Argument patterns Flashcards
Conjunction
conjunction is a statement if the form
P and Q
“I am running, and it’s sunny”
made up of two conjuncts
disjunction
Any statement P or Q
“Either the movie night was cancelled or my friends said they were going to show up”
made up of disjuncts
Negation
Not P
~P
It is NOT sunny
Conditional
if P, then Q
‘If it rains, the picnic will be cancelled”
“if jones committed the murder, the butler is sad”
If my friends don’t show up to movie night will be cancelled
Biconditional
A biconditional is a statement if the from
P if and only Q
You can enter the club if only if you have Id
Argument by Elimination
- P or Q
- ~P
- Q (from 1,2)
Either the bus comes or I have to walk home
the bus did not come
Therefore, I walked home
False argument by elimination?
- P or Q
- you assert P
- Q
Looks similar, but invalid
Either the bus comes or I have to walk home
I walked home
therefore, the bus didn’t come (this is invalid)
Conjunction
- P
- Q
- p and Q (from 1,2)
Joe is working out and eating at the same time
joe is eating
Affirming the Antecedent
- if P, then Q
- P
- Q (from 1,2)
If P is true, then Q has to be true
if I’m going to the movies then I will buy popcorn
I went to movies
therefore, I bought popcorn
Denying the consequent
- If P then Q
- ~Q
- ~P (from 1,2)
If jack goes to Egypt then he will visit the pyramids
Jack did not visit the pyramids
therefore Jack did not go to Egypt
If I’m hungry then I will eat
I didn’t eat
therefore I am not hungry
is an example of
Denying the Antecedent
- If P, then Q
- ~P
- ~Q
THIS IS INVALID
If I smoke weed, then my eyes will be red
my eyes are red
therefore, I smoked weed
This is an example of ?
Affirming the Consequent
- If P, then Q
- Q
- P
THIS IS INVALID
What does Hypothetical syllogism look like?
- If P, then Q
- If Q, then R
- If P then R (from1,2)
If I commit a crime then I will go to jail
If I go to jail then I won’t be able to see family
therefore, if I commit a crime I won’t be able to see family
Contraposition
- If P, then Q
- If ~Q
- then ~P (from1)
If I commit a crime then I will go to jail
if I don’t commit a crime,
then I won’t go to jail
Universal Modus Ponens
- All A’s are B’s
- x is an A
- x is B
Example:
All new TTC buses have wifi inside
This is a new TTC bus
Therefore, this TTC bus has wifi installed
Universal Modus Tollens
- All A’s are B’s
- x is not B
- x is not A
All new new phones are fast
The Iphone 2 is not fast
therefore, the Iphone 2 is not a new phone
Universal Hypothetical Syllogism
- All A’s are B’s
- All B’s are C’s
- All A’s are C’s
All pizza’s are made with dough
Anything made with dough has water
therefore, All pizza’s have water
Universal Ruling out
- No A’s are B’s
- x is an A**
- x is not a B
No cars can fly
Tesla is car
therefore, Tesla’s can’t fly
All dogs are mean
Jim is not a dog
therefore, Jim is not mean
an example of….
- All A’s are B’s
- x is not A
INVALID
All dogs are mean
Hercules is mean
therefore, Hercules is a dog.
is an example of..
All A’s are B’s
x is a B
x is not an A
INVALID
