Syllogisms
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 2^{8} = 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]
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[edit]
Examples[edit]
Barbara (AAA-1)[edit]
Celarent (EAE-1)[edit]
Similar: Cesare (EAE-2)
Calemes (AEE-4) |
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Calemes is like Celarent with S and P exchanged. |
Darii (AII-1)[edit]
Similar: Datisi (AII-3)
Dimatis (IAI-4) |
---|
Dimatis is like Darii with S and P exchanged. |
Ferio (EIO-1)[edit]
Similar: Festino (EIO-2), Ferison (EIO-3), Fresison (EIO-4)
Baroco (AOO-2)[edit]
Bocardo (OAO-3)[edit]
Barbari (AAI-1) [edit]
Bamalip (AAI-4) |
---|
Bamalip is like Barbari with S and P exchanged: |
Celaront (EAO-1)[edit]
Similar: Cesaro (EAO-2)
Camestros (AEO-2)[edit]
Similar: Calemos (AEO-4)
Felapton (EAO-3)[edit]
Similar: Fesapo (EAO-4)