Foundations of Logic: Concepts and Reasoning Principles

Etymology of Logic

From the Greek word logos, meaning 'proposition' or 'reason'.

What is Logic?

It is the study of methods and principles for distinguishing good reasoning from bad.

Central Problem of Logic

The central problem of logic is the distinction between right and wrong reasoning.

Premises and Conclusions

Proposition

A proposition is a statement that can be true, false, or indeterminate. It is usually the expression of a judgment.

Structure of a Proposition

• Subject
• Verb (Copula)
• Predicate

Distinction: Questions and Exclamations

Unlike propositions, questions and exclamations do not assert something that can be true or false.

The Notion of Inference

Inference is the process by which one arrives at a conclusion or statement based on other propositions accepted as the starting point of the process.

The inference process provides a rationale.

Elements of Reasoning Structure

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Conclusion on Reasoning

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Indicators of Premises

• Because
• Since
• For
• Given that
• For that reason

Indicators of Conclusions

• So
• Therefore
• Thus
• Hence
• Consequently
• It follows that
• We can conclude that

Informal Fallacies

Informal fallacies are arguments that are incorrect because their form is irrelevant or their content is misleading, failing to support the conclusion.

Logical Principles

These are fundamental laws governing the process of reasoning. They establish general principles, often considered self-evident or derived from intuition, that underpin the rules of logic.

Deductive Reasoning

In deduction, particular truths are inferred from general truths. Deductive arguments are assessed as valid or invalid, rather than right or wrong.

Categorical Propositions

Typical Forms

• Universal affirmative (A)
• Universal negative (E)
• Particular affirmative (I)
• Particular negative (O)

Modes (Quantity and Quality)

Categorical propositions are classified by their quantity (universal or particular) and quality (affirmative or negative). These are often remembered by the Latin terms 'AffIrmo' (A, I) and 'nEgO' (E, O).

Structure of a Categorical Proposition

• Quantifier
• Subject
• Copula (verb)
• Predicate

Categorical Syllogisms

Structure and Components

A categorical syllogism consists of three parts: a major premise, a minor premise, and a conclusion.

Key terms:

• Major Term (P): The predicate of the conclusion, found in the major premise.
• Minor Term (S): The subject of the conclusion, found in the minor premise.
• Middle Term (M): Appears in both premises but not in the conclusion.

The predicate of the conclusion is the major term of the syllogism, and the subject of the conclusion is the minor term of the syllogism.

Determining Mode and Figure

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Inductive Reasoning

In induction, general truths are inferred from particular truths. Inductive arguments provide conclusions that are probable, not certain.