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Syllogism Test

Two statements, one conclusion: decide whether the conclusion has to be true if both statements are.

Type
Logic
Takes
about 3-5 min
Result in
correct

Syllogisms

~3-5 min

  1. Read two statements about made-up things, then a conclusion.
  2. Decide: if both statements are true, must the conclusion be true too?
  3. 10 items, half that follow and half that don't. A diagram explains each one.

Y and N answer from the keyboard. Judge the logic, not whether it sounds likely.

Your result: — / 10

How it's measured

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How does the syllogism test work?

Each item gives you two statements and a conclusion, all about made-up groups such as zorps and bims. Your job is to decide whether the conclusion follows: whether it must be true whenever both statements are true. Answer It follows or It doesn't, and a Venn diagram then shows why.

There are 10 items, new every game: 5 where the conclusion follows and 5 where it doesn't, in a random order. Y and N answer from the keyboard.

How is your Syllogism Test result calculated?

Your result is the number of items you judged correctly, out of 10, with the time you took. It is split into the ones that follow and the ones that don't, so you can see whether you lean towards yes or no. Guessing would get about 5 right, so a score near that means the logic isn't clicking yet.

No published average exists for this exact set of items, so there is no rating. Every answer is checked by the game's own code, which tries every possible arrangement of the three groups.

What does it mean for a conclusion to follow?

A conclusion follows when there is no possible situation in which both statements are true and the conclusion is false. It is about the form of the argument, not about whether the conclusion is true in the real world. If you can picture one case that fits both statements but breaks the conclusion, it doesn't follow.

  • All A are B, all B are C, so all A are C. Follows: everything in A is inside B, which is inside C.
  • All A are B, all C are B, so all A are C. Doesn't follow: A and C can both sit inside B without overlapping.
  • All A are B, so all B are A. A common slip: there can be B that aren't A.
  • Some A are B. In logic, “some” means at least one, and possibly all. It doesn't tell you that some A are not B.

Why are the words made up?

So that what you already believe can't do the work. People judging syllogisms tend to accept conclusions they find believable and reject ones they don't, whatever the logic says: the belief bias. Evans, Barston and Pollard showed it in three experiments in 1983 (Memory & Cognition), and found it was stronger for arguments that don't follow than for ones that do. With nonsense words there is nothing to believe, only the form.

How are the answers checked?

With Venn diagrams, introduced by John Venn in 1880. Three overlapping circles split the groups into seven regions, and each region either has members or is empty. The game tries all 128 ways of filling them, keeps the ones where both statements are true, and checks the conclusion in each.

Counting the same way, there are 256 possible syllogisms of this kind. 15 are valid if “all” makes no claim that anything exists, and 24 if every group is taken to have members, as in the traditional logic going back to Aristotle. The 9 that depend on that choice never appear in this test, so every item has one answer. The site's tests check both counts.

For more reasoning puzzles, try the Logic Grid Puzzle or the Verbal Analogy Test.

Questions

What is a syllogism?
An argument with two statements, called premises, and a conclusion drawn from them, each saying how two groups relate: all, no, some, or some not. For example: all dogs are mammals, all mammals are animals, so all dogs are animals.
Is a conclusion that follows always true?
Only if the statements are true. A valid argument guarantees that true statements give a true conclusion; it says nothing about statements that are false. That is why this test asks only whether the conclusion follows.
Does "some" mean "not all"?
No. In logic "some" means at least one, and it allows all. "Some zorps are bims" is still true if every zorp is a bim.
What does the Venn diagram after each item show?
Each circle is a group. Shaded parts must be empty if both statements are true. When the conclusion doesn't follow, dots mark the parts with members in one case where both statements hold and the conclusion fails.
What is a good score on the syllogism test?
There is no published average for this set of items. Guessing gets about 5 of 10, and 9 or more only about once in 93 tries, so a score that high means you are reasoning from the form.
Is this the syllogism part of an aptitude test?
No, it is a practice puzzle in the same spirit. Real tests use their own items, wording and time limits, so a score here doesn't predict a score there.