Syllogisms of another important set of forms use affirmative

Names for the Valid Syllogisms premises (only one of which is universal) to derive a particular
affirmative conclusion:
A careful application of these rules to the 256 possible forms of
categorical syllogism (assuming the denial of existential import) The first in this group is AII-1 ("Darii"):
leaves only 15 that are valid. Medieval students of logic, relying on
syllogistic reasoning in their public disputations, found it convenient All M are P.
to assign a unique name to each valid syllogism. These names are Some S are M.
full of clever reminders of the appropriate standard form: their initial Therefore, Some S are P.
letters divide the valid cases into four major groups, the vowels in
order state the mood of the syllogism, and its figure is indicated by Converting the minor premise produces another valid form, AII-3
(complicated) use of m, r, and s. Although the modern interpretation ("Datisi"):
of categorical logic provides an easier method for determining the
validity of categorical syllogisms, it may be worthwhile to note the All M are P.
fifteen valid cases by name: Some M are S.
Therefore, Some S are P.
The most common and useful syllogistic form is "Barbara", whose
mood and figure is AAA-1:
The second pair begins with "Disamis" (IAI-3):
All M are P.
Some M are P.
All S are M.
All M are S.
Therefore, All S are P.
Therefore, Some S are P.

Instances of this form are especially powerful, since they are the
Converting the major premise in this case yields "Dimaris" (IAI-4):
only valid syllogisms whose conclusions are universal affirmative
propositions. Some P are M.
All M are S.
A syllogism of the form AOO-2 was called "Baroco": Therefore, Some S are P.
All P are M.
Some S are not M. Only one of the 64 distinct moods for syllogistic form is valid in all
Therefore, Some S are not P. four figures, since both of its premises permit legitimate
conversions:
The valid form OAO-3 ("Bocardo") is:
Begin with EIO-1 ("Ferio"):
Some M are not P.
No M are P.
All M are S.
Some S are M.
Therefore, Some S are not P.
Therefore, Some S are not P.

Four of the fifteen valid argument forms use universal premises

Converting the major premise produces EIO-2 ("Festino"):
(only one of which is affirmative) to derive a universal negative
conclusion: No P are M.
Some S are M.
One of them is "Camenes" (AEE-4): Therefore, Some S are not P.
All P are M.
No M are S. Next, converting the minor premise of this result yields EIO-4
Therefore, No S are P. ("Fresison"):
No P are M.
Converting its minor premise leads to "Camestres" (AEE-2): Some M are S.
Therefore, Some S are not P.
All P are M.
No S are M.
Therefore, No S are P. Finally, converting the major again leads to EIO-3 ("Ferison"):
No M are P.
Another pair begins with "Celarent" (EAE-1): Some M are S.
Therefore, Some S are not P.
No M are P.
All S are M.
Therefore, No S are P. Notice that converting the minor of this syllogistic form will return
us back to "Ferio."
Converting the major premise in this case yields "Cesare" (EAE-2):
No P are M.
All S are M.
Therefore, No S are P.
"Barbara" "Datisi"
Name given by medieval logicians to any categorical Name given by medieval logicians to a categorical
syllogism whose standard form may be designated as syllogism with the standard form AII-3.
AAA-1.
Example: Since all bookstores are places that sell popular
Example: All finches are birds, and all cardinals are novels and some bookstores are coffee shops, it follows
finches, so all cardinals are birds. that some coffee shops are places that sell popular novels.
"Baroco" "Disamis"
Name given by medieval logicians to a categorical Name given by medieval logicians to a categorical
syllogism whose standard form is AOO-2. syllogism whose standard form may be designated as IAI-
3.
Example: All cats are furry mammals, but some housepets
are not furry mammals, so some housepets are not cats. Example: Some nutritious dinners are vegetarian delights,
and all nutritious dinners are well-rounded meals, so some
"Camenes"
well-rounded meals are vegetarian delights.
Name given by medieval logicians to a categorical
syllogism whose standard form is AEE-4. "Dimaris"
Name given by medieval logicians to any categorical
Example: All first-degree murders are premeditated
syllogism whose standard form is IAI-4.
homicides, but no premeditated homicides are actions
performed in self-defence, so it follows that no actions Example: Some beloved household pets are golden
performed in self-defence are first-degree murders. retrievers, and since all golden retrievers are dogs, it must
follow that some dogs are beloved household pets.
"Camestres"
Name given by medieval logicians to any categorical "Ferio"
syllogism whose standard form may be designated as Name given by medieval logicians to any categorical
AEE-2. syllogism whose standard form may be designated as
EIO-1.
Example: All terriers are dogs, while no cats are dogs, so
no cats are terriers. Example: No mendicant friars are wealthy patrons of the
arts, but some medieval philosophers are mendicant friars,
so some medieval philosophers are not wealthy patrons of
"Celarent"
the arts.
Name given by medieval logicians to any categorical
syllogism whose standard form may be designated as "Festino"
EAE-1. Name given by medieval logicians to a categorical
syllogism with the standard form EIO-2.
Example: No cold-blooded animals are furry pets, even
though all reptiles are cold-blooded animals; therefore, no Example: No people deserving of our admiration and
reptiles are furry pets. praise are inveterate liars, but some wealthy industrialists
are inveterate liars; therefore, some wealthy industrialists
"Cesare"
are not people deserving of our admiration and praise.
Name given by medieval logicians to a categorical
syllogism whose standard form is EAE-2. "Fresison"
Name given by medieval logicians to any categorical
Example: Since no truly peaceful nations are places where
syllogism whose standard form may be designated as
basic human rights are inadequately defended, while all
EIO-4.
countries torn by ethnic strife are places where basic
human rights are inadequately defended, it follows that no Example: Since no fish are mammals while some animals
countries torn by ethnic strife are truly peaceful nations. that live in water are mammals, it follows that some
animals that live in water are not fish.
"Darii"
Name given by medieval logicians to any categorical "Ferison"
syllogism whose standard form may be designated as AII- Name given by medieval logicians to any categorical
1. syllogism whose standard form is EIO-3.
Example: All logicians are philosophers, and some serious Example: Since no people who admire Marx are political
scholars are logicians, so some serious scholars are conservatives and some people who admire Marx are
philosophers. South Carolinians, it follows that some South Carolinians
are not political conservatives.