W2: Argument mapping and evaluation

What are complex arguments?

A set of arguments consisting of intermediate conclusion(s) which act as the premise to support a main conclusion at the end

What are the 2 conditions for a good argument?

1. Its premises must be true

2. Its premises must be connected to its conclusion in the right way

How is this a bad argument: “Canberra is the capital of Australia. Therefore, Tokyo is the capital of Japan.”

The premise does not support the conclusion (even though it is true)

What is a good argument NOT the same as??

Good ≠ persuasive (bad arguments can also persuade)

Validity and soundness (no definition)

What are the conditions for a valid argument?

3 ways to phrase:

1. impossible for its conclusion to be false while ALL its premises are true (aka conclusion must follow all premises)

2. impossible for ALL premises to be true while the conclusion is false

3. it IS contradictory if the premises are true while the conclusion is false

What does a valid argument ‘force’ you to do?

A valid argument forces you to accept the conclusion IF you accept the the premises (if not you contradict yourself; incoherent)

Going back to the Canberra and Tokyo example, is that argument valid?

No, the conclusion possibly being false (Tokyo is not the capital of Japan) does not contradict the premise being true (Canberra is the capital of Aus)

What are the 3 rules/forms of valid arguments? (just identify, no need any background knowledge)

1. Modus Ponens (affirming the antecedent)

2. Modus Tollens (denying the consequent)

3. BARBARA

What is Modus Ponens?

1. If A, then B (if Bob studied, he will pass the exam)

2. A (Bob studied)

3. ∴ B (So, he will pass the exam) 

What is Modus Tollens?

1. If A, then B (if Bob studied, he will pass the exam)

2. Not B (Bob did not pass the exam) 

3. ∴ Not A (So, Bob did not study)

What is BARBARA?

1. All Fs are G (all mammals are warm blooded)

2. All Hs are F (cats are mammals) 

3. ∴ All Hs are G (cats are warm blooded) 

What are the 2 rules/forms of invalid arguments?

1. Affirming the consequent

2. Denying the antecedent

What is the format for affirming the consequent?

1. If A, then B (if Bob studied, he will pass the exam)

2. B (Bob passed the exam)

3. ∴ A (So, Bob studied)

• Bob could have passed the exam through other means

What is the format for denying the antecedent?

1. If A, then B (if Bob studied, he will pass the exam)

2. Not A (Bob did not study) 

3. ∴ Not B (He will not pass the exam) 

• He could still pass the exam without studying

Suppose all the sub-arguments in a complex arguments are valid, does this mean the argument as a whole is valid too?

Yes

Suppose one of the sub-arguments in a complex arguments is invalid, does this mean the argument as a whole is invalid too?

No, if at least one of the routes of premise>int conclusion is valid, the main conclusion is still valid (still have to check the validity of all routes)

What are the 2 types of arguments?

1. Deductive arguments

2. Inductive arguments

What are deductive arguments?

Arguments that aim for guaranteed certainty; validity (e.g. mathematical and logical proofs)

What are inductive arguments?

Arguments that are invalid, but aims for probable support and argument strength

What are the two common types of inductive arguments?

1. Inductive generalisation

2. Inference to the best explanation (IBE) (“Abduction”)

What is inductive generalisation?

Arguments that generalise to all/most cases from past experience/majority stats

What 2 aspects are important for inductive generalisation?

Sample size and quality (for representativeness)

What is this argument called: “Each morning, the sun has risen out of the east. So, the sun will rise out of the east tomorrow” 

An argument by analogy

What does the format of arguments by analogy look like?

1. a has feature F

2. b resembles a, in some relevant way

3. ∴ b has feature F

What is the difference between an inductive generalisation and an analogy based on the previous example?

• An argument from analogy moves from observed cases to a claim about one particular new case (because that case is similar to the others)

• An inductive generalisation moves from observed cases to a claim about all or most cases (“the sun will always rise from the east”)

In what setting is arguments by analogy commonly used in?

Moral and legal debates

But what is good about inductive arguments in general?

They are strong

What is the general consensus to a strong inductive argument?

If the premises make it hard to believe the conclusion could be false

What is IBE?

An argument with

1. Some observed evidence

2. A hypothesis that explains them

What do the premises and conclusion act as?

• Premises: observations/explanations

• Conclusion: hypothesis

What are the 3 types of explanations?

1. Causal

2. Constitutive

3. Teleological

What are the 3 types of explanations based on?

1. Causal - based on mechanisms (“the bridge collapsed because of the earthquake”)

2. Constitutive - based on definitions (“17 is a prime no. as it is divisible by itself and 1”)

3. Teleological - based on an agent’s goal (“Bob is studying in order to do well for his exam”)

What makes an explanation better than another?

A simple explanation with fewer surprising assumptions is better

What are the 2 conditions for a sound argument?

1. It is valid

2. Its premises are ALL true

What do you do when you spot an invalid argument?

Look to bridge the gap between the premise(s) and conclusion by coming up with a hidden premise (refer to ipad notes)

What is the relationship between hidden premises, validity and soundness?

Adding an extra hidden premise can improve the validity of an invalid argument, BUT doesn’t improve soundness IF the premises are false

Objection (no definition)

What are the 2 ways to criticise an argument? (// what makes an argument good)

1. Show that at least one of its premises is false

2. Show that the premises are not connected to the conclusion in the right way

How do you prove the falsity of a premise?

Disagree with it using another separate argument

How do you display it on an argument map?

The conclusion of the separate argument points towards the premise you’re trying to disagree with

How do you prove that the premises and conclusion are not connected correctly?

Through principles of validity/inductive strength/alternative reasoning

How do you display it on an argument map?

The alternative reasoning points towards the middle of the conclusion arrow

What is an objection to an objection called?

A rebuttal

How do you display it on an argument map?

The rebuttal point point towards the objection point