Reason & Argument
Lecture 3
Lecture Synopsis
1. Recap: validity, soundness & counterexamples, induction.
2. Arguing for a should conclusion.
3. Complications with using should.
(1) Recap: validity &
soundness
Last week:
Features of a good argument (n.b. technical
terms!):
Validity: an argument is valid if and only if when
the premises are true, the conclusion is true.
Soundness: an argument is sound if and only if
it is valid & its premises are true.
(1) Recap
Testing & Criticising Arguments
Thus, to show an argument is faulty, you can
either show that:
1. It is invalid: the conclusion does not follow
from the premises.
2. It is unsound: one or more of its premises is
false.
(Notice that if an argument is invalid, then it is
automatically unsound.)
(1) Recap
How to...
Testing for & criticising Validity:
Look at the form or pattern of the argument
Does it exemplify a syllogism (always valid)?
Or a fallacy (always invalid)?
OR: Can you produce a counter-example?
i.e. an instance of the argument with true premises
but a false conclusion.
Soundness:
Try to think of a counter-example
A case that shows a premise is false.
(1) Recap
Valid & Invalid Patterns
Valid (Syllogisms):
Modus Ponens
Modus Tollens
Hypothetical Syllogism
Disjunctive Syllogism (and many others...)
Invalid (Fallacies):
Affirming the Consequent
Denying the Antecedent (and many others)
(1) Recap
Errata
Disjunctive Syllogism:
X or Y
Not – X
So Y
Also a valid instance:
X or Y
Not–Y
So X
(1) Recap
Errata
Affirming the consequent
•(S1)
If he is a thief, then he would look uncomfortable.
•(S2)
He looks uncomfortable.
•(S3)
So he is a thief.
Named after the second premise! (The same goes for
denying the antecedent)
Invalid because: there are other antecedents (‘reasons
why’) for the consequent ‘he would look uncomfortable’.
(1) Recap
Counter-examples
For soundness:
Think of a case that shows a premise is false.
For validity:
Show how the same form or pattern of reasoning,
when employed with different (true) premises, can
lead to a false conclusion.
(1) Recap
Induction
•
Every zebra we have ever observed has black and white
stripes.
•
So all zebras have black and white stripes.
Induction is ampliative, unlike deduction, i.e. it goes beyond
or adds to the information in the premises/observations
Strictly invalid, thus it carries no guarantee of the truth of its
conclusion (cf. Hume’s famous ‘problem of induction’)
Arguments can still be inductively strong (supported by
many observations)
Terminology
Sentences or premises can be conditionals
(with antecedents & consequents), conjunctions
(conjuncts) and disjunctions (disjuncts).
Premises can be true or false.
(Only) arguments can be valid or invalid, sound
or unsound. (e.g. premises can’t be valid or
invalid, sound or unsound)
(1) Recap
Summary
You have learned the meaning of validity &
soundness and other technical terms.
You have learned how to use these terms in
constructing & criticising arguments.
Now you need to practice identifying and testing
for them!
Tutorials: try all the exercises in McKay.
(2) Arguing for a ‘should’ conclusion
A special case:
An argument is typically designed to establish
a matter of fact.
Sometimes however, you want to establish
that someone should or ought to think
something or to act in some way.
In some of these cases, the logic is different.
(2) Should
Exceptions
We are not worried about straightforward cases
like this:
•If
everyone is ready, then we should begin the meeting.
•Everyone
•So
is ready.
we should begin the meeting.
(2) Should
Invalid examples
•
John should do the work his boss asked him to
do.
•
John can only do his work if he stops playing
Tetris.
•
So John should stop playing Tetris.
(2) Should
Invalid examples
•
Paul wants to get a promotion.
•
Paul will get a promotion if he works really hard.
•
So Paul should work really hard.
(2) Should
Invalid examples
•
George wants to become the company’s CEO.
•
The only way to become the company’s CEO
is to invest heavily in company stock.
•
So George should invest heavily in company
stock.
(2) Should
Common Features
A premise about what someone wants or should
achieve.
A premise about how that thing can be attained or
achieved.
A conclusion about what we should do.
What makes a good ‘should’ argument?
Can such arguments be valid?
(2) Should
The Success Condition
Will the suggested action achieve the outcome?
e.g. working hard may not lead Paul to get a
promotion.
(Perhaps someone else is already a shoo-in)
The ‘SC’ here:
Working really hard will lead to Paul getting a
promotion.
(2) Should
The Optimal Means Condition
Is the action you think Paul should perform, the
best way for him to achieve the outcome?
e.g. working really hard might not be the best
way to get a promotion.
In this case, the ‘OMC’ would be:
Working really hard is the best way to get
a promotion.
(2) Should
The EJM Condition
Does the end justify the means?
•Ringo
wants a nuclear warhead.
•The
best way to get a nuclear warhead is to find a black
market arms dealer.
•Ringo
should find a black market arms dealer.
The EJM here:
All things considered, acquiring a nuclear warhead is
better than not acquiring one.
(2) Should
A ‘Should’ Pattern
Combining these three caveats or conditions yields a
promising pattern for should arguments:
•Success
Condition (SC): Doing Y will achieve X.
•Optimal
Means (OMC): Doing Y is the best way to
achieve X.
•End
Justifies Means (EJM): All things considered,
doing Y and achieving X is better than not achieving X.
(2) Should
A Valid Schema
•
SC: P’s doing Y will achieve X.
•
OMC: Person P’s doing Y is the best way to achieve X.
•
EJM: All things considered, P’s doing Y and achieving X is better than not
achieving X.
•
(To secure validity, we need to add: If OMC, EJM and SC, then P should
do Y)
•
Therefore: P should do Y.
•
When evaluating should arguments, ask yourself whether each
condition is fulfilled.
(2) Should
Example
We should execute murderers, because doing so will prevent them
from killing again:
•SC
(stated): Executing murderers will prevent them from killing
again.
•OMC
(unstated): Executing murderers is the best way to prevent
them from killing again.
•EJM
(unstated): Executing murderers and preventing them from
killing again is better than not preventing them from killing again.
•Conclusion:
We should execute murderers.
(2) Should
Example
You should buy a lottery ticket, because you won’t win
unless you play.
•SC
(unstated): If you buy a lottery ticket, you will win.
•OMC
(directly implied by the stated premise): Buying a
lottery ticket is the best (the only) way to win.
•EJM
(not stated): Buying a lottery ticket and winning is
better than not winning.
•Conclusion:
•
You should buy a lottery ticket.
That reconstruction has a glaringly false premise.
Here is another try.
(2) Should
A more charitable
interpretation...
•
SC (unstated): If you buy a lottery ticket, you will have
a chance to win.
•
OMC (directly implied by the stated premise): Buying
a lottery ticket is the best (the only) way to have a
chance to win.
•
EJM (not stated): Buying a lottery ticket and having a
chance to win is better than not having a chance to
win.
•
Conclusion: You should buy a lottery ticket.
(2) Should
Example
We should release almost all prisoners, because doing so is the
only way to cut down on prison costs.
•SC
(unstated): Releasing almost all prisoners will cut down on
prison costs.
•OMC
(directly implied by the stated premise): Releasing almost all
prisoners is the best (the only) way to cut down on prison costs.
•EJM
(not stated): Releasing almost all prisoners and cutting down
on prison costs is better than not cutting down on prison costs.
•Conclusion:
We should release almost all prisoners.
(2) Arguing for a ‘Should’ Conclusion
Summary
In some cases, the logic of ‘should’ is different from
standard patterns of validity (the patterns are strictly
invalid).
An easy way to construct a strong ‘should’ argument
is to follow the pattern: SC, OMC, EJM, therefore...
And evaluating it is easy too: are these conditions
present and correct?
(3) Complications
Using ‘should’ can get complicated...
Uncertainty
The lottery/job interview case.
Balancing probabilities - risks and
rewards.
Evaluative Terms
What You Have Learned
Today
1. Recap
Arguments are valid/invalid, sound/unsound; premises are
true/false.
2. Arguing for a should conclusion.
Optimal Means Condition (OMC), End-Justifies-the-Means (EJM),
Success Condition (SC), the valid schema.
3. Complications
Uncertainty, Evaluative Terms.