## Deductive Reasoning

**Definition**:

**Deductive reasoning is a logical process that moves from specific facts to a general conclusion.** The premises or reasons that were given, must be logically valid for the conclusion to be correct. Deductive reasoning is used in mathematics and scientific investigations.

In **Mathematics**, deductions are made based on axioms, or self-evident truths.

In **Scientific** **investigations**, deductive reasoning is used to test hypotheses.

In **Research**, deductive reasoning is used to develop hypotheses and test those hypotheses.

### Deductive Logic Arguments

**A Deductive Argument, in logic, is an argument in which a conclusion follows necessarily from the premises**. The conclusion is said to be deduced from the premises.

Deductive arguments are also called valid arguments, because if the premises are true, then the conclusion must be true. In order to be a valid argument, the premises must be logically connected to the conclusion by a logical principle such as modus ponens or modus tollens.

#### Example of Deductive Logic Arguments

Premise | All insects have exactly six legs. |

Premise | Spiders have eight legs. |

Conclusion | Therefore, spiders are not insects. |

### Types of Deductive Reasoning

There are three types of **Deductive Reasoning**

- Syllogism
- Modus ponens
- Modus tollens

#### Syllogism

**In deductive reasoning, a syllogism is a three-part argument consisting of a premise, a conclusion, and a reason for the conclusion.**

The premises of a syllogism must be logically valid; that is, they must lead logically to the conclusion for the given argument. The most common form of syllogism is modus ponens, Latin for “mode of putting.” In modus ponens, the conclusion is logically implied by the premises.

Syllogisms are valid in deductive reasoning because they allow us to move from general statements to specific conclusions.

**Example**

Suppose we know that all mammals are animals and that all dogs are mammals. We can then conclude that all dogs are animals. This type of reasoning allows us to build up our knowledge base by moving from general statements to more specific conclusions.

#### Modus Ponens

**In modus ponens, a valid Deductive Reasoning principle, if one premise is true, then the conclusion must be true.**

The principle is based on the idea that if something can be inferred from a given set of facts, then it must be true. In order for modus ponens to work, both the premises and the conclusion must be logically valid.**Example**:

All humans are mortal.

Smith is a human.

Therefore, Smith is mortal.

#### Modus Tollens

**Modus tollens is a type of deductive reasoning that uses a conditional statement to determine whether the consequent is true.** It is also known as the “denying the consequent” fallacy.

The basic premise of modus tollens is that if the consequent is false, then the antecedent must be false as well. This type of reasoning can be used to disprove a hypothesis or to show that a statement is not valid.

**Example**:

If the temperature is too hot then the water will not be freeze.

## When to use Deductive Reasoning

When you’re trying to solve a problem, it can be helpful to use deductive reasoning. Deductive reasoning starts with a general principle and then applies it to specific cases. This type of reasoning is often used in mathematics and logic.

For example, imagine you’re trying to figure out how many people are in a room. You might start by assuming that everyone in the room is an adult. You can then apply this principle to specific cases, such as counting the number of people who are sitting down or standing up.

Deductive reasoning can also be used when making decisions. For instance, imagine you’re considering whether or not to buy a new car. You might start by assuming that the car will be reliable and last for several years.

### Advantages of Deductive Reasoning

There are many advantages to using deductive reasoning.

- One of the most important is that it can be used to help identify and solve problems.
- Deductive reasoning can also help you to see relationships between things that may not be obvious at first glance.
- It can help you to come up with new ideas and solutions.

### Disadvantages of Deductive Reasoning

Some of the Disadvantages of using Deductive reasoning are:

- Deductive reasoning can be misleading. If the premises of an argument are false, the conclusion may also be false.
- Deductive reasoning can lead to rigidity and inflexibility. People who rely too heavily on deductive reasoning can become closed-minded and unwilling to consider other points of view.
- It can be time-consuming. It can take a lot of time to come up with a valid argument and test all the possible implications of the premises.