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) |
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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) |
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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)