1) Quiz due tonight (Wednesday night)! Check Canvas this p.m.
2) Submit homework assignments via lecture page on Canvas. (Yes, the reverse of what we originally told you. But your life will be easier now: you'll submit everything via the lecture page.)
PLAN FOR TODAY
1) Brief review, validity and soundness, deductive vs. inductive
Focus on common mistakes in homework
2) Brief intro to modus ponens (not Otis ponens... he bites)
We will revisit this (and other inference rules) in lecture, but learning MP will help you make arguments with hidden premises valid
3) Examples from the homework, Lesson 3.1 (just one or two)
Small group discussion & class discussion
Look at the examples I've picked but remember, I take requests
4) Examples from homework, Lesson 3.2
Focus on Part B, your answers to the question
Small group discussion & class discussion: evaluating arguments
Refer to the two tips I list below & review the method for running a reductio
Lesson 3.1
Stuff to cover:
TWO OF THE MOST IMPORTANT TERMS YOU WILL LEARN IN THIS CLASS. YES I AM YELLING.
1) Validity (sufficiency): Assuming the premises are true, the conclusion MUST be true
*FORM, NOT CONTENT
*TRUTH VALUE OF PREMISES IS IRRELEVANT
This is a valid deductive argument:
P1) If the moon is made of green cheese then I'm a monkey's uncle
P2) The moon is made of green cheese
C) I'm a monkey's uncle
Side note - How to be friends with philosophers, Part 2
In Part 1, I complained about the common and improper use of the phrase "begging the question."
*Eye twitch*
Like "begging the question," while you're in this class you should treat "valid" as a technical term
Valid refers to the logical relationship between the premises and conclusion in a deductive argument.
Given this, the following phrases make no sense:
"That's a valid point"
"That premise is valid"
"You have a valid concern"
Exception: You may say "That is a valid inference."
2) Soundness: The argument is valid and the premises are actually true.
*SOUND ENTAILS VALID
Related: there is no such thing as an invalid, sound argument
No need to evaluate an invalid argument for soundness.
Think of it like that sign at the amusement park:
Validity is like being 42" tall.
If you're 42" tall, we'll check to see if you have any other conditions that preclude getting on the ride.
Similarly, if we determine an argument is valid, we'll check to see if it's sound (if the premises are true).
Invalidity is like being less than 42" tall.
If you're less than 42" tall, it's pointless to check whether anything else prohibits you from riding. You can't get on the ride.
Similarly, if we determine an argument is invalid, it's pointless to check for soundness; it can't be sound (by definition).
Terms, continued:
Deductive arguments: Valid +/- sound, or invalid
GUARANTEED CONCLUSIONS
Inductive arguments: Strong vs. weak, invalid by definition
PROBABLE CONCLUSIONS
REPEAT AFTER ME: INDUCTIVE ARGUMENTS ARE INVALID BY DEFINITION
Valid argument forms: examples
(Don't be scared of formal logic!)
Note: We are not going to go over these in discussion (except modus ponens) but you should refer back to these pictures when you are trying to figure out a) Whether an argument is valid, or b) How to make an argument valid.
Invalid inferences (aka, formal fallacies): examples
Method for determining validity/invalidity:
1) Assume all the premises are true
2) See if the conclusion MUST be true*
*Tip: try to find a counterexample, i.e., an instance in which all of the premises are true, but the conclusion is false. If you find a counterexample, boom. The argument is invalid.
Homework Qs for class discussion
Part A
Is this argument valid or invalid? Sound or unsound?
4. All limimus eat pamumas. Frank is a limimu. Therefore,
Frank eats pamumas.
Part B (Groups):
(a) Is the argument valid or invalid?
(b) If it isn't valid, explain why not
(c) If the argument is inductive, say whether it is a strong, medium, or weak inductive argument (your answer to 'b' will help you decide).
11. Every time I come home, the downstairs neighbors' dogs bark. When I come home tonight they'll bark.
12. If you're not sure how to do this homework assignment you should see your TA. If you plan on seeing your TA but can't make their office hours, you should see if they can meet you at another time. Mary isn't sure how to do this homework and can't make office hours, therefore Mary should see if her TA can meet at another time.
13. Everyone likes ice cream. Some people like Donald Trump. Therefore, some people like ice cream and Donald Trump.
14. Some people like ice cream and some people like Donald Trump. Therefore, some people like both ice cream and Donald Trump.*
*Let's talk about the form of this argument
P1) Some animals are cats
P2) Some animals are dogs
C) Therefore, some animals are both cats and dogs
Good reasoning?
Lesson 3.2
Stuff to cover:
Enthymemes (hidden premises)
Making inductive arguments deductively valid
(Related: Principle of charity <-- This term should be familiar)
Tip #1: To make an argument with hidden premises deductively valid, MODUS PONENS IT.
Many (most, for our purposes) arguments can be reconstructed in modus ponens form, e.g.:
7. Aspartame is bad for you because it isn't natural.
P1) Aspartame isn't natural
P2) If something's not natural, it's bad for you <-- enthymeme
C) Aspartame is bad for you
Tip #2: You can use any of the four valid inference rules I explained above (MP, MT, DS, UI) to construct a valid argument. STICK WITH THOSE. BE WARY OF OTHERS.
Reductio ad absurdum, or reductio, for short
(Latin: "Reduce to absurdity")
Running a reductio:
1) Assume ("for the sake of argument") all the premises of an argument are true
2) Show that absurd and/or contradictory results follow.
If you show that an argument has absurd implications (a successful reductio) you show there's good reason to doubt the conclusion
Keep Tip #1, Tip #2, and the method for running a reductio in mind when we evaluate these arguments:
Homework, Part B
Increasingly, moral philosophers and others agree that the practice of factory farming animals for meat is morally wrong (and indefensible). If you disagree, suggest a reason or argument in defense of the practice then make your argument valid by supplying the hidden premise (enthymeme). If you agree that factory farming isn't morally defensible, support your conclusion with a short argument and make your argument valid. Be prepared to present your arguments in your recitation section.
GROUP EXERCISE
1) Fill in the missing premise that makes the argument valid
2) Evaluate the truth value of the premises
Arguments for
Argument 1: I like it.
(P1) Meat tastes good and eating it gives me pleasure.
(C) Eating factory farmed meat is morally permissible.
Argument 2: We need to eat meat.
(P1) We need to eat meat.
(C) Therefore, eating factory farmed meat is morally
permissible.
Argument 3: Other animals eat meat.
(P1) Animals eat other animals and we don't say it's morally
wrong.
(C) Therefore, it's morally permissible for humans to eat
meat.
Argument 4: The historical argument
(P1) Historically humans have always eaten meat.
(C) It is morally permissible to eat factory farmed
meat.
Arguments against
Argument
1: Wrong to kill innocents
P1)
It is wrong to kill innocent animals
C)
Therefore, factory farming is wrong
Argument
2: The Golden Rule
P1)
We wouldn't treat people like that
C)
Therefore, factory farming is wrong
Argument
3: Suffering is wrong
P1)
Factory farming causes animal suffering
C)
Therefore, factory farming is wrong
Argument
4: It's unhealthy
P1)
Factory farming creates health risks for humans
C)
Therefore, factory farming is wrong
***Extra credit (one bonus point) for the ambitious. The answer to the question at the end of this case is "no." The answer is no because you can run a reductio on the computer scientist's argument. Explain.
A computer scientist announces that he's constructed a computer program that can play the perfect game of chess: he claims that this program is guaranteed to win every game it plays, whether it plays black or white, with never a loss or a draw, and against any opponent whatsoever. The computer scientist claims to have a mathematical proof that his program will always win, but the proof runs to 500 pages of dense mathematical symbols, and no one has yet been able to verify it. Still, the program has just played 20 games against Gary Kasparov and it won every game, 10 as white and 10 as black. Should you believe the computer scientist's claim that the program is so designed that it will always win against every opponent?