What is deductive reasoning and why do people often make errors of logic

Nowadays we are faced with an enormous variety of problems solving and reasoning. Reasoning is based on a system of formal logic. Formal logic consists of the abstract rules and theory of logical reasoning that logicians have developed over the years. However, both are activities of thinking.

Researchers have used many forms of different reasoning. One of them is deductive reasoning. Deductive reasoning is when you progress from things you know or assume to be true – called ‘premises’ – to conclusions that must follow from these premises. Also analyse arguments to see if they are valid. There are many cases where premises appear to be true in conclusion or alternatively nonsensical.

The most famous example of deduction is:

‘Socrates is a man.

All men are mortal.

Therefore, Socrates is mortal.’

The first two statements are premises, and the third statement is a conclusion. The first two are true, the conclusion must be true.

Deductive – reasoning problems are proceeding through the other types of thinking problems.

For example conditional reasoning is when the reasoner comes to conclusion based on proposition. Propositional logic doesn’t admit any uncertainty about the truth. Conditional reasoning consists of modus ponens (an important rule of inference), modus tollens (another major rule of inference), affirmation of the consequent (differences of meaning between propositional logic and ordinary language, with use of ‘If ‘) and denial of the antecedent (people think about conclusion as a valid, but is invalid).

Another type of thinking, which has been studied for over 2000 years, is syllogistic reasoning. Syllogism is deductive argument that is drawing conclusion from two statements. The most common quantifiers used for premises and conclusion are: all; some; no; and some…. not. For instance:

All men are soldiers.

All soldiers are alcoholics.

Therefore, all men are alcoholics.

People may be likely to make decisions based on biases that lead them to make errors in syllogistic reasoning. There is belief bias in which people were 100% confident in their answers, they were correct only between 60 to 70%. According to Klaurer, Musch and Naumer (2000) there are factors, which have influence on syllogistic reasoning:

Base – rate effect:

The performance of syllogistic reasoning is influenced by the perceived probability of syllogism being valid,

Atmosphere effect: if both premises are same, the conclusion is expected to be the same,

Conversion error: is regarded as an example of atmosphere effect, in which one statement is converted into different form of statement.

There are many questions about deductive reasoning. For example:

Why do we make errors on tasks of deductive reasoning? What factors affect the errors we make? The answer for this is in theoretical approaches as in the abstract- rule theories. The abstract-rule approach was originally proposed by Braine (1978;p.360) was that people comprehend the premises of an argument and then turn them into abstract rules from which they make inferences. Braine introduced three main kinds of possible errors:

1.) Comprehension errors – the premises are presented on an incorrect fashion

2.) Heuristic inadequacy – reasoning action failing to locate the right line of reasoning

3.) Processing errors – happen when the memory of a participant is overload.

In fact, people have a logical reasoning, except for extraneous effect from the comprehension of statement or the limitations of working memory. In Braine theory, the affirmation of consequent error occurs due to a conversion error. According to Braine et al. (1984), we assume other people will provide us with the information we need to know. People have a mental rule corresponding to modus ponens so syllogisms based on modus ponens are easy to handle, and pose no comprehension problems. But, Byrne (1989) showed that this is not always true.

Johnson-Laird is a representative, of one of the most influential theory to deductive reasoning, which is mental model. According to him (1999,p.116), ‘Each mental model represents a possibility, and its structure and content capture what is common to the different ways in which the possibility might occur.’ That basically mean, a mental model draws a possible state-of-affairs in the world. One of Johnson-Laird’s main assumptions is the principle of truth that he incorporated into this theory. He claims that people should minimise the quantity of information on working memory and to build a mental model that represent only what is true, and what is false.

The abstract-rule theory is one of the main theories of deductive reasoning, which contests that errors are made when people misunderstand the reasoning task. It based on many experimental researches on deductive reasoning, which are limited and under-specified. The second one calls a mental model approach, which argue that errors are made when the full set of mental models is not constructed. It supported by empirical evidence.

Most people perform mistakenly on deductive reasoning task, but it doesn’t mean the humans are illogical and irrational on grounds of the normative system problem, the interpretation problem, and the external validity problem. There is a big gap between the relatively successful nature of our reasoning used in everyday life and the reasoning in the laboratory, which is unavailing.

Deductive reasoning is basically a process in which we deduce the conclusion that follows from premises. However, even in deductive reasoning, errors are still made. I believed that people are intelligent beings. The reason why we make errors is because we are not familiar with a task or a task is not well presented clearly or we are affected by our beliefs.