Logical Deduction

Deduction means deriving new, necessarily true statements from existing statements (premises). This is the foundation of logical reasoning.

What is the Essence of Deduction?

• If the initial statements are true, the conclusion must also be true.
• Deduction is based on formal rules, not content.
• This ensures that the reasoning is always valid.

Simple Example

• Premise 1: "All humans are mortal."
• Premise 2: "Socrates is human."
• Conclusion: "Socrates is mortal."

This is a classic deductive argument: the conclusion is necessarily true if the initial statements are true.

Formal Notation

This means: from premises P1, P2, …, Pn, conclusion Q can be derived. The ⊢ symbol denotes logical derivation.

Deductive Validity

A conclusion is deductively valid if it is impossible for the premises to be true and the conclusion false.

Summary

Deduction is a conclusion in which a necessarily true conclusion follows from true premises. This is the basis of proofs in mathematics and logic.

Practice Exercise