Editing Syllogism (section)

==Basic structure==
A categorical syllogism consists of three parts:
# Major premise
# Minor premise
# Conclusion/Consequent

Each part is a [[categorical proposition]], and each categorical proposition contains two categorical terms.<ref>{{cite web|url=http://www.philosophypages.com/dy/c.htm#capro |title=Philosophical Dictionary: Caird-Catharsis |publisher=Philosophypages.com |date=2002-08-08 |access-date=2009-12-14}}</ref> In Aristotle, each of the premises is in the form "All S are P," "Some S are P", "No S are P" or "Some S are not P", where "S" is the subject-term and "P" is the predicate-term:

* "All S are P," and "No S are P" are termed [[Universal proposition|''universal'' propositions]];
* "Some S are P" and "Some S are not P" are termed [[Particular proposition|''particular'' propositions]].

More modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the ''major term'' (i.e., the [[Predicate (grammar)|predicate]] of the conclusion); in a minor premise, this is the ''minor term'' (i.e., the subject of the conclusion). For example:

:'''Major premise''': All humans are mortal.
:'''Minor premise''': All Greeks are humans.
:'''Conclusion/Consequent''': All Greeks are mortal.

Each of the three distinct terms represents a category. From the example above, ''humans'', ''mortal'', and ''Greeks'': ''mortal'' is the major term, and ''Greeks'' the minor term. The premises also have one term in common with each other, which is known as the ''middle term''; in this example, ''humans''. Both of the premises are universal, as is the conclusion.

:'''Major premise''': All mortals die.
:'''Minor premise''': All men are mortals.
:'''Conclusion/Consequent''': All men die.

Here, the major term is ''die'', the minor term is ''men'', and the middle term is ''mortals''. Again, both premises are universal, hence so is the conclusion.

=== Polysyllogism ===
{{Main|Polysyllogism}}
A polysyllogism, or a '''sorites''', is a form of argument in which a series of incomplete syllogisms is so arranged that the predicate of each premise forms the subject of the next until the subject of the first is joined with the predicate of the last in the conclusion. For example, one might argue that all lions are big cats, all big cats are predators, and all predators are carnivores. To conclude that therefore all lions are carnivores is to construct a sorites argument.