Deductive argument

Deductive argument

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William holds a degree in philosophy from the Federal University of Santa Maria (UFSM), specializes in teaching and works as a philosophy teacher in high school.
January 31, 2021 - 4 min read

What is a deductive argument

A deductive argument is the one in which conclusion necessarily follows from the reasons or premises. That means that, if the premises are true, the conclusion will also be true, since there is no possibility that it is false. This is the strongest type of argument that exists, because if we accept the premises, we also have to accept the conclusion.

This is a classic example of a deductive argument:

Every man is mortal.

Socrates is a man.

Socrates is mortal.

It is impossible the conclusion that “Socrates is mortal” to be false if the premises are true. That is, if all men are mortal and Socrates is a man, he must also be mortal. To deny this would be to commit a contradiction.

It is common to say from deductive arguments that the conclusion is already contained, implicitly, in the premises. When drawing a conclusion in a deductive way, what we are doing is to make explicit the information already present in the premises. Consider the example above again. The conclusion “Socrates is moral” was already present, implicitly, in the information contained in the premises of the argument.

What defines a deductive argument unmistakably is the fact that it is the only type of argument that generates absolute certainty or, as it is said in logic, that the conclusion is necessary. The other arguments, such as arguments from analogy , inductive , from authority and others, are arguments whose premises justify the conclusion with some probability. However, even with true premises, the conclusions of these arguments can still prove to be false. The same is not true of deductive arguments.

Meaning of “deduct”

It is common to see the word “deduct” being used in different everyday situations. The dictionary gives the following meaning to it “to conclude (something) by reasoning, to infer”. In this sense, we say that a person deduced that his phone, which is not waterproof, would stop working, because it falls into the pool.

This is the best known use of “deduct”, but, as you may have noticed, when we speak of “deductive argument” we are saying something else with “deductive”.

Thus, in common usage, “to deduce” means “to draw a conclusion”. In logic, “to deduce” means “to draw a conclusion that is necessarily true if the premises are true”.

Uses of deductive arguments

There are some common forms of deductive arguments that are important to know in order to understand in which situations these types of arguments are used and how to recognize it. We will explore three of them: arguments based on mathematics, definitions and syllogisms.

Arguments based on mathematics

Arguments based on mathematics are those that operate with arithmetic or geometric calculations. Thus, mathematics is a type of accurate knowledge that uses deductive arguments quite frequently in its statements. In addition, when reasoning about mathematical issues, we generally make deductions. For example, if there are 25 students in the class, I know that 5 more students have entered and I conclude that the class will have 30 students, I am doing a deductive reasoning. My conclusion is necessarily true, as it follows from the sum of 25 and 5.

Arguments based on definitions are those whose conclusion is inferred from the meaning of a phrase or word used in the premises. An interesting example of this type of deductive argument can be found in philosophy. Many philosophers sought to produce evidence for the existence of God from a pure analysis of the meaning of that word and thus offer a deductive argument to justify its existence.

The argument can be summarized as follows: God means, among other things, “to be perfect”. For something to be perfect, it must exist, otherwise it would be imperfect. Therefore, it is necessary that God exists.

This is a deductive argument because the conclusion depends solely on the meaning of the word “perfect” and “God”. If we agree with the meanings attributed to these words in the premises, that is, “God is a perfect being” and “something perfect necessarily exists”, then we have to accept the conclusion that “God exists.”

Finally, syllogisms are deductive arguments with two premises and one conclusion. The following argument is an example:

Every cat has four legs.

Tony is a cat.

So, Tony has four legs.

This type of argument has been studied since Aristotle and is a of the main topics studied by logic.

References

Walton, Douglas. Informal Logic: A Pragmatic Approach. Cambridge: Cambridge University Press, 2008.

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