### Sea Shells

```Mediate Inference
Mediate Inference
• Commonly called as argument
• Has two major types:
–Deduction/Deductive
Arg./Syllogism
• Categorical Syllogism
• Hypothetical Syllogism
Mediate Inference
–Induction
• Induction by complete
enumeration
• Induction incomplete
enumeration
• Induction by analogy
Categorical Syllogism
• is an argument which proceeds from
statements concerning the
relationship of two terms, to a
conclusion concerning the
relationship of two terms to each
other.
• All its propositions are categorical
propositions (A,E,I,O).
Example
All poets are creative.
M
P
Some artists are poets.
S
M
Ergo, some artists are creative.
S
P
Ordinary language
arguments
No, that girl is not Leyla because she
has short hair, while Leyla has long
hair.
Di lagi na modagan nga sakyanan kay
way gasolina
Where there’s smoke there’s fire;
there’s no fire in the warehouse
because there’s no smoke there.
Ordinary language
arguments
No, that girl is not Leyla because she has
short hair, while Leyla has long hair.
No person identical to Leyla is a person who
has short hair.
All persons identical to that girl are persons
who have short hair
So, no person identical to that girl is a person
identical to Leyla.
Ordinary language
arguments
Di lagi na modagan nga sakyanan kay
way gasolina. (The car won’t run
because it has no gas)
All cars without gas are cars that won’t
run.
All cars identical to that car are cars
without gas.
So, all cars identical to that car are cars
that won’t run.
Ordinary language
arguments
Arguments in the ordinary language can
be translated to the basic categorical or
hypothetical syllogism.
Syllogisms (categorical or hypothetical)
are basic forms of arguments
Hence, the analysis of categorical
syllogism
Example
All poets are creative.
Mu +
Pp
Some artists are poets.
Sp +
Mp
Ergo, some artists are creative.
Sp
+
Pp
Example
Since most 18-year-old lads registered for the
Barangay polls and all who are registered for
the Barangay polls are voters, then most 18year-old lads are voters.
All who are registered for the Barangay polls
Mu + Pp
are voters.
Most 18-year-old lads registered for the
Sp + Mp
Barangay polls.
Ergo, most 18-year-old lads are voters.
Sp + Pp
For Analysis
No legislator has judiciary power. Thus, no
senator has judiciary power because they are
legislators
Mu – Pu
No legislator has judiciary power.
Su + Mp
Every senator is a legislator.
Thus, no senator has judiciary power. Su – Pu
For Analysis
Not all religious movements are Christians. Thus,
some fundamentalists are Christians because
some religious movements are fundamentalists.
Not all religious movements are Christians.
Mp – Pu
Some religious movements are fundamentalists.
Mp + Sp
Thus, some fundamentalists are Christians.
Sp + Pp
Rules of valid syllogism
1. There must be three and only three terms
2. The middle term must not occur in the
conclusion
3. The major or minor term may not be
universal in the conclusion if it is only
particular in the premises
4. The middle term must be used as a
universal at least once.
5. Two negative premises yield no valid
conclusion
Rules of valid syllogism
6. If both premises are affirmative the
conclusion must be affirmative
7. If one premise is negative the conclusion
must be negative
8. If one premise is particular the conclusion
must be particular
9. From two particular premises no valid
conclusion can be draw
Rules of valid syllogism
There must be three and only three terms
possible violation:
Mandaue is next to Cebu
Consolacion is next to Mandaue
Ergo, Consolacion is next to Cebu
Change in supposition
Man begins with M.
Joseph is a man.
So, Joseph begins with M.
Rules of valid syllogism
Equivocation
A Pail holds water.
This argument holds water.
So, this argument is a pail.
Rule 2. The middle term must not occur in the
conclusion
Misplaced middle term
Rule 3. The major or minor term may not be
universal in the conclusion if it is only
particular in the premise
Rules of Valid syllogism
Illicit Minor; Illicit Major
Rule 4. The middle term must be used
as a universal at least once.
-Undistributed middle term
Rule 5. Two negative premises yield no
valid conclusion
-Exclusive premises
Rule 6. If both premises are affirmative
the conclusion must be affirmative
Rules of Valid syllogism
negative conclusion out of
affirmative premises
Rule 7. If one premise is negative the
conclusion must be negative
affirmative conclusion out of a
negative premise
Rule 8. If one premise is particular the
conclusion must be particular
-universal conclusion out of a
particular premise