Welcome to Logic – Not That Thing Your High-School Debate Team Called ‘Thinking’
So you wandered into the shrine of formal thought because you like tidy arguments, or a meme made you curious, or someone told you ‘logic’ is where the answers live. Before you post your GIF of ‘duck = all properties’ or ask whether quantum mechanics makes ‘or’ mean something different, let me save you a little social embarrassment: this place is more like a library of engineering standards for reasoning than a motivational poster about being ‘rational’.
I spend my time rooting through the detritus of sloppy analogies and finding the islands of robust, useful structure underneath. Here are a few friendly mistakes people make, why they are seductive, and what the actual neighborhoods of logic look like.
Not everything that sounds similar belongs to the same house
You’ve seen the meme about ‘what they teach you’ and ‘what they don’t’. Cute, but often a category error. Logic gives us tools for these confusions: quantifiers, negation, scope, and the distinction between partitions (a universe-of-discourse claim) and orderings (preferences, rankings). Mixing those up is like asking whether a screwdriver can be integrated into a sonnet — entertaining, but not helpful.
Proof by resonance: lovely rhetoric, shaky epistemology
People rely on ‘proof by resonance’: something fits all your intuitions, so it must be right. That’s seductive because it feels like closure. Technically, it’s necessary-and-sufficient conditions plus isomorphism and invariance. Definitions are messy, contexts shift, and ‘all relevant contexts’ is almost never explicit. Resonance is a fine heuristic and a poor substitute for rigor.
Where people are actually working (and arguing) right now
Contemporary logic is a city with very different districts:
– Proof and type theory: proofs as objects you compute with; home to programming languages and proof assistants.
– Model theory: which structures satisfy which sentences; algebraic and combinatorial.
– Computability and complexity: what can be computed and how efficiently.
– Modal and dynamic logics: necessity, knowledge, time, change.
– Substructural logics and paraconsistency: rethinking structural rules and handling contradictions without explosion.
– Category theory and categorical logic: the abstract plumbing that relates different systems.
– Quantum logic and foundations: where inference meets noncommuting observables.
– Logic and AI: formal methods, specification, and questions about mechanized reasoning.
Each area asks different questions and uses different tools. Treating them as interchangeable is like using a butter knife to fix your car.
Cross-disciplinary glimpses
These conversations are where the magic happens: stability theory linking algebra and definability, category theory offering a morphism-first viewpoint, proof theory informing complexity through resource accounting, and quantum logic forcing philosophy to ask whether logic is empirical.
A small rant
Stop trying to fold quantum mechanics, circuit debugging, and meme-logic under one umbrella and then demand consistency. Use the right vocabulary—quantifiers, negation, isomorphism, invariance—and be suspicious of absolute claims. Definitions are tools: sharpen them, replace them when needed, and don’t get romantically attached just because one ‘feels right’.
Where to start if you want in
Read surveys and the Stanford Encyclopedia of Philosophy. Try a technical primer like Enderton or Boolos & Jeffrey for basics. Pick a subfield that tickles you and follow recent proceedings (LICS, ASL journals) and arXiv preprints. Talk to practitioners: logic rewards curiosity, patience, and tolerance for pedantry.
Parting thought
Logic is less about one true way to think and more about building neighborhoods where certain questions are answerable and others are intentionally ignored. Different logics illuminate different aspects of the world and our reasoning about it.
So: which piece of your intuitive reasoning would you be most scared to formalize, and why? What would formalizing it force you to admit about how you actually think?
