Assignment #6: Formal Methods II: Categorical Logic

1. Read Van Cleave, section 2.14; do exercise set 18.

2. Read 2.17; do exercise set 21.

Practice Quiz #2

 We will review this practice quiz on Monday, March 23; we will have quiz #2 on Wednesday, March 25

1. Reproduce the chart for induction and deduction.

2. Write a sound deductive inference.

3. Write a strong inductive inference.

4. Translate into formal symbolic language:

a. I will go to the party only if you will go (use I and Y).

b. It is not both sunny and warm today (use S and W).

c. It is neither sunny nor warm today (use S and W)

5. Is the following inference valid or invalid:

If A then B; not A, therefore, not B.

Show validity using the 8 rules of deduction:

1. Q

2. P   /therefore, (Q or R) and P

1. If A then B

2. not B and not C  /therefore, not A and not C

1. If D or E, then A and B

2. D   /therefore, B

1. If P then Q

2. P or (R and S)  

3. not Q and not T   /therefore, R

Translate and show validity using the 8 rules of deductive reasoning:

If you care about your education, you will succeed; and if you succeed, your years at MCLA will be spent wisely. You do care about your education, and you will either fail to spend your years at MCLA wisely or you will reap one of life's greatest rewards. It follows that you will reap that reward. (use C, S, Y, R)

Assignment #5: Formal Proofs

Read: Van Cleave, section 2.11. Do exercise sets 16 & 17.

8 Rules of valid inference:

Modus Ponens (MP)

p⊃q,
p
∴
q

 Modus Tollens (MT)

 p⊃q,
~q
∴
~p

 Disjunctive Syllogism (DS)

p∨q,
~p
∴
q

 or, if desired,

p∨q,
~q
∴
p

Simplication (Simp)

p.q
∴
p

 or, if desired,

p.q
∴
q

Conjunction (Conj)

p,
q
∴
p.q

Hypothetical Syllogism (HS)

p⊃q,
q⊃r
∴
p⊃r

Addition(Add)

 p

∴
p∨q

 Constructive Dilemma (CD)

(p⊃q),
(r⊃s),
p∨r
∴
q∨s

 

 

Sample Quiz #1

Sample Quiz #1

Reminder: Quiz #1 is scheduled for this Friday, 2/27.

1. What is a logical argument?

2. List 2 premise indicator words and 2 conclusion indicator words.

3. Distinguish arguments from explanations among the following:

a. “All dogs are reptiles; Fido is a dog; therefore, Fido is a reptile.” B. “Go to your room, because you have been bad, and all bad persons must go to their rooms.”  C. “Water freezes at 32 degrees because the molecules get so cold that they slow down enough to hook onto each other, forming a solid crystal.”

4. What are the possible ways an argument can be unsound?

5. True or false?  “A sound deduction may have one false premise.”

6. Reproduce the chart for induction and deduction. 

7. Compose an enthymeme, then supply the missing premise.

8. Translate into formal symbolic language:

a. It is Friday and it is not raining. (use F and R)

b. My name is not Bob or Sally. (use B and S)

c. Next week, we will meet on Monday or Wednesday, but not Tuesday or Thursday. (use M, W, T, R)

d. I'll have some cake or ice cream, but not both. (use C and I)

9. Write an argument that attempts to leap over the “is-ought gap.”  What missing premise would make it valid?

10. Reproduce the truth table for "and".

 

Assignment #4: Formal Methods I: Propositional Logic

 Read and do exercises, Van Cleave, 2.1-2.5 & 2.7

Assignment #3: Validity, Soundness, Strength, Enthymemes, Is-ought gap

Begin reading and working through the exercises in Van Cleave, 1.3; and 1.6-1.9

Supplemental (on the is-ought gap):

Thesis XII Online: Volume 22.1

Note: I will not hold class on Wednesday, February 18th.  (Monday the 16th is a holiday; I will hold class on Friday the 20th).

Assignment #2 The nature of an argument

Things to do:

1. We will discuss the very nature of critical thinking and philosophy in our next class; then move on to: 

2. Read Van Cleave, 1.1-1.2.  In your notebook dedicated to this class, do all of the exercises.  Bring questions/comments to class.