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.

Thank you!!