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Reduction of the Categorical Syllogism
Chapter 16
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.
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.
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.
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.
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.
Examples:
ConvertendE- No virtue is viceE- No animal are
tress.I- Some Filipinos
are millionaires.I- Some
government officials are corrupt.
ConverseE- No vice is virtue.E- No tress are
animals.I- Some millionaires
are Filipinos.I- Some corrupt are
government officials.
o Figure 2 – FESTINOE- 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.
o Figure 4 – FRESISONE- No lazy person is creative;I- But, some creative individuals
are artists;O- Some artists are not lazy
persons.Reductiono Figure 1 – FERIO
E- No creative person is lazy;I- But, some artists are creative;O- Some artists are not lazy
persons.
P- Per accidens
oThe letter P signifies the proposition indicated by the previous vowel should be converted per accidens (accidental conversion).
oConvertend A- All roses are
plants.A- A hammer is a
tool.I- Some living
things are plants.
I- Some females are mothers.
oConverseI- Some plants are
roses.I- Some tools are
hammer.A- All plants are
living things.A- All mothers are
females.
o Figure 3- DARAPTIA- All Dominican Priest are cerebral;A- But, all Dominican priests are deep
thinkers.I- Some deep thinkers are cerebral. Reductiono Figure 1- DARIIA- All Dominican priest are cerebral;A- But, some deep thinkers are Dominican
priest;
I- Some deep thinkers are cerebral.
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.Reductiono 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.
M- mutation.
oThe premises have to be interchanged so that the original major premise becomes the minor premise and vice versa.
oFigure 4- DIMARISI- Some lawyers are liars;A- But, all liars are immoral;I- Some immoral are lawyers.ReductionoFigure 1- DARII A- All liars are immoral;I- But, some lawyers are liars;I- Some lawyers are immoral.
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.Reductiono Figure 1- CELARENTE- No rich businessman is a student;A- But, all political aspirants are rich
businessmen;E- No political aspirants are students.
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.
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.Reductiono 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.
o Figure 2- BAROCOA- All Filipinos are hospitable;O- But, some youth delegates are not
hospitable;O- Some youth delegates are not
Filipinos.Reductiono Figure 1 – BARBARAA- All Filipinos are hospitable;A- But, all youth delegates are Filipinos;A- All youth delegates are hospitable.
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