Abelard 1150 AD

1. A Short & Imprecise History of Logic Abelard 1150 AD Chrysippus 260 BC William of Ockham 1310 David Hume 1750 C.S Peirce 1860 Gottlob Frege 1880 Alfred Tarski 1950 2000 Years ! Aristotle 360 BC Euclid 300 BC Galen 150 William of Sherwood 1240 George Boole 1840 John Venn 1870 Kurt Goedel 1950

2. Logic is the science of reasoning, proof, thinking, or inference. • Logic allows us to analyze a piece of reasoning and determine whether it is correct or not. • We use Logic to determine soundness, validity, and cogency of an argument. Logic is the science of correct argument. Logic: What is it?

3. On Argument “An argument is a connected series of statements intended to establish a proposition”

4. Why do we care about argument? Intelligence Analysts Argue for a Living!

5. 3 Components to an Argument 2. Inference 1. Premises 3. Conclusion

6. The Premise • Explicitly stated propositions which can be inferred to a justified conclusion. • Boy bands are useless. • Useless things must be blasted into the cold, dark, emptiness of space.

7. The Conclusion • End state of an argument, drawn from previously established premises. • Boy bands must be blasted into the cold, dark emptiness of space.

8. The Inference • A process (or form) which allows “movement” to Conclusion. • Not a statement • You can’t see it • Justifies your case for blasting the boy bands into space.

9. Conclusion Indicators • therefore • wherefore • thus • consequently • we may infer • accordingly • we may conclude • it must be that • for this reason • so • entails that • hence • it follows that • implies that • as a result

10. Premise Indicators • since • as indicated by • because • for • in that • may be inferred from • as • given that • seeing that • for the reason that • inasmuch as • owing to

11. Premise Indicators Expectant mothers should never use recreational drugs, since the use of these drugs can jeopardize the development of the fetus. The use of recreational drugs can jeopardize the development of the fetus. Therefore, expectant mothers should never use recreational drugs.

12. Premise Indicators It is vitally important that wilderness areas be preserved, for wilderness provides essential habitat for wildlife, including endangered species, and it is a natural retreat from the stresses of daily life. Wilderness provides essential habitat for wildlife, including endangered species, and it is a natural retreat from the stresses of daily life. Therefore, it is vital that wilderness areas be preserved.

13. Conclusion Indicators Not only does the national defense depend upon the space program, but most any NASA initiative will more than pay for itself through technological spin-offs. Further, at current funding levels the program cannot fulfill its anticipated potential. Consequently, the space program deserves increased expenditures in the years ahead.

14. Conclusion Indicators When individuals voluntarily abandon property, they forfeit any expectation of privacy in it that they might have had. therefore, a warrantless search or seizure of abandoned property is not unreasonable under the Fourth Amendment.

15. Basic Types of Reasoning Deductive GeneralParticular Inductive ParticularGeneral Abductive Evidence/FactsBest Explanation

16. Abductive Reasoning Inference to the best explanation. • Concerned with singular events & corresponding evidence • No conditional or universal statements involved

17. Inductive Reasoning • Specific  General • a form of reasoning that makes generalizations based on individual instances “An observant man can learn by an accurate and systematic examination of all that came in his way. From a drop of water, a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other. So all life is a great chain, the nature of which is known whenever we are shown a single link of it.” SH This ice (any ice I have ever touched) is cold.  All ice is cold. This billiard ball (and 100/100 billiard balls struck with a cue) moves when struck with a cue.  All billiard balls struck with a cue, move.

18. Deductive Reasoning • General  Specific • Reasoning which moves from given statements (premises), which are assumed to be true, to conclusions, which must be true if the premises are true. * If one is a U.S. Marine, then one is rifleman. * Mike is a U.S. Marine. * Mike is a rifleman

19. Propositional Logic • Simplest construct for deduction, most illustrative of basics • Based on statements which are either true or false • Statements which have “truth value” • These are propositions: • The Russian navy deploys SLBMs • Bob Blair enjoys prancing to the sounds of a Pan flute. • A Gaboon Viper is not harmful. • Robert Mugabe is not nice. • Arnold Schwarznegger starred in Terminator

20. Not Propositions • Where is Ankara? (question) • Let’s go to the theater. (proposal) • I suggest you get contacts. (suggestion) • Turn off the TV. (command) • Fantastic! (exclamation)

21. Operators V “or” Disjunction “and”Conjunction “if…then” Conditional “therefore” Conclusion ~ “not” Negation

22. The Russian navy deploys SLBMs R • Mr. Hansen wears Brazilian undergarments. S • A Gaboon Viper is dangerous. V • Robert Mugabe is a kind and gentle soul. M • Arnold Schwarznegger starred in Terminator. Y

23. The 19 Rules of Inference 10. De Morgan's Theorem (De M) 11. Commutation (Com.) 12. Association (Assoc.) 13. Distribution (Dist) 14. Double Negation (D.N.) 15. Transposition (Trans.) 16. Material Implication (M. Imp.) 17. Material Equivalence (M. Equi) 18. Exportation (Exp.) 19. Tautology (Taut.) 1. Disjunctive Syllogism (D.S.) 2. Modus Ponens (M.P.) 3. Modus Tollens (M.T.) 4. Hypothetical Syllogism (H.S.) 5. Constructive Dilemma (C.D) 6. Absorption (Abs.) 7. Simplification (Simp.) 8. Conjunction (Conj.) 9. Addition (Add.)

24. 1. Disjunctive Syllogism (D.S.) 2. Modus Ponens (M.P.) 3. Modus Tollens (M.T.)

25. Disjunctive Syllogism Either you saw Terminator, or you saw Cloverfield You didn’t see Terminator. Therefore, you saw Cloverfield. P v Q ~P  Q

26. Modus Ponens Ifyou saw Terminator, thenyou saw Arnold Schwarznegger. You saw Terminator. Therefore, you saw Arnold Schwarznegger. P  Q P Q

27. Modus Tollens Ifyou saw Terminator, thenyou saw Arnold Schwarznegger. You did not see Arnold Schwarznegger. Therefore, you did not see Terminator. P  Q ~Q  ~P

28. -Either Akula # 1 or Victor # 4 will deploy.The Akula will not deploy.Therefore, the Victor will deploy. Modus Ponens Modus Tollens Disjunctive None of the above

29. If a nation is a member of NATO, it deploys troops to operations.Romania is a member of NATO.Therefore, Romania deploys troops to operations. Modus Ponens Modus Tollens Disjunctive None of the above

30. If Backfire airframe # 7 launches, it will communicate with its base.No communications with base occurred.Therefore, Backfire airframe #7 didn’t launch. Modus Ponens Modus Tollens Disjunctive None of the above

31. If Kosovo declares independence, Serbia will protest to the U.N.Kosovo declared independence.Serbia will protest to the U.N. Modus Ponens Modus Tollens Disjunctive None of the above

32. If an apple has worms, we can’t make calvadosout of it. There are worms in the apple.We must make mezcal instead. Modus Ponens Modus Tollens Disjunctive None of the above

33. Formal Fallacies

34. Affirming the Consequent Fallacy Ifyou saw Terminator, thenyou saw Arnold Schwarznegger. You saw Arnold Schwarznegger. Therefore, you saw Terminator. P  Q Q  P

35. Denying the Antecedent Fallacy Ifyou saw Terminator, thenyou saw Arnold Schwarznegger. You did not see Terminator. Therefore, you did not see Arnold Schwarznegger. P  Q ~P  ~Q

36. Soundness & Validity • A Valid argument has proper form. • A Sound argument is valid, has true premises, and thus, a true conclusion. So: A Sound argument is always Valid; but a Valid argument is not always Sound.

38. Inductive Strength • This barrel contains 100 apples. • Three apples selected at random were found to be ripe. • Therefore, probably all 100 apples are ripe. • This barrel contains 100 apples. • Eighty apples selected at random were found to be ripe. • Therefore, probably all 100 apples are ripe. True Premises + Strong Argument = Cogent Argument Strength is a matter of degrees (probabilistic) Premises need to be comprehensive

39. Why We Need Logic

40. Now do you love Logic? Yes No Abstain