Formal Systems
Symbolic structure and proof
If-then statements, truth tables, syllogisms, quantified proofs, line-by-line natural deduction. The structural core underneath every argument.
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A complete logic curriculum
Lessons that teach you to build proofs, weigh evidence, and spot bad arguments — with detailed feedback on every response you write.
What makes this different
Every unit reads like a real course. You are taught the ideas before you are asked to apply them.
Cross-modal reasoning
Most courses teach one kind of thinking. We teach all the ones you actually use.
What you'll learn
Formal Systems
If-then statements, truth tables, syllogisms, quantified proofs, line-by-line natural deduction. The structural core underneath every argument.
Reasoning Under Uncertainty
Most real arguments don't prove — they support. Generalize from examples, pick the best explanation, and update your beliefs as new evidence arrives.
How it works
Careful exposition, worked examples, formalization patterns. Not a rule list to memorize.
Write proofs and arguments. Get specific feedback on exactly where the reasoning breaks.
Progress across 74 lessons and 15 units shows what to study next.
Full curriculum
Fourteen units in sequence. Start with Foundations, then move through formal systems, reasoning under uncertainty, and applied decision logic.
What reasoning is and why structure matters
How to construct, classify, and evaluate definitions rigorously
Why some conclusions follow necessarily
How class statements support traditional deductive reasoning
How whole statements combine into logically assessable structures
How internal sentence structure changes formal reasoning
Reasoning about what must, might, and could have been
From fundamental inferential failures to specific species across modes of reasoning
How to reason well under uncertainty
How priors, likelihoods, and evidence interact in rational belief revision
How to compare explanations without confusing them with proofs
How to reason from a problem state to a workable next move
How rational agents choose when outcomes depend on chance
The mathematical scaffolding that makes formal reasoning possible
How to defend what a text really says — and how to answer those who explain it away
Not sure where to start?
Ten reasoning questions. Get personalized unit recommendations.
Start diagnosticFree to start. Your first lesson is one click away.
Conceptual Control
Spot the fallacies that keep showing up in bad arguments. Write definitions that hold up. The skills that connect formal logic to real conversations.