Reason & ArgumentLecture 3

Lecture Synopsis

1.Recap: validity, soundness & counter-examples, 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.

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

Disjunctive Syllogism:

X or Y

Not – X

So Y

Also a valid instance:

X or Y

Not–Y

So X

Errata

(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

(1) Recap

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.

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)

(1) Recap

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.

Exceptions

We are not worried about straightforward cases like this:

• If everyone is ready, then we should begin the meeting.

• Everyone is ready.

• So 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) Should

(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.