs
- express its own consistency
- diagonalize
- reflect even indirectly
Reflection is not banned.
It is simply out of scope.
B.5 Mathematics as Engineering (Again)
From an engineering perspective:
- PA is like unrestricted recursion
- Presburger arithmetic is like bounded loops
Both have uses.
Only one is safe as infrastructure.
Presburger predicativism therefore treats arithmetic strength the way engineers treat power tools:
Use the weakest one that gets the job done.
Everything stronger is labeled experimental.
B.6 What Still Works
Within Presburger predicativism, one still has:
- counting and scheduling
- linear constraints
- semilinear sets
- verification and model checking
- resource-bounded reasoning
- termination guarantees
This is the arithmetic actually used in:
- formal verification
- SMT solvers
- safety-critical systems
- control and planning
MUTH merely admits this openly.
B.7 One-Sentence Summary
Presburger predicativism is the decision to stop arithmetic at the point where it remains useful, decidable, and silent about itself.
Or, in MUTH’s voice:
If it adds, keep it. If it multiplies, justify it. If it reflects, don’t ship it.
iHack, therefore iBlog 
Leave a comment