Formalising Arguments Flashcards
What is a very simple example of a valid argument involving and?
P1: Brazil is in South America and Kenya is in Africa
Conc: Brazil is in South America
What is the previous argument valid?
Because it just asserts two claims, stuck together with the word ‘and’.
If the premise is true, it can only be because…
Both of those claims are true
So, in particular, the first of those claims must be what?
True
So, if the premise is true, the conclusion is…
Also true
In turn, the argument is…
Valid
All arguments with this form are what?
P1: A and B
Conc: A
Valid
What is the argument:
P1: A
P2: B
Conc: A and B
Valid
What is the issue with this argument?
P1: This morning I had tea and cake’;
Conc: ‘This morning I had tea’
The premises must be written in full sentences.
I.e., This morning I had tea and this morning I had cake
What is it reasonable to think with the sentence ‘This morning I had tea and cake’?
That I had tea and cake together at the same time, whilst the second sentence loses that implication
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?
Lose its implication that Stan and Ollie can only lift the box together, not separately.
An ‘AND’ sentence states that…
Both of the premises are true.
An ‘OR’ sentence states that…
At least one of the two sentences are true
The ‘OR’ operator gives us a simple argument form:
P1: A
Conc: A or B
Give an example of:
P1: A
Conc: A or B
P1: Cats drink milk;
Conc: Cats drink milk or Cats drink orange juice
Arguments with this form are what?
Always valid, regardless of whether the two sentences are actually true, or whether they’re related to each other at all
Is this argument form valid or invalid?
P1: A or B
Conc: A
Invalid
Why is an argument with the following form not valid?
P1: A or B
Conc: A
The premise only tells us that at least one of the two sentences are true, but it does not tell us which one
Sometimes, in ordinary language, when we say ‘OR’ in what way?
Exclusive or inclusive
What is an exclusive or?
They’re not both true:
‘The bird on the fence is either a crow or a raven’
What is an inclusive or?
We allow that one, or the other, or both options might be true:
‘It will rain on Thursday or Friday’
In logic, what is ‘OR’?
Always inclusive
There are also valid forms of argument in which we need to assert that something is?
False
Give an example of an argument that asserts that something is false.
P1: Birds eat cabbages or Birds eat insects
P2: Birds don’t eat cabbages;
Conc: Birds eat insects
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
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
What is the notation form of ‘modus ponens’?
P1: If A then B;
P2: A;
Conc: B
What is the notation form of ‘modus tollens’?
P1: If A then B
P2: B is not true;
Conc: A is not true
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
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
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
What is the symbol for:
A and B
A & B
What is the symbol for:
A or B
A V B
What is the symbol for:
It’s not true that A
¬ A
What is the symbol for:
If A then B
A → B
