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)
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1 | ![]() Barbara |
![]() Barbari |
![]() Darii |
![]() Ferio |
![]() Celaront |
![]() Celarent |
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2 | ![]() Festino |
![]() Cesaro |
![]() Cesare |
![]() Camestres |
![]() Camestros |
![]() Baroco |
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3 | ![]() Darapti |
![]() Datisi |
![]() Disamis |
![]() Felapton |
![]() Ferison |
![]() Bocardo | ||||||||
4 | ![]() Bamalip |
![]() Dimatis |
![]() Fesapo |
![]() Fresison |
![]() Calemes |
![]() Calemos |
Graphical elements
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[edit | edit source]Barbara (AAA-1)
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Celarent (EAE-1)
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Similar: Cesare (EAE-2)
Calemes (AEE-4) |
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![]() Calemes is like Celarent with S and P exchanged. |
Darii (AII-1)
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Similar: Datisi (AII-3)
Dimatis (IAI-4) |
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![]() Dimatis is like Darii with S and P exchanged. |
Ferio (EIO-1)
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Similar: Festino (EIO-2), Ferison (EIO-3), Fresison (EIO-4)
Baroco (AOO-2)
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Bocardo (OAO-3)
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Barbari (AAI-1)
[edit | edit source]![](https://cdn.statically.io/img/upload.wikimedia.org/wikipedia/commons/thumb/8/8b/Modus_Barbari.svg/300px-Modus_Barbari.svg.png)
Bamalip (AAI-4) |
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![]() Bamalip is like Barbari with S and P exchanged: |
Celaront (EAO-1)
[edit | edit source]![](https://cdn.statically.io/img/upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Modus_Celaront.svg/300px-Modus_Celaront.svg.png)
Similar: Cesaro (EAO-2)
Camestros (AEO-2)
[edit | edit source]![](https://cdn.statically.io/img/upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Modus_Camestros.svg/300px-Modus_Camestros.svg.png)
Similar: Calemos (AEO-4)
Felapton (EAO-3)
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Similar: Fesapo (EAO-4)
Darapti (AAI-3)
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