Formal Logic Flashcards
For any proposition A we can form the negation of that proposition, which simply asserts what?
That A is not true
How do we write negation?
‘It’s not true that A’, or ‘A is not true’
What is the negation of ‘Birds eat cabbages’?
‘It’s not true that birds eat cabbages.’
What two things must the sentence and its negation be?
Inconsistent and exhaustive
Define inconsistent.
Incompatible - both cannot be true
Define exhaustive.
No other possibilities - cannot both be false
What aren’t the sentences ‘wild mushrooms are delicious’ and ‘wild mushrooms are dangerous’?
Not inconsistent - they can both be true
What aren’t the sentences ‘That bird is a crow’ and ‘That bird is a raven’?
Not exhaustive - they can both be false
Give an example of a conditional.
‘If it’s raining then I should take my umbrella’
For any two proposition A and B, how do we write it as a conditional?
If A then B
‘If A then B’ is what?
A proposition
What is a proposition?
Something that can be true or false
Whether a particular sentence with the form ‘If A then B’ is true or false depends on what?
Whether A and B are true or false
What is the ‘IF’ part of the sentence called?
The antecedent
What should you think of the antecedent as?
A condition that may or may not be satisfied
What is the ‘THEN’ part of the sentence called?
The consequent
What should you think of the consequent as?
Something that supposedly follows from that condition
What does the condition ‘If A then B’ not say?
That A is true, and it doesn’t say that B is true
What does the conditional ‘If A then B’ assert?
The relationship between A and B
Sometimes we use an ‘If… Then…’ sentence when A does what to B?
When A causes or influences B.
E.g. ‘If it rains then I’ll stay at home’
‘If you drink more coffee then you won’t sleep well’
Sometimes we use ‘If… then…’ to show what?
That the direction of causation goes from B to A
E.g. ‘If my keys aren’t here then I left them at home’
‘If these fingerprints match then you’re guilty’
Sometimes there no direct what between A and B?
Sometimes there’s no direct cause or physical relation between them at all
E.g. ‘If the thermometer goes up then I’ll buy ice-cream’
What is the best way to think of ‘If A then B’?
‘Knowing that A was true would tell you that B is true’
Give the formalised version of modus ponens argument.
P1: If A then B
P2: A
Conc: B
Give the formalised version of modus tollens argument.
P1: If A then B
P2: B is not true
Conc: A is not true
Give an example of modus tollens.
P1: If there’s an elephant in the room then we can see an elephant
P2: It’s not true that we can see an elephant
Conc: It’s not true that there’s an elephant in the room
Is the following argument valid? What is this called?
P1: If A then B
P2: B
Conc: A
This is invalid and is called affirming the consequent
Is the following argument valid? What is this called?
P1: If A then B
P2: A is not true
Conc: B is not true
This is invalid and is called denying the antecedent
Give an example of affirming the consequent.
P1: If it’s raining then the windows are wet
P2: The windows are wet
Conc: It’s raining
Give an example of denying the antecedent.
P1: If it’s raining then the windows are wet
P2: It’s not true that it’s raining
Conc: It’s not true that the windows are wet
What are logic operators sometimes also called?
Logical connective
What is the logical operator for A and B?
&
What is the logical operator for A or B?
V
What is the logical operator for If A then B?
=>
What is the logical operator for It’s not true that A?
¬
What is the difference between arithmetic operators and logical operators?
The latter don’t act on numbers but sentences
We can think of sentences here as what?
Truth values
What are truth values?
Whether or not a proposition is true or false
How do we write truth values?
T for true; F for false
Given two propositions ‘A’ and ‘B’ what sentence can we form with conjunction?
A&B
A&B is true when?
When both A and B are true
If we know the truth value of either A or B, then we can do what?
Tell whether A&B is true or false.
What are the four possibilities we have to consider with A&B?
T T | T
T F | F
F T | F
F F | F
What does this do?
A B | A&B
—————
T T | T
T F | F
F T | F
F F | F
Show that the sentences are not related or relevant to each other
Give two propositions ‘A’ and ‘B’ what sentence can we form with disjunction?
AVB
A V B is true when what?
At least one of A and B are true
So, if we know the truth value of A, we know what?
Whether A V B is true
What are the four possibilities we have to consider with A V B?
T T | T
T F | T
F T | T
F F | F
What does this do?
A B | AVB
—————
T T | T
T F | T
F T | T
F F | F
Show that A V B is inclusive and that the truth of A V B does not tell us of the truth of the individual propositions
Given the proposition ‘A’ we can form what with negation?
¬A
¬A is true when?
A is false
What are the two possibilities we have to consider with ¬A
T | F
F | T
Given two propositions A and B, we can form what with the conditional?
A=>B
What are the four possibilities we have to consider with A=>B?
T T | T
T F | F
F T | T
F F | T
