Syllogisms

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This page illustrates syllogisms in three different ways:

  • With Venn diagrams, that show in which intersections of the three sets objects do not (black), can (white) or do (red) exist.
  • With Euler diagrams, which are like Venn diagrams with empty regions removed. (Only small diagrams on top of the table.)
  • The gist of this page is the reduction of this first-order logic topic to zeroth-order logic using binary square matrices that are essentially 8-ary logical connectives. There are 8 intersections of the three sets, and each intersection can either contain elements or not. So there are 28 = 256 situations that can be the case. Each statement (premise or conclusion) can be denoted by the set of situations in which it is true.

All Syllogisms (table of contents)[edit]

Modus Barbara (Euler).svg Modus Barbari (Euler).svg Modus Bamalip (Euler).svg Modus Darapti (Euler).svg Modus Darii (Euler).svg Modus Disamis (Euler).svg Modus Felapton (Euler).svg Modus Ferio (Euler).svg Modus Celaront (Euler).svg Modus Celarent (Euler).svg Modus Camestres (Euler).svg Modus Camestros (Euler).svg Modus Baroco (Euler).svg Modus Bocardo (Euler).svg
1 Modus Barbara.svg
Barbara
Modus Barbari.svg
Barbari
Modus Darii.svg
Darii
Modus Ferio.svg
Ferio
Modus Celaront.svg
Celaront
Modus Celarent.svg
Celarent
2 Modus Festino.svg
Festino
Modus Cesaro.svg
Cesaro
Modus Cesare.svg
Cesare
Modus Camestres.svg
Camestres
Modus Camestros.svg
Camestros
Modus Baroco.svg
Baroco
3 Modus Darapti.svg
Darapti
Modus Datisi.svg
Datisi
Modus Disamis.svg
Disamis
Modus Felapton.svg
Felapton
Modus Ferison.svg
Ferison
Modus Bocardo.svg
Bocardo
4 Modus Bamalip.svg
Bamalip
Modus Dimatis.svg
Dimatis
Modus Fesapo.svg
Fesapo
Modus Fresison.svg
Fresison
Modus Calemes.svg
Calemes
Modus Calemos.svg
Calemos

Graphical elements[edit]

Venn diagram and corresponding cubic Hasse diagram, used in the diagram on the right
The 256 situations that can be the case (minterms)
Light vertices indicate that an area is empty, dark vertices indicate that there is at least one element.

Examples[edit]

Barbara (AAA-1)[edit]

Venn diagrams
Minterms


Celarent (EAE-1)[edit]

Venn diagrams
Minterms

Similar: Cesare (EAE-2)

Darii (AII-1)[edit]

Venn diagrams
Minterms

Similar: Datisi (AII-3)

Ferio (EIO-1)[edit]

Venn diagrams
Minterms

Similar: Festino (EIO-2), Ferison (EIO-3), Fresison (EIO-4)

Baroco (AOO-2)[edit]

Venn diagrams
Minterms

Bocardo (OAO-3)[edit]

Venn diagrams
Minterms

Barbari (AAI-1) [edit]

Venn diagrams

Celaront (EAO-1)[edit]

Venn diagrams

Similar: Cesaro (EAO-2)

Camestros (AEO-2)[edit]

Venn diagrams

Similar: Calemos (AEO-4)

Felapton (EAO-3)[edit]

Venn diagrams
Minterms

Similar: Fesapo (EAO-4)

Darapti (AAI-3)[edit]

Venn diagrams
Minterms