Assignment #7: Formal Methods II: Categorical Logic

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

2. Read 2.17; do exercise set 21.

Reminder: Quiz #2, next Monday, November 3.  The quiz will consist of 5 problems lifted from exercise 17 in Van Cleave.

Assignment #6: Formal Proofs

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

(Also complete the 6 translations + proofs handed out on Friday.)

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

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 #5: "not both" "neither nor" and conditionals

Reminder; Quiz #1, Monday, 10/6

Read and do exercises for Van Cleave, 2.5 & 2.7

Assignment #4: Formal Methods I: Propositional Logic

 Read and do exercises, Van Cleave, 2.1-2.4

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

Assignment #2 The nature of an argument

Things to do:

1. We will continue discussing the nature of philosophy/critical thinking in our next session.  

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

Assignment #1: Handout CPE, syllabus, defininitions

Things to do:

1. Research the term "philosophy" and the phrase "critical thinking."  Find definitions that strike you as inclusive and instructive and bring them to class in a dedicated (section of a) notebook.

2. Review Handout CPE and the syllabus; raise any questions about these documents in our next class.