Deductive Method

We explain what the deductive method is, how it originated and its classification. Also, what are its characteristics and examples.

What is the deductive method?

A method or deductive reasoning is known as a type of logical reasoning which is characterized by necessarily inferring a conclusion from a series of premises.

The validity of the argument is given by the form of the argument, as well as its truth character: the truth of the premises implies the truth of the conclusion. It is impossible for the premises to be true and the conclusion false.

For example:

Premise 1. All men are mortal.
Premise 2. Socrates is a man.
Conclusion. Socrates is mortal

As can be seen in the example, if we start from the statement that all men are mortal, and then take a particular case, in which we affirm that Socrates is a man, we must necessarily deduce that Socrates is mortal.

If the reasoning is carried out in a valid and correct manner, and if the premises from which it is based are not only valid but also true, will always return valid and correct results. To guarantee this, deductive reasoning is governed by inference rules or transformation rules.

Due to its form, guarantee of validity and intuitive proximity (that is, it is deduced naturally), deductive reasoning is one of the most used modes of reasoning in mathematics and in many other hard sciences.

See also: Argumentation

Origin of the deductive method

The use of deductive reasoning is attributed to Aristotlewho made the first particular records of a specific form of deductive reasoning: the syllogism.

In the 17th century, philosophers such as Descartes, Spinoza, and Leibniz reformulated many of the definitions that revolved around inferential logic and deductive reasoning. The work of Descartes stands out mainlywho redefined the method to find the formal constitution of scientific knowledge.

In this way, deductive reasoning It also served as the foundation for the composition of the scientific methodwithout which the contemporary notion of science would not exist.

Uses of the deductive method

The deductive method can be used in different ways:

• Direct use and immediate conclusion. These are those cases in which the conclusion is obtained from a single necessary premise. This premise is an axiom: it is used as a starting point accepted by the scientific community to develop any theory. For example, the law of causality considered as an axiom maintains that every action is a consequence of a cause that precedes it.
• Indirect use and mediate conclusion. These are those cases in which the conclusion is obtained from two or more premises: a major one, which contains a universal proposition, and a minor one, which includes a particular proposition. In this case the conclusion is inferred from the observation of both premises. The syllogism is an example of reasoning with indirect use and immediate conclusion.

Why is the deductive method important?

Deductive reasoning is one of the most used reasonings in everyday life. It is also fundamental for the formulation of certain types of logic, such as symbolic or propositional logic.

In propositional logic, for example, lie the foundations of formal systems like the one that gave rise to computing. This is because mathematics uses deductive reasoning by relying on its fixed and immutable rules.

Features of the deduction

It is understood by a deduction to obtaining valid conclusionsverifiable, communicable, based on one or more general premises. For example, to deduce that from a premise that states that p then qhave:

p then q (general premise)
p (particular premise)
q (particular conclusion)

Deductive reasoning is characterized by the following:

• It starts from a general premise to go towards the particular.
• Perform top-down reasoning.
• The premises anticipate the conclusion that they already contain in themselves.
• The validity of the argument is given by its form: the truth of the premises guarantees the truth of the conclusion.

Invalid reasoning or sophistry

Sophistry or invalid reasoning is understood to mean those reasoning that on the surface seems valid and true but when inspecting the validity of its structure, it is observed that the truth of the conclusion is not guaranteed by the truth of the premises. They are also known as fallacies.

For example:

Premise 1. If it is raining, it is hot.
Premise 2. It's hot.
Conclusion. Therefore, it is raining.

In this example we can see how a conclusion is derived from the premises whose truth is neither logically necessary nor guaranteed by what precedes it: it may happen that it is hot and it does not rain.

Differences with the inductive method

The inductive method is a reasoning that goes from the particular to the general. Thus, the fundamental difference between the deductive and inductive methods is based on the logical path that each one proposes:

• The deductive method starts from general premises towards a particular conclusion. The conclusions are contained in the premises.
• The inductive method does the opposite, that is, it starts from particular premises to try to extrapolate a law or a general conclusion. The conclusions are obtained from a formulation of laws based on a generalization.

In addition to this logical movement, there are other differences whose formality is less. Induction, for example, uses observation, recording and contrasting information to build general premises that serve as a basis for what is stated. In this reasoning we observe a leap of faith that can never occur in deductive reasoning: nothing can be stated that is not derived as a logical consequence of what has already been said.

Variations of the deductive method

There are some specific derivations of the deductive method that are used in formal sciences. These are the empirical-analytical method, the hypothetical-deductive method and abductive reasoning:

• The empirical-analytical method. It is a scientific research model based on empirical logic and experimentation. It also includes the observation and controlled replication of natural phenomena, in pursuit of their statistical analysis.
• Abductive reasoning. It is one that, based on the description of a specific fact of which one has knowledge, arrives at any hypothesis. That is, abductive reasoning arrives at a probable explanation of a fact based on the premises that are held or known.
• The hypothetico-deductive method. It is the reasoning model that supports the scientific method. It is the research path that allows a degree of certainty and reliability in scientific knowledge. To do this, the hypothetico-deductive method consists of several essential steps:

• Observation of nature to study.
• Creation of a hypothesis that explains its phenomena.
• Deduction of elementary propositions or consequences of the hypothesis itself.
• Experimental verification of the validity of the conclusions.

Examples of the deductive method

We can think of examples of deductive reasoning used in everyday life. For example:

• TO. 1. Birds fly.
  2. The sparrow is a bird.
  3.The sparrow flies.
• b. 1. All men are mortal.
  2. Martin is a man.
  3. Martin is mortal.
• c. 1. Whenever it rains there are clouds in the sky.
  2. It rains.
  3. There are clouds in the sky.

Continue with: Scientific Knowledge

References

• Gamut, LTF, & Durán, C. (2002). Introduction to logic. Buenos Aires, Argentina: Eudeba.
• “Deductive reasoning” on Wikipedia.
• “Deductive method” in Methods.
• “Deductive method” in Soviet Philosophical Dictionary.
• “Deductive method” in Definición.de.
• “Deductive Reasoning vs. Inductive reasoning” in LiveScience.