Deductive Logic

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Introduction[edit]

—Tools for evaluating consistency

Logic makes consistency visible.

Deductive logic provides a system of tools and techniques that allow the truth-values of certain classes of statements—known as propositions— to be evaluated for consistency. Beginning with propositions known to be true or false, deductive logic allows us to derive other statements with known truth-values. It also allows us to identify incorrectly attributed truth-values and inconsistencies.

Learning deductive logic provides a basic theoretical foundation that is helpful when studying more complex (and less exact) forms of logic.

Objectives

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The objectives of this course are to help students:

  1. Learn terms commonly used in logical analysis,
  2. Recognize statements that form propositions,
  3. Create propositions and construct valid arguments,
  4. Learn to recognize and evaluate truth functions, also known as truth operations,
  5. Determine the truth-value of various propositions,
  6. Use logical connectives to transform systems of truth functions and propositions into alternative statements having equivalent truth-values,
  7. Analyze systems of proposition to evaluate the consistency of their truth-values,
  8. Solve logic puzzles,
  9. Transform certain natural language sentences into equivalent symbolic statements,
  10. Begin establishing a foundation for studying more complex logical analysis.

The course contains many hyperlinks to further information. Use your judgment and these link following guidelines to decide when to follow a link, and when to skip over it. Each of the top level headings below are linked to course materials; it is important to follow these links.

This course is part of the Applied Wisdom curriculum and of the Clear Thinking curriculum.

If you wish to contact the instructor, please click here to send me an email or leave a comment or question on the discussion page.

Non-contradiction[edit]

Aristotle's Law of non-contradiction can be stated as:

The most certain of all basic principles is that contradictory propositions are not true simultaneously.

Aristotle says that without the principle of non-contradiction we could not know anything that we do know.[1][2] This principle forms the foundation of reason, and especially of deductive logic. The goal of deductive logic is to derive the most powerful claims possible within the law of non-contradiction.

Truth Functions[edit]

Arguments and Validity[edit]

Inference Rules[edit]

Equivalent Schemata[edit]

Categorical Sentence Schemata[edit]

Logic Puzzles[edit]

Further Reading[edit]

Many books on logic include sections on deductive logic. Search for these and choose any that seem helpful. The following books were used to develop this course.

  • Michalos, Alex C. (November, 1969). Principles of Logic. Prentice Hall. pp. 433. ISBN 978-0137094028. 
  • Copi, Irving M.; Cohen, Carl (June 20, 2001). Introduction to Logic. Prentice Hall. pp. 647. ISBN 978-0130337351. 
  • Weston, Anthony (November 14, 2008). Rulebook for Arguments. Hackett Publishing Co, Inc. pp. 104. ISBN 978-0872209541. 

References[edit]

  1. Aristotle on Non-contradiction, Stanford Encyclopedia of Philosophy
  2. Contradiction, Stanford Encyclopedia of Philosophy.

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