Recently I have presented a publication: Introduction to Aristotelian logic wich content would help, to whom proposed it, to answer the following problem:

What conclusion can be drawn from these two premises ?:

• All steemians are content creators
• No plagiarists are steemians

In this entry the solution of the problem will be given, so whoever wants to try to solve it by himself should not read it. But from the solution to the problem we will delve a little more into this world of logic.

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Invalid syllogisms

The syllogisms to be valid must comply with some rules, such as: If a premise is particular, the conclusion must be particular; if a premise is negative, the conclusion must be negative; at least one premise must be affirmative... So a syllogism that does not comply with any of the rules would be invalid.

Perhaps proving the validity of a syllogism is not so simple, but it is demonstrating that a syllogism is invalid. We should simply find two true premises that, when applied to the syllogism, yield a false conclusion.

Suppose you want to defend as conclusion for these two premises: "Some plagiarists are content creators".
Then we have:

All steemians are content creators
No plagiarists are steemians
Conclusion: Some plagiarists are content creators

But let's see now the generic form of that syllogism:

All A are B
No C are A
Conclusion: Some C are A

Although we can already see that it does not comply with any of the rules mentioned above, it is simpler to check its invalidity by conveniently replacing the arguments.
Let's say that A will be dogs; B: animals and C: cats.
Then we will have:

All dogs are animals (true premise)
No cats are dogs (true premise)
Some cats are dogs (false conclusion)

So then the validity of that syllogism was refuted.

Another response that has ventured is: "No plagiarists are content creators".
Let's see it:

All steemians are content creators
No plagiarists are steemians
Conclusion: No plagiarists are content creators

The generic form of this proposal is:

All A are B
No C are A
Conclusion: No C are B

Using the same replacements that we have left before we have:

All dogs are animals (true premise)
No cats are dogs (true premise)
No cats are animals (false conclusion)

Therefore this is an invalid syllogism.

Solution to the problem

To find and be able to visualize the conclusion from the premises of this problem, it is advisable to previously make an immediate inference about each of these premises (see in Introduction...).

Premises:

• All A are B
• No C are A

On the first premise (All A are B) I apply the conversion by limitation (which is actually a combination of the notions of subalternation and conversion) and it remains: Some B are A.

The second premise (No C are A) by simple conversion can be transformed into: No A are C.

In this way the syllogism remains:

Some content creators are steemians
No steemians are plagiarists
Some content creators are not plagiarists

See how the deduction made now is evident.

Penguins are birds that do not fly

It is interesting to note that this syllogism, which appears to us to be somewhat elusive, may have all been used at some point in our lives. And we use it automatically when we find some exception to some statement that until then we took for granted.

Penguins

A good example of this can be found in the first concept that we form of birds, because we almost always grow by associating birds with flight. A child could believe the premise "All birds fly" true. But one day somebody mentions to that child that penguins are birds and that they do not fly. So, what would be the syllogism that encloses the deductive reasoning of that child?

All penguins are birds
No penguins are fliers (or what is the same: No fliers are penguins)
Conclusion: Some birds are not fliers

Another similar example could be the following:

All fungal species are living beings
No species of fungus are animals or vegetables
Conclusion: Some living beings are not animals or vegetables

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I hope that this brief tour of Aristotelian logic has entertained you. In a future publication it will be explained why this syllogism that is valid in the traditional logic, it is not in the modern logic that originates with George Boole.

—Who? George Bush?
—No no. Do not be scared ... It is not about George Bush Sr. or Jr. Nothing to do with that family. The mathematician George Boole.

Until next time.

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Bibliography

• COPY Irving M. (1962) Introduction to logic