2. Reduction of the categorical
syllogism is the process of
expressing in the First Figure
syllogism that are validly
expressed in the other figures.
Logicians considered the First
Figure as the perfect figure and
the others as the imperfect
ones.
3. Reduction consists in finding the
presupposition necessary to reach
a valid conclusion.
It has to be noted that reduction
is not required for recognizing the
validity of the so-called imperfect
figures; we recognized their
validity even before their
reduction to the first reduction.
4. Process of reduction.
1. Each mood begins with one of
these four letters: B,C,D and F.
2. Moods in the other figures
beginning with one of these letters
may be reduced to the mood of the
First Figure having the same
initial.
5. 3. The consonants s, p, m, and c are
the key consonants indicating the
logical operation to be performed
in order to obtain a syllogism in
one of the four moods of the
first figure. Here are the key
consonants and their role in the
reduction of the categorical
syllogism.
6. S – simple conversion.
The consonant S indicates that the
proposition indicated by the
previous vowel should be converted
simply. Recall that in simple
conversion, the subject and the
predicate are transposed. The
quality and quantity remain the
same.
7. Examples:
Convertend
E- No virtue is vice
E- No animal are
tress.
I- Some Filipinos are
millionaires.
I- Some government
officials are
corrupt.
Converse
E- No vice is virtue.
E- No tress are
animals.
I- Some millionaires
are Filipinos.
I- Some corrupt are
government
officials.
8. o Figure 2 – FESTINO
E- No terrorists are virtuous;
I- But, some policemen are virtuous;
O- Some policemen are not terrorists.
Reduction
o Figure 1 – FERIO
E- No virtuous are terrorists;
I- But, some policemen are virtuous;
O- Some policemen are not terrorists.
9. o Figure 4 – FRESISON
E- No lazy person is creative;
I- But, some creative individuals
are artists;
O- Some artists are not lazy
persons.
Reduction
o Figure 1 – FERIO
E- No creative person is lazy;
I- But, some artists are creative;
O- Some artists are not lazy persons.
10. P- Per accidens
oThe letter P signifies the
proposition indicated by the
previous vowel should be
converted per accidens
(accidental conversion).
11. o Convertend
A- All roses are
plants.
A- A hammer is a
tool.
I- Some living
things are plants.
I- Some females
are mothers.
o Converse
I- Some plants are
roses.
I- Some tools are
hammer.
A- All plants are
living things.
A- All mothers are
females.
12. o Figure 3- DARAPTI
A- All Dominican Priest are cerebral;
A- But, all Dominican priests are deep
thinkers.
I- Some deep thinkers are cerebral.
Reduction
o Figure 1- DARII
A- All Dominican priest are cerebral;
A- But, some deep thinkers are Dominican
priest;
I- Some deep thinkers are cerebral.
13. o Figure 4 – FESAPO
E- No public servant is a source of anomaly;
A- But, the source of anomaly are those that
are in power;
O-Some that are in power are not public
servants.
Reduction
o Figure 1- FERIO
E- No source of anomaly is a public servant.
I- But, some that are in power are sources of
anomaly;
O- Some that are in power are not public
servants.
14. M- mutation.
oThe premises have to be
interchanged so that the
original major premise
becomes the minor
premise and vice versa.
15. o Figure 4- DIMARIS
I- Some lawyers are liars;
A- But, all liars are immoral;
I- Some immoral are lawyers.
Reduction
o Figure 1- DARII
A- All liars are immoral;
I- But, some lawyers are liars;
I- Some lawyers are immoral.
16. o Figure 2 – CAMESTRES
A- All political aspirants are rich
businessmen;
E- But, no student is a rich businessman;
E- No student is a political aspirants.
Reduction
o Figure 1- CELARENT
E- No rich businessman is a student;
A- But, all political aspirants are rich
businessmen;
E- No political aspirants are students.
17. C- contradictory of the original conclusion.
oThis is to be substituted for
the contradictory of the
premise preceding C. ( Note:
You get first the contradictory
of two O- proposition in the
syllogism; then, substitute one
for the other.
18. o Figure 3- BOCARDO
O- Some government employees are not
punctual;
A- But, all government employees are
candidates for promotion;
O- Some candidates for promotion are not
punctual.
Reduction
o Figure 1 – BARBARA
A- All candidates for promotion are punctual;
A- But, all government employees are
candidates for promotion;
A- All government employees are punctual.
19. o Figure 2- BAROCO
A- All Filipinos are hospitable;
O- But, some youth delegates are not
hospitable;
O- Some youth delegates are not Filipinos.
Reduction
o Figure 1 – BARBARA
A- All Filipinos are hospitable;
A- But, all youth delegates are Filipinos;
A- All youth delegates are hospitable.
