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Syllogisms

All wugs are daxes; some daxes are feps. Does it follow that some wugs are feps? Judge conclusions about made-up kinds, from two premises to long chains.

  • Logic
  • Untimed
  • 12 levels

How it plays

You get premises about made-up kinds — wugs, daxes, feps — and a conclusion. Decide whether the conclusion must be true whenever the premises are. Assume every kind has at least one member.

The words are nonsense so that nothing sounds believable: with real kinds, people judge whether a conclusion seems true rather than whether it follows.

Levels add kinds to the chain, then "no", "some" and "some … not", then shuffle the premises out of order. When a conclusion does not follow, the working names the thing the premises allow that breaks it.

Keys

Space starts and skips ahead · 1–9 pick · Enter submits · Esc stops. On a phone, tap.

What it trains

This practises telling what follows from what is merely compatible. It trains this kind of judgement; it is not evidence of better reasoning in general.

Learn

How to get better at syllogisms: the method, the techniques, what each new level asks of you, and the traps the wrong answers are made of.

Your approach to each question

  1. Read the conclusion first and note its two kinds, which comes first, and its form: all, no, some, or some … not. When you must pick the conclusion yourself, the two kinds to watch are the two ends of the chain.
  2. Draw each premise as you read it. “All wugs are daxes” is an arrow, wug → dax. “No” and “some” are links that work both ways; mark them as such.
  3. Follow the chain from one kind in the conclusion to the other. The premises always link the two ends through every kind between, one step at a time.
  4. Then try to break it: imagine a world where every premise is true and the conclusion false. If you can build one, it does not follow; if every attempt fails, it does.

Techniques and tricks

  • Follow the arrows for “all”

    “All X are Y” is an arrow from X to Y. “All A are C” follows only if you can walk from A to C along arrows, every one pointing the way you walk.

    e.g. All wugs are daxes; all daxes are feps. So all wugs are feps — but not that all feps are wugs.

  • Every kind has members

    In this game every kind is assumed to exist. So “All wugs are daxes” also gives “Some wugs are daxes” and “Some daxes are wugs”. Any arrow path gives a “some” both ways.

    e.g. All daxes are wugs; all daxes are feps. Some wugs are feps follows, because the daxes are both.

  • One “no” at the end of the arrows

    If arrows lead from A into a kind that is shut off from C by a “no”, then no A are C. If the arrow points the other way, only “some … not” survives.

    e.g. All wugs are daxes; no daxes are feps: no wugs are feps. All daxes are wugs; no daxes are feps: only some wugs are not feps.

  • “Some” needs arrows leading away

    A “some” link carries forward only along arrows leaving it. Some A are B and all B are C gives some A are C; an arrow pointing back into B gives nothing.

    e.g. Some wugs are daxes; all daxes are feps: some wugs are feps.

  • Two negatives give nothing

    A chain with two “no” or “some … not” links says nothing at all about its two ends. Spot two negatives and answer “It does not follow” for any conclusion about those ends.

  • Build the counter-example

    To show it does not follow, make up one thing that fits every premise and breaks the conclusion. The working does exactly this when you miss, so copy its shape.

    e.g. All wugs are daxes; all feps are daxes. A dax that is a fep but not a wug fits both — so “all feps are wugs” fails.

As the levels climb

  • You start with three kinds and only “all”. Each level then changes one thing, in turn: one more kind in the chain, a new form, the premises shuffled out of order, the clock tightened — round and round until each change is used up.
  • The forms arrive in order: “all”, then “no”, then “some”, then “some … not”. Each new one brings its own direction rules; learn them on short chains before the chain grows.
  • The kinds grow up to “Most kinds in a chain”. A long chain is still a series of links between neighbours; reduce it one step at a time from one end, carrying a single relation.
  • Shuffled premises mean you must rebuild the chain before reading it: find the premise that mentions one end of the conclusion, then the one that shares its other kind.
  • The clock closes to 80%, 65% and then 55% of 8 seconds plus 5 for each kind, with 40% more on “Which conclusion follows?”. It only applies if you turn “Time pressure” on.

Traps to avoid

  • The reversed “all”: “All wugs are daxes” does not mean all daxes are wugs. A conclusion that turns an arrow round reads naturally and is wrong.
  • The shared middle: all wugs are daxes and all feps are daxes says nothing about wugs and feps. Two arrows into the same kind link nothing.
  • Turning “some … not” round: some wugs are not daxes does not give some daxes are not wugs. Of the four forms, only “no” and “some” can be read both ways.
  • Forgetting that kinds exist: “Some daxes are wugs” does follow from “All wugs are daxes” here. Do not reject a “some” just because no premise says “some”.
  • On “Which conclusion follows?”, the wrong options are chosen to be about the same two kinds as the right one. Check each against the arrows; do not pick by the words.

How to practise

  • Keep “Question” on “Does this conclusion follow?” to learn the rules, then switch to “Which conclusion follows?”, which makes you test several conclusions against the same premises.
  • Set “Most kinds in a chain” to 3 or 4 while the new forms arrive, then raise it towards 9.
  • After every “does not follow”, read the counter-example in the working and say it aloud. Being able to build one is the whole skill.

Levels

It is untimed unless you turn the clock on. There are 12 levels with the default settings, and the counter stops at the real top. Your level is judged on your last ten answers, every ten: 90% moves you up, below 80% moves you down, which holds most people near four in five right.

All of it is in the settings beside Start — how many answers a judgement looks at and how often it recalibrates, the thresholds, the time, which questions, how many options, and whether you see each verdict at once or review them together at the judgement. You can also jump to any level.

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