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Logic and Critical Thinking > Formalising Arguments > Flashcards

Formalising Arguments Flashcards

1
Q

What is a very simple example of a valid argument involving and?

A

P1: Brazil is in South America and Kenya is in Africa
Conc: Brazil is in South America

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2
Q

What is the previous argument valid?

A

Because it just asserts two claims, stuck together with the word ‘and’.

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3
Q

If the premise is true, it can only be because…

A

Both of those claims are true

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4
Q

So, in particular, the first of those claims must be what?

A

True

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5
Q

So, if the premise is true, the conclusion is…

A

Also true

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6
Q

In turn, the argument is…

A

Valid

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7
Q

All arguments with this form are what?
P1: A and B
Conc: A

A

Valid

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8
Q

What is the argument:
P1: A
P2: B
Conc: A and B

A

Valid

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9
Q

What is the issue with this argument?
P1: This morning I had tea and cake’;
Conc: ‘This morning I had tea’

A

The premises must be written in full sentences.
I.e., This morning I had tea and this morning I had cake

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10
Q

What is it reasonable to think with the sentence ‘This morning I had tea and cake’?

A

That I had tea and cake together at the same time, whilst the second sentence loses that implication

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11
Q

What does rewriting the sentence ‘Stan and Ollie can lift this box’ to ‘Stan can lift this box and Ollie can lift this box’ do?

A

Lose its implication that Stan and Ollie can only lift the box together, not separately.

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12
Q

An ‘AND’ sentence states that…

A

Both of the premises are true.

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13
Q

An ‘OR’ sentence states that…

A

At least one of the two sentences are true

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14
Q

The ‘OR’ operator gives us a simple argument form:

A

P1: A
Conc: A or B

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15
Q

Give an example of:
P1: A
Conc: A or B

A

P1: Cats drink milk;
Conc: Cats drink milk or Cats drink orange juice

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16
Q

Arguments with this form are what?

A

Always valid, regardless of whether the two sentences are actually true, or whether they’re related to each other at all

17
Q

Is this argument form valid or invalid?
P1: A or B
Conc: A

A

Invalid

18
Q

Why is an argument with the following form not valid?
P1: A or B
Conc: A

A

The premise only tells us that at least one of the two sentences are true, but it does not tell us which one

19
Q

Sometimes, in ordinary language, when we say ‘OR’ in what way?

A

Exclusive or inclusive

20
Q

What is an exclusive or?

A

They’re not both true:
‘The bird on the fence is either a crow or a raven’

21
Q

What is an inclusive or?

A

We allow that one, or the other, or both options might be true:
‘It will rain on Thursday or Friday’

22
Q

In logic, what is ‘OR’?

A

Always inclusive

23
Q

There are also valid forms of argument in which we need to assert that something is?

A

False

24
Q

Give an example of an argument that asserts that something is false.

A

P1: Birds eat cabbages or Birds eat insects
P2: Birds don’t eat cabbages;
Conc: Birds eat insects

25
Q

How would one write the argument:
P1: Birds eat cabbages or Birds eat insects
P2: Birds don’t eat cabbages;
Conc: Birds eat insects

A

P1: A or B
P2: A is not true
Conc: B

26
Q

Why is this argument valid?
P1: A or B
P2: A is not true
Conc: B

A

Premise 1 says at least one of the two sentences is true;
Premise 2 says that A is not true;
The only option (B) must therefore be true

27
Q

What is the notation form of ‘modus ponens’?

A

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

28
Q

What is the notation form of ‘modus tollens’?

A

P1: If A then B
P2: B is not true;
Conc: A is not true

29
Q

Give an example of modus tollens

A

P1: If the dog sees a stranger then the dog will bark;
P2: The dog isn’t barking
Conc: The dog does not see a stranger

30
Q

Give an example of modus ponens

A

P1: If it is raining then the windows are wet;
P2: The windows are not wet;
Conc: It’s not raining

31
Q

By giving words symbols (notation), what is the benefit?

A

We can escape the temptation to read them as conventional English words with their common connotations

32
Q

What is the symbol for:
A and B

A

A & B

33
Q

What is the symbol for:
A or B

A

A V B

34
Q

What is the symbol for:
It’s not true that A

A

¬ A

35
Q

What is the symbol for:
If A then B

A

A → B

Logic and Critical Thinking (8 decks)

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