CS/SE 2211: Laws of Thought and Deductive Reasoning

Study Notes

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

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")

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

Steps to construct a logical diagram:
1. Identify the components (premises and conclusions)
2. Use a mark (e.g., number) to represent each component
3. Use arrow heads to indicate the relationship among components
4. Properly represent the logical relationship

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

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

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)