Lecture 4 Flashcards
What is an argument?
a set of statements, one of which the (conclusion) is taken to be supported by the remaining statement (the premises)
what is a deductive argument?
a deductive argument intends to provide logically conclusive support for the conclusion
What is Deductive validity ?
- An argument is deductively valid if and only if it not possible for all premises to be true and conclusion false
- if all the premises were true, the conclusion would have to be true too
- the conclusion logically follows the premises
How do we test whether an argument is valid or not?
- imagine that all the premises are true. does this guarantee that the conclusion has to be true as well?
- if the conclusion could be false, then it’s an invalid argument
What is conjuction?
conjunction is a statement if the form
P and Q
“I am hungry and it’s raining”
made up of two conjuncts
What is disjunction?
Any statement P or Q
“Either the picnic was cancelled or it was sunny”
Jones committed the murder or the butler did”
made up of disjuncts
What is negation?
Not P
~P
It is NOT sunny
What is conditional?
if P, then Q
‘If it rains, the picnic will be cancelled”
“if jones committed the murder, the butler is sad”
What is bi-conditional?
A biconditional is a statement if the from
P if and only if Q
You can enter the club if only if you have Id
Argument by Elimination example
- P or Q
- ~P
- Q (from 1,2)
If it wasn’t the the butler, then it was Jones
Example of invalid argument by elimination?
- P or Q
- you assert P
- Q
Looks similar, but invalid
Either lefty or righty committed crime
Lefty committed the crime
Rightly didn’t commit the crime
How can we gauruntee that righty had nothing to do with it
They might have collaborated
How do we use the word OR in arguments?
We use OR: inclusive
Example of a conjunction argument?
- P
- Q
- p and Q (from 1,2)
It is raining and I am wet
from that you can validly conclude that it is raining
Affirming Antecedent argument pattern
- if P, then Q
- P
- Q (from 1,2)
If Ryerson is a great uni, then many students apply there
Ryerson is a great uni
many students apply there
Denying the consequent example
- If P then Q
- ~Q
- ~P (from 1,2)
If Jim committed the murder then he used his gun on Tuesday
he didn’t use his gun on Tuesday
He’s innocent
Denying the Antecedent example
- If P, then Q
- ~P
- ~Q
If Einstein invented the computer, he’s a genius
2. Einstein did not invent the computer
3. Einstein is not a genuis
Affirming the consequent
- If P, then Q
- Q
- P
If Einstein invented the computer, then he’s a genius
Einstein is a genuis
he invented the computer
Hypothetical syllogisim example
- If P, then Q
- If Q, then R
- If P then R (from1,2)
If donald trump loses the election, joe biden wins
If joe Biden wins, his supporters will be happy
If donald trump loses, biden supporters will be happy
Contraposition example
- If P, then Q
- If ~Q then ~P (from1)
If donald loses the election, joe biden wins
therefore, joe biden doesn’t win, then doanls doesn’t lose the election
Universal Modus Ponens refer to attributes
- All A’s are B’s
- x is an A
- x is B
Example:
All students are hardworking.
Omar is a student
Omar is hardworking
Uiversal Hypothetical Syllogism example
- All A’s are B’s
- All B’s are C’s
- All A’s are C’s
example: All whales are mammals
all mammals are animals
All whales are animals
Universal Ruling out
- No A’s are B’s
- x is an A
- x is not a B
Example: No children are perfectl behaved at all times
Jacob is a child
Jacob is not perfectly behaved at all times
Invalid pattern example
- All A’s are B’s
- x is not A
- X is not B
All students are hardworking
Himari is not a student
Himari is not hardworking
All A’s are B’s
x is a B
x is not an A
IS THIS VALID?
All students are hardworking
Himari is hard working
Himari is a student
Invalid.
