Lesson 4
Critical Thinking
In This Lesson
1. Logical Reasoning
Logical reasoning is the ability to analyze information and draw valid conclusions.
Types of Reasoning
Deductive Reasoning
General to specific; if premises are true, conclusion must be true.
All mammals are warm-blooded.
Dogs are mammals.
Therefore, dogs are warm-blooded.
Inductive Reasoning
Specific to general; conclusion is probable but not certain.
The sun rose today.
The sun rose yesterday.
Therefore, the sun will rise tomorrow.
Conditional Statements
- If-Then: If P, then Q (P ā Q)
- Converse: If Q, then P (not always true)
- Inverse: If not P, then not Q (not always true)
- Contrapositive: If not Q, then not P (always true if original is true)
Example: If it rains, the ground gets wet.
Contrapositive: If the ground is not wet, it did not rain. ā
2. Arguments & Conclusions
Understanding how to analyze arguments and identify valid conclusions.
Parts of an Argument
- Premise: A statement that provides evidence or reasons
- Conclusion: The statement being supported by the premises
- Assumption: Unstated premise that the argument relies on
Signal Words
Premise Indicators:
because, since, given that, for, as, due to, the reason is
Conclusion Indicators:
therefore, thus, hence, so, consequently, it follows that
Evaluating Arguments
- Identify the conclusion
- Identify the premises/evidence
- Check if premises support the conclusion
- Look for hidden assumptions
- Consider alternative explanations
3. Logical Fallacies
Fallacies are errors in reasoning that weaken arguments.
Common Fallacies
- Ad Hominem: Attacking the person instead of the argument.
"You can't trust his opinion on climate change; he's not a scientist."
- Straw Man: Misrepresenting someone's argument to make it easier to attack.
"You want to reduce military spending? So you don't care about national security!"
- False Dilemma: Presenting only two options when more exist.
"You're either with us or against us."
- Hasty Generalization: Drawing conclusions from insufficient evidence.
"I met two rude people from that city; everyone there must be rude."
More Fallacies to Know
- Appeal to Authority: Using an authority figure as evidence without expertise
- Appeal to Emotion: Using emotions instead of logic to persuade
- Circular Reasoning: The conclusion is used as a premise
- Red Herring: Introducing irrelevant information to distract
- Slippery Slope: Claiming one event will lead to extreme consequences
- Post Hoc: Assuming causation from correlation (after this, therefore because of this)
4. Pattern Recognition
Identifying patterns in sequences, series, and relationships.
Number Sequences
- Arithmetic: Add/subtract a constant
2, 5, 8, 11, 14... (add 3)
- Geometric: Multiply/divide by a constant
3, 6, 12, 24, 48... (multiply by 2)
- Fibonacci-like: Each term is sum of previous terms
1, 1, 2, 3, 5, 8, 13...
- Square/Cube numbers: Perfect squares or cubes
1, 4, 9, 16, 25... (nĀ²)
Letter/Word Patterns
- Alphabetical: Based on position in alphabet
A, C, E, G, ? (skip one letter = I)
- Word analogies: Relationship between word pairs
Hot : Cold :: Light : ? (Dark - opposites)
Pattern-Finding Strategy
- Look at differences between consecutive terms
- Look at ratios between consecutive terms
- Check for alternating patterns
- Consider multiple operations combined
- Check position-based patterns
5. Analytical Skills
Strategies for analyzing information and solving problems systematically.
Data Interpretation
- Read carefully: Note titles, labels, units, and scales
- Identify trends: Look for increases, decreases, or patterns
- Compare data: Note similarities and differences
- Draw conclusions: What does the data show?
- Be skeptical: Consider what the data doesn't show
Problem-Solving Techniques
- Break it down: Divide complex problems into smaller parts
- Work backwards: Start from the desired result
- Eliminate options: Rule out clearly wrong answers
- Use examples: Test with specific cases
- Draw diagrams: Visualize the problem
Critical Questions to Ask
- What is the main point or conclusion?
- What evidence supports this claim?
- Are there any assumptions being made?
- Could there be alternative explanations?
- What information is missing?
- Is the source reliable?
USTET Critical Thinking Tips
- āPractice logical puzzles - Sudoku, logic grids, brain teasers.
- āRead critically - Analyze arguments in news articles and editorials.
- āLearn to identify fallacies - Spot weak reasoning in everyday discussions.
- āPractice pattern recognition - Number and letter sequences.
Congratulations!
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