Deductive Reasoning

What is deductive reasoning?

The deductive reasoning is a form of argument where a premise, considered valid, directed towards a particular conclusion will also be valid. Deductive reasoning is said to go from the general to the particular.

The premise of deductive reasoning is usually accepted as a law, or as a general principle that is always true, and since the conclusion is inferred from this premise, the conclusion will also be valid. In other words, the conclusion will necessarily be true.

Let’s take an example

: “People who don’t eat meat are vegetarians. Mauricio does not eat meat. So Mauricio, necessarily, is a vegetarian ”.

With deductive reasoning, specific phenomena or facts can be understood, and it is a very widespread reasoning among scientists (mathematicians, physicists, biologists, etc.); However, this type of reasoning does not provide more information, it only corroborates or confirms the premise or axiom.

Let us remember that the premise is, according to logic, that proposition that is found before the conclusion and from which one starts to reach that conclusion, and that the axiom is a proposition that is always taken as evident and from which it is not it requires an advance demonstration.

If the premises of deductive reasoning are true, the conclusions always will be. If they are not, deductive reasoning can lead to a fallacy, that is, to false reasoning.

For example

: “All the boxers are Korean. Mohamed Ali was a boxer. Mohamed Ali was Korean ”(Mohamed Ali was a very famous American boxer in the 1960s). Here we see that the premise, being false, leads to a false conclusion.

Characteristics of deductive reasoning

Premises and conclusion

Deductive reasoning is always made up of a major and minor premise, and then the conclusion. One of the most famous arguments is the following: “All men are mortal (major premise); Socrates is mortal (minor premise), ergo Socrates is mortal (conclusion) ”.

The premises are always true

Since one of the conditions for deductive reasoning to exist is that its premises are true, then they always will be. Its premises are accepted as laws or axioms.

The conclusions are accepted as valid

As we explained in the introduction, since the premises are true, the conclusions will necessarily also be true, as long as it is assumed that the reasoning process is correct.

No new information

The conclusion is a corroboration of the premises, it only shows a truth that is already given in the premises. When we say: “Cats meow. I have a pet that meows. So my pet is a cat ”, what we do is reaffirm the truth contained in the premise, and understand that this pet is a cat.

The form contains the validity

We have said that the conclusion is valid because the premises are. As the conclusion does not provide more information, then its validity always depends on the form of the reasoning, not on its content.

For the conclusion to be valid, there must be internal coherence between the parts of the reasoning, between the premises and the conclusion.

It can lead to fallacies

This characteristic is derived from the previous one: if the premise is false, the conclusion will also be false. In other words, if due process of deductive reasoning is not followed, fallacies will arise.

For example: “All women have long hair. Gonzalo has long hair. Gonzalo is a woman ”. We see how from an uncertain premise a conclusion that is not true is generated.

Necessarily inferred conclusion

In all deductive reasoning, the conclusion will always be inferred from the premises given above.

It is used in the scientific method

Deductive reasoning is used in the scientific method to test hypotheses and theories.

Types of deductive reasoning

In deductive reasoning, three types can be seen: the syllogism, the modus tollendo tollens and the modus ponendo ponens .

Syllogism

This is the deductive reasoning par excellence, in which the first premise is the major, the second minor, and the third the conclusion. Example:

  • Human beings have feelings (major premise).
  • Mariana and Luis have feelings (minor premise).
  • Mariana and Luis are necessarily human beings (conclusion).

Modus tollendo tollens

It is also called “denial of the consequent.” It occurs when, given a conditionality of the first premise, it is rejected in the second. The scheme would be as follows: If A implies B, but B is not true, then A is not true. Example:

  • If the water boils there will be steam (premise 1).
  • There is no steam (premise 2).
  • So the water is not boiling (conclusion).

Modus putting ponies

It is also called “assertion of the antecedent.” It is characterized, like the previous type, by an initial conditionality of the first premise, where the second confirms it. His scheme would be: If A implies B, and if A is true, then B is also true. Example:

  • If the pregnancy is nine months, the child will be born full term (premise 1).
  • The child was born at nine months (premise 2).
  • So the child was born full term (conclusion).

Differences between deductive and inductive reasoning

Both are arguments widely used by researchers, philosophers and scientists, and even in the same investigation there may be an application of the two. However, both present substantial differences.

Directionality of reasoning: “Top down” vs. “Bottom up”

Deductive reasoning is “top down”, which goes down, that is, from the general to the particular.

Inductive reasoning is “bottom up”, upwards, that is, from the particular to the general.

Application areas

The deductive applies to the formal sciences (logic, mathematics, etc.) and the inductive to the experimental and social sciences.

Characteristics

Deductive reasoning establishes conclusions based on generalizations, while inductive reasoning is based on observing facts and phenomena, and generalizes from these observations.

The deductive conclusions are always valid and rigorous, while in the inductive they are probable, they are not valid by themselves. The deductive does not generate new knowledge, and the inductive does.

Examples of deductive reasoning

Example 1

  • All turtles are green.
  • Morro is a turtle.
  • Morro is green.
If we start from the premise that all turtles are green, and Morro is a turtle, then we will necessarily have to infer that Morro is green because it is a turtle.

Example 2

  • Cheese is a dairy derivative.
  • Dairy derivatives contain calcium.
  • Cheese contains calcium.
If dairy products contain calcium, and cheese is, then the cheese will contain calcium.

Example 3

  • The soccer school admits girls and boys from 6 years old.
  • My son wants to learn soccer at that school and he is 5 years old.
  • My son will not be admitted to soccer school yet.
As the school has an age limit, until that limit is reached, it will not admit any child who does not meet it.

Example 4

  • Iván must pass the final exam to become an engineer.
  • Ivan passed the exam.
  • Then Ivan will graduate as an engineer.
When the condition of premise 1 that is given in premise 2 is fulfilled, the conclusion is that Ivan will be an engineer because he passed the exam.

Example 5

  • Manuel’s children are tall.
  • Juan is Manuel’s son.
  • Juan is tall.
If Juan is Manuel’s son, and his sons are tall, then the conclusion is that Juan is tall because he is Manuel’s son.

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