Deductive vs Non-Deductive Arguments 2 Chapter 3 (continued)

Deductive and Non-Deductive Arguments Deductive arguments: if the premises are true, the conclusions MUST be true (is guaranteed to be true) Non-Deductive arguments: If the premises are true, the conclusion is NOT necessarily true (not guaranteed to be true)

Overview Deductive Arguments Sound Valid Invalid Valid Arg: sound or unsound Invalid Arg: always unsound

Valid Deductive Argument Valid: the conclusion MUST be true ASSUMING the premises are true Invalid: not valid: assuming the premises are true, the conclusions COULD be false.

Sound Deductive Arguments Sound: valid argument AND premises are true Unsound: not valid or premises are not true All invalid arguments are unsound When we want to prove something we want sound arguments

Valid with true premises (Sound***) Valid with false premises Examples Valid with true premises (Sound***) Valid with false premises Invalid with true premises Invalid with false premises

Examples of Deductive Arguments Mathematical Proofs: E.g. Geometry Physics Proofs: E.g. Newtonean physics Moral / Political Arguments

Geometry and Pythagorean Theorem Axioms of Geometry A straight line segment can be drawn joining any two points. Any straight line segment can be extended indefinitely in a straight line. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center. All right angles are congruent. any straight line and a point not on it, there is only one straight line which passes through that point and never intersects the first line.   Pythagorean Theorem: (a2+b2=c2) area of both square triangle side are equal to area of hypothenuse Pythagoras’ proof is a long deductive argument, where his theorem is a conclusion and the axioms are the premises. All theorems of geometry are proven by deductive arguments

Moral / Political Arguments Libertarian Argument: Taxation is slavery Taxation = Sdfsdf So, taxing citizens is slavery.

Deductive Logic (Ch. 5)

Chapter 5: Deductive Logic Valid Argument Form 1 Chapter 5: Deductive Logic

Plan for Today Deductive (Valid) Arguments: the conclusion MUST be true assuming the premises are true. Today: Review Deductive Argument Forms from Last Week Today: Go Over Invalid Arguments Forms (Fallacies)

From Ordinary Language to Argument Form Remove Non-Claims Identify Indicator Words Add Implicit Premises Identify Simple or Complex Argument Form Form ONLY

Modus Ponens Ordinary Language Argument Form If the economy is bad, then church attendance will increase. The economy is in bad. So, church attendance will increase Argument 1. If the economy is bad (p), then church attendance will increase (q) 2. The economy is bad (p) 3. So, church attendance will increase (q) Form Modus Ponens If p, then q p So, q

Modus Tollens Ordinary Language Argument Form If I am in New Orleans, I must be in the United States. But, I’m not in the United States. So, I can’t be in New Orleans. Argument 1. If I am in New Orleans (p), then I must be in the United States (q) 2. I am not in the United States (not q) 3. So, I am not in New Orleans (not p) CONTENT + FORM Form Modus Tollens If p, then q Not q So, not p

Categorical Syllogism Ordinary Language All fish are sea-creatures. And, since all sea-creatures are animals, it must be that all fish are animals Argument 1. All fish (A) are sea-creatures (B) 2. All sea-creatures (B) are animals (C) 3. So, all fish (A) are animals (C) Form Categorical Syllogism All A are B All B are C All C are B

Disjunctive Syllogism Ordinary Language Either Michael has brown hair or blue eyes. I know he doesn’t have brown hair. So, he has blue eyes Argument 1. Either Michael has brown hair (p) or Michael has blue eyes (q). 2. I know he doesn’t have brown hair (not p) 3. So, he has blue eyes (q) Form Disjunctive Syllogism p or q not p So, q

Chain Argument Ordinary Language Argument Form The Chain Argument … 1. If I get a job this summer (p), then I will have lots of money(q) 2. If I have lots of money (q), then I will impress my friends (r) 3. So, if I get a job this summer (p), then I will impress my friends (r) Form The Chain Argument If p then q If q then r So, if p then r

Examples Either I’m in NYC or I’m in Vancouver. I’m not in Vancouver. So, I’m in NYC. All pigs are animals. All animals can fly. So, All pigs can fly. If I get a tattoo, I’ll be cool. If I’m cool then I’ll be successful. So, if I get a tattoo, I’ll be successful. If I go to Vegas, I’ll be rich. I will never be rich. So, I’ll not go to Vegas. Disjunctive Syllogism Categorical Syllogism Chain Argument Modus Tollens

Summary: Valid Deductive Forms The Chain Argument If p then q If q then r So, if p then r Modus Ponens If p, then q p So, q Modus Tollens If p, then q Not q So, not p Disjunctive Syllogism p or q not p So, q Categorical Syllogism All A are B All B are C All C are B