Deductive Reasoning Characteristics, Types and Examples

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Sherman Hoover

The deductive reasoning It is a type of logical thinking in which a particular conclusion is drawn from general premises. It is a way of thinking opposed to inductive reasoning, by which a series of laws are inferred by observing concrete facts.

This type of thinking is one of the fundamental bases of various disciplines such as logic and mathematics, and it has a very important role in most of the sciences. For this reason, many thinkers have tried to develop the way in which we use deductive thinking so that it produces as few mistakes as possible..

Some of the philosophers who have most developed deductive reasoning were Aristotle and Kant. In this article we are going to see the most important characteristics of this way of thinking, as well as the types that exist and the differences it has with inductive reasoning..

Article index

  • 1 Components
    • 1.1 Plot
    • 1.2 Proposition
    • 1.3 Rules of inference
  • 2 Features
    • 2.1 True conclusions
    • 2.2 Appearance of fallacies
    • 2.3 Does not provide new knowledge
    • 2.4 Validity vs. truth
  • 3 Types
    • 3.1 Modus ponens
    • 3.2 Modus tollens
    • 3.3 Syllogisms
  • 4 Differences between deductive and inductive reasoning
  • 5 Examples
    • 5.1 Example 1
    • 5.2 Example 2
    • 5.3 Example 3
    • 5.4 Example 4
  • 6 References

Components (edit)

In order to draw a logical conclusion using deductive thinking, we have to have a number of elements. The most important are the following: argument, proposition, premise, conclusion, axiom and rules of inference. Next we will see what each of these consists of.

Argument

An argument is a test used to confirm that something is true or, conversely, to show that it is something false.

It is a discourse that allows expressing reasoning in an orderly way, in such a way that its ideas can be understood in the simplest way possible..

Proposition

Propositions are phrases that speak about a concrete fact, and of which it can be easily verified if they are true or false. For this to be true, a proposition must include only one idea that can be empirically tested..

For example, "right now it is night" would be a proposition, because it only contains a statement that does not admit ambiguities. That is, either it is totally true or it is totally false.

Within deductive logic, there are two types of propositions: the premises and the conclusion.

Premise

A premise is a proposition from which a logical conclusion is drawn. Using deductive reasoning, if the premises contain correct information, then the conclusion will necessarily be valid.

However, it should be noted that in deductive reasoning one of the most common failures is to take as certain premises that in reality are not. Thus, even though the method is followed to the letter, the conclusion will be wrong.

Conclution

It is a proposition that can be deduced directly from the premises. In philosophy and mathematics, and in the disciplines in which deductive reasoning is used, it is the part that gives us the irrefutable truth about the subject we are studying.

Axiom

Axioms are propositions (usually used as a premise) that are assumed to be evidently true. For this reason, contrary to most of the premises, a prior proof is not required to affirm that they are true..

Inference rules

Inference or transformation rules are the tools by which a conclusion can be drawn from the initial premises.

This element is the one that has undergone the most transformations over the centuries, with the aim of being able to use deductive reasoning more and more effectively..

Thus, from the simple logic that Aristotle used, by changing the inference rules, we went to the formal logic proposed by Kant and other authors such as Hilbert..

Characteristics

By its very nature, deductive reasoning has a number of characteristics that are always met. Next we will see the most important.

True conclusions

As long as the premises from which we start are true, and we follow the process of deductive reasoning correctly, the conclusions we draw are 100% true.

That is, contrary to all other types of reasoning, what is deduced from this system cannot be refuted..

Appearance of fallacies

When the method of deductive reasoning is erroneously followed, conclusions appear that appear to be true but are not really so. In this case, logical fallacies would arise, conclusions that seem true but are not valid..

Does not bring new knowledge

By its very nature, inductive reasoning does not help us to generate new ideas or information. On the contrary, it can only be used to extract ideas hidden within the premises, in such a way that we can affirm them with total certainty.

Validity vs. truth

If the deductive procedure is correctly followed, a conclusion is considered valid regardless of whether the premises are true or not.

On the contrary, to affirm that a conclusion is true, the premises must also be it. Therefore we can find cases in which a conclusion is valid but not true.

Types

There are basically three ways we can draw conclusions from one or more premises. They are as follows: modus ponensmodus tollens and syllogisms.

Modus ponens

The modus ponens, Also known as an antecedent statement, it applies to certain arguments made up of two premises and a conclusion. Of the two premises, the first is conditional and the second is the confirmation of the first.

An example would be the following:

- Premise 1: If an angle has 90º, it is considered a right angle.

- Premise 2: Angle A has 90º.

- Conclusion: A is a right angle.

Modus tollens

The modus tollens follows a similar procedure to the previous one, but in this case the second premise states that the condition imposed in the first is not met. For example:

- Premise 1: If there is fire, there is also smoke.

- Premise 2: No smoke.

- Conclusion: There is no fire.

The modus tollens it is at the base of the scientific method, since it allows to falsify a theory through experimentation.

Syllogisms

The last way deductive reasoning can be done is through a syllogism. This tool consists of a major premise, a minor premise, and a conclusion. An example would be the following:

- Major premise: All humans are mortal.

- Minor premise: Peter is human.

- Conclusion: Peter is mortal.

Differences between deductive and inductive reasoning

Deductive and inductive reasoning are contrary in many of their elements. Unlike formal logic, which draws particular conclusions from general facts, inductive reasoning serves to create new and general knowledge by observing a few concrete cases.

Inductive reasoning is another of the bases of the scientific method: through a series of particular experiments, general laws can be formulated that explain a phenomenon. However, this requires the use of statistics, so the conclusions do not have to be 100% true.

That is, in inductive reasoning, we can find cases in which the premises are totally correct, and even so the inferences we make from them are wrong. This is one of the main differences with deductive reasoning.

Examples

Next we will see several examples of deductive reasoning. Some of these follow the logical procedure in the correct way, while others do not..

Example 1

- Premise 1: All dogs have hair.

- Premise 2: John has hair.

- Conclusion: Juan is a dog.

In this example, the conclusion would be neither valid nor true, since it cannot be deduced directly from the premises. In this case, we would be facing a logical fallacy.

The problem here is that the first premise only tells us that dogs have hair, not that they are the only creatures that do. Therefore, it would be a sentence that provides incomplete information.

Example 2

- Premise 1: Only dogs have hair.

- Premise 2: John has hair.

- Conclusion: Juan is a dog.

In this case we are faced with a different problem. Although now the conclusion can be drawn directly from the premises, the information contained in the first of these is false.

Therefore, we would find ourselves before a conclusion that is valid, but is not true..

Example 3

- Premise 1: Only mammals have hair.

- Premise 2: John has hair.

- Conclusion: Juan is a mammal.

Contrary to the two previous examples, in this syllogism the conclusion can be drawn directly from the information contained in the premises. Also, this information is true.

Therefore, we would find ourselves before a case in which the conclusion is not only valid, but is also true.

Example 4

- Premise 1: If it's snowing, it's cold.

- Premise 2: It's cold.

- Conclusion: It's snowing.

This logical fallacy is known as the consequent statement. This is a case in which, despite the information contained in the two premises, the conclusion is neither valid nor true because the correct procedure of deductive reasoning has not been followed..

The problem in this case is that the deduction is being done in reverse. It is true that whenever it is snowing, it has to be cold, but not whenever it is cold it has to snow; therefore, the conclusion is not well drawn. This is one of the most frequent mistakes when using deductive logic.

References

  1. "Deductive Reasoning" in: Definition Of. Retrieved on: June 04, 2018 from Definition Of: definicion.de.
  2. "Definition of Deductive Reasoning" in: Definition ABC. Retrieved on: June 04, 2018 from ABC Definition: definicionabc.com.
  3. "In philosophy, what is deductive reasoning?" in: Icarito. Retrieved on: June 04, 2018 from Icarito: icarito.cl.
  4. "Deductive Reasoning vs. Inductive Reasoning ”in: Live Science. Retrieved on: June 04, 2018 from Live Science: livescience.com.
  5. "Deductive reasoning" in: Wikipedia. Retrieved on: June 04, 2018 from Wikipedia: en.wikipedia.org.

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