Hypothetical syllogism: concept, characteristics and examples

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

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

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

There are different types of syllogisms, classified into four figures. They all have the three terms mentioned, being able to find up to 256 different syllogism modes. Among those, only 19 are considered legitimate. The syllogisms have given rise to the appearance of fallacies, which are produced by misusing the logical elements established in them.

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Aristotelian logic and syllogisms

As noted above, Aristotle is the first to start theorizing about the concept of syllogism. The Greek philosopher uses this term when he deals with the so-called Aristotelian judgments.

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

in his book First analytics and in the compilation the organon It is where the thinker expresses all his contributions on the subject.

hypothetical syllogism

Definition

The classical definition indicates 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 poses is a conditional case, and valid or invalid terms may appear.

According to propositional logic, which uses logical connectors to join concepts, the hypothetical is 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 areas of life. It is enough for someone to reflect to make a decision so that, unconsciously, they are using them. For example:

“If I don’t pay taxes, I will be committing a crime.

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

So if I don’t pay my taxes, I could go to jail.»

Formulation

When talking about logic, formulations or notations are those formulas that are used to facilitate their use. They are very common in schools, as they work to remember the structure of the syllogism.

As a general rule, the notation of hypotheticals is as follows:

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

To make the formula more understandable, it can be summarized as follows:

If A is, B is.

If B is, C is.

Then if A is, C is.

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) a logical conclusion can be inferred.

Example

“If I fall asleep in the morning, I will be late for work.

If I’m late for work, they’ll call me out.

So if I oversleep in the morning, I’ll get noticed at work.»

2- Mixed hypothetical syllogism

The mixed hypothesis mixes 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 ponenswould result in a syllogism like this:

“If it’s sunny, then it’s day.

It is sunny.

Therefore, it is daytime.»

Example of negative mixed syllogism

the refusal modus tollens would be as follows:

“If the moon rises, then it is night.

It is not at night.

Therefore, we do not see the moon.

3- Disjunctive hypothetical syllogism

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

Example

“If A is, B is or C is.

It is so that B is.

Therefore C is not.

Examples of hypothetical syllogisms

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’t look for a job.

If you don’t look for a job, then no one is going to hire you.

Then, if my sister is at home, nobody is going to hire her”.

second example

“If men are nice, then everyone likes them.

If everyone likes them, then they will have many friends.

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

third example

“If I don’t wake up, I can’t go to the party.

If I don’t go to the party, I won’t have fun.

So if I don’t wake up I won’t have fun.»

fourth example

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

If you know ways to derive valid arguments, then you can learn to make valid arguments.

Therefore, if you study logic, then you can learn to make valid arguments.»

References

abc. Law of hypothetical syllogism. Retrieved from abc.com.py
Delira Bautista, Jose. The hypothetical syllogism in human thought. Recovered from uaa.mx
Beuchot, Mauricio. Introduction to logic. Recovered from books.google.es
Philosophy-index. Hypothetical syllogism. Retrieved from philosophy-index.com
Dr Naugle. Hypothetical Syllogisms. Retrieved from dbu.edu
Concept crucible. Lessons in logic hypothetical syllogism. Retrieved from conceptcrucible.com
Lear, Jonathan. Aristotle and Logical Theory. Recovered from books.google.es
Harris, Robert. Deduction. Retrieved from virtualsalt.com

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