1) Exam #1 Friday (10/7)
-Study guide & practice exam posted on Canvas
-Review old homework assignments & come see me with questions
-Review quizzes: If you don't understand an answer, come see me
E.g.... Only 38% of students got this question right on the quiz:
What best describes the following argument in regards to kind, logical force, and premise acceptability?
Most students who do all the homework assignments and have zero
absences do well on the exam. Therefore, Megan will do well on the exam
because she did all the homework assignments and hasn't missed a single
class. (Assume it's true that Megan is a student, that she did all the homework assignments, and didn't miss any classes).
+0.55
Discrimination Index
A table of student answers
| Answer Text | Number of Respondents | Percent of respondents selecting this answer |
|
|---|
| Inductive, cogent. |
| 38 % |
|
|---|
| Inductive, strong but uncogent. |
| 17 % |
|
|---|
| Deductive and valid. |
| 8 % |
|
|---|
| Deductive and sound. |
| 34 % |
|
|---|
| Deductive, valid but not sound. |
| 4 % |
|
|---|
-EXAM #1 REVIEW SESSION
Thursday (10/6) 6-8pm, Shatzel Hall 317
*If you can't make the review session, come see me, Ami, or John
2) MP, MT, AC, DA
-Formalizing arguments
-Review
-Practice questions
3) Test review
-Practice questions
MP, MT, AC, DA
(Refer back to last blog post)
-Review: conditional statements
If the cat is on the mat, then the cat is asleep
M = The cat is on the mat
A = The cat is asleep
Formalized:
M > A (If M, then A)
The part of a conditional that follows "if" is called the antecedent
In this example, the antecedent is "The cat is on the mat"
The part of a conditional that follows "then" is called the consequent.*
*Note that sometimes, "then" is implicit. E.g., if someone told you, "If the cat is on the mat, the cat is asleep," you would infer "then" in front of "the cat is asleep" even though it's not stated.
In this example, the consequent is "The cat is asleep"
It may help to label the antecedent and the consequent when you formalize the argument, as below:
Pay special attention to the second formulation!
Order doesn't matter
Whatever comes after the "if" is the antecedent
Whatever comes after the "then" (sometimes implicit) is the consequent
English does not capture the logical dependence order. Logical notation does.
In short:
When you put the argument in logical form, you always put the ANTECEDENT FIRST and the CONSEQUENT SECOND
A > C
(If antecedent, then consequent)
Thus, "The cat is asleep if the cat is on the mat" in logic speak is also:
M > A
-Formalizing arguments, review
Symbols
> (conditional) = "If...then..."
Example:
A > B = If A, then B
~ (negation) = "Not"*
Example:
~C = Not C
*Whenever a premise contains a negative (not, won't, didn't, etc.) use the ~ to indicate
E.g. It is not raining = ~R
Method:
1) Figure out what the conclusion is
2) Figure out what the premises are
(Label, underline, diagram, put the argument in standard form... whatever you need to do to keep track of what's what)
3) Make a translation key*
*You don't have to do this when Ami indicates what letters you should use, but in other cases you need to indicate what the letters you choose symbolize
4) Symbolize the argument in premise-conclusion form
5) DOUBLE CHECK: TRANSLATE YOUR SYMBOLIZATION BACK INTO ENGLISH TO SEE IF IT MAKES SENSE!! <-- This will help you catch errors
Example:
If the cat is on the mat, then the cat is asleep. The cat is on the mat. Therefore, the cat is asleep.
P1) If the cat...
P2) The cat is on the mat
C) The cat is asleep
Key:
M= The cat's on the mat
A = The cat's asleep
P1) M > A
P2) M
C) A
-VALID INFERENCE RULES:
If the premises are true, the conclusion MUST BE TRUE
*You cannot find counterexamples to these arguments
Modus ponens:
P1) A>B
P2) A
C) B
P1) If the cat is on the mat, the cat is asleep
P2) The cat is on the mat
C) The cat is asleep
Modus tollens:
P1) A>B
P2) ~B
C) ~A
P1) If the cat is on the mat, the cat is asleep
P2) The cat is not asleep
C) The cat is not on the mat
-INVALID INFERENCES (NOPE NOPE NOPE)
*You can find counterexamples to these arguments!
Bad/AC: Affirming the consequent
(Modus ponens gone wrong)
P1) A>B
P2) B
C) A <-- does not follow
P1) If the cat is on the mat, the cat is asleep
P2) The cat is asleep
C) The cat is on the mat
Counterexample: It is not necessarily true that the cat is on the mat, because the cat could be asleep elsewhere. My cat sleeps on my bed, on the kitchen table, in the windowsill, on my laptop, on the couch, in her cat tree... (where do cats not sleep???)
Bad/DA: Denying the antecedent
(Modus tollens gone wrong)
P1) A>B
P2) ~A
C) ~B <-- does not follow
P1) If the cat is on the mat, then the cat is asleep
P2) The cat is not on the mat
C) The cat is not asleep
Counterexample: See explanation above. It is not necessarily true that the cat is not asleep, because the cat could be asleep elsewhere (for instance, on my clean laundry).
(For all you dog lovers, here is a picture of a dog on a mat)
Note regarding negatives: Pay attention to the form of the argument. Don't let negatives throw you off!
This argument is also in modus ponens form:
~M > A
~M
______
A
Modus tollens:
~M > A
~A
______
~~M
Bad/AC:
~M > A
A
______
~M
Bad/DA:
~M > A
~~M
______
~A
Practice
(From Homework 3.3)
a) Symbolize the argument (use the first letter of the underlined word and '~' for negation).
(b) Is the argument valid? If it is, cite whether it's modus tollens or modus ponens. If it isn't, cite whether it's denying the antecedent (DA) or affirming the consequent (AC).
4. You don't want to be my lover because if you want be my lover you gotta get with my friends. And last night when I asked you to get with my friends, you said "no."
9. You won't have to drown your sorrows if you do well on the test. You don't have to drown your sorrows, therefore you did well on the test.
More examples:
1. If it barks, it's a dog. It doesn't bark. Therefore, it's not a dog.
2. You're going to do well on the test if you study. You study. Therefore, you're going to do well on the test.
3. If there's smoke, there's fire. There's no smoke, because there's no fire.
4. This dish tastes awful. You must've put too much salt in it. If you put too much salt in a dish, it always tastes awful.
More practice:
MP, MT, DA, AC
(a) Identify the missing premise then (b) put the argument into standard premise-conclusion form. (c) Evaluate the argument for soundness. (d) See if you can construct a reductio (where applicable).
1.
P1) Historically humans have always eaten meat.
C) It is morally permissible to eat factory farmed meat.
2.
P1) Factory farming creates health risks for humans.
C) Therefore, factory farming is wrong.
Practice question for Exam #1:
If you want to do well then you should bring your TA cookies. You didn’t bring your TA cookies. Therefore, you don’t want to do well. P1. P2. C. Valid/Invalid:_______________. Reasoning Pattern: _________.
Comprehensive practice question for Exam #1
(a) Put the following arguments into standard premise-conclusion form (just write the first 3 words of each premise). Number the premises according to their position in the original arguments.
(b) Identify whether the premises are convergent, serial, or linked
(c) Identify whether the argument is inductive or deductive and its logical force (valid, invalid, strong, weak)
(d.i.) Determine which premises are acceptable, questionable, unacceptable using the various criteria we’ve discussed in class (5 for acceptability, 3 for questionable, 3 for unacceptable).
(d. ii) If a premise is questionable say what information you’d need in order to accept it.
(e) Diagram the arguments in the space next to where you write the premises.
1. In recent years, health trends became a mark of status. For example, a high-end health food store (Whole Foods) grew into a supermarket-chain juggernaut. Designer clothing is now yoga-wear. Also, refusing to eat gluten is a way to show one’s status.
(a). P1.
P2.
P3.
C.
(b) Premises are all: Linked, convergent, serial (circle).
(c) P1 in relation to the conclusion is: (circle the correct answers) i. Inductive vs Deductive ii. Valid, Invalid, Strong, Weak
P2 in relation to the conclusion is: i. Inductive vs Deductive ii. Valid, Invalid, Strong, Weak
P3 in relation to the conclusion is: i. Inductive vs Deductive ii. Valid, Invalid, Strong, Weak
(d) P1. Acceptable/Questionable/Unacceptable because:
P2. Acceptable/Questionable/Unacceptable because:
P3. Acceptable/Questionable/Unacceptable because:
(e) Diagram:
