Inferring means extracting a proposition as a conclusion from others. O syllogism it is the argument that, according to Aristotle, has three characteristics: it is mediated, deductive and necessary.
O syllogism é mediated, as it is not immediately apprehended from perception, but must use reasoning to understand the real. É deductive because it starts from the truth of universal premises to arrive at other premises. And is required, because it establishes a causal chain between the premises.
The premises, to form a syllogism, should be distributed as follows:
- The first premise, called the major premise, must contain the major term and the middle term;
- The second premise, called the minor premise, must contain the middle term and the minor term;
- The conclusion must contain the terms major and minor.
Below are some rules for a better understanding of the form of syllogism:
1. The syllogism must always contain three terms: the largest, the smallest and the average;
2. The middle term must be part of the premises and never of the conclusion and must be taken at least once in its entirety;
3. No term can be longer in the conclusion than in the premises, because then, it will be concluded more that what is allowed, that is, one of the premises must always be universal and necessary, positive or negative.
4. The conclusion cannot contain the middle term (see item 2);
5. From two negative premises, nothing can be concluded. The middle term will not have linked the extremes;
6. Of two affirmative premises, the conclusion must be affirmative, of course;
7. Of two particular propositions, nothing can be concluded (see item 2);
8. The conclusion always accompanies the “weak” part, that is, if there is a negative premise, the conclusion will be negative. If there is a particular premise, the conclusion will be private. If there are both, the conclusion must be negative and private.
In this way, you can configure some modes of syllogism in Aristotle:
THE. All propositions are affirmative universals.
Ex.:
All men are mortal.
All Brazilians are men.
Therefore, all Brazilians are mortal.
This is the famous perfect syllogism, because it demonstrates the necessary link between individual, species and genus. That's what science aims at.
B. The major premise is universally negative, the minor premise is universally affirmative, and the conclusion is universally negative.
Ex.:
No star is perishable.
All stars are stars.
Therefore, no star is perishable.
Ç. The major premise is universally affirmative, the minor premise is privately affirmative, and the conclusion is privately affirmative.
Ex.:
All men are mortal.
John is a man.
Therefore, John is mortal.
D. The major premise is universally negative, the minor premise is particularly affirmative, and the conclusion is particularly negative.
Ex.:
No king is loved.
Henry VII is a king.
Therefore, Henry VII is not loved.
Of course, by the possibilities, there are up to 64 ways to produce an argument or syllogism, but in practice, these are its most used forms. Remembering that these rules are used to make the famous predicate calculus in what we call Aristotelian formal logic.
By João Francisco P. Cabral
Brazil School Collaborator
Graduated in Philosophy from the Federal University of Uberlândia - UFU
Master's student in Philosophy at the State University of Campinas - UNICAMP
Source: Brazil School - https://brasilescola.uol.com.br/filosofia/figuras-silogismo-algumas-regras-para-seu-entendimento.htm