sentence (syntactically independent grammatical unit) questioncommandstatement “this is a class in...

Sentence(syntacticallyIndependent

grammatical unit)

Question Command Statement

“This is a class

in logic.”“I enjoy logic.” “Today is

Friday.”

Argument

• Argument is an attempt to persuade someone of something, by giving reasons or evidence for accepting a particular conclusion

Premise

A premise is a statement that an argument claims will induce or justify a conclusion

How to Recognize Arguments?How to Recognize Arguments?

Conclusion Indicators

• Therefore• Hence• Thus• So• Accordingly• In consequence• Proves that• As a result• For this reason

Premise Indicators

• Since• Because• For• As• Follows from• As shown by• Inasmuch as

Argument Vs Explanation

• Premise – P• Conclusion – Q

“Q because P”

Validity

Validity refers to a relation between propositions.

Validity

• Validity never applies to any single proposition by itself.

Validity

• P -> Q• Logical Necessity• Deductive/Inductive?

Truth & Falsity

• Truth and Falsity are attributes of individual propositions.

Valid Vs True

Truth and falsity are attributes of individual propositions or statements, validity and invalidity are attributes of arguments.

Valid Arguments, True Propositions

• All mammals have lungs• All whales are mammals• Therefore all whales have lungs

Valid Arguments, False Propositions

• All four-legged creatures have wings.• All spiders have four legs.• Therefore, all spiders have wings.

Invalid Arguments, True Propositions

• If I owned all the gold in Fort Knox, then I would be wealthy.

• I do not own all the gold in Fort Knox.• Therefore, I am not wealthy

Invalid Arguments, True Premisses, False Conclusion

• If Bill Gates owned all the gold in Fort Knox, then Bill Gates would be wealthy.

• Bill Gates does not own all the gold in Fort Knox.

• Therefore Bill Gates is not wealthy

Valid Arguments, False Premisses, True Conclusion

• All fishes are mammals.• All whales are fishes.• Therefore all whales are mammals.

Invalid Arguments, False Premisses, True Conclusion

• All mammals have wings• All whales have wings.• Therefore, all whales are mammals.

Invalid Arguments, False Premisses, False Conclusion

• All mammals have wings• All whales have wings• Therefore all mammals are whales

Lessons

• When an argument is valid, and all of its premisses are true, we call it “sound”.

Lessons

• Truth or falsity of an argument’s conclusion does not by itself determine the validity or invalidity of that argument.

• The fact that an argument is valid does not gurantee the truth of its conclusion.

• If an argument is valid and its premisses are true, we may be certain that its conclusion is true also.

• If an argument is valid and its conclusion is false, not all of its premisses can be true.