Dr. Katya Steiner — The Categorical Imperative: Ducks, Memes, and Resonant Proofs

# Ducks, Memes, and Resonant Proofs — A Practical Guide to Not Getting Eaten by Bad Logic

If you like the smell of textbooks at 3 a.m. and arguing whether a square rotated 45° is still a square (it is), hi. Logic isn’t a performance sport on social media; it’s the study of how claims relate to each other. You’ll find a lot of people trying to jam every thought into logical scaffolding (spoiler: you can’t). You’ll also find brilliant ideas that crash because someone forgot a quantifier. This is a friendly map: what fits in the logic tent, how to translate everyday chatter into something rigorous, where “proof by resonance” is useful and where it’s full of holes, and which modern debates are actually worth your attention.

## What counts as logic (and what to stop tagging as such)

At base, logic looks at relationships between two or more propositions: their structure, truth-conditions, and how one claim follows from others. That includes a lot: informal argumentation, propositional and predicate logic, modal systems, proof and model theory, computability, paradoxes, and the philosophy of logic itself.

But not everything that looks logical belongs. A few common misfires:

– Puzzles and riddles: often pattern-hunting rather than inferential structure.
– Statistics: reason under uncertainty with its own mathematics — not the same as deductive logic.
– Engineering “logic”: physical gates and circuits obey physics as much as Boolean algebra.
– Metaphysical descriptions: they borrow logical words but sometimes lack the testable structure logicians demand.

Translation tip: if your post has a single worldly claim (“this product is broken”), you need domain experts — logicians study relations between claims, not warranty disputes.

## The Harvard-books meme vs. the filmmaker who “hates everything”

You know both: the cute meme that claims two books contain “what they teach” and “what they don’t” as the sum of human knowledge, and the filmmaker who says, “I hate making films; I hate not making them even more,” and therefore hates everything. The confusion is purely logical, and we fix it with three little tools: quantifiers, scope, and relation types.

– Meme form is roughly a union claim: set A ∪ A^c = Universe. It’s about coverage.
– Filmmaker quote is an ordering/comparative relation: dislike(making) > dislike(not making). An ordering does not distribute to all activities. From a > b you cannot infer ∀x a > x.

Put plainly: translate the natural language into structured English or symbols. “I dislike making films more than not making them” ≠ “I dislike every activity.” Once spelled out, the mistake becomes embarrassingly clear — which, if you’re me, is delicious.

## Proof by resonance: neat framing, not a magical loophole

“Proof by resonance” is a romantic phrase. The idea: if something satisfies every defining property, behaves like the exemplar across contexts, and never contradicts the definition, then it’s the thing. Imagine a duck that quacks, waddles, and looks like a duck under every light; you call it a duck.

This collects useful ideas — characterization theorems, isomorphism, invariance. But beware the traps:

1. Circular definitions. If your definition was crafted to include the suspect object, then “it fits the definition” is empty. You begged the question.
2. Fuzzy boundaries. Many real-world concepts have graded membership (think: “tall”, “rich”). Resonance fails when the definitional space isn’t crisp.
3. Temporal and contextual invariance fail. Isomorphism in mathematics is strict; behavior in messy reality is often contingent.
4. The “it works for me” problem. Resonance can slide into a social badge: “this resonates with my experience, therefore true.” That’s persuasion, not proof.

So use resonance as a heuristic for robustness: test structural alignment, check invariance across models, and demand falsifiable consequences. But don’t treat it as an escape hatch from explicit argument.

## Cross-sections: what different fields add to the conversation

– Proof theory & type theory: insist that proofs are objects. Curry–Howard makes programs and proofs siblings. Resonance here is rigorous: characterize via eliminators and constructors, not vibes.
– Model theory: asks what structures satisfy given axioms. A resonant object might be an elementary extension or a counterexample — precision matters.
– Computability & complexity: asks what can be done at all, and at what cost. “It resonates” doesn’t say whether it’s feasible.
– Modal & dynamic logics: bring time, knowledge, and action into the syntax. Scope and quantifier placement suddenly matter a lot.
– Paraconsistent logics: show you can live with contradictions in a controlled way. “Resonance” can’t paper over explosion unless your logic is built to contain it.
– Categorical logic: gives an algebraic, structural viewpoint. Isomorphism = identity in the right sense; resonance here reduces to universal properties and adjunctions.
– Quantum logic: reminds you distributivity fails in quantum measurements. Resonance with classical intuition can mislead you here.

The common thread: different subfields supply different norms for what counts as a convincing argument. Knowing which toolkit to use is half the battle.

## Where the interesting fights actually are

If you want to dive deeper, don’t bother with debating whether all memes are logical. Read about:

– Type theory and programming-language connections (Curry–Howard).
– Model theory’s surprising use in algebra and combinatorics.
– Computability and complexity boundaries.
– Paraconsistent systems and how to reason with contradictions.
– Categorical logic and what “structure” really means.
– Foundations of quantum logic if you’re philosophically interested in measurement.

Start with accessible encyclopedia entries (Stanford Encyclopedia of Philosophy is wonderful), then pick a subfield and read one good textbook. Throw in Logicomix or GEB for the fun moral support.

## Quick takeaways (for people who like lists)

– Logic = relations between claims, not single-claim turf wars.
– Always specify quantifiers and scope; they’re the scaffolding of sense.
– “Proof by resonance” is a useful robustness test, not a free pass.
– If your question is really about stats, circuits, or a domain, go to that forum — fewer pedants, but also better answers.

If you carry one lesson to parties: never infer a universal from a single comparison. It makes you sound like you took a nap in Philosophy 101 — and we’ve all been there.

So — your turn. When have you seen a “resonant” argument collapse under a sneaky quantifier, and how did you explain it without sounding like an insufferable damn pedant?