Reasoning Trainers — 8 tools
Practice, not just demonstration. Each tool here scores, times or guides you. If you can pass the Wason Selection Trainer on all 12 variants without peeking, you probably don't need this page.
Cognitive Bias Sniffer
Paste a paragraph of reasoning. We score it for the cognitive biases most often seen in everyday prose: anchoring, availability, confirmation, sunk-cost, hindsight and a few others.
How to interpret the score
Each match adds to a red-flag index. Low scores (0–2) usually mean the prose contains hedges and self-correction. A score of 4+ is a sign that the writer is unlikely to update even on strong counter-evidence — which is exactly when biases take over. Numbers are heuristic, not diagnostic.
The matcher is keyword + pattern based — a sentence with "I knew it all along" gets hindsight bias, regardless of whether hindsight is in fact involved. So treat the output as a checklist to consider, not as evidence.
Wason Selection Trainer
Twelve rule variants — abstract ones where most people miss, and cheater-detection ones where most people get it right. The contrast is the lesson.
Why most people fail the abstract but pass the cheating version
This is one of the most-cited findings in cognitive psychology. Cosmides & Tooby argued the human brain is better at detecting social-cheating patterns than at pure conditional logic. Subsequent replications and challenges exist (see e.g. Oaksford & Chater's "pragmatic reasoning schemas") but the lesson for you: re-frame a rule into a real-world scenario you're invested in, and you reason about it better.
The trainer's purpose is not to score you against the population, but to make you notice the difference between a "feeling right" answer and a logically derived one.
Modus Ponens / Tollens Speed Trainer
A two-minute drill. Detect whether a given rule + premise yields the conclusion by MP, MT, neither, or a fallacy. Streaks tracked locally; no leaderboards.
Proof by Contradiction Workshop
Pick a statement. The workshop walks you through the recipe: assume the negation, derive a clash, conclude. It scores each step.
How the recipe works
- State the claim you want to prove.
- Temporarily assume the negation (this is the "suppose for contradiction" step).
- Combine that assumption with any axioms/definitions and derive a contradiction.
- Discard the assumption; conclude the original claim.
If you can't reach a contradiction in a few minutes, you're missing a case or an axiom. The workshop won't fill the gap for you — it nudges you to look again.
Why this is harder than it looks
The first time you write a proof by contradiction, the mental step of dropping the assumption is the hard one. Beginners want to keep the false premise in the conclusion. Treat the assumption like a rented tool: you use it, then you return it.
Counter-example Generator
Type a universal claim ("all primes are odd") and we either confirm it or produce a counter-example from a small knowledge base.
What's in the knowledge base?
Hand-curated facts about primes, weekdays, continents, basic geometry. We did not try to plug in a knowledge graph or Wikipedia API; the small, verifiable scope is what makes the tool trustworthy. If you want a counter-example on a domain we don't know about, you'll have to teach us (or write your own).
AGM Belief-Revision Lab
The Alchourrón–Gärdenfors–Makinson model: see what happens to your belief set when you expand, contract, or revise with a new piece of evidence.
The 8 AGM postulates in plain English
Closure · Success · Inclusion · Vacuity · Consistency · Preservation · Super-additivity · Vacuity 2.0. We check the first four by default and tell you when your revision violates one.
Logical Sequence Predictor
Type any number sequence. Predictor fits the top three formula candidates (linear, quadratic, geometric …) and shows the next five terms.
Multiple formulas often fit the same prefix — how we decide
Given a finite prefix, the problem is underdetermined: any sequence can be extended in countless ways. We try finite-difference patterns (linear if 1st differences are constant, quadratic if 2nd are, etc.), then a geometric/exponential scan, then a periodic scan, then a linear-recurrence (order ≤ 3) test by least squares on the recurrence coefficients. The list is ranked by fit error on the prefix; predictions beyond the prefix are extrapolations, not "the" answer.
Inductive vs Deductive Side-by-Side
Same problem, two reasoning styles. See exactly what each method can promise and what it cannot.
Deductive lane
Given a guaranteed rule, derive the only-possible conclusion. Result is certain.
Inductive lane
Given observations only, propose the most plausible rule and quantify uncertainty. Result is a bet.