Dfn. Syllogism. This is a three-line argument with two premises and one conclusion in which there are only three terms.
All donuts are delicious treats. Some junk foods are delicious treats. Therefore, some junk food are donuts.
The three terms are: donuts, delicious treats, & junk oof.
First, there is the issue of validity . The argument is structurally correct (so that if the premises were true, the conclusion could not be false).
All leopards have spots. All spotted animals wish they had stripes. Therefore, all leopards wish they had stripes.
NOTE: If the two premises were true, the conclusion would have to be true too.
An argument is sound if
(1) the argument is valid
(2) the premises are actually true.
All leopards are cats. No cat is a squirrel. Therefore, no leopard is a squirrel.
Form 1: “All A is B.” Universal positive
“ All cockatoos are birds that can talk.”
Form 2: “No A is B.” Universal negative “No cockatoo is a duck.”
Form 3: “A is/is not B.” Universal positive/negative “Australia is a place with many cockatoos.”
This includes where A has only one member “That baby cockatoo is a darling bird.”
Form 1: “Some A is B” Particular positive
“ Some chefs are good bakers.”
Form 2: “Some A is not B” Particular negative
“ Some fish are not rainbow trout.”
Form 3: “x% of A is/is not B” Particular positive/negative. Where x 100 or 0.
“ 64% of women are tea drinkers.”
In analyzing a syllogism, it’s usually best to rewrite the premises and the conclusion in the form of categorical propositions .
These are :
A: All P are Q. All basketball players are athletes.
E: No P is Q. No violinist is a football player.
I: Some P is Q. Some gymnasts are shy people.
O: Some P is not Q. Some mountain climbers are not stamp collectors.
NOTE: The letters A, E, I, and O are handy ways to abbreviate these 4 forms.
A categorical syllogism is a syllogism in which the premises and the conclusion are categorical claims.
All racoons are pesky animals. No pesky animal is a good pet. Therefore, no raccoon is a good pet
The standard form of a categorical syllogism is a syllogism stated in the order of major premise, minor premise, and then the conclusion.
This gives us a uniform way to set out syllogisms so they are easy to assess, and we aren’t scrambling trying to figure out what’s what.
Categorical Syllogism in Standard Form
Here’s a categorical syllogism in standard form.
No vampires are morning people. Some morning people are folks who like scrambled eggs for breakfast. Therefore, no folks who like scrambled eggs for breakfast are vampires.
NOTE: The major premise is the premise that contains the predicate term (=major term) found in the conclusion.
The second premise is called the minor premise and it contains the subject term (=minor term) found in the conclusion. Both premises have a linking term (= middle term) that does not appear in the conclusion.
The middle term is the term that is found only in the premises, not the conclusion.
P = Predicate of the conclusion Major term
S = Subject of the conclusion Minor term
M = Term found in both premises Middle term
The Figures of the Syllogism
M P P M M P P M
S M S MM S M S
S P S P S P S P
FIGURE 1 FIGURE 2 FIGURE 3 FIGURE 4
Step down M’s on right M’s on left step up
Mood and Figure
The mood of the syllogism is found after the syllogism is in categorical standard form. Then you just read the abbreviations (A,E,I, O) of the universal/particular and positive/negative propostions. The figure is found by the location of the middle term.
Some vegetarians are cheese-eaters. All bicyclists are cheese-eaters. Therefore, some bicyclists are vegetarians.
The MOOD of the syllogism is: IAI. The figure is figure 2 (M’s on right). So the mood and figure is written:
Distribution of a term refers to how much of the class (the subject or the predicate) is being referred to in the propostion.
It’s easy to find: Claims that are all-or-nothing (A and E claims) refer to all of the subject class. Claims that are particular (I and O claims) refer to only some. So the SUBJECT IS DISTRIBUTED in universal claims—but not particular claims.
Claims that are positive (A and I) do not distribute the PREDICATE —the predicate is only distributed in negative claims (E and O).
PROPOSITION DISTRIBUTED TERM(S):
All P is Q subject
No P is Q subject and predicate
Some P is Q nothing
Some P is not Q predicate
RULES OF THE SYLLOGISM
Rule 1: The middle term must be distributed at least once.
Rule 2: If a term is distributed in the conclusion, it must also be distributed in its corresponding premise Illicit major : When the major term is distributed in the conclusion, but is not distributed in the major premise Illicit minor: When the minor term is distributed in the conclusion, but is not distributed in the minor premise
Note: A valid syllogism does not requires the conclusion to have its terms distributed. But if a term is distributed in the conclusion, then it must also be distributed in its corresponding premise.
Rules of the Syllogism con.
Rule 3: At least one premise must be positive. (Two negative premises = invalid argument)
Rule 4: If the syllogism has a negative premise, there must be a negative conclusion, and vice versa.
Rule 5: If both of the premises are universal, the conclusion must also be universal. And if the conclusion is universal, both premises must be universal as well.
(You cannot have two universal premises with a particular conclusion and you cannot have a universal conclusion unless both premises are also universal.)