Argument and Analysis
Arguments

An argument is a set of claims put forward as
reasons to believe some statement.
Arguments

An argument is a set of claims put forward as
reasons to believe some statement.
The reasons are given in the premisses
 The statement they support is the conclusion

Arguments

An argument is a set of claims put forward as
reasons to believe some statement.
The reasons are given in the premisses
 The statement they support is the conclusion

An argument
If children like ice-cream, and Bob is a child,
then Bob likes ice-cream
Arguments

An argument is a set of claims put forward as
reasons to believe some statement.
The reasons are given in the premisses
 The statement they support is the conclusion

An argument in standard form
P1
Children like ice-cream
P2
Bob is a child
C
Bob likes ice-cream
Arguments

Two kinds of arguments

Deductive - conclusion doesn’t tell us more about the
world than the premisses
Arguments

Two kinds of arguments

Deductive - conclusion doesn’t tell us more about the
world than the premisses

Inductive – does claim to tell us more
Arguments

Two kinds of arguments

Deductive - conclusion doesn’t tell us more about the
world than the premisses


If children like ice-cream, and Bob is a child, then
Bob likes ice-cream
Inductive – does claim to tell us more
Arguments

Two kinds of arguments

Deductive - conclusion doesn’t tell us more about the
world than the premisses


If children like ice-cream, and Bob is a child, then
Bob likes ice-cream
Inductive – does claim to tell us more

All the swans I have seen are black. Therefore all
swans are black
Deductive Arguments

Validity

If the premisses are true then the conclusion must
be true

Note: if the premisses are false then the conclusion may
be false
Deductive Arguments

Validity

If the premisses are true then the conclusion must
be true


Note: if the premisses are false then the conclusion may
be false
Soundness

The argument is valid and the premisses are true

Note: the conclusion must be true
Deductive Arguments

Logic

Some arguments are valid just because of their form
All men are mortal
Socrates is a man
Socrates is mortal
Deductive Arguments

Logic

Some arguments are valid just because of their form
All men are mortal
Socrates is a man
Socrates is mortal
All A are B
C is an A
C is B
Deductive Arguments

Not Logic

Some arguments are not valid just because of their
form
Socrates is a bachelor
Socrates is unmarried.
Deductive Arguments

Not Logic

Some arguments are not valid just because of their
form
Socrates is a bachelor
Socrates is unmarried
A is a B
A is C
Deductive Arguments
Disproving Validity


Method 1 — The Counterexample Method
Deductive Arguments
Disproving Validity


Method 1 — The Counterexample Method
(i)
Determine the pattern of the argument to be
criticised
Deductive Arguments
Disproving Validity


Method 1 — The Counterexample Method
(i)
Determine the pattern of the argument to be
criticised
Construct a new argument with:
(ii)
(a) the same pattern
(b) obviously true premises; and
(c) an obviously false conclusion.
Deductive Arguments
Disproving Validity


Method 1 — The Counterexample Method
Example
If God created the universe then the theory of evolution is wrong
The theory of evolution is wrong
God created the universe
Deductive Arguments
Disproving Validity


Method 1 — The Counterexample Method
Example
If A then B
B
A
Deductive Arguments
Disproving Validity


Method 1 — The Counterexample Method
Example
If Stephen is a wombat then Stephen is a mammal
Stephen is a mammal
Stephen is a wombat
T
T
F!
Deductive Arguments
Disproving Validity


Method 2 — Invalidating Possible Situations
Deductive Arguments
Disproving Validity


Method 2 — Invalidating Possible Situations
Describe a possible situation in which the
premises are obviously true and the conclusion is
obviously false
Deductive Arguments
Disproving Validity


Method 2 — Invalidating Possible Situations
Example
(Fallacy of Affirming the Consequent)
If my car is out of fuel it won’t start
My car won’t start
My car is out of fuel
Deductive Arguments
Disproving Validity


Method 2 — Invalidating Possible Situations
Example
(Fallacy of Affirming the Consequent)
My car will indeed not start without fuel (it is a fuel-driven car) and the
electrical system needed to start the car has been taken out for repairs
(so it won't start). Yet the car has a full tank of petrol.
Deductive Arguments
Disproving Validity


Method 2 — Invalidating Possible Situations
Example
(Fallacy of Denying the Antecedent)
If the committee addresses wilderness values it must address
naturalness
It will not address wilderness values
It need not address naturalness
Deductive Arguments
Disproving Validity


Method 2 — Invalidating Possible Situations
Example
(Fallacy of Denying the Antecedent)
Wilderness value involves, amongst other things, naturalness (Federal legislation
actually defines 'wilderness value' this way). Moreover, the Committee's terms
of
reference do not include consideration of wilderness value (so it
won't address
it). Yet the Committee is explicitly formed to consider
naturalness (to feed their
findings into those of other Committees, so that
a joint finding can be made
regarding wilderness values)
Deductive Arguments
Fallacies


Are errors which look a lot like valid arguments
Deductive Arguments
Fallacies


Are errors which look a lot like valid arguments
Example
(Fallacy of Affirming the Consequent)
Form:
If P then Q
Q
P
Deductive Arguments
Fallacies


Are errors which look a lot like valid arguments
Example
(Fallacy of Affirming the Consequent)
Form:
Resembles:
If P then Q
If P then Q
Q
P
P
Q
(Modus Ponens)
Deductive Arguments
Fallacies


Are errors which look a lot like valid arguments
Example
(Fallacy of Denying the Antecedent)
Form:
If P then Q
~P
~Q
Deductive Arguments
Fallacies


Are errors which look a lot like valid arguments
Example
(Fallacy of Denying the Antecedent)
Form:
Resembles:
If P then Q
If P then Q
~P
~Q
~Q
~P
(Modus Tollens)
Inductive Arguments
Two kinds



Argument from Analogy
Inference to Best Explanation
Inductive Arguments

Argument from Analogy
Consider a watch. A watch exhibits (a) complexity of parts; (b) suitability
to fulfil a certain function (i.e. telling the time); and (c) its complexity is
what enables it to fulfil this function. These three features are extremely
unlikely to have come about by accident. No one on seeing a watch would
think it the product of chance. Even seeing it for the first time, one would
conclude that it is the product of design by some intelligent being.
But many things in nature we observe (e.g. the eye) are similarly complex,
fulfil a function (e.g. seeing) and their complexity enables them to fulfil
this function.
So it is reasonable to suppose that they too are made by an intelligent
being
Inductive Arguments

Argument from Analogy
P1
P2
P3
C
A watch has (a), (b), (c).
The world has (a), (b), (c).
Watches require a watch-maker
The world requires a world-maker
Inductive Arguments

Argument from Analogy
P1
P2
P3
C
The Object has properties P1,P2,…,Pn
The Analogue also has P1,P2,…,Pn
The analogue has property P
Therefore the object has property P
Inductive Arguments

Argument from Analogy (as a deduction)
P1
P2
P3
P4*
P
C
The Object has properties P1,P2,…,Pn
The Analogue also has P1,P2,…,Pn
The analogue has property P
If A & B share P1,P2,…,Pn they share
Therefore the object has property P
Inductive Arguments
Evaluating Arguments from Analogy


Are the premisses true?
Inductive Arguments
Evaluating Arguments from Analogy



Are the premisses true?
Is the analogy strong?
Inductive Arguments
Evaluating Arguments from Analogy



Are the premisses true?
Is the analogy strong?

Are P1,P2,…,Pn relevant to P?
Inductive Arguments
Evaluating Arguments from Analogy



Are the premisses true?
Is the analogy strong?


Are P1,P2,…,Pn relevant to P?
Are there disanalogies?
Inductive Arguments
Evaluating Arguments from Analogy



Are the premisses true?
Is the analogy strong?



Are P1,P2,…,Pn relevant to P?
Are there disanalogies?
Is the conclusion too strong?
Inductive Arguments

Inference to Best Explanation
You return home to find your door broken and some valuable items
missing. This cries out for explanation. Possible explanations include:
(1)A meteorite struck your door and vaporised your valuables,
(2) friends are playing a joke on you,
(3) a police Tactical Response Group entered your house mistakenly, and
(4) you were robbed.
Explanation 4 seems the best, so you conclude you were robbed.
Inductive Arguments

Inference to Best Explanation
P1
P2
C
Phenomenon A is observed
Explanation X explains A and does so
better than any rival explanation
X is the case
Inductive Arguments
Evaluating Inference to Best Explanation


Is there anything that needs explaining?
Inductive Arguments
Evaluating Inference to Best Explanation



Is there anything that needs explaining?
What is the ‘best’ explanation?

Evaluate for Strength
Inductive Arguments
Evaluating Inference to Best Explanation



Is there anything that needs explaining?
What is the ‘best’ explanation?

Evaluate for Strength

Does it really explain?
Inductive Arguments
Evaluating Inference to Best Explanation



Is there anything that needs explaining?
What is the ‘best’ explanation?

Evaluate for Strength


Does it really explain?
Is it more widely applicable?
Inductive Arguments
Evaluating Inference to Best Explanation



Is there anything that needs explaining?
What is the ‘best’ explanation?

Evaluate for Strength



Does it really explain?
Is it more widely applicable?
Is it as simple as possible?
Inductive Arguments
Evaluating Inference to Best Explanation



Is there anything that needs explaining?
What is the ‘best’ explanation?

Evaluate for Strength




Does it really explain?
Is it more widely applicable?
Is it as simple as possible?
Is it conservative of prior beliefs?
Inductive Arguments
Evaluating Inference to Best Explanation



Is there anything that needs explaining?
What is the ‘best’ explanation?

Evaluate for Strength





Does it really explain?
Is it more widely applicable?
Is it as simple as possible?
Is it conservative of prior beliefs?
Have we checked all the reasonable explanations?