Formal Logic Flashcards

1
Q

For any proposition A we can form the negation of that proposition, which simply asserts what?

A

That A is not true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

How do we write negation?

A

‘It’s not true that A’, or ‘A is not true’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is the negation of ‘Birds eat cabbages’?

A

‘It’s not true that birds eat cabbages.’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What two things must the sentence and its negation be?

A

Inconsistent and exhaustive

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Define inconsistent.

A

Incompatible - both cannot be true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Define exhaustive.

A

No other possibilities - cannot both be false

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What aren’t the sentences ‘wild mushrooms are delicious’ and ‘wild mushrooms are dangerous’?

A

Not inconsistent - they can both be true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What aren’t the sentences ‘That bird is a crow’ and ‘That bird is a raven’?

A

Not exhaustive - they can both be false

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Give an example of a conditional.

A

‘If it’s raining then I should take my umbrella’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

For any two proposition A and B, how do we write it as a conditional?

A

If A then B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

‘If A then B’ is what?

A

A proposition

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is a proposition?

A

Something that can be true or false

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Whether a particular sentence with the form ‘If A then B’ is true or false depends on what?

A

Whether A and B are true or false

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is the ‘IF’ part of the sentence called?

A

The antecedent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What should you think of the antecedent as?

A

A condition that may or may not be satisfied

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the ‘THEN’ part of the sentence called?

A

The consequent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What should you think of the consequent as?

A

Something that supposedly follows from that condition

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What does the condition ‘If A then B’ not say?

A

That A is true, and it doesn’t say that B is true

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

What does the conditional ‘If A then B’ assert?

A

The relationship between A and B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Sometimes we use an ‘If… Then…’ sentence when A does what to B?

A

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’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Sometimes we use ‘If… then…’ to show what?

A

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’

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Sometimes there no direct what between A and B?

A

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’

23
Q

What is the best way to think of ‘If A then B’?

A

‘Knowing that A was true would tell you that B is true’

24
Q

Give the formalised version of modus ponens argument.

A

P1: If A then B
P2: A
Conc: B

25
Give the formalised version of modus tollens argument.
P1: If A then B P2: B is not true Conc: A is not true
26
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
27
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
28
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
29
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
30
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
31
What are logic operators sometimes also called?
Logical connective
32
What is the logical operator for A and B?
&
33
What is the logical operator for A or B?
V
34
What is the logical operator for If A then B?
=>
35
What is the logical operator for It's not true that A?
¬
36
What is the difference between arithmetic operators and logical operators?
The latter don't act on numbers but sentences
37
We can think of sentences here as what?
Truth values
38
What are truth values?
Whether or not a proposition is true or false
39
How do we write truth values?
T for true; F for false
40
Given two propositions 'A' and 'B' what sentence can we form with conjunction?
A&B
41
A&B is true when?
When both A and B are true
42
If we know the truth value of either A or B, then we can do what?
Tell whether A&B is true or false.
43
What are the four possibilities we have to consider with A&B?
A B | A&B --------------- T T | T T F | F F T | F F F | F
44
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
45
Give two propositions 'A' and 'B' what sentence can we form with disjunction?
AVB
46
A V B is true when what?
At least one of A and B are true
47
So, if we know the truth value of A, we know what?
Whether A V B is true
48
What are the four possibilities we have to consider with A V B?
A B | AVB --------------- T T | T T F | T F T | T F F | F
49
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
50
Given the proposition 'A' we can form what with negation?
¬A
51
¬A is true when?
A is false
52
What are the two possibilities we have to consider with ¬A
A | ¬A ----------- T | F F | T
53
Given two propositions A and B, we can form what with the conditional?
A=>B
54
What are the four possibilities we have to consider with A=>B?
A B | A=>B --------------- T T | T T F | F F T | T F F | T