Pass Facilitator Answer Sheet

PASS FACILITATOR ANSWER SHEET

Logic questions

Analysing arguments for validity

This exercise is fun and should help students develop their scientific writing techniques and will help deconstruct multiple choice questions. We can also use the answers in the session to show some descriptive statistics.

Time: 5-10 minutes for questionnaire, then roughly 10 mins to go through answers, and 10 mins to discuss.

Procedure:

- The questions should be done individually and then the scores tallied quickly (The quick answer key is at the end of this document).

- One PASS facilitator should go to each of the students and tally the data (on the tally sheet provided) and display the tabulated and/or graphed data on the white board for the class to see.

- Meanwhile the other PASS facilitator can work through the problems with the group with the help of the long answer key.

A good argument should be convincing. An argument is a set of statements consisting of premises (the data/information) and a conclusion (inferred from the data).You should find your self believing the claim, or at least finding the conclusion reasonable. This entails several things:

·  that the premises are acceptable or reasonable (likely to be true)

·  that the evidence or reasons are relevant to the claim

·  that the reasons provide sufficient grounds to lead us to accept the claim.

These things are based on logic. Logic is the analysis and appraisal of arguments. The best introduction to logic is to DO some logic problems, give them a try – DON’T WORRY most people get a lot of them wrong.

Each problem gives you premises (data/information) and asks which conclusion follows logically. Don't worry about whether the premises are true; instead, ask yourself, "If these premises WERE true, then what else would HAVE to be true?"

1. All humans are mortal.
Socrates is human.
So ???

{1} - Socrates is mortal. (CORRECT ANSWER)
{2} - Socrates is Greek.
{3} - None of these validly follows.

2. Some cave dwellers use fire.
All who use fire have intelligence.
So ???

{ 1 } - All who have intelligence use fire.
{ 2 } - Some cave dwellers have intelligence.
{ 3 } - All cave dwellers have intelligence.
{ 4 } - None of these validly follows.

1 This is invalid (try plugging in "calculus" for "..."):

All who use ... have intelligence.
So all who have intelligence use ....

2 Right! If SOME of them use fire, and ALL who do this have intelligence, then SOME of them have intelligence.

It might be that they ALL have intelligence. But we can't conclude this from the premises, since we only know that SOME of them use fire.

3 "All" in the conclusion is too strong. Maybe only a few cave dwellers use fire -- and only these few have intelligence.

4 No, we can draw a conclusion.

3. If you overslept, you'll be late.
You aren't late.
So ???

{ 1 } - You didn't oversleep.
{ 2 } - You're late.
{ 3 } - You did oversleep.
{ 4 } - None of these validly follows.

1 Correct, the premise states that you are not late, therefore you must not have overslept

2 Huh? The second premise says that you aren't late!

3 Given the premises, "You did oversleep" has to be false.

4 No, we can draw one of the conclusions.

4. No one held for murder is given bail.
Smith isn't held for murder.
So ???

{ 1 } - Smith is given bail.
{ 2 } - Smith isn't given bail.
{ 3 } - Smith is innocent.
{ 4 } - None of these validly follows.

1 Maybe Smith isn't given bail -- because maybe he's held for something else (like kidnapping) for which bail is denied. Or maybe he's not held for anything at all.

2 Maybe he's held for a minor offence and so is given bail

3 Are you his lawyer?

4 We can't tell from the premises whether he is given bail. For all we know, he might be a kidnapper and the law might deny bail to kidnappers.

5. No court that suppresses evidence is impartial.
Some courts subject to political pressure suppress evidence.
So ???

{ 1 } - Some courts subject to political pressure aren't impartial.
{ 2 } - No courts subject to political pressure are impartial.
{ 3 } - Some courts subject to political pressure are impartial.
{ 4 } - None of these validly follows.

1 By the second premise, there are courts subject to political pressure that suppress evidence. By the first premise, these courts aren't impartial. So some courts subject to political pressure aren't impartial.

2 No" in the conclusion is too strong. Maybe some courts subject to political pressure are honest and impartial -- and resist the political pressure.

3 This conclusion might be true. But we can't prove it from our premises!

4 No, we can draw one of the conclusions.

6. Every revolution is a trade disruption.
Some trade disruptions cause financial anxiety.
So ???

{ 1 } - All trade disruptions cause financial anxiety.
{ 2 } - Some revolutions cause financial anxiety.
{ 3 } - Some revolutions don't cause financial anxiety.
{ 4 } - None of these validly follows.

1 We can't conclude this from the premises. The second premise has "Some."

2 Not necessarily! The second premise tells us only that SOME trade disruptions cause financial anxiety. Those that do this need not be revolutions.

3 We can't conclude this from the premises. We know that SOME (at least one) trade disruption causes financial anxiety. But, for all we know, maybe ALL of them cause financial anxiety.

4 Given our premises, we can't draw any of these conclusions.

7. Anyone who has just lost a lot of blood is likely to faint.
No one who is likely to faint is a safe pilot.
So ???

{ 1 } - Everyone who has just lost a lot of blood is a safe pilot.
{ 2 } - No one who has just lost a lot of blood is a safe pilot.
{ 3 } - All safe pilots have just lost a lot of blood.
{ 4 } - None of these validly follows.

1 No! Such people might faint!

2 By the first premise, if you just lost a lot of blood then you might faint. By the second premise, if you might faint then you wouldn't make a safe pilot. So if you just lost a lot of blood then you wouldn't make a safe pilot. You might faint!

3 No! Such pilots might faint!

4 No, we can draw one of the conclusions.

8. If there’s knowledge, then either some things are known without proof

or we can prove every premise by previous arguments infinitely.
We can't prove every premise by previous arguments infinitely.
There's knowledge.
So ???

{ 1 } - Some things are known without proof.
{ 2 } - Everything that's known is provable.
{ 3 } - There's no knowledge.
{ 4 } - None of these validly follows.

1 Aristotle (the first logician) used this to argue that every argument ultimately rests on unproven premises.

2 The premises prove the opposite of this!

3 Huh? The third premise says that there's knowledge!

4 No, we can draw one of the conclusions.

9. No person desiring to help others is reluctant to make sacrifices.
Some masochists aren't reluctant to make sacrifices.
So ???

{ 1 } - Some masochists don't desire to help others.
{ 2 } - All masochists desire to help others.
{ 3 } - Some masochists desire to help others.
{ 4 } - None of these validly follows.

1 We can't conclude this from the premises. Maybe ALL masochists desire to help others

2We can't conclude this from the premises.

3 Not necessarily! The second premise tells us that SOME masochists aren't reluctant to make sacrifices. These masochists might not care about others. They might make sacrifices just because they like to do so. The premises don't tell us that they desire to help others.

4Given our premises, we can't draw any of these conclusions.

This one is difficult!

10. Only language users employ generalizations.
Not a single animal uses language.
At least some animals reason.
So ???

{ 1 } - Not all reasoning beings employ generalizations.
{ 2 } - Only reasoning beings employ generalizations.
{ 3 } - No reasoning beings employ generalizations.
{ 4 } - None of these validly follows.

1 John Stuart Mill used this to argue that reasoning doesn't require generalizations (statements using "all" or "no"). We could rephrase the conclusion as "Some reasoning beings don't employ generalizations." This one is difficult!

2 To draw this conclusion, we'd need a further universal premise linking reasoning beings with language users or with animals.

3 "No" in the conclusion is too strong. Notice that the last premise is about SOME reasoning beings.

4 No, we can draw one of these conclusions.

You just finished the pretest that I give to my logic class on their first day.

Most people who haven't studied logic get about half the problems wrong. Untrained logical intuitions tend to be unreliable. A logic course can sharpen your logical intuitions and teach you various ways to test whether reasoning is valid.

I designed this pretest for a friend in psychology who wanted to test sex-differences in reasoning. Despite the common belief that females are less logical than males, my friend found that both groups did equally well.