Syllogism determines a deductive argument or reasoning, which is made up of three interconnected propositions.
In philosophy, syllogism is a doctrine that belongs to Aristotelian logic and is based on deduction.
Aristotle (384 BC-322 BC) used this method in the study of logical argumentation.
The syllogism theory was presented by him in his work “ Analytica Priora ” (First Analytical).
Did you know?
From the Greek, the term syllogism ( syllogisms ) means “conclusion” or “inference”.
Examples of syllogism
Example 1 :
Every man is mortal.
Socrates is a man.
Socrates is deadly.
Example 2 :
Every Brazilian is South American.
Every northeastern is Brazilian.
Therefore, all Northeasterners are South American.
Example 3 :
Every politician is a liar.
José is a politician.
Therefore, José is a liar.
Composition of Aristotelian Syllogism
The first and second propositions are called premises and the last is the conclusion:
- Major premise (P 1 ): declaratory, where all M is P .
- Minor premise (P 2 ): Indicative, where S is M .
- Conclusion : the union of the first two assumptions, it is possible to deduce the third proposition, where S is P .
Syllogism Terms
Syllogism consists of three terms :
- Major Term : also called the major extreme, it appears in the major premise, being the predicate term of the conclusion. It is represented by P .
- Minor Term : also called the minor extreme, it appears in the minor premise, being the term subject of the conclusion. It is represented by S .
- Medium Term : it appears in both premises, however, it does not appear in the conclusion. It is represented by M .
False syllogism
The fallacy is considered a “false syllogism” since it is invalid in the construction of categorical syllogisms.
Thus, the fallacy is a misleading argument, a misconception or a false belief.
Example :
All swans are not black.
Some birds are swans.
Therefore, all birds are not black.
For the above propositions to be considered a syllogism, the conclusion should be: Some birds are not black.
This is because the conclusion of the syllogism always follows the negative or particular premise, and in this case, “some”.
Rules for Construction of Syllogism
We must take into account that there are some rules for the construction of categorical syllogism, that is, so that they are valid and do not fall into the fallacy problem.
Regarding the syllogism terms we have:
1 . The three terms (major, minor and medium) used for the construction of a syllogism must have the same meaning:
Every lion is a mammal.
Some people are lion .
Therefore, some people are mammals.
In this case, the term “lion” was used in two ways: the animal and the sign. This syllogism is not valid because it contains four terms: lion (animal); lion (sign); mammals and people.
2 . At the conclusion of a syllogism, the middle term does not appear, only the largest and the smallest term:
No canid is feline.
Every canid is a carnivore.
Therefore, this canid is not a feline carnivore.
Thus, the example above is not a syllogism but a formal fallacy.
3 . Throughout its length, the medium term must appear at least once:
All fruits are vegetables.
All vegetables are vegetables.
Therefore, all vegetables are fruits.
In this case of formal fallacy, we have that vegetables (such as fruit or vegetables) are a part of the total extent of vegetables.
4 . In the conclusion of the syllogism, the terms major and minor cannot come up to a greater extent than in the premises:
Any violent act is reprehensible.
Many human beings commit violent acts.
Therefore, all human beings are reprehensible.
In this case, the conclusion of the syllogism should be: Many human beings are reprehensible.
Regarding the syllogism propositions , we have:
5 . When a syllogism presents two affirmative premises, the conclusion must also be affirmative:
All cats are mammals.
All mammals are vertebrates.
Therefore, some vertebrates are not felines.
In this example, the conclusion of the syllogism should be: Some vertebrates are felines.
6 . When a syllogism presents two negative premises, nothing can be concluded:
No mother is insensitive.
Some women are not mothers.
Therefore, some women are insensitive.
In this case of formal fallacy, there is an unjustified conclusion and therefore it is not a syllogism.
7 . When a syllogism presents two particular premises, nothing can be concluded:
Some salespeople are not honest.
Some Brazilians are salespeople.
Therefore, some Brazilians are not honest.
We have above an example that violates the syllogism rule, from an inconclusive proof.
8 . The conclusion of a syllogism will always follow the weakest part, that is, the negative and / or particular premise:
All cats are not white.
Some cats are cats.
Therefore, all cats are not white.
In the example above, the conclusion of the syllogism should be: Some cats are not white.
Types of Syllogism
According to Aristotelian syllogism, there are two types of syllogism:
- Dialectical syllogism : based on hypothetical or uncertain judgments. In this case, the syllogism is used in the studies of rhetoric and persuasion and refers to opinions.
- Scientific syllogism : based on scientific arguments, which contain the value of truth in both premises and conclusions.
Legal syllogism
In the area of law, syllogism is used as a tool for the conclusion of facts. This type of syllogism is classified into:
- Presentation of the major premise
- Presentation of the facts
- Conclusion by legislation
Example of legal syllogism :
Killing someone is a crime and the murderer must be punished.
Joana killed someone.
Therefore, Joana must be punished.