In a previous entry I left the following challenge:

What can you conclude from the following premises?:

1. All steemians are content creators.
2. No plagiarists are steemians.

The solution to this problem may not be obvious to us. It may be necessary to introduce some basic notions of logic to solve it. Here we go…

Aristotle

Syllogisms

A syllogism is a deductive reasoning that starts from two premises to arrive at a conclusion.

The following may be the most well-known and repeated syllogism in the history of syllogisms:

All men are mortal.
Socrates is a man.
Conclusion: Socrates is mortal.

In its generic form it would be:

All A are B
All C are A
Conclusion: All C are B.

Categorical propositions

Every syllogism is composed of two premises and a conclusion. Both the premises and the conclusion are categorical propositions, which means that they are enunciations in which one class is related to another; in particular, they affirm or deny that one class is contained in the other, partially or totally.

Given this definition, we can understand that there are four categorical propositions:

1. All S are P
2. No S are P
3. Some S are P
4. Some S are not P

The first two propositions are called universal since they preach on the total of the set S (Subject), while the last two are particular since they are limited to preaching on some (or at least one) of the members of S.

Immediate inferences

An immediate inference is one that can be made from a single proposition. Let's see the cases of immediate inference that there are.

Inferences by opposition

It is called inferences as opposed to those that arise from the following table:

(Image taken from the book Introduction to logic of Irving M. Copy)

In general these inferences are obvious, as if I consider it true that All S are P I can not really consider that No S are P.

Perhaps it should be clarified that the truth of an universal follows the truth of the particular that preaches the same quality, but not the other way around (the error in those who generalize). Also, the falsity of a particular follows the falsehood of an universal, but not the other way around (to say that it is false that all ICOs are a fraud does not mean that it is false that some are).

Inferences by conversion

These are those in which a simple exchange between the subject and the predicate of a proposition operates. For example, if I say that no dog is a cat, I can say with equal truth value that no cat is a dog.
It is interesting to note that the conversion of the universal proposition All S are P can not be All P are S (of the proposition all odd are numbers not followed all numbers are odd) But within the framework of Aristotelian logic what is known as conversion by limitation is applied, that is, the conversation results in a particular proposition: Some P are S (some numbers are odd).

Conversions:

Original	Converse
All S are P	Some S are P (by limitation)
No S are P	No P are S
Some S are P	Some P are S
Some S are not P	(does not have a converse)

Inferences for obversion
These arise from considering the concept of complement, that is, the denial of the original class or group. For example, if the class or group A is the set of all prime numbers, its complement will be the group of all numbers that are not prime numbers.

Obversions:

Original	Obverse
All S are P	No S are non P
No S are P	All S are non P
Some S are P	Some S are not non P
Some S are not P	Some S are non P

Now, did you find the solution to the problem?

You can share it in the comments.