There are lots of examples of each of the 24 correct syllogism forms to be found on the internet, and lots of references to the fact that there are 256 possible syllogism forms. But nowhere could I find examples of logically incorrect syllogisms. So I decided (September 2015) to write a program to generate them all. I don't know why -- maybe someone else will be tickled by some of the more absurd ones below.
The program to generate them follows after the list.
The Key:
Each syllogism form is listed with its Figure type and its three linkages:
(A=All, E=No, I=Some, O=Some Not)
If a form is logical then it is in bold and its Medieval mnemonic is listed.
A “weak” form can be supplanted by a stronger form (See Barbara vs. Barbari)
An “existential” form is logical only if the middle element has at least one member.
e.g.: No jockeys in this room are women; All jockeys in this room are short people;
Therefore: Some short people in this room are not women. (3eao: Felapton)
(is only necessarily true if there’s at least one jockey in the room)
The software that generated this list did not check whether the major or minor premise is correct or incorrect, only whether the conclusion is logical.
thus you might find statements such as: “all humans are women; some men are humans; therefore, some men are women,” which is a logical statement given the incorrect premises. Most syllogisms below are both incorrect and illogical.
The List
1aaa (Barbara)
All pets are furry beasts.
All rabbits are pets.
Therefore, all rabbits are furry beasts.
-----------------------
1aae
All chairs are furniture.
All stools are chairs.
Therefore, no stools are furniture.
-----------------------
1aai (Barbari) [weak] [existential]
All musicologists are scholars.
All musicians are musicologists.
Therefore, some musicians are scholars.
-----------------------
1aao
All animals are rational beings.
All people are animals.
Therefore, some people are not rational beings.
-----------------------
1aea
All delicious foods are platos.
No tacos are delicious foods.
Therefore, all tacos are platos.
-----------------------
1aee
All insects are animals.
No spiders are insects.
Therefore, no spiders are animals.
-----------------------
1aei
All pets are furry beasts.
No rabbits are pets.
Therefore, some rabbits are furry beasts.
-----------------------
1aeo
All animals are rational beings.
No people are animals.
Therefore, some people are not rational beings.
-----------------------
1aia
All animals are rational beings.
Some people are animals.
Therefore, all people are rational beings.
-----------------------
1aie
All insects are animals.
Some spiders are insects.
Therefore, no spiders are animals.
-----------------------
1aii (Darii)
All pets are furry beasts.
Some rabbits are pets.
Therefore, some rabbits are furry beasts.
-----------------------
1aio
All musicologists are scholars.
Some musicians are musicologists.
Therefore, some musicians are not scholars.
-----------------------
1aoa
All chairs are furniture.
Some stools are not chairs.
Therefore, all stools are furniture.
-----------------------
1aoe
All insects are animals.
Some spiders are not insects.
Therefore, no spiders are animals.
-----------------------
1aoi
All plants are fungi.
Some flowers are not plants.
Therefore, some flowers are fungi.
-----------------------
1aoo
All plants are fungi.
Some flowers are not plants.
Therefore, some flowers are not fungi.
-----------------------
1eaa
No chairs are furniture.
All stools are chairs.
Therefore, all stools are furniture.
-----------------------
1eae (Celarent)
No pets are furry beasts.
All rabbits are pets.
Therefore, no rabbits are furry beasts.
-----------------------
1eai
No insects are animals.
All spiders are insects.
Therefore, some spiders are animals.
-----------------------
1eao (Celaront) [weak] [existential]
No chairs are furniture.
All stools are chairs.
Therefore, some stools are not furniture.
-----------------------
1eea
No insects are animals.
No spiders are insects.
Therefore, all spiders are animals.
-----------------------
1eee
No insects are animals.
No spiders are insects.
Therefore, no spiders are animals.
-----------------------
1eei
No women are humans.
No men are women.
Therefore, some men are humans.
-----------------------
1eeo
No insects are animals.
No spiders are insects.
Therefore, some spiders are not animals.
-----------------------
1eia
No delicious foods are platos.
Some tacos are delicious foods.
Therefore, all tacos are platos.
-----------------------
1eie
No musicologists are scholars.
Some musicians are musicologists.
Therefore, no musicians are scholars.
-----------------------
1eii
No animals are rational beings.
Some people are animals.
Therefore, some people are rational beings.
-----------------------
1eio (Ferio)
No pets are furry beasts.
Some rabbits are pets.
Therefore, some rabbits are not furry beasts.
-----------------------
1eoa
No plants are fungi.
Some flowers are not plants.
Therefore, all flowers are fungi.
-----------------------
1eoe
No women are humans.
Some men are not women.
Therefore, no men are humans.
-----------------------
1eoi
No women are humans.
Some men are not women.
Therefore, some men are humans.
-----------------------
1eoo
No pets are furry beasts.
Some rabbits are not pets.
Therefore, some rabbits are not furry beasts.
-----------------------
1iaa
Some pets are furry beasts.
All rabbits are pets.
Therefore, all rabbits are furry beasts.
-----------------------
1iae
Some chairs are furniture.
All stools are chairs.
Therefore, no stools are furniture.
-----------------------
1iai
Some chairs are furniture.
All stools are chairs.
Therefore, some stools are furniture.
-----------------------
1iao
Some musicologists are scholars.
All musicians are musicologists.
Therefore, some musicians are not scholars.
-----------------------
1iea
Some delicious foods are platos.
No tacos are delicious foods.
Therefore, all tacos are platos.
-----------------------
1iee
Some musicologists are scholars.
No musicians are musicologists.
Therefore, no musicians are scholars.
-----------------------
1iei
Some plants are fungi.
No flowers are plants.
Therefore, some flowers are fungi.
-----------------------
1ieo
Some insects are animals.
No spiders are insects.
Therefore, some spiders are not animals.
-----------------------
1iia
Some delicious foods are platos.
Some tacos are delicious foods.
Therefore, all tacos are platos.
-----------------------
1iie
Some plants are fungi.
Some flowers are plants.
Therefore, no flowers are fungi.
-----------------------
1iii
Some women are humans.
Some men are women.
Therefore, some men are humans.
-----------------------
1iio
Some pets are furry beasts.
Some rabbits are pets.
Therefore, some rabbits are not furry beasts.
-----------------------
1ioa
Some chairs are furniture.
Some stools are not chairs.
Therefore, all stools are furniture.
-----------------------
1ioe
Some chairs are furniture.
Some stools are not chairs.
Therefore, no stools are furniture.
-----------------------
1ioi
Some insects are animals.
Some spiders are not insects.
Therefore, some spiders are animals.
-----------------------
1ioo
Some musicologists are scholars.
Some musicians are not musicologists.
Therefore, some musicians are not scholars.
-----------------------
1oaa
Some musicologists are not scholars.
All musicians are musicologists.
Therefore, all musicians are scholars.
-----------------------
1oae
Some chairs are not furniture.
All stools are chairs.
Therefore, no stools are furniture.
-----------------------
1oai
Some musicologists are not scholars.
All musicians are musicologists.
Therefore, some musicians are scholars.
-----------------------
1oao
Some pets are not furry beasts.
All rabbits are pets.
Therefore, some rabbits are not furry beasts.
-----------------------
1oea
Some plants are not fungi.
No flowers are plants.
Therefore, all flowers are fungi.
-----------------------
1oee
Some animals are not rational beings.
No people are animals.
Therefore, no people are rational beings.
-----------------------
1oei
Some pets are not furry beasts.
No rabbits are pets.
Therefore, some rabbits are furry beasts.
-----------------------
1oeo
Some insects are not animals.
No spiders are insects.
Therefore, some spiders are not animals.
-----------------------
1oia
Some plants are not fungi.
Some flowers are plants.
Therefore, all flowers are fungi.
-----------------------
1oie
Some pets are not furry beasts.
Some rabbits are pets.
Therefore, no rabbits are furry beasts.
-----------------------
1oii
Some women are not humans.
Some men are women.
Therefore, some men are humans.
-----------------------
1oio
Some plants are not fungi.
Some flowers are plants.
Therefore, some flowers are not fungi.
-----------------------
1ooa
Some insects are not animals.
Some spiders are not insects.
Therefore, all spiders are animals.
-----------------------
1ooe
Some women are not humans.
Some men are not women.
Therefore, no men are humans.
-----------------------
1ooi
Some animals are not rational beings.
Some people are not animals.
Therefore, some people are rational beings.
-----------------------
1ooo
Some plants are not fungi.
Some flowers are not plants.
Therefore, some flowers are not fungi.
-----------------------
2aaa
All humans are women.
All men are women.
Therefore, all men are humans.
-----------------------
2aae
All animals are insects.
All spiders are insects.
Therefore, no spiders are animals.
-----------------------
2aai
All furniture are chairs.
All stools are chairs.
Therefore, some stools are furniture.
-----------------------
2aao
All rational beings are animals.
All people are animals.
Therefore, some people are not rational beings.
-----------------------
2aea
All furry beasts are pets.
No rabbits are pets.
Therefore, all rabbits are furry beasts.
-----------------------
2aee (Camestres)
All scholars are musicologists.
No musicians are musicologists.
Therefore, no musicians are scholars.
-----------------------
2aei
All fungi are plants.
No flowers are plants.
Therefore, some flowers are fungi.
-----------------------
2aeo (Camestros) [weak] [existential]
All furry beasts are pets.
No rabbits are pets.
Therefore, some rabbits are not furry beasts.
-----------------------
2aia
All furniture are chairs.
Some stools are chairs.
Therefore, all stools are furniture.
-----------------------
2aie
All fungi are plants.
Some flowers are plants.
Therefore, no flowers are fungi.
-----------------------
2aii
All humans are women.
Some men are women.
Therefore, some men are humans.
-----------------------
2aio
All animals are insects.
Some spiders are insects.
Therefore, some spiders are not animals.
-----------------------
2aoa
All platos are delicious foods.
Some tacos are not delicious foods.
Therefore, all tacos are platos.
-----------------------
2aoe
All furry beasts are pets.
Some rabbits are not pets.
Therefore, no rabbits are furry beasts.
-----------------------
2aoi
All platos are delicious foods.
Some tacos are not delicious foods.
Therefore, some tacos are platos.
-----------------------
2aoo (Baroco)
All furniture are chairs.
Some stools are not chairs.
Therefore, some stools are not furniture.
-----------------------
2eaa
No platos are delicious foods.
All tacos are delicious foods.
Therefore, all tacos are platos.
-----------------------
2eae (Cesare)
No platos are delicious foods.
All tacos are delicious foods.
Therefore, no tacos are platos.
-----------------------
2eai
No furry beasts are pets.
All rabbits are pets.
Therefore, some rabbits are furry beasts.
-----------------------
2eao (Cesaro) [weak] [existential]
No rational beings are animals.
All people are animals.
Therefore, some people are not rational beings.
-----------------------
2eea
No fungi are plants.
No flowers are plants.
Therefore, all flowers are fungi.
-----------------------
2eee
No fungi are plants.
No flowers are plants.
Therefore, no flowers are fungi.
-----------------------
2eei
No rational beings are animals.
No people are animals.
Therefore, some people are rational beings.
-----------------------
2eeo
No fungi are plants.
No flowers are plants.
Therefore, some flowers are not fungi.
-----------------------
2eia
No rational beings are animals.
Some people are animals.
Therefore, all people are rational beings.
-----------------------
2eie
No fungi are plants.
Some flowers are plants.
Therefore, no flowers are fungi.
-----------------------
2eii
No furry beasts are pets.
Some rabbits are pets.
Therefore, some rabbits are furry beasts.
-----------------------
2eio (Festino)
No animals are insects.
Some spiders are insects.
Therefore, some spiders are not animals.
-----------------------
2eoa
No humans are women.
Some men are not women.
Therefore, all men are humans.
-----------------------
2eoe
No scholars are musicologists.
Some musicians are not musicologists.
Therefore, no musicians are scholars.
-----------------------
2eoi
No platos are delicious foods.
Some tacos are not delicious foods.
Therefore, some tacos are platos.
-----------------------
2eoo
No fungi are plants.
Some flowers are not plants.
Therefore, some flowers are not fungi.
-----------------------
2iaa
Some scholars are musicologists.
All musicians are musicologists.
Therefore, all musicians are scholars.
-----------------------
2iae
Some platos are delicious foods.
All tacos are delicious foods.
Therefore, no tacos are platos.
-----------------------
2iai
Some platos are delicious foods.
All tacos are delicious foods.
Therefore, some tacos are platos.
-----------------------
2iao
Some humans are women.
All men are women.
Therefore, some men are not humans.
-----------------------
2iea
Some fungi are plants.
No flowers are plants.
Therefore, all flowers are fungi.
-----------------------
2iee
Some fungi are plants.
No flowers are plants.
Therefore, no flowers are fungi.
-----------------------
2iei
Some scholars are musicologists.
No musicians are musicologists.
Therefore, some musicians are scholars.
-----------------------
2ieo
Some furry beasts are pets.
No rabbits are pets.
Therefore, some rabbits are not furry beasts.
-----------------------
2iia
Some humans are women.
Some men are women.
Therefore, all men are humans.
-----------------------
2iie
Some platos are delicious foods.
Some tacos are delicious foods.
Therefore, no tacos are platos.
-----------------------
2iii
Some furry beasts are pets.
Some rabbits are pets.
Therefore, some rabbits are furry beasts.
-----------------------
2iio
Some platos are delicious foods.
Some tacos are delicious foods.
Therefore, some tacos are not platos.
-----------------------
2ioa
Some fungi are plants.
Some flowers are not plants.
Therefore, all flowers are fungi.
-----------------------
2ioe
Some platos are delicious foods.
Some tacos are not delicious foods.
Therefore, no tacos are platos.
-----------------------
2ioi
Some rational beings are animals.
Some people are not animals.
Therefore, some people are rational beings.
-----------------------
2ioo
Some fungi are plants.
Some flowers are not plants.
Therefore, some flowers are not fungi.
-----------------------
2oaa
Some scholars are not musicologists.
All musicians are musicologists.
Therefore, all musicians are scholars.
-----------------------
2oae
Some rational beings are not animals.
All people are animals.
Therefore, no people are rational beings.
-----------------------
2oai
Some humans are not women.
All men are women.
Therefore, some men are humans.
-----------------------
2oao
Some furniture are not chairs.
All stools are chairs.
Therefore, some stools are not furniture.
-----------------------
2oea
Some furniture are not chairs.
No stools are chairs.
Therefore, all stools are furniture.
-----------------------
2oee
Some rational beings are not animals.
No people are animals.
Therefore, no people are rational beings.
-----------------------
2oei
Some animals are not insects.
No spiders are insects.
Therefore, some spiders are animals.
-----------------------
2oeo
Some rational beings are not animals.
No people are animals.
Therefore, some people are not rational beings.
-----------------------
2oia
Some furry beasts are not pets.
Some rabbits are pets.
Therefore, all rabbits are furry beasts.
-----------------------
2oie
Some furry beasts are not pets.
Some rabbits are pets.
Therefore, no rabbits are furry beasts.
-----------------------
2oii
Some furniture are not chairs.
Some stools are chairs.
Therefore, some stools are furniture.
-----------------------
2oio
Some furniture are not chairs.
Some stools are chairs.
Therefore, some stools are not furniture.
-----------------------
2ooa
Some humans are not women.
Some men are not women.
Therefore, all men are humans.
-----------------------
2ooe
Some fungi are not plants.
Some flowers are not plants.
Therefore, no flowers are fungi.
-----------------------
2ooi
Some rational beings are not animals.
Some people are not animals.
Therefore, some people are rational beings.
-----------------------
2ooo
Some humans are not women.
Some men are not women.
Therefore, some men are not humans.
-----------------------
3aaa
All musicologists are scholars.
All musicologists are musicians.
Therefore, all musicians are scholars.
-----------------------
3aae
All musicologists are scholars.
All musicologists are musicians.
Therefore, no musicians are scholars.
-----------------------
3aai (Darapti) [existential]
All women are humans.
All women are men.
Therefore, some men are humans.
-----------------------
3aao
All chairs are furniture.
All chairs are stools.
Therefore, some stools are not furniture.
-----------------------
3aea
All animals are rational beings.
No animals are people.
Therefore, all people are rational beings.
-----------------------
3aee
All animals are rational beings.
No animals are people.
Therefore, no people are rational beings.
-----------------------
3aei
All animals are rational beings.
No animals are people.
Therefore, some people are rational beings.
-----------------------
3aeo
All animals are rational beings.
No animals are people.
Therefore, some people are not rational beings.
-----------------------
3aia
All chairs are furniture.
Some chairs are stools.
Therefore, all stools are furniture.
-----------------------
3aie
All insects are animals.
Some insects are spiders.
Therefore, no spiders are animals.
-----------------------
3aii (Datisi)
All delicious foods are platos.
Some delicious foods are tacos.
Therefore, some tacos are platos.
-----------------------
3aio
All chairs are furniture.
Some chairs are stools.
Therefore, some stools are not furniture.
-----------------------
3aoa
All insects are animals.
Some insects are not spiders.
Therefore, all spiders are animals.
-----------------------
3aoe
All musicologists are scholars.
Some musicologists are not musicians.
Therefore, no musicians are scholars.
-----------------------
3aoi
All delicious foods are platos.
Some delicious foods are not tacos.
Therefore, some tacos are platos.
-----------------------
3aoo
All insects are animals.
Some insects are not spiders.
Therefore, some spiders are not animals.
-----------------------
3eaa
No musicologists are scholars.
All musicologists are musicians.
Therefore, all musicians are scholars.
-----------------------
3eae
No animals are rational beings.
All animals are people.
Therefore, no people are rational beings.
-----------------------
3eai
No insects are animals.
All insects are spiders.
Therefore, some spiders are animals.
-----------------------
3eao (Felapton) [existential]
No musicologists are scholars.
All musicologists are musicians.
Therefore, some musicians are not scholars.
-----------------------
3eea
No musicologists are scholars.
No musicologists are musicians.
Therefore, all musicians are scholars.
-----------------------
3eee
No women are humans.
No women are men.
Therefore, no men are humans.
-----------------------
3eei
No chairs are furniture.
No chairs are stools.
Therefore, some stools are furniture.
-----------------------
3eeo
No animals are rational beings.
No animals are people.
Therefore, some people are not rational beings.
-----------------------
3eia
No insects are animals.
Some insects are spiders.
Therefore, all spiders are animals.
-----------------------
3eie
No musicologists are scholars.
Some musicologists are musicians.
Therefore, no musicians are scholars.
-----------------------
3eii
No chairs are furniture.
Some chairs are stools.
Therefore, some stools are furniture.
-----------------------
3eio (Ferison)
No women are humans.
Some women are men.
Therefore, some men are not humans.
-----------------------
3eoa
No musicologists are scholars.
Some musicologists are not musicians.
Therefore, all musicians are scholars.
-----------------------
3eoe
No women are humans.
Some women are not men.
Therefore, no men are humans.
-----------------------
3eoi
No animals are rational beings.
Some animals are not people.
Therefore, some people are rational beings.
-----------------------
3eoo
No musicologists are scholars.
Some musicologists are not musicians.
Therefore, some musicians are not scholars.
-----------------------
3iaa
Some pets are furry beasts.
All pets are rabbits.
Therefore, all rabbits are furry beasts.
-----------------------
3iae
Some chairs are furniture.
All chairs are stools.
Therefore, no stools are furniture.
-----------------------
3iai (Disamis)
Some insects are animals.
All insects are spiders.
Therefore, some spiders are animals.
-----------------------
3iao
Some musicologists are scholars.
All musicologists are musicians.
Therefore, some musicians are not scholars.
-----------------------
3iea
Some delicious foods are platos.
No delicious foods are tacos.
Therefore, all tacos are platos.
-----------------------
3iee
Some pets are furry beasts.
No pets are rabbits.
Therefore, no rabbits are furry beasts.
-----------------------
3iei
Some plants are fungi.
No plants are flowers.
Therefore, some flowers are fungi.
-----------------------
3ieo
Some pets are furry beasts.
No pets are rabbits.
Therefore, some rabbits are not furry beasts.
-----------------------
3iia
Some musicologists are scholars.
Some musicologists are musicians.
Therefore, all musicians are scholars.
-----------------------
3iie
Some insects are animals.
Some insects are spiders.
Therefore, no spiders are animals.
-----------------------
3iii
Some pets are furry beasts.
Some pets are rabbits.
Therefore, some rabbits are furry beasts.
-----------------------
3iio
Some musicologists are scholars.
Some musicologists are musicians.
Therefore, some musicians are not scholars.
-----------------------
3ioa
Some plants are fungi.
Some plants are not flowers.
Therefore, all flowers are fungi.
-----------------------
3ioe
Some plants are fungi.
Some plants are not flowers.
Therefore, no flowers are fungi.
-----------------------
3ioi
Some musicologists are scholars.
Some musicologists are not musicians.
Therefore, some musicians are scholars.
-----------------------
3ioo
Some chairs are furniture.
Some chairs are not stools.
Therefore, some stools are not furniture.
-----------------------
3oaa
Some animals are not rational beings.
All animals are people.
Therefore, all people are rational beings.
-----------------------
3oae
Some pets are not furry beasts.
All pets are rabbits.
Therefore, no rabbits are furry beasts.
-----------------------
3oai
Some women are not humans.
All women are men.
Therefore, some men are humans.
-----------------------
3oao (Bocardo)
Some delicious foods are not platos.
All delicious foods are tacos.
Therefore, some tacos are not platos.
-----------------------
3oea
Some delicious foods are not platos.
No delicious foods are tacos.
Therefore, all tacos are platos.
-----------------------
3oee
Some animals are not rational beings.
No animals are people.
Therefore, no people are rational beings.
-----------------------
3oei
Some chairs are not furniture.
No chairs are stools.
Therefore, some stools are furniture.
-----------------------
3oeo
Some animals are not rational beings.
No animals are people.
Therefore, some people are not rational beings.
-----------------------
3oia
Some chairs are not furniture.
Some chairs are stools.
Therefore, all stools are furniture.
-----------------------
3oie
Some animals are not rational beings.
Some animals are people.
Therefore, no people are rational beings.
-----------------------
3oii
Some insects are not animals.
Some insects are spiders.
Therefore, some spiders are animals.
-----------------------
3oio
Some musicologists are not scholars.
Some musicologists are musicians.
Therefore, some musicians are not scholars.
-----------------------
3ooa
Some animals are not rational beings.
Some animals are not people.
Therefore, all people are rational beings.
-----------------------
3ooe
Some delicious foods are not platos.
Some delicious foods are not tacos.
Therefore, no tacos are platos.
-----------------------
3ooi
Some delicious foods are not platos.
Some delicious foods are not tacos.
Therefore, some tacos are platos.
-----------------------
3ooo
Some plants are not fungi.
Some plants are not flowers.
Therefore, some flowers are not fungi.
-----------------------
4aaa
All animals are insects.
All insects are spiders.
Therefore, all spiders are animals.
-----------------------
4aae
All furniture are chairs.
All chairs are stools.
Therefore, no stools are furniture.
-----------------------
4aai (Bamalip) [existential]
All humans are women.
All women are men.
Therefore, some men are humans.
-----------------------
4aao
All furniture are chairs.
All chairs are stools.
Therefore, some stools are not furniture.
-----------------------
4aea
All animals are insects.
No insects are spiders.
Therefore, all spiders are animals.
-----------------------
4aee (Calemes)
All animals are insects.
No insects are spiders.
Therefore, no spiders are animals.
-----------------------
4aei
All animals are insects.
No insects are spiders.
Therefore, some spiders are animals.
-----------------------
4aeo (Calemos) [weak] [existential]
All platos are delicious foods.
No delicious foods are tacos.
Therefore, some tacos are not platos.
-----------------------
4aia
All furniture are chairs.
Some chairs are stools.
Therefore, all stools are furniture.
-----------------------
4aie
All platos are delicious foods.
Some delicious foods are tacos.
Therefore, no tacos are platos.
-----------------------
4aii
All fungi are plants.
Some plants are flowers.
Therefore, some flowers are fungi.
-----------------------
4aio
All scholars are musicologists.
Some musicologists are musicians.
Therefore, some musicians are not scholars.
-----------------------
4aoa
All humans are women.
Some women are not men.
Therefore, all men are humans.
-----------------------
4aoe
All furniture are chairs.
Some chairs are not stools.
Therefore, no stools are furniture.
-----------------------
4aoi
All humans are women.
Some women are not men.
Therefore, some men are humans.
-----------------------
4aoo
All rational beings are animals.
Some animals are not people.
Therefore, some people are not rational beings.
-----------------------
4eaa
No platos are delicious foods.
All delicious foods are tacos.
Therefore, all tacos are platos.
-----------------------
4eae
No scholars are musicologists.
All musicologists are musicians.
Therefore, no musicians are scholars.
-----------------------
4eai
No rational beings are animals.
All animals are people.
Therefore, some people are rational beings.
-----------------------
4eao (Fesapo) [existential]
No animals are insects.
All insects are spiders.
Therefore, some spiders are not animals.
-----------------------
4eea
No platos are delicious foods.
No delicious foods are tacos.
Therefore, all tacos are platos.
-----------------------
4eee
No platos are delicious foods.
No delicious foods are tacos.
Therefore, no tacos are platos.
-----------------------
4eei
No animals are insects.
No insects are spiders.
Therefore, some spiders are animals.
-----------------------
4eeo
No fungi are plants.
No plants are flowers.
Therefore, some flowers are not fungi.
-----------------------
4eia
No platos are delicious foods.
Some delicious foods are tacos.
Therefore, all tacos are platos.
-----------------------
4eie
No fungi are plants.
Some plants are flowers.
Therefore, no flowers are fungi.
-----------------------
4eii
No fungi are plants.
Some plants are flowers.
Therefore, some flowers are fungi.
-----------------------
4eio (Fresison)
No rational beings are animals.
Some animals are people.
Therefore, some people are not rational beings.
-----------------------
4eoa
No scholars are musicologists.
Some musicologists are not musicians.
Therefore, all musicians are scholars.
-----------------------
4eoe
No furry beasts are pets.
Some pets are not rabbits.
Therefore, no rabbits are furry beasts.
-----------------------
4eoi
No rational beings are animals.
Some animals are not people.
Therefore, some people are rational beings.
-----------------------
4eoo
No platos are delicious foods.
Some delicious foods are not tacos.
Therefore, some tacos are not platos.
-----------------------
4iaa
Some platos are delicious foods.
All delicious foods are tacos.
Therefore, all tacos are platos.
-----------------------
4iae
Some furry beasts are pets.
All pets are rabbits.
Therefore, no rabbits are furry beasts.
-----------------------
4iai (Dimatis)
Some fungi are plants.
All plants are flowers.
Therefore, some flowers are fungi.
-----------------------
4iao
Some fungi are plants.
All plants are flowers.
Therefore, some flowers are not fungi.
-----------------------
4iea
Some furry beasts are pets.
No pets are rabbits.
Therefore, all rabbits are furry beasts.
-----------------------
4iee
Some humans are women.
No women are men.
Therefore, no men are humans.
-----------------------
4iei
Some rational beings are animals.
No animals are people.
Therefore, some people are rational beings.
-----------------------
4ieo
Some humans are women.
No women are men.
Therefore, some men are not humans.
-----------------------
4iia
Some fungi are plants.
Some plants are flowers.
Therefore, all flowers are fungi.
-----------------------
4iie
Some platos are delicious foods.
Some delicious foods are tacos.
Therefore, no tacos are platos.
-----------------------
4iii
Some furniture are chairs.
Some chairs are stools.
Therefore, some stools are furniture.
-----------------------
4iio
Some furry beasts are pets.
Some pets are rabbits.
Therefore, some rabbits are not furry beasts.
-----------------------
4ioa
Some rational beings are animals.
Some animals are not people.
Therefore, all people are rational beings.
-----------------------
4ioe
Some rational beings are animals.
Some animals are not people.
Therefore, no people are rational beings.
-----------------------
4ioi
Some rational beings are animals.
Some animals are not people.
Therefore, some people are rational beings.
-----------------------
4ioo
Some rational beings are animals.
Some animals are not people.
Therefore, some people are not rational beings.
-----------------------
4oaa
Some rational beings are not animals.
All animals are people.
Therefore, all people are rational beings.
-----------------------
4oae
Some scholars are not musicologists.
All musicologists are musicians.
Therefore, no musicians are scholars.
-----------------------
4oai
Some scholars are not musicologists.
All musicologists are musicians.
Therefore, some musicians are scholars.
-----------------------
4oao
Some scholars are not musicologists.
All musicologists are musicians.
Therefore, some musicians are not scholars.
-----------------------
4oea
Some rational beings are not animals.
No animals are people.
Therefore, all people are rational beings.
-----------------------
4oee
Some furniture are not chairs.
No chairs are stools.
Therefore, no stools are furniture.
-----------------------
4oei
Some furniture are not chairs.
No chairs are stools.
Therefore, some stools are furniture.
-----------------------
4oeo
Some humans are not women.
No women are men.
Therefore, some men are not humans.
-----------------------
4oia
Some furry beasts are not pets.
Some pets are rabbits.
Therefore, all rabbits are furry beasts.
-----------------------
4oie
Some humans are not women.
Some women are men.
Therefore, no men are humans.
-----------------------
4oii
Some furniture are not chairs.
Some chairs are stools.
Therefore, some stools are furniture.
-----------------------
4oio
Some fungi are not plants.
Some plants are flowers.
Therefore, some flowers are not fungi.
-----------------------
4ooa
Some scholars are not musicologists.
Some musicologists are not musicians.
Therefore, all musicians are scholars.
-----------------------
4ooe
Some furniture are not chairs.
Some chairs are not stools.
Therefore, no stools are furniture.
-----------------------
4ooi
Some fungi are not plants.
Some plants are not flowers.
Therefore, some flowers are fungi.
-----------------------
4ooo
Some furry beasts are not pets.
Some pets are not rabbits.
Therefore, some rabbits are not furry beasts.
-----------------------
The (Python3) code to generate the list:
# -*- coding: utf-8 -*-
######################
# syllogisms.py -- generate all possible syllogisms,
# whether valid or not
#
# Copyright 2015, Michael Scott Cuthbert (cuthbert@mit.edu)
# Released freely under a BSD license.
from __future__ import print_function
# change these to make it funny...
sylloExamples = [('men', 'women', 'humans'),
('people', 'animals', 'rational beings'),
('stools', 'chairs', 'furniture'),
('spiders', 'insects', 'animals'),
('musicians', 'musicologists', 'scholars'),
('rabbits', 'pets', 'furry beasts'),
('flowers', 'plants', 'fungi'),
('tacos', 'delicious foods', 'platos')
]
import random
from collections import OrderedDict
class Figure:
def __init__(self, type=None):
self.figureType = type
self.conclusion = ["S", "P"]
if type == 1:
self.major = ["M", "P"]
self.minor = ["S", "M"]
self.conclusion = ["S", "P"]
elif type == 2:
self.major = ["P", "M"]
self.minor = ["S", "M"]
self.conclusion = ["S", "P"]
elif type == 3:
self.major = ["M", "P"]
self.minor = ["M", "S"]
self.conclusion = ["S", "P"]
elif type == 4:
self.major = ["P", "M"]
self.minor = ["M", "S"]
self.conclusion = ["S", "P"]
class Mood:
linkMapping = {"a": "all ",
"e": "no ",
"i": "some ",
"o": "some ",
}
postVerbLink = {"a": "",
"e": "",
"i": "",
"o": "not "}
def __init__(self, links):
self.links = links
self.majorLink = links[0]
self.minorLink = links[1]
self.conclusionLink = links[2]
logical = OrderedDict([("1aaa","barbara"), ("1eae","celarent"),
("1aii","darii"), ("1eio","ferio"),
("1aai","barbari"), ("1eao","celaront"),
("2eae","cesare"), ("2aee","camestres"), ("2eio","festino"),
("2aoo","baroco"), ("2eao","cesaro"), ("2aeo","camestros"),
("3aii","datisi"), ("3iai","disamis"), ("3eio","ferison"),
("3oao","bocardo"), ("3eao","felapton"), ("3aai","darapti"),
("4aee","calemes"), ("4iai", "dimatis"), ("4eio","fresison"),
("4aeo","calemos"), ("4eao", "fesapo"), ("4aai","bamalip")
])
# existential fallacy -- requires at least one member of the set to exist.
existential = set(["1aai", "1eao", "2eao", "2aeo", "3eao", "3aai", "4aeo", "4eao", "4aai"])
# weakened -- it is possible to make a stronger statement about the claims
# all instead of some, no instead of some not.
weakened = existential - set(["3eao", "3aai", "4eao", "4aai"])
wordType = {"S": "subject",
"M": "middle",
"P": "predicate"}
class Syllogism:
def __init__(self, figure, mood, syllowords=None):
self.figure = Figure(figure)
self.mood = Mood(mood)
if syllowords is None:
syllowords = random.choice(sylloExamples)
self.subject = syllowords[0]
self.middle = syllowords[1]
self.predicate = syllowords[2]
def generate(self):
allSentences = []
for sentence in ("major", "minor", "conclusion"):
sOut = ""
if sentence == "conclusion":
sOut = "Therefore, "
linkage = getattr(self.mood, sentence + "Link")
linkWord = self.mood.linkMapping[linkage]
if sOut == "":
linkWord = linkWord.capitalize()
sOut += linkWord
sFormat = getattr(self.figure, sentence)
wt = wordType[sFormat[0]]
sOut += getattr(self, wt)
sOut += " are "
sOut += self.mood.postVerbLink[linkage]
wt = wordType[sFormat[1]]
sOut += getattr(self, wt)
sOut += ". "
allSentences.append(sOut)
return("\n".join(allSentences))
def generateAll():
for i in range(1,5):
for a in "aeio":
for b in "aeio":
for c in "aeio":
shorthand = "{0}{1}".format(i, a+b+c)
print(shorthand, end="")
if shorthand in logical:
print(" (" + logical[shorthand].capitalize() + ")", end="")
if shorthand in weakened:
print(" [weak]", end="")
if shorthand in existential:
print(" [existential]", end="")
print("")
s = Syllogism(i, a+b+c)
print(s.generate())
print("-----------------------\n")
if __name__ == '__main__':
generateAll()
5 comments:
Love it! :-)
I am surprised that a musician works with logic and programming! Nice work, thank you.
3iai (Disamis) is valid and should be in bold.
Ah
Hmmmmmm
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