Lecture 9 Flashcards
What is a conditional claim?
if P then Q)
- P is antecedent and Q is the consequent .
- A conditional claim does not assert that the antecedent or the consequent is true.
If Susan is a sister, then Susan has a sibling. is an example of
the antecedent being true, then consequent is probably true.
If Adam is basketball player he is over six feet tall. is an example of
antecedent being true, the consequent is neither guaranteed to be true nor probably true
If today is Thursday, then monkeys like bananas. You should——- this premise
reject this premise
What is the general test for conditionals
- imagine/suppose/pretend that the antecedent
is true, and then ask yourself: what does that tell us about the consequent? - If the consequent has to be true, then you should believe the conditional.
- If consequent is not guaranteed to be true, then you should disbelieve the
conditional - If you can’t tell then you should suspend judgment
Examples for Necessary and sufficient conditions
Sometimes we reason about what to believe or do by thinking about what is necessary or sufficient for what.
- The restaurant claims to provide excellent service, but if you did, then their waiter would pay attention to detail. Their waiter never pay any attention so the restaurant does not provide good service (NECESSARY)
- robbing this casino is one way to become a millionaire so I plan to do it (SUFFICIENT)
- keeping my grass green requires lots of fertilizer, so I’m going to spread some fertilizer this weekend. (NECESSARY)
- whenever there is a fire there is sure to be oxygen (NECESSARY)
What are Necessary conditions
When X is absent, Y cannot occur.
When P is false, Q must also be false
X: Oxygen X: Unmarried
Y: Fire Y: Bachelor
How to test necessary conditions?
Could you have Y without X?
Could Q be true while P is false?
P: Oxygen is present P: Jim is unmarried
Q: Fire occurs Q: Jim is a bachelor
What are Sufficient condition?
- When X is the case, Y must be the case .
- When P is true, Q must also be true
X: you get an A in the class P: fifi is poodle
Y: you pass the class Q fifi is a dog
What is the test for sufficient conditions?
- The test: could X be present, without Y occurring?
- Could P be true while Q is false?
- If the answer is that you have a sufficient condition.
- a key connection: A is sufficient for B= B is necessary for A
Diffrent ways to state conditonals?
- We can say the same thing by reversing the order of the consequent and antecedent and negating both of them
- If P then Q
If not Q then not P - If Trudeau is the prime minster then he’s a politician.
- If Trudeau is not a politician then he is not the prime minister.
What is the rule of thumb in defintions?
Rule of thumb: the higher the stakes, the more precision is needed.
Why must we use good definitons?
- Sloppiness about definitions can lead to bad arguments,
misunderstandings, confusion, etc.
When is definition too narrow?
- A definition is too narrow if it excludes things that it shouldn’t exclude.**
- e.g., “a student is someone enrolled at a university”’
- too narrow, you can be a highschool student
When is definition too broad?
- A definition is too board if it includes things that should not,**
- e.g., “a computer is an electronic device with a screen”
- too broad, includes T.V and GPS.
