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Logical Thinking

Q: What is a fallacy in logic?

A fallacy in logic is an error in reasoning that undermines the validity of an argument. Fallacies often arise when an argument appears persuasive but lacks logical coherence or factual accuracy. They are categorized into types such as: Fallacies of relevance: Arguments where the premises are not related to the conclusion (e.g., ad hominem). Fallacies of defective induction: Conclusions drawn from insufficient or biased evidence (e.g., hasty generalization). Fallacies of ambiguity: Misleading arguments due to vague or ambiguous language (e.g., equivocation).

Learn critical thinking and logical reasoning to create valid arguments, avoid logical fallacies, and solve real-world problems using tools like if-then implications and Aristotle’s logic.

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Overview

Content

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Critical and logical thinking are essential in today’s democratic society and professional organizations. This course lays a foundation for these skills by embedding logic into everyday language and situations. You will learn to create logically valid arguments, recognize and avoid logical fallacies, and focus on the form of an argument rather than its content. You’ll explore how to prove the validity or invalidity of arguments and understand the historical development of logic from Aristotle’s syllogism to modern predicate logic. By the end of the course, you’ll be equipped to tackle real-world problems more effectively using logical operators, if-then implications, and other tools in logical reasoning. You’ll gain skills in using logic and language judiciously in both your professional and civic life.

Critical and logical thinking are essential in today’s democratic society and professional organizations. This course lays a fou...Show More

WHAT YOU'LL LEARN

A strong foundation in critical thinking and its relationship to problem-solving in real-world problems

An understanding of logical fallacies, such as fallacies of relevance and ambiguity, and learning to recognize them in everyday arguments

The ability to structure a logical argument and evaluate it based on the laws of logic and building blocks like categorical syllogism and categorical propositions

Proficiency in resolving real-world problems through knowledge and reasoning using modern logic and its tools, including logical operators and if-then implications

A strong foundation in critical thinking and its relationship to problem-solving in real-world problems

TAKEAWAY SKILLS

Logic building

Content

37 Lessons8 Quizzes

Introduction to Logical Thinking

2 Lessons

Learn logical structures, enhance reasoning skills, and explore practical logic applications in everyday scenarios.

A Nugget from the World of Logic

The Logical Flow of the Course on Logic

Fallacies in Logic

5 Lessons

Unpack logical fallacies examples, including fallacies in logic, fallacies of relevance, and fallacies of ambiguity, to improve your fallacies argument.

Fallacies and Fallacious Arguments

Fallacies of Relevance

Fallacies of Defective Induction

Fallacies of Ambiguity

Exercise: Recognize and Apply Invalid Everyday Arguments

Logical Argument

6 Lessons

Understand how language conveys logical arguments, using if-then implications and logical operators to construct clear and valid reasoning.

Logic and Language

Syntax and Semantics

Complicating Sentences Using Logical Operators

The IF-THEN Implication

Build a Logical Argument

Exercise: Recognize an Argument

What Is Logic?

7 Lessons

Explore what logic is. Its laws of logic, key building blocks, and how knowledge and reasoning ensure validity in arguments.

The Definition and Scope of Logic

Building Blocks of Logic

Validity and Truth

Discover the Laws of Logic

Knowledge and Reasoning

Logician vs. Scientist

Exercise: Recognize Valid Arguments in Everyday Life

First Theory of Logic: Aristotle’s Logic

3 Lessons

Explore Aristotle’s logic, categorical propositions, and categorical syllogism forms for assessing argument validity.

Categorical Propositions

Categorical Syllogism and Forms

First Mechanization for Validity

Second Theory of Logic: Propositional Logic

7 Lessons

Learn propositional logic with syllogism, truth tables, rules of inference, rules of substitution, and natural deduction proof.

Relaxing Some Constraints of Syllogism

Symbols and Connectives

Validity through Truth Tables

Rules of Inference

Rules of Substitution

Proofs by Natural Deduction

Exercise: Truth Table Knowledge

Third Theory of Logic: Predicate Logic

3 Lessons

Piece together predicate logic, focusing on quantifiers and validation rules for constructing valid logical arguments.

Predicate Logic

Predicate Functions and Quantifiers

Validity through Predicate Logic

Logical Reasoning in Action

3 Lessons

Apply logical reasoning in legal cases, problem-solving, puzzle-solving, and computing logic.

Logic in a Legal Case

Logic in Problem Solving and Puzzles

Logic in Computing

Wrap Up

1 Lessons

Grasp the fundamentals of articulating real-life situations, recognizing fallacies, and fostering logical thinking.

Logical Milestone

Certificate of Completion

Showcase your accomplishment by sharing your certificate of completion.

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Frequently Asked Questions

What is logical thinking?

Logical thinking is the ability to analyze a situation systematically, evaluate evidence, and draw sound conclusions based on reasoning and facts. It involves creating valid arguments, identifying logical relationships, and solving problems using structured and coherent approaches.

What is a fallacy in logic?

A fallacy in logic is an error in reasoning that undermines the validity of an argument. Fallacies often arise when an argument appears persuasive but lacks logical coherence or factual accuracy. They are categorized into types such as:

Fallacies of relevance: Arguments where the premises are not related to the conclusion (e.g., ad hominem).
Fallacies of defective induction: Conclusions drawn from insufficient or biased evidence (e.g., hasty generalization).
Fallacies of ambiguity: Misleading arguments due to vague or ambiguous language (e.g., equivocation).

What is an example of a proposition in logic?

A proposition is a declarative statement that is either true or false but not both. Example: All humans are mortal. This is a proposition because it expresses a clear statement with a truth value.

What is a predicate term in logic?

A predicate term in logic is the part of a statement that describes a property, characteristic, or relationship about the subject. In predicate logic, it is often represented as a function or a relation.

**Example:** In the statement “All cats are mammals,” the predicate term is “are mammals,” which describes the property of the subject “cats.”