What is a verbal syllogism?

A verbal syllogism is an argument made of two premises and a conclusion, using words such as all, some and no; the test asks whether the conclusion must follow from the premises, regardless of whether it sounds true.

Syllogisms test deductive reasoning and the ability to resist belief bias: accepting a conclusion because it is believable rather than because it is valid. They date back to Aristotle and still appear in aptitude and graduate admissions tests.

By What's Your IQ · Published 3 Oct 2026 · Updated 3 Oct 2026

Format: Two premises, one conclusion: valid or invalid?
Statement types: All, No, Some, Some … not
Possible forms: 256, of which 15 are valid in modern logic
Measures: Deduction, resisting belief bias
This test: Free, timed, with an explanation for every item

What is a syllogism?

A syllogism is an argument with two premises and a conclusion, each saying how two groups relate (all, no, some, some … not), and it is valid only if the conclusion must be true whenever the premises are. Validity is about structure, not truth: an argument can be valid with a false conclusion, or invalid with a true one.

Syllogism items test deductive reasoning: following what strictly follows from given statements while ignoring what you believe. They appear in aptitude tests, admissions tests and logic courses.

By What's Your IQ · Published 3 Oct 2026 · Updated 3 Oct 2026

Format: Two premises and a conclusion; decide valid or invalid
Statement types: All, No, Some, Some … not
Possible forms: 256, of which 15 are valid in modern logic
Measures: Deduction and resistance to belief bias
This test: 12 arguments, 12 minutes, free

Only four kinds of statement

Every premise in the test is one of these.

All A are BEvery A sits inside B. Doesn't tell you all B are A.

No A are BThe two groups never overlap.

Some A are BAt least one A is also a B. Possibly all are.

Some A are not BAt least one A lies outside B.

How to check any syllogism

Don't ask "does this sound right?" Ask "can I picture a world where both premises are true and the conclusion is false?"

1Swap words for lettersStudents, athletes, tall → S, M, P. Belief can't pull you once the words are gone.

2Try to break itPicture a world where both premises are true but the conclusion is false. Put people in only the places the premises allow.

3DecideIf you can build that world, it's invalid. If every attempt forces the conclusion to be true, it's valid.

Rule of thumb: two "some" premises, or two negative premises, never give a valid conclusion.

Syllogism lab

Build any of the 256 forms. It finds a counterexample if one exists.

PREMISE 1

PREMISE 2

CONCLUSION

FIGURE (TERM ORDER)

1Some musicians are poets.

2All musicians are students.

∴Some students are poets.

Valid: Disamisfigure 3 · IAINo arrangement of students, musicians and poets can make both premises true and this conclusion false. Medieval logicians named this form Disamis; the vowels spell its statement types.

Uses modern logic: "All A are B" doesn't assume any A exist. That's why forms like Darapti (All M are P, all M are S ∴ some S are P) show as invalid here but counted as valid for Aristotle.

Valid or invalid?

12 arguments · 12 minutes · ignore whether it's true in real life

Some conclusions are true in the real world but don't follow; some are false but do. Treat the premises as the only facts that exist.

Argument 1 of 12

00:00

PREMISE 1All dogs are mammals.

PREMISE 2All mammals are animals.

THEREFOREAll dogs are animals.

0/12Worth another go after the traps below.Belief bias didn't catch you · 29854926:45

Plain logic0/4Loose 'some'0/2Reversed 'all'0/2Belief bias0/3'Not B' trap0/1

All dogs are mammals.All mammals are animals.∴ All dogs are animals.Valid · you said nothingA chain of 'all': dogs sit inside mammals, which sit inside animals.

All roses are flowers.Some flowers fade quickly.∴ Some roses fade quickly.Invalid · you said nothingThe flowers that fade quickly might not include any roses. Nothing links the 'some' to roses.

No fish are mammals.All sharks are fish.∴ No sharks are mammals.Valid · you said nothingSharks sit entirely inside fish, and fish share nothing with mammals.

All cats have tails.This animal has a tail.∴ This animal is a cat.Invalid · you said nothingHaving a tail doesn't make something a cat; dogs have tails too. This reverses the 'all'.

All birds can fly.Penguins are birds.∴ Penguins can fly.Valid · you said nothingFalse in real life, but it follows from the premises. Valid isn't the same as true.

Some teachers are musicians.All musicians are creative.∴ Some teachers are creative.Valid · you said nothingThe teachers who are musicians are, through that, creative.

All addictive things are expensive.Some cigarettes are cheap.∴ Some cigarettes are not addictive.Valid · you said nothingAny cheap cigarette can't be expensive, so it can't be addictive. It sounds wrong; it's still valid.

All vitamins are healthy.Some pills are healthy.∴ Some pills are vitamins.Invalid · you said nothingBelievable but invalid: the healthy pills could all be non-vitamins.

Some students are athletes.Some athletes are tall.∴ Some students are tall.Invalid · you said nothingTwo 'some' premises never guarantee a link. The tall athletes might not be the students.

No reptiles have fur.Some pets have fur.∴ Some pets are not reptiles.Valid · you said nothingThe furry pets can't be reptiles.

All squares are rectangles.Some rectangles are not squares.∴ Some squares are not rectangles.Invalid · you said nothingThe second premise says something about rectangles, not squares; and the first rules this out.

Some managers are not engineers.All engineers are graduates.∴ Some managers are not graduates.Invalid · you said nothingThe non-engineer managers could still be graduates. 'Not in B' doesn't mean 'not in C'.

Four ways a conclusion fools you

Each one is in the test above.

Belief biasAll birds can fly. Penguins are birds. ∴ Penguins can fly.Judge the structure, not the world. Swap the words for A, B, C and look again.

Reversing 'all'All cats have tails. This has a tail. ∴ It's a cat.'All A are B' never means 'all B are A'. Draw A inside B and check the leftover space.

Two loose 'somes'Some students are athletes. Some athletes are tall. ∴ Some students are tall.If both premises say 'some', nothing is guaranteed. The overlaps can miss each other.

'Not B' isn't 'not C'Some managers aren't engineers. All engineers are graduates. ∴ Some managers aren't graduates.Being outside a small circle doesn't put you outside the bigger one around it.

71% vs 10%How often people accepted an invalid argument when its conclusion was believable versus unbelievable, in Evans, Barston & Pollard's belief-bias study [1].

2,300 years of the same puzzle

c. 350 BCAristotle, Prior AnalyticsDefines the syllogism and sorts arguments into figures by where the middle term sits.

c. 1250Latin mnemonic namesBarbara, Celarent, Darii, Ferio…: the vowels in each name encode its three statement types.

1880sVenn's diagramsJohn Venn's overlapping circles make it possible to check validity by shading regions.

1983Belief bias measuredEvans, Barston & Pollard show people accept invalid arguments far more when the conclusion is believable.

256Possible forms4 statement types for each of 3 lines, times 4 figures.

24Valid for AristotleWhen 'All A are B' is taken to imply some A exist.

15Valid in modern logicThe forms the lab above marks as valid.

4FiguresThe ways the middle term can be placed across the two premises.

Verbal analogiesRelationships between words rather than groups.

Verbal reasoningTrue, false or cannot say on real passages.

Numerical reasoningThe same careful reading, with tables and charts.

References

Evans, J. St B. T., Barston, J. L., & Pollard, P. (1983). On the conflict between logic and belief in syllogistic reasoning. Memory & Cognition, 11(3), 295–306.
Johnson-Laird, P. N., & Bara, B. G. (1984). Syllogistic inference. Cognition, 16(1), 1–61.
Khemlani, S., & Johnson-Laird, P. N. (2012). Theories of the syllogism: A meta-analysis. Psychological Bulletin, 138(3), 427–457.

True isn't the same as follows.