RULES OF SYLLOGISM.pdf

Logic

1. RULES OF SYLLOGISM

2. THE EIGHT RULES
TheseeightrulesaregroupedintoRulesonTerms(1-4)andRulesonProposition(5-8).
RULEONE:Theremustbethreeandonlythreeterms.
◦*Asyllogismestablishestheidentityornon-identityoftheminorandthemajortermonthe
basisoftheirrespectiverelationtoacommonthirdtermormiddleterm.Asyllogismwith
fourtermsdoesnotestablishasequence.
◦EXAMPLE:
Everymanisrational,
butPeterisaman,
Therefore,Peterisrational.

3. •A syllogism having four terms is called a “logical quadruped” (four feet).
1. Arithmetical Additionis adding a fourth term
Example:
Every Dog is an animal,
But every cactus is a plant,
Therefore, (no possible conclusion because the premises are not related to each other)
2. Equivocationis giving a term two or more meanings resulting in having a fourth term which
destroys the sequence
Example:
A pitcher is a water container,
But Mr. Sanders is a pitcher.
Therefore, Mr. Sanders is a water container.
3. Changing supposition consists changing the point of view or usage of a term
Example:
A mother is a woman giving birth, (real supposition)
but a nun is a mother, (metaphorical)
therefore, a nun is a woman giving birth.

4. RULE TWO: No term must have greater extension in the conclusion than
it has in the premises.
This applies to the minor and major terms. Any of them may not be a universal term in the
conclusion if it is a particular term in the premise.
*illicit minor –when the over-extended term is the minor term
*illicit major –when the over -extended term is the major term
a.) ILLICIT MINOR
Example:
Every girl is a female,
But every girl is a young person, (particular)
Therefore, every young person is a female. (universal)

5. b.)ILLICITMAJOR
Example:
Somecandiesarechocolate,(particular)
Butnofruitisachocolate,
Therefore,nofruitisacandy.(universal)
RULETHREE:Themiddletermmustnotappearintheconclusion .
Themiddletermservesasthecommonthirdtermwhichrelatestheminorandthe
majorterms.Therefore,ithasnoplaceintheconclusion. Itiseasytoseeifthemiddle
termisintheconclusionbecauseitcomesoutthreetimesinthesyllogism.
Example:
Every student is a learner ,
Buteverylearnerisanachiever,
Therefore,everylearnerisastudent.(misplacedmiddle)

6. RULE FOUR: The middle term must be universal at least once.
Because a particular term signifies an indeterminate portion of a whole, what it says
does not necessarily apply to the whole totality. An error of this rule is called
“undistributed middle”
Example:
Every man is
human being, (particular)
But every scientist is a human being, (particular)
Therefore, every scientist is a man.
The middle term “human being” is a particular term since it is a predicate of both
affirmative propositions.

7. RULE FIVE: Two affirmative premises yield an affirmative conclusion.
The conclusion will always be an affirmative when the premises are affirmative.
Violation of this rule is called “negative affirmation” since it denies what should be
affirmed in the conclusion.
Example:
Some women are writers,
But all writers are educated,
Therefore,
some educated are women.

8. RULE SIX: Two negative premises will produce no conclusion.
When both premises are negatives, nothing is stated so that nothing could be
concluded. Call this error –‘double negation”
Example:
No stone is an organism,
But no stone is edible,
Therefore, ( no conclusion possible).

9. RULESEVEN:Ifonepremiseisnegative,theconclusionmustbe
negative;ifonepremiseisparticular,theconclusionmustbe
particular.
Since the conclusion comes from the premises, it cannot declare more than what is
implied in the premises. Error of this rule is “affirmed negation”
Example;
No tree is able to walk, (negative)
But an acacia is a tree,
Therefore, an acacia is able to walk. (affirmative)

10. RULE EIGHT: When both premises are particular, there is
no conclusion.
Two particular premises will not establish a sequence. It leads to the error of “undistributed
middle” or ‘‘illicit major”
Example:
Some trees are tall,
But some men are tall, (undistributed middle)
Therefore, some men are trees.
Some trees are tall,
But some tall (things) are not buildings,
Therefore, some buildings are not trees. (illicit major)