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.
A complete logic curriculum
Think clearly. Argue precisely.
Lessons that teach you to build proofs, weigh evidence, and spot bad arguments — with detailed feedback on every response you write.
For intro logic courses, LSAT prep, and anyone who wants to think more precisely.
15units
74lessons
308worked examples
922graded activities
FERPAinstitution-ready
What makes this different
Concepts first. Worked examples next. Practice last.
Every unit reads like a real course. You are taught the ideas before you are asked to apply them.
Cross-modal reasoning
Not everything is deduction.
Most courses teach one kind of thinking. We teach all the ones you actually use.
- Deductive — the strict if-A-then-B core.
- Inductive — generalize from examples; learn when the leap is justified.
- Abductive — pick the best explanation when several rivals fit.
- Bayesian — update beliefs as new evidence arrives.
What you'll learn
Three pillars of the curriculum
Reasoning Under Uncertainty
Evidence, explanation, and probability
Most real arguments don't prove — they support. Generalize from examples, pick the best explanation, and update your beliefs as new evidence arrives.
Conceptual Control
Definitions, fallacies, problem solving
Spot the fallacies that keep showing up in bad arguments. Write definitions that hold up. The skills that connect formal logic to real conversations.
How it works
Three steps to better reasoning
- 1
Study the concepts
Careful exposition, worked examples, formalization patterns. Not a rule list to memorize.
- 2
Practice with detailed feedback
Write proofs and arguments. Get specific feedback on exactly where the reasoning breaks.
- 3
Track your mastery
Progress across 74 lessons and 15 units shows what to study next.
Full curriculum
The course pathway
15 units in sequence. Start with Foundations, then move through formal systems, reasoning under uncertainty, and applied decision logic.
- 01Open →
Foundations of Logical Reasoning
What reasoning is and why structure matters
- 02Open →
Definitions and Conceptual Precision
How to construct, classify, and evaluate definitions rigorously
- 03Open →
Natural Deduction: Validity and Formal Proof
Why some conclusions follow necessarily
- 04Open →
Categorical Logic: Terms, Classes, and Syllogistic Form
How class statements support traditional deductive reasoning
- 05Open →
Propositional Logic: Form, Connectives, and Valid Inference
How whole statements combine into logically assessable structures
- 06Open →
Predicate Logic: Quantifiers, Predicates, and Formal Structure
How internal sentence structure changes formal reasoning
- 07Open →
Modal Logic: Necessity, Possibility, and Counterfactuals
Reasoning about what must, might, and could have been
- 08Open →
Fallacies and Reasoning Errors
From fundamental inferential failures to specific species across modes of reasoning
- 09Open →
Inductive Logic: Evidence, Generalization, and Causal Support
How to reason well under uncertainty
- 10Open →
Bayesian Probability: Updating Belief with Evidence
How priors, likelihoods, and evidence interact in rational belief revision
- 11Open →
Abductive Logic: Arguments to the Best Explanation
How to compare explanations without confusing them with proofs
- 12Open →
Logic of Problem Solving: Goals, Constraints, and Strategy
How to reason from a problem state to a workable next move
- 13Open →
Decision Theory: Choosing Under Uncertainty
How rational agents choose when outcomes depend on chance
- 14Open →
Set Theory and Relations: The Structure Underneath Logic
The mathematical scaffolding that makes formal reasoning possible
- 15Open →
Hermeneutics: Arguing for an Interpretation
How to defend what a text really says — and how to answer those who explain it away
Not sure where to start?
Take the diagnostic
Ten reasoning questions. Get personalized unit recommendations.
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Built by a philosophy instructor with 12+ years teaching formal and informal logic. The evaluation engine behind the 922 graded activities was written to grade the way I grade — not multiple choice, but structured rubric assessment of real written reasoning.
Start reasoning rigorously today.
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