# Deductive reasoning

The deductive reasoning is mainly formed by those arguments which their conclusions inferred on the premises . Formally the deduction forms to be a series of finite formulas which are designated as a conclusion to the sequence of questions that are formulated and answered in a logical and sequential way.

## What is deductive reasoning?

Deductive reasoning is the mental process by which a series of ideas is reasoned and structured in order to reach a conclusion. The logical method of deduction is carried out by the need to reach the conclusion of a previously raised premise.

• Definition
• Characteristics of deductive reasoning
• What is it for
• Types of deductive reasoning
• Criticisms of deductive reasoning
• Examples

## Definition

The deductive reasoning is formed as a result of mental activity that lets you take a series of conclusions from one or more premises. This concept tells us that once we have started from what we believe is the general , we can arrive at the particular as an end point.

## Characteristics of deductive reasoning

In order to understand deductive reasoning , we must understand the series of characteristics that it encompasses, such as:

#### Argument

This is the reason, or the proof that allows the justification or refutation of something. In other words, it is the discourse by which the premise will be carried out.

#### Proposition

This includes the entities that provide the truth values within the argument. It is in this section where you can talk about a true or false proposition.

#### Premise

It is defined as any purpose in which the conclusion is due . If the argument is valid initially, the premise itself will indicate them to us, so it would cease to be a premise, to become an argument.

#### Conclution

At this point in the conversation , we can already have the logical point of everything, and therefore the end of the previous premise. It must be taken into account that for a proposition to take the role of conclusion, there must not be a fortuitously valid argument, it will only be enough to be at the end for it to take that place.

#### Axiom

It complies with being the proposition which is taken as evident and for which it is not necessary to have a previous demonstration.

## What is it for

Deductive reasoning is  most often used in mathematics for solving puzzles such as Sudoku . It can be used daily to reach those logical conclusions that we know are true, but for which we need a series of steps and facts to corroborate. It is based initially on the belief system of the person , as well as the cognitive capacity that the user has to reach the conclusion of a premise.

## Types of deductive reasoning

There are three basic ways by which we can obtain conclusions, these are:

• Modus ponens:  which is known as the antecedent statement. It is applied in certain arguments which are initially formed by two premises and a conclusion.
• Modus tollens: consists of u procedures very similar to the one mentioned above with the difference that in the second premise it is affirmed but the condition that was imposed in the first is not met .
• Syllogism : a final way in which deductive reasoning can be reachedis through a syllogism , in which we are faced with a major premise, a minus and a conclusion.

## Criticisms of deductive reasoning

In general, this type of thoughts is moved only by those that is the particular, its deduction is only based on those general premises which help it to reach a particular conclusion as long as its deductive argument is valid towards that conclusion by the drift this premise

## Examples

Some examples of deductive reasoning are as follows:

#### Example 1

• Premise 1: All cats have hair.
• Premise 2: Arturo has hair.
• Conclusion: Arturo is a cat.

Here we can see how the conclusion can be valid as it may not, since it is impossible to deduce directly from the premises. In this example, we are faced with a logical fallacy .

#### Example 2

• Premise 1: Only cats have hair.
• Premise 2: Arturo has hair.
• Conclusion: Arturo is a cat.

In this example we have a totally different problem. The information is invalid even though we can draw a conclusion directly from the premises.

#### Example 3

• Premise 1: Only mammals have hair.
• Premise 2: John has hair.
• Conclusion: Juan is a mammal.

In this example we do come to a valid conclusion.