Unit 1: Introduction to Logic

Logic: Nature and Scope

What is Logic?

The word "Logic" comes from the Greek word "logos," which can mean "reason," "discourse," "word," or "study."

Logic is the systematic study of the principles of correct reasoning.

It is not the study of *how* people actually think (that's psychology). Instead, it is the study of *how* people *ought* to think if they want to reason correctly. Its main goal is to distinguish good arguments (correct reasoning) from bad arguments (incorrect reasoning).

Nature of Logic

• A Science: Logic is a science because it is a systematic and organized body of knowledge.
• An Art: Logic is also an art because it teaches us the *skill* or *technique* of reasoning correctly.
• Normative: Logic is a normative science, not a positive one. A positive science (like biology) describes *what is*. A normative science (like logic or ethics) prescribes *what ought to be*. Logic sets the "norms" or "rules" for correct reasoning.
• Formal: Logic is concerned with the form (or structure) of an argument, not its content (or subject matter). This is a crucial point that will be explained in "Truth and Validity."

Scope of Logic

The scope of logic is vast. It is the "scaffolding" of all other fields of study, from mathematics and science to law and philosophy. The syllabus for this paper focuses on Traditional or Aristotelian Logic, which is a type of Deductive Logic.

The main types of logic are:

1. Deductive Logic: The study of arguments where the conclusion is claimed to follow from the premises with absolute necessity. If the premises are true, the conclusion *must* be true. (This is the focus of this course).
2. Inductive Logic: The study of arguments where the conclusion is claimed to follow from the premises with probability. The premises support the conclusion but do not guarantee it. (e.g., scientific reasoning).

Truth and Validity

This is the most important distinction in all of deductive logic. It separates the *content* of an argument from its *structure*.

Truth (and Falsity)

• Truth and Falsity are properties of propositions (statements).
• A proposition is a declarative sentence that is either true or false (e.g., "The sky is blue," "All cats are mammals").
• Truth is the correspondence of a proposition to reality (a "fact").

Validity (and Invalidity)

• Validity and Invalidity are properties of deductive arguments.
• An argument is not "true" or "false." A proposition is not "valid" or "invalid."
• An argument is valid if its conclusion follows necessarily from its premises. This means: IF the premises are true, the conclusion MUST be true.
• An argument is invalid if its conclusion does not follow necessarily from its premises. This means: It is *possible* for the premises to be true and the conclusion to be false.