Week 7: Conditionals Flashcards
(30 cards)
What is a conditional statement?
A conditional is a statement of the form “If A, then B”, symbolized as A → B, where A is the antecedent and B is the consequent. It expresses a dependence between two propositions.
What does “A → B” mean in propositional logic?
It means that if A is true, then B must also be true. It does not mean B causes A, or that A and B are both true — only that if A is true, B must follow.
What is Modus Ponens?
Valid form of inference:
If A, then B (A → B)
A
∴ B
✅ Example:
If it rains, the ground gets wet.
It rains.
∴ The ground gets wet.
Why is Modus Ponens valid?
Because it directly affirms the antecedent and applies the rule stated in the conditional. If A is true and A guarantees B, then B must also be true.
What is Modus Tollens?
Valid form of inference:
- If A, then B (A → B)
- Not B (¬B)
- ∴ Not A (¬A)
✅ Example:
If the light is on, then the switch is up.
The light is not on.
∴ The switch is not up.
Why is Modus Tollens valid?
If B must be true whenever A is true, then finding that B is false shows that A cannot be true either.
What is “Affirming the Consequent”?
Invalid (fallacious) reasoning:
- If A, then B
- B
- ∴ A ❌
Example:
If it’s a dog, it has four legs.
It has four legs.
∴ It’s a dog. (Could be a cat or a table)
Why is “Affirming the Consequent” a fallacy?
Because the truth of the consequent does not guarantee the truth of the antecedent — other causes may lead to B.
What is “Denying the Antecedent”?
Invalid (fallacious) reasoning:
- If A, then B
- Not A
- ∴ Not B ❌
Example:
If it is snowing, it is cold.
It is not snowing.
∴ It is not cold. (It could be cold without snow)
Why is “Denying the Antecedent” a fallacy?
Because even if A is false, B could still be true due to other conditions. A being false doesn’t rule out B.
What is a sufficient condition?
A condition that guarantees the outcome.
“If A, then B” → A is a sufficient condition for B.
What is a necessary condition?
A condition that must be true for something else to happen.
“If A, then B” → B is a necessary condition for A.
How are sufficient and necessary conditions confused?
Mistaking a necessary condition for a sufficient one (or vice versa) leads to fallacies like affirming the consequent or denying the antecedent.
What is Reductio ad Absurdum?
A proof method where you assume the opposite of what you want to prove and show it leads to a contradiction — thereby refuting the assumption
Give a Reductio ad Absurdum example.
Claim: √2 is irrational.
Assume √2 is rational = a/b.
Square both sides → 2 = a²/b² → a² = 2b².
Leads to contradiction about parity (even/odd).
∴ √2 is irrational.
Why is Reductio ad Absurdum powerful in logic?
It forces a contradiction from an assumption, showing the assumption cannot be true. It’s foundational in formal logic and mathematics.
What is an indicative conditional?
A conditional used to state what is actually or likely true.
Example: If Oswald didn’t kill JFK, someone else did.
What is a subjunctive (counterfactual) conditional?
A conditional used to describe what could have happened under different circumstances.
Example: If Oswald had not killed JFK, someone else would have.
What’s the key difference between indicative and subjunctive conditionals?
Indicative is based on actual facts; subjunctive is hypothetical, referring to what might be the case in alternate worlds.
Why are subjunctive conditionals harder to evaluate logically?
They depend on judgments about what would happen in non-actual scenarios, requiring assumptions about background context and causal laws.
What is the Wason Selection Task?
A psychological test to see how people handle conditional reasoning.
Rule: If there is a vowel on one side, there is an even number on the other.
What does the Wason Task reveal?
People often fail to apply Modus Tollens and only check for confirming evidence, not falsifying it.
How does confirmation bias affect conditional reasoning?
We tend to seek evidence that confirms a rule (turning over vowel cards) and neglect testing disconfirming cases (like turning over an odd number).
What is the formal structure of a conditional in logic?
“A → B” reads: If A is true, then B must be true.
It is false only when A is true and B is false.
