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

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?

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
How would one write the argument: P1: Birds eat cabbages or Birds eat insects P2: Birds don't eat cabbages; Conc: Birds eat insects
P1: A or B P2: A is not true Conc: B
26
Why is this argument valid? P1: A or B P2: A is not true Conc: B
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
What is the notation form of 'modus ponens'?
P1: If A then B; P2: A; Conc: B
28
What is the notation form of 'modus tollens'?
P1: If A then B P2: B is not true; Conc: A is not true
29
Give an example of modus tollens
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
Give an example of modus ponens
P1: If it is raining then the windows are wet; P2: The windows are not wet; Conc: It's not raining
31
By giving words symbols (notation), what is the benefit?
We can escape the temptation to read them as conventional English words with their common connotations
32
What is the symbol for: A and B
A & B
33
What is the symbol for: A or B
A V B
34
What is the symbol for: It's not true that A
¬ A
35
What is the symbol for: If A then B
A → B