Syllogism

Names for the Valid Syllogisms

Syllogisms of another important set of forms use affirmative 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 All M are P. syllogistic reasoning in their public disputations, found it convenient Some S are M. to assign a unique name to each valid syllogism. These names are 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 All M are P. validity of categorical syllogisms, it may be worthwhile to note the Some M are S. fifteen valid cases by name: 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 only valid syllogisms whose conclusions are universal affirmative propositions. A syllogism of the form AOO-2 was called "Baroco": All P are M. Some S are not M. Therefore, Some S are not P. The valid form OAO-3 ("Bocardo") is: Some M are not P. All M are S. Therefore, Some S are not P. Four of the fifteen valid argument forms use universal premises (only one of which is affirmative) to derive a universal negative conclusion: One of them is "Camenes" (AEE-4): All P are M. No M are S. Therefore, No S are P. Converting its minor premise leads to "Camestres" (AEE-2): All P are M. No S are M. Therefore, No S are P. Another pair begins with "Celarent" (EAE-1): No M are P. All S are M. Therefore, No S are P. Converting the major premise in this case yields "Cesare" (EAE-2): No P are M. All S are M. Therefore, No S are P.

Converting the major premise in this case yields "Dimaris" (IAI-4): Some P are M. All M are S. Therefore, Some S are P. Only one of the 64 distinct moods for syllogistic form is valid in all four figures, since both of its premises permit legitimate conversions: Begin with EIO-1 ("Ferio"): No M are P. Some S are M. Therefore, Some S are not P. Converting the major premise produces EIO-2 ("Festino"): No P are M. Some S are M. Therefore, Some S are not P. Next, converting the minor premise of this result yields EIO-4 ("Fresison"): No P are M. Some M are S. Therefore, Some S are not P. Finally, converting the major again leads to EIO-3 ("Ferison"): No M are P. Some M are S. Therefore, Some S are not P. Notice that converting the minor of this syllogistic form will return us back to "Ferio."

"Barbara" Name given by medieval logicians to any categorical syllogism whose standard form may be designated as AAA-1. Example: All finches are birds, and all cardinals are finches, so all cardinals are birds. "Baroco" Name given by medieval logicians to a categorical syllogism whose standard form is AOO-2.

"Datisi" Name given by medieval logicians to a categorical syllogism with the standard form AII-3. Example: Since all bookstores are places that sell popular novels and some bookstores are coffee shops, it follows that some coffee shops are places that sell popular novels. "Disamis" Name given by medieval logicians to a categorical syllogism whose standard form may be designated as IAI3.

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.