FINAL TERM
Syllogism
Syllogism
✓From the word syn (together) and logein (to think)- “to think
together”
✓oral or written expression of an inference or reasoning
✓it is also called argumentation
✓a process of proving a statement
✓form of discourse which logically deduces, induces or
produces new proposition or conclusion from 2
✓previously known propositions.
All men are rational;
Example of But Pedro is a man;
syllogism Therefore, Pedro is rational.
1. Categorical Syllogism – The
premises and conclusion are
categorical propositions that
either affirm or deny without
General qualification
Types of
Syllogism
2. Hypothetical Syllogism – the
major premise is a
hypothetical proposition.
A. Premises – the 2 previously known propositions
presumed to be true.
1. Major Premise (Mp) – the proposition
pronouncing the general law and containing the
Elements of
major term.
2. Minor Premise (mp) – the proposition
Categorical pronouncing the particular instance and containing
the minor term.
Syllogism
B. Conclusion- the proposition containing the result
of reasoning.
- the new proposition coming out from the two
premises.
- expresses the agreement or disagreement
between the minor term and the major term.
C. Terms – the 3 terminologies found in the
premises and conclusion
Elements of 1. Major Term (P) – predicate of the conclusion
and predicate of the major premise.
Categorical 2. Minor Term (S) – subject of the conclusion
Syllogism and of the minor premise
3. Middle Term (M) – the term mediating
between the two other terms.
- can be found in both premises but not in the
conclusion.
Other symbols include:
(u) – universal
(p) - particular
(+) - affirmative copula
(-) - negative copula
Sample of Syllogism with symbols
(M) (P)
(Mp) All trees are plants;
(S) (M)
(mp) But, Narra is a tree;
(S) (P)
( C ) Therefore, Narra is a plant.
1. Three terms only, each term must be univocal.
- categorical syllogism must only have 3 propositions
that must contain 3 terms ( P, S, M )
* if not followed it will commit a violation
called: 4-term syllogism/excess term and ambiguous
Rules of middle term
Categorical Example: 4-term/excess term violation
Syllogism (M1) (P)
All plants are organic;
(S) (M2)
But, all stones are minerals;
(S) (P)
Therefore, all stones are organic.
Rules of Categorical Syllogism
2. Major and or minor term can be universal in the conclusion, provided it is or they are also
universal in the premises.
Violation: Illicit (P) or Illicit (S)
Example: Illicit (P) Illicit (S)
(Mu) (Pp) (Mu) (Pp)
Animals are organisms; Congressmen are politicians;
(Su) (Mu) (Mu) (Sp)
But, Plants are not animals; But, Congressmen are men;
(Su) (Pu) (Su) (Pp)
Therefore, Plants are not organisms All men are politicians.
Rules of Categorical Syllogism
3. Middle Term must be universal at least once.
Violation: Undistributed Middle
Result: Some conclusions will be (T), some will be (F)
(Pu) (Mp) (Pu) (Mp)
Example: All men are mortal; All men are mortal;
(Su) (Mp) (Su) (Mp)
But, All Ilonggos are mortal; But, All pigs are mortal;
(Su) (Pp) (Su) (Pp)
Therefore, All Ilonggos are men. (T) Therefore, All pigs are men. (F)
Rules of Categorical Syllogism
4. If one premise is particular, conclusion must be particular.
Example: All men are rational;
But, Some animals are men;
Therefore, all animals are rational.
Rules of Categorical Syllogism
5. No two particular premises
Example: Some students are Filipinos;
But, Some Ilonggos are not students;
Therefore, Some Ilonggos are not Filipinos.
Rules of Categorical Syllogism
6. Affirmative premises should have affirmative conclusion.
Example:
All Christians are believers
But, Some gamblers are Christians;
Therefore, All gamblers are not believers.
7. If one premise is negative, conclusion
must also be negative
Rules of Example:
Categorical All doves are birds;
Syllogism But, all dogs are not doves;
Therefore, Some dogs are birds.
8. No two negative premises.
Rules of Example:
Categorical No animal is a stone;
Syllogism But, No diamond is an animal;
Therefore, No diamond is a stone.
Syllogistic Figure –
Figures of arrangement of syllogism
Categorical based on the positioning of
Syllogism the Middle Term (M) in the
premises.
1.Figure 1 [Sub-Pre]
2.Figure 2 [Pre-Pre]
3.Figure 3 [Sub-Sub]
4.Figure 4 [Pre-Sub]
✓The Middle Term is the Subject of the Major Premise and the
Predicate of Minor Premise.
✓ “The Perfect Syllogism”, Re: Aristotle, because the basic
formula of syllogism is applied normally and naturally.
FIGURE 1 ✓Models of all forms of argumentation.
(F1) – [ SUB
– PRE ] (M) (P)
Mp – M P Plants are organisms;
(S) (M)
mp – S M Roses are plants;
(S) (P)
C - S P Roses are organisms.
FIGURE 2 (F2) - [ PRE – PRE ]
✓The Middle Term is the Predicate of the Major Premise and Predicate of Minor
Premise.
(P) (M)
Mp - P M All men are not immortal beings;
(S) (M)
mp - S M Some creatures are immortal beings;
(S) (P)
C - S P Some creatures are not men.
FIGURE 3 (F3) - [ SUB - SUB ]
✓The Middle Term is the Subject of the Major Premise and the Minor Premise.
(M) (P)
Mp - M P Dogs are not cats;
(M) (S)
mp - M S Dogs are pets;
(S) (P)
C - S P Some Pets are not cats.
FIGURE 4 (F4) - [ PRE - SUB ]
✓The Middle Term is the Predicate of the Major Premise and the Subject of Minor
Premise
Mp - P M Senators are politicians;
mp - M S Politicians are propagandist;
C - S P Some propagandists are senators.
The arrangement of the Premises
according to quantity and quality
Syllogistic The combination or pairing of the 4
Moods forms of proposition
If A, E, I, O proposition are paired
with each other, there will be 16
possible pairs that can be produced.
The 16 pairs of combination
*The valid pairs are in capital letters
*the invalid pairs are in small letters
Pair nos. 6, 8, 14, and 16 are invalid. They violate rule No. 8 – No two negative premises.
Pair nos. 11, 12, 15 are invalid. They violate rule No. 5 – No two particular premises.
Pair no. 10 is invalid. It violates rule No. 2 – P and S must not be (u)in the conclusion if they are (p) in
the premises.
*Only 8 valid pairs are left. But they are not totally valid in all figures.
*When the 8 valid pairs are combined with the syllogistic figures, some will be invalidated in certain
figure. This is because, there are special rules for figures and there are times that they are violated.
Rules for Figures
• FIGURE 1 – A, B M P
A. Major premise must be universal S M
B. Minor premise must be affirmative S P
*If rules A and B are followed, 4 valid moods can be created. They are represented by the
Latin mnemonic devise below:
bArbArA cElArEnt dArII fErIO
Figure 1
Figure 1
FIGURE 2- A,B
A- Major premise must be universal
B- At least must be negative
*With these 2 rules applied, out of 8 possible valid moods, only 4
remain valid.
cEsArE cAmEstrEs fEstInO bArOcO
Figure 2
Figure 2
FIGURE 3- B, D, E
B- Minor premise must be affirmative M P
D- At least one premise must be universal M S
E- Conclusion must be particular S P
**Applying the 3 rules for F3, out of the 8 possible valid moods, only 6
remain valid.
dArApTI dAtIsI dIsAmIS
fElAptOn bOcArdO fErIsOn
Figure 3
All scholars are studious;
But, All scholars are achievers;
Therefore, Some achievers are studious
No liars are honest;
But, Some liars are lawyers;
Therefore, _______________________.
Many Christians are charitable
But, All Christians are believers;
Therefore, _______________________.
FIGURE 4- F, G, H
F. If major premise is affirmative, minor premise must be universal
G. If minor premise is affirmative, conclusion must be particular
H. If one premise (and conclusion) is negative, major premise must
be universal.
** Applying these 3 rules for F4, out of the 8 possible valid moods,
only 5 remain valid.
brAmAntIp dImArIs cAmEnEs fEsApO frEsIsOn
Figure 4
Angels are not mortal beings;
But, some mortal beings are God-fearing;
Therefore, Some God-fearing beings are not angels.
All As are letters
But, Some letters are Bs
Therefore, Some Bs are As
All brutes are not rational animals;
But, All rational animals are men;
Therefore, _______________________
