Deductive vs. Inductive Arguments Jason Chang Critical Thinking

Lecture Outline Two types of reasoning Deductive arguments Inductive arguments Common misconceptions Determining whether deductive or inductive

Two Types of Reasoning Reasoning Using information, evidence, or claims(s) to arrive at further information, evidence, or claim(s)

Two Types of Reasoning (P1) John’s fingerprints are on the murder weapon. (P2) John’s DNA was found at the murder scene. (P3) The murder victim owed John money. Therefore, John probably committed the murder.

Two Types of Reasoning (P1) Triangle OAH is a right triangle (P2) O = 3 (P3) A = 4 (P4) A2 + B2 = C2 Therefore, H = 5 O = 3 A = 4

Two Types of Reasoning Necessary reasoning Probabilistic reasoning (P1) Triangle OAH is a right triangle (P2) O = 3 (P3) A = 4 (P4) A2 + B2 = C2 Therefore, H = 5 (P1) John’s fingerprints are on the murder weapon. (P2) John’s DNA was found at the murder scene. (P3) The murder victim owed John money. Therefore, John probably committed the murder. Necessary reasoning Probabilistic reasoning

Two Types of Reasoning Necessary reasoning Deductive reasoning Probabilistic reasoning Inductive reasoning

Deductive Arguments Premises Deductive argument Conclusion An argument in which it is thought that the conclusion necessarily follows from the premises

Deductive Arguments (P1) All men are mortal. (P2) Socrates is a man. Therefore, (C) Socrates is mortal.

Deductive Arguments (P1) Either John or Sally committed the murder. (P2) We know that Sally did not commit the murder. Therefore, (C) John committed the murder.

Deductive Arguments (P1) A = B (P2) B = C Therefore, (C) A = C

Inductive Arguments Premises Inductive argument Conclusion An argument in which it is thought that the conclusion probably follows from the premises

Inductive Arguments (P1) She stayed up all night partying. (P2) She drank heavily and had a hangover in the morning. (P3) She did not eat breakfast. Therefore, (C) She probably will not ace the test.

Inductive Arguments (P1) It did not snow in San Jose on July 4 in 2014. (P2) It did not snow in San Jose on July 4 in 2013. (P3) In fact, for the past 100 years, it did not snow in San Jose on July 4. Therefore, (C) Next July 4, it will probably not snow in San Jose.

Years it did not snow in San Jose on July 4 Inductive Arguments (P3) In fact, for the past ??? years, it did not snow in San Jose on July 4. Therefore, (C) Next July 4, it will probably not snow in San Jose. Certainty Confidence that it will not snow next July 4 Years it did not snow in San Jose on July 4

Common misconceptions

Common misconceptions Deductive and inductive arguments must have true premises FALSE!

Common misconceptions (P1) All women are rich. (P2) Socrates is a woman. Therefore, (C) Socrates is rich.

Common misconceptions (P1) In my life, all the dogs I have witnessed are red. Therefore, (C) All dogs are red.

Common misconceptions Deductive and inductive must have “good” reasoning FALSE!

Common misconceptions (P1) Triangle OAH is a right triangle (P2) O = 3 (P3) A = 4 (P4) A2 + B2 = C2 Therefore, H = 5 (P1) Triangle OAH is a right triangle (P2) O = 3 (P3) A = 4 (P4) A2 + B2 = C2 Therefore, H = 7

Common misconceptions (P1) In my life, I have known only one person from New Zealand. (P2) She was not intelligent. Therefore, (C) All New Zealanders lack intelligence.

Determining whether deductive or inductive

Determining whether deductive or inductive Method #1: Indicator words Deductive indicators “Necessarily” “Must” “Certainly” “Absolutely” Inductive indicators “Probably” “Likely” “Plausible” “Reasonable to conclude”

Determining whether deductive or inductive Method #2: Type of reasoning Sometimes it is useful simply to observe the strength the conclusion is thought to follow from the premises.

Determining whether deductive or inductive (P1) All men are mortal. (P2) Socrates is a man. Therefore, (C) Socrates is mortal. DEDUCTIVE (P1) Some fruits are green objects. (P2) Some fruits are green apples. Therefore, (C) Some fruits are green apples. ???

Determining whether deductive or inductive Sometimes it is difficult to distinguish between: An inductive argument A deductive argument with bad reasoning (P1) Some fruits are green. (P2) Some fruits are green apples. Therefore, (C) Some fruits are green apples.

Determining whether deductive or inductive Method #3: Argument form Notice the argument form This is the easiest and fastest way to determine whether an argument is deductive or inductive

Determining whether deductive or inductive Common deductive argument forms Argument from mathematics (except from statistics) Argument from definition Syllogism (categorical, hypothetical, disjunctive) Modus ponens and modus tollens Scientific argument that applies general law

Determining whether deductive or inductive Common inductive argument forms Prediction Generalization Causal inference Argument from analogy Argument from authority Scientific argument of observation to general law