Professional Development

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PD 20
Engineering Workplace Skills: Developing Reasoned Conclusions

Unit 04 Understanding Arguments

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“That's just your opinion”

?

The Earth is sphere-like

That’s just your opinion

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Aren’t all opinions equally good?

Politically, maybe...

...but not from a logical point of view

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Aren’t all opinions equally good?

Assume that nobody’s opinion is wrong in a debate.

All opinions are correct

Your opinion is wrong

Smith

Jones
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Aren’t all opinions equally good?
No! Not all opinions are equally good.
Assume that nobody’s opinion is wrong in a debate. If Smith is right, then Smith must concede that Jones is right…

Which is to say that Smith is wrong.
All opinions are correct Your opinion is wrong

Smith

Jones
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Aren’t all opinions equally good?
Global warming... Claim: Humans are contributing to global warming
Numerous scientific studies suggest that humans are causing an increase in greenhouse gasses

Only a sciencehating capitalist would disagree

Smith

Jones
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What is an Argument?

An argument is a set of premises which are given to support a conclusion

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Example

Jairaj

Premise 1

All uWaterloo Engineering students are hard workers. Jairaj is a uWaterloo Engineering student. Conclusion Hence, Jairaj is a hard worker.
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Premise 2

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Example

Premise 1

All uWaterloo Engineering students are hard workers.

Premise 2

Jairaj is a uWaterloo Engineering student.

Conclusion

Hence, Jairaj is a hard worker.

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Types of arguments
Deductive Arguments Ampliative Arguments

Premise 1 if true Premise 2

Premise 1 true Premise 2

Conclusion

true

Conclusion

false true

- Truth is guaranteed

- Defeasible - Premises lend credence

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Evaluating Deductive Arguments
Deductive Arguments

Premise 1 Premise 2

Validity:
If the premises are true, then the conclusion must also be true

Conclusion

Soundness:
An argument is sound if (1) It is a valid argument, and (2) Its premises are true

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All sound arguments are valid arguments
If it is sound, it is also valid

Sound Arguments

Valid Arguments

It can be valid but not be sound

But not all valid arguments are sound arguments
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Examples

Example 1
P1 P2 C All cats are animals Boots is a cat

true true true

Example 2
P1 P2 C All cats are dogs Boots is a cat

false true false

Hence, Boots is an animal

Hence, Boots is a dog

Valid and Sound

Valid but not Sound

- Start with true premises - Distinguish between form and content
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Examples
Let S, P, and B be variables
Example 1
P1 P2 C All S are P B is a S Hence, B is a P

Example 2
P1 P2 C All S are P B is a S Hence, B is a P

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How do we evaluate a deductive argument?

1) Analyze the argument form

Sound Internal Arguments

2) Evaluate the truth of the premises and conclusion

External

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Analyzing Argument Forms
Logical Vocabulary
The logical form of an argument depends on the logical vocabulary used in the premises and conclusion

Logical Vocabulary

...and... Alice is in Toronto and Hamish is in Ottawa. ...or... Either I got the job or Bob got the job. If Anish is in Montreal then he is in Quebec. If...then... not... It is not the case that chlorine is a garnish.

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Analyzing Argument Forms

Once we understand the logical structure of the argument, we can look for counter examples
Counter Example Try and come up with an argument where:

(1) The logical form is the same

(2) The premises are obviously true

(3) The conclusion is obviously false

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Example of a Counter Example
(P1) If the bear patrol is working, then there won’t be any bears around.

Argument

(P2) There aren’t any bears around.

(C) Hence, the bear patrol is working.

Counter Example

(P1) If I’m the richest man in the world, then there won’t be any bears around me.

true true

(P2) There aren’t any bears around me.

(C) Hence, I’m the richest man in the world.

false

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Summary
Not all opinions, beliefs, or claims are equal Claims need to be backed up with good arguments There are different types of arguments Evaluating deductive arguments is a two-part process: 1. Analyze logical form Check the logical vocabulary A good deductive argument is truth-preserving 2. Evaluate truth Evaluating truth is an external process
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Logic Courses at uWaterloo

PHIL 240 Introduction to Formal Logic

PHIL 342 Non-Classical Logics

PMATH 330 Introduction to Mathematical Logic

PMATH 432 First Order Logic and Computability

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