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Questions and Answers
What is the difference between an error in a premise and a fallacy?
What are the two broad groupings of arguments that fallacies can belong to?
What is the name of the deductive fallacy that occurs when someone denies the antecedent?
What is an example of an inductive fallacy?
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What is the term for an argument that is logically valid and has all true premises?
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What is the term for an argument that is logically valid but has one or more false premises?
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What is the purpose of checking for consistency among the premises?
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What is the term for an argument that is not logically valid?
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What is an example of affirming the consequent?
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What is the main difference between deductive and inductive fallacies?
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Study Notes
Laws of Thought
- Laws of thought are fundamental principles for logical reasoning, debated by philosophers for centuries
- Five laws of thought:
- Law of Identity: Everything is identical to itself (e.g., if something is A, then it is A)
- Law of Non-contradiction: Nothing can be both A and not A (e.g., a square cannot be both a square and not a square)
- Law of Excluded Middle: Everything is either A or not A (e.g., a thing is either a square or not a square)
- Law of Commutativity for Conjunction: The order of statements joined by "and" does not affect the truth or falsity of the conjunction
- The Index Law: Asserting a statement is equivalent to its assertion in conjunction with itself
Claims and Arguments
- Claim: A statement that can be determined as true or false (e.g., "Watching TV from a close distance harms eyesight")
- Argument: A set of claims that has a central or principle claim and other claims that support it (e.g., "We are in for an unusually hot summer because the data from Meteorological Office shows lower temperature in the region in the previous year")
Inductive Arguments
- Example 1: 99% of residents in a town have credit cards, so Sunil, a resident, will likely have a credit card (strong inductive reasoning)
- Example 2: Two snakes seen were brown, so all snakes in the locality are brown (weak inductive reasoning)
- Strength of inductive reasoning depends on the probability of the conclusion
Diagramming Arguments
- Steps to construct a logical diagram:
- Identify the components (premises and conclusions)
- Use a mark (e.g., number) to represent each component
- Use arrow heads to indicate the relationship among components
- Properly represent the logical relationship
Validity and Invalidity
- Validity: If both premises are true, the conclusion must be true
- Invalidity: If both premises are false, the conclusion may be true or false
- Table showing possible validity and invalidity scenarios:
- Premises: True, Conclusion: True → Possible
- Premises: True, Conclusion: False → Not Possible
- Premises: False, Conclusion: True → Possible
- Premises: False, Conclusion: False → Possible
Soundness and Unsoundness
- Sound argument: Both valid and all premises true
- Unsound argument: Violates either validity or premise truth (or both)
Consistency
- A set of statements is consistent if there is at least one possible situation where every member is true
- A set of statements is inconsistent if no such possibility exists
Evaluating Arguments
- Check for validity and soundness
- Check for consistency among premises
Fallacies
- Error in a premise: Factual error
- Error in reasoning: Fallacy
- Two broad categories of fallacies:
- Deductive Fallacies (e.g., denying the antecedent, affirming the consequent)
- Inductive Fallacies (e.g., illicit or hasty generalization)
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Description
This quiz covers the fundamentals of laws of thought, claims, and arguments in the context of deductive reasoning and logic programming. It's designed for Bachelor of Science (Hons) students in CS, SE, and IT.
