Validity, Soundness, Strength, Cogency Jason Chang Critical Thinking

Lecture Outline I.Background II.Deductive argument terminology III.Inductive argument terminology

Background We have been focusing on two types of arguments Deductive arguments Inductive arguments

Background The labels “deductive” and “inductive” refer to the type of argument NOT whether the argument has good reasoning NOT whether the argument has true premises

Background Deductive argument with bad reasoning (P1) All U.S. presidents have been men. (P2) I am a man. Therefore, I was a U.S. president. Inductive argument with bad reasoning (P1) The murder victim owed John money. (P2) John was in town on the night of the murder. Therefore, John probably committed the murder.

Background Deductive argument with false premises (P1) All men are cheaters. (P2) Mary is a man. Therefore, Mary is a cheater. Inductive argument with false premises (P1) It has snowed in San Jose for the past 100 days. Therefore, It will probably snow tomorrow.

Background We will now introduce labels that refer to the quality of the argument Whether the argument is “good” or “bad”

Labels for “good” and “bad” deductive arguments

Deductive argument terminology Definition A valid argument is a deductive argument with good reasoning The conclusion follows necessarily from the premises VALID

Deductive argument terminology Definition An invalid argument is a deductive argument with bad reasoning The conclusion does not follow necessarily from the premises INVALID

Deductive argument terminology (P1) All men are mortal. (P2) Socrates is a man. Therefore, Socrates is mortal. (P1) If the 49ers win, I will be happy. (P2) If I am happy, I will dance. Therefore, If the 49ers win, I will dance. Both are valid arguments – the conclusion follows necessarily from the premises

Deductive argument terminology (P1) All X are Y. (P2) Z is an X. Therefore, Z is a Y. (P1) If X, then Y. (P2) If Y, then Z. Therefore, If X, then Z. Are these valid arguments?

Deductive argument terminology Validity concerns whether the argument has good reasoning NOT whether the premises are actually true

Deductive argument terminology It is possible to have a valid argument with false premises (P1) If it rains, frogs will fall from the sky. (P2) If frogs fall from the sky, the world will end. Therefore, If it rains, the world will end. OH NO!

Deductive argument terminology Possibilities for valid arguments TRUE PREMISESFALSE PREMISES TRUE CONCLUSION FALSE CONCLUSION (P1) All men are mortal. (P2) Socrates is a man. Therefore, Socrates is mortal. (P1) All wines are soft drinks. (P2) Coke is a wine. Therefore, Coke is a soft drink. (P1) If it rains, frogs will fall from the sky. (P2) If frogs fall from the sky, the world will end. Therefore, If it rains, the world will end. ?

Deductive argument terminology A valid argument is an argument in which the conclusion necessarily follows from the premises This means that there is zero possibility that the conclusion is false if all the premises are true. (If this was possible, the conclusion would not follow necessarily)

Deductive argument terminology (P1) All students who ace the exam will pass the class. (P2) You passed the class. Therefore, You must have aced the exam. Is it possible to envision a scenario in which the premises are true but conclusion false? If so, the conclusion does not follow necessarily from the premises. The argument is INVALID.

Deductive argument terminology Possible to envision true premises and false conclusion? (P1) If you love him, you will stay with him. (P2) You chose to stay with him. Therefore, You love him. INVALID

Deductive argument terminology Recap of major points A valid argument is a deductive argument in which the conclusion follows necessarily from the premises Validity does NOT concern whether the premises are actually true The conclusion of a valid argument must be true if the premises are true

Deductive argument terminology Definition A sound argument is a valid argument with all true premises SOUND

Deductive argument terminology Definition An unsound argument is a deductive argument that: (1) Is invalid, OR (2) Has false premises, OR (3) Both 1 and 2 UNSOUND

Deductive argument terminology (P1) If you are a student at this school, you attend a school in California. (P2) You are a student at this school. Therefore, You attend a school in California. Conclusion follows necessarily from premises Premises are true The argument is SOUND

Deductive argument terminology VALIDINVALID SOUND (P1) (P2) Therefore, (C) X UNSOUND (P1) (P2) Therefore, (C) (P1) (P2) Therefore, (C)

Labels for “good” and “bad” inductive arguments

Inductive argument terminology Definition A strong argument is an inductive argument with good reasoning The conclusion follows probably from the premises STRONG

Inductive argument terminology Definition A weak argument is an inductive argument with bad reasoning The conclusion does not follow probably from the premises WEAK

Inductive argument terminology (P1) In 98 of the 100 trials conducted, all rats who received the drug Nitosol developed cancer. Therefore, The drug probably causes cancer in rats. This is a strong argument – the conclusion follows probably from the premises

Inductive argument terminology (P1) In 8 of the 100 trials conducted, all rats who received the drug Nitosol developed cancer. Therefore, The drug probably causes cancer in rats. This is a weak argument – the conclusion does not follow probably from the premises

Can a strong argument have false premises? Inductive argument terminology

Yes! Strength concerns whether the argument has good reasoning – NOT whether the premises are actually true (P1) In all 100 trials, the red pen has floated to the ceiling when let go. Therefore, Next time I let go, the pen will probably float to the ceiling.

Inductive argument terminology Possibilities for strong arguments TRUE PREMISESFALSE PREMISES PROBABLY TRUE CONCLUSION PROBABLY FALSE CONCLUSION (P1) All dogs I have seen cannot fly. Therefore, Probably all dogs can’t fly. (P1) All women I have met are over 5 feet tall. Therefore, The next woman I meet will be over 5 feet tall. (P1) All U.S. presidents have died in office Therefore, The next U.S. president will die in office. ?

Just like for validity… We can determine whether an argument is strong by envisioning the premises to be true and then asking a question about the conclusion. Inductive argument terminology

(P1) I met 3 Parisians while visiting Paris. (P2) All 3 were smokers. Therefore, All Parisians are smokers. Is it possible to envision a scenario in which the premises are true but conclusion probably false? If so, the conclusion does not follow probabilistically from the premises. The argument is WEAK.

Inductive argument terminology Strong Weak (P1) In 50 of the 100 trials conducted, all rats who received the drug Nitosol developed cancer. Therefore, The drug probably causes cancer in rats. (P1) In 98 of the 100 trials conducted, all rats who received the drug Nitosol developed cancer. Therefore, The drug probably causes cancer in rats. (P1) In 8 of the 100 trials conducted, all rats who received the drug Nitosol developed cancer. Therefore, The drug probably causes cancer in rats. Unlike validity, there are degrees of strength

Inductive argument terminology Definition A cogent argument is a strong argument with all true premises The conclusion follows probably from the premises COGENT

Inductive argument terminology Definition An uncogent argument is an inductive argument that: (1) Is weak, OR (2) Has false premises, OR (3) Both 1 and 2 UNCOGENT

Deductive argument terminology STRONGWEAK COGENT (P1) (P2) Therefore, (C) X UNCOGENT (P1) (P2) Therefore, (C) (P1) (P2) Therefore, (C)