Formal vs. informal reasoning

Some people think that all good arguments consist essentially of formal logical inferences or syllogisms. But if you look closely, you quickly notice that arguing has little to do with formal logical reasoning.

Logical reasoning can be divided into two groups: formal and informal reasoning. Both are important for critical thinking, but have different areas of application and methods.

Formal reasoning

Formal reasoning is based on explicit rules and structures that are independent of the content of the arguments. It concentrates on the form or structure of an argument and often uses symbolic notation.

Characteristics of formal reasoning:

• Use of formal systems such as predicate logic or propositional logic
• Strict rules for valid inferences
• Independence from the specific content
• Precision and unambiguity
• The possibility of formal proof

Example of formal reasoning (syllogism): Premise 1: All A are B. Premise 2: All B are C. Conclusion: All A are C.

This argument pattern is valid independently of the specific content. It does not matter what A, B and C stand for — the conclusion follows necessarily from the premises.

Informal reasoning

Informal reasoning refers to arguments in natural language that are not fully formalized. It takes into account the context, background knowledge and implicit assumptions.

Characteristics of informal reasoning:

• Use of natural language
• Consideration of context and background knowledge
• Inclusion of implicit premises
• Flexibility and adaptability
• Application in everyday discussions and debates

Example of informal reasoning: "The lawn is wet. It must have rained during the night."

This argument contains implicit assumptions (e.g. that rain is the most probable cause of a wet lawn) and is based on everyday knowledge and experience.

Differences and areas of application

The main differences between formal and informal reasoning are:

1. Precision vs. flexibility: Formal reasoning is more precise, but less flexible; informal reasoning is more flexible, but possibly less precise.

2. Explicitness vs. implicitness: Formal reasoning makes all assumptions explicit; informal reasoning can contain implicit assumptions.

3. Area of application: Formal reasoning is often used in mathematics, formal logic and theoretical computer science; informal reasoning is predominant in everyday discussions, politics, ethics and many other fields.

Both types of reasoning have their strengths and weaknesses:

• Formal reasoning offers precision and clarity, but can be too rigid in complex real-world situations.
• Informal reasoning is more flexible and more context-related, but can be more prone to fallacies and ambiguities.

For critical thinking it is important to understand both types of reasoning and to apply them appropriately depending on the context.