Logic

1. Logic HUM 200 Basic Logical Concepts Lectures taken from Copi, I., & Cohen, C. (2009). HUM200: Introduction to logic: 2009 custom edition (13th ed.). Upper Saddle River, NJ: Pearson/Prentice Hall.

2. Objectives • When you complete this lesson, you will be able to: • Define logic • Describe the different types of propositions • Recognize premise and conclusion indicators • Distinguish arguments from explanations • Differentiate between deductive and inductive arguments • Differentiate between validity and truth

3. What Logic Is • Study of methods and principles used to distinguish correct from incorrect reasoning • Use of objective criteria to evaluate arguments • The logician is interested in an argument’s form and quality

4. Propositions • Assert that something is, or is not, the case • Must be either true or false • Differ from questions, commands, and exclamations • Have a more formal form than some ordinary language sentences • “Leslie won the election” • “The election was won by Leslie” • Both make the same assertion

5. Propositions, continued • Simple proposition • Makes only one assertion • “It is raining” • Compound proposition • Contains two or more simple propositions • “The British were at the gates of Hamburg and Bremen”

6. Propositions, continued • Disjunctive (Alternate) proposition • At least one of the component propositions must be true • “Circuit courts are useful, or they are not useful” • Hypothetical (Conditional) proposition • Is false only when the antecedent is true and the consequent is false • “If God did not exist, it would be necessary to invent Him”

7. Arguments • Any group of propositions of which one is claimed to follow from the others • Linked by inference • Components • Premise • Used to support some other proposition • Conclusion • Proposition that the premises support • Example • “No one was present when life first appeared on earth.” (Premise) • “Therefore any statement about life’s origins should be considered as theory, not fact.” (Conclusion)

8. Therefore Hence So Accordingly In consequence Consequently Proves that As a result For this reason Thus For these reasons It follows that I conclude that Which shows that Which means that Which entails that Which implies that Which allows us to infer that Which points to the conclusion that We may infer Conclusion Indicators

9. Since Because For As Follows from As shown by Inasmuch as As indicated by The reason is that For the reason that May be inferred from May be derived from May be deduced from In view of the fact that Premise Indicators

10. Arguments and Explanations • Explanations appear to be arguments because they contain common indicators • Therefore is the name of it called Babel; because the Lord did there confound the language of all the earth. – Gen. 11:19

11. Deductive and Inductive Arguments • Deductive argument • Makes the claim that its conclusion is supported by its premises • Inductive argument • Claims to support its conclusion only with some degree of probability

12. Deductive and Inductive Arguments, continued • Deductive arguments • Valid argument • If its premises are true, its conclusion must be true • Invalid argument • Argument claim is incorrect • Classical logic • Techniquesbased on works of Aristotle to analyze deductive arguments • Modern symbolic logic • Mathematical symbols areusedto visualize the argument

13. Deductive and Inductive Arguments, continued • Inductive arguments • Premises support their conclusions with probability • The terms validity and invalidity do not apply • May be strengthened or weakened by additional information

14. Validity and Truth • Validity • Refers to the relationship between propositions • Does not apply to a single proposition • Truth • Asserts what really is the case • Applies only to propositions

15. Validity and Truth, continued • Example I • Valid argument with only true propositions • All mammals have lungs. • All whales are mammals. • Therefore all whales have lungs.

16. Validity and Truth, continued • Example II • Valid argument with only false propositions • All four-legged creatures have wings. • All spiders have four legs. • Therefore all spiders have wings.

17. Validity and Truth, continued • Example III • Invalid argument with only 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.

18. Validity and Truth, continued • Example IV • Invalid argument with true propositions and a 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.

19. Validity and Truth, continued • Example V • Valid argument with false premises and a true conclusion • All fishes are mammals. • All whales are fishes. • Therefore all whales are mammals.

20. Validity and Truth, continued • Example VI • Invalid argument with false premises and a true conclusion • All mammals have wings. • All whales have wings. • Therefore all whales are mammals.

21. Validity and Truth, continued • Example VII • Invalid argument with all false propositions • All mammals have wings. • All whales have wings. • Therefore all mammals are whales.

22. Validity and Truth, continued • Possible combinations

23. Validity and Truth, continued • Sound argument • Valid argument and true premises • Conclusion must be true

24. Summary • Logic • Propositions • Arguments • Premise and conclusion indicators • Explanations • Deductive and inductive arguments • Validity and truth