Hypothetical syllogism: Main Characteristics (With Examples)

A hypothetical syllogism is one that starts from several judgments based on hypotheses and ends up drawing a valid conclusion when relating them to each other. It is a tool used in the logic very present in any type of experience, since it allows to extrapolate relationships between interconnected facts.

In general, syllogisms are defined as part of deductive reasoning. There are several types and all are formed by three premises: a first considered major, a second minor and, finally, a third that would be in which the generated conclusion is established to relate the previous ones.

Aristotle, the first philosopher who formulated a theory about syllogisms

The first thinker who formulated a theory about syllogisms was Aristotle. This philosopher is considered as the father of logic. The syllogisms remain as one of the main modes of human reasoning and are usually represented using a kind of mathematical formula to help understand them better.

There are different types of syllogisms, classified into four figures. All have the three mentioned terms, and up to 256 different syllogisms can be found. Among those, only 19 are considered legitimate. The syllogisms have given rise to the appearance of fallacies, which occur by misusing the logical elements established in them.

Aristotelian logic and syllogisms

As noted earlier, Aristotle is the first to begin to theorize about the concept of syllogism. The Greek philosopher uses this term when dealing with so-called Aristotelian judgments.

To do so, he begins to study the relationship between different terms, uniting them and drawing conclusions: logic has been born, called for a long time Aristotelian in honor of its creator.

In his book First analytical and in the compilation The organon is where the thinker expresses all his contributions on the subject.

Hypothetical syllogism

Definition

The classical definition points out that hypothetical syllogisms are a class or rule of inference with which to draw conclusions. In this case, and hence its hypothetical name, what it raises is a conditional case, with valid or invalid terms appearing.

According to the propositional logic, which uses logical connectors to join the concepts, the hypothetical in a type of syllogism from which an inference can be drawn.

In the field of the history of logic, it has been established that these syllogisms are the predecessors of the theory of consequences.

In any case, the argumentation presented by these syllogisms makes them very frequent in all vital areas. It is enough that someone reflects to make some decision so that, unconsciously, they are using them. For example:

"If I do not pay taxes, I will be committing a crime.

If I commit a crime, I could go to jail.

Therefore, if I do not pay the taxes, I could go to jail."

Formulation

When speaking of logic, formulations or notations are those formulas that are used to facilitate their use. They are very frequent in the teaching centers, since they work to remember the structure of the syllogism.

As a general rule, the hypothetical notation is as follows:

1st premise: P -> Q
2nd premise: Q -> R
Conclusion: P -> R.

For the formula to be more comprehensible, it can be summarized as follows:

If A is, B is.

If B is, C is.

Then, if A is, C is.

The 3 main types of hypothetical syllogisms

Within the hypothetical syllogisms there are several different types that, although they share the same structure and characteristics, have small differences.

1- Pure hypothetical syllogism

It is the one that has been explained previously, in which the logical structure is maintained without any change with respect to the rule.

In this way, knowing both the first premise (A and B) and the second (B and C) can infer a logical conclusion.

Example

"If I fall asleep in the morning, I'll be late for work.

If I'm late for work, they'll call my attention.

Therefore, if I fall asleep in the morning, they will call attention to me at work."

2- Mixed hypothetical syllogism

The mixed mixes the hypothesis of the first premise with a second and a third categorical. They can be negative or positive, with different structures.

Example of affirmative mixed syllogism

The affirmative, called modus ponens , it would translate into a syllogism like this:

"If it's sunny, then it's daytime.

It is sunny.

Therefore, it is day."

Example of negative mixed syllogism

The negative modus tollens it would be as follows:

"If the moon rises, then it's night.

It is not night.

Therefore, we do not see the moon."

3- Disjunctive hypothetical syllogism

It mixes the hypothesis and the disjunctive in its main premise. If this occurs, a hypothetical disjunctive syllogism is generated. Like the mixed ones, they have a positive and a negative form, with the same names that were pointed.

Example

"If A is, B is or C is.

It is so that B is.

Then, C is not."

Examples of syllogisms hypothetical

Sometimes it is not easy to understand the concept of syllogism, so the best way to resolve any doubt is to see some examples:

First example

"If my sister is at home, then she can not look for work.

If you do not look for a job, then nobody will hire you.

Then, if my sister is at home, nobody will hire her."

Second example

"If men are kind, then they all fall well.

If they all fall well, then they will have many friends.

Then, if the men are kind, then they will have many friends."

Third example

"If I do not wake up, I can not go to the party.

If I do not go to the party, I will not have fun.

Then, if I do not wake up, I will not have fun."

Fourth example

"If you study logic, you will know ways to deduce valid arguments.

If you know ways to deduce valid arguments, then you can learn to raise valid arguments.

Therefore, if you study logic, then you can learn to raise valid arguments."

References

1. abc. Law of the hypothetical syllogism. Retrieved from abc.com.py
2. Delira Bautista, José. The hypothetical syllogism in human thought. Recovered from uaa.mx
3. Beuchot, Mauricio. Introduction to logic. Recovered from books.google.es
4. Philosophy-index Hypothetical syllogism. Retrieved from philosophy-index.com
5. Dr. Naugle. Hypothetical Syllogisms. Recovered from dbu.edu
6. Crucible concept. Lessons in logic hypothetical syllogism. Retrieved from conceptcrucible.com
7. Lear, Jonathan. Aristotle and Logical Theory. Recovered from books.google.es
8. Harris, Robert. Deduction Retrieved from virtualsalt.com