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Formal Logic · Free
Syllogism Checker
Check the validity of any categorical syllogism. Enter the major premise, the minor premise, and the conclusion using the four standard quantifiers (All / No / Some / Some… are not). The tool identifies the figure, mood, and standard name (Barbara, Celarent, Darii, …), reports validity under both modern and traditional Aristotelian interpretation, and — when invalid — explains exactly which of the five rules of syllogism is violated.
Used in: Categorical Logic. The full lesson walks through the four standard forms (A, E, I, O), the distribution rule for each, and how the five rules of syllogism work as a closed test for validity.
Major premise
are
Minor premise
are
Conclusion
are
Reference: the 24 traditionally valid syllogisms
Of the 256 possible mood-figure combinations, 24 are valid under traditional Aristotelian logic. 15 of those remain valid under modern (Boolean) interpretation; the other 9 require existential import — they assume the subject class is non-empty, which modern logic doesn't take for granted.
Figure 1
- Barbara (AAA-1) — valid (both interpretations)
- Celarent (EAE-1) — valid (both interpretations)
- Darii (AII-1) — valid (both interpretations)
- Ferio (EIO-1) — valid (both interpretations)
- Barbari (AAI-1) — valid (traditional only)
- Celaront (EAO-1) — valid (traditional only)
Figure 2
- Cesare (EAE-2) — valid (both interpretations)
- Camestres (AEE-2) — valid (both interpretations)
- Festino (EIO-2) — valid (both interpretations)
- Baroco (AOO-2) — valid (both interpretations)
- Cesaro (EAO-2) — valid (traditional only)
- Camestros (AEO-2) — valid (traditional only)
Figure 3
- Darapti (AAI-3) — valid (traditional only)
- Disamis (IAI-3) — valid (both interpretations)
- Datisi (AII-3) — valid (both interpretations)
- Felapton (EAO-3) — valid (traditional only)
- Bocardo (OAO-3) — valid (both interpretations)
- Ferison (EIO-3) — valid (both interpretations)
Figure 4
- Bramantip (AAI-4) — valid (traditional only)
- Camenes (AEE-4) — valid (both interpretations)
- Dimaris (IAI-4) — valid (both interpretations)
- Fesapo (EAO-4) — valid (traditional only)
- Fresison (EIO-4) — valid (both interpretations)
- Camenos (AEO-4) — valid (traditional only)