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Philosophy 103: Introduction to Logic
Test: Symbolic Logic

Topic: Theory Construction in Economics

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SYMBOLIC LOGIC  TEST PART III 
STATEMENT FORMS 

RETURN TO TEST ON SYMBOLIC LOGIC INDEX PAGE


Part III:  Statement Forms.  Test the corresponding statement-forms of any three of the four higher-level laws and characterize them as being a tautology, a contingent statement or a self-contradictory statement.

On the basis of your analysis, would you reject any of the higher-level laws your test?


Answer to Part III--A.

Prof. Userer's First Law: Form 
 is equivalent  [(S  and  R)  or  (S  and  notR)]  is equivalent  [(s  and  r)  or  (s  and  notr)]

r s and r notr s and notr (s and r) or (sandnotr)

s  is equivalent [(s and r) or (s andnotr)]

1 T T   T   F   F T   T  
2 T F   F   F   F     F       T    
3 F T   F   T   T T   T  
4 F F   F   T   F F   T  
 

Prof. Userer's First Law lacks empirical content--his First Law is a tautology.


Answer to Part III--B.

Prof. Userer's Second Law:

 

Form

[V  or  (R   and T)]  implies  (U  and  T)

[v  or  (r  and  t)]  implies  (u and   t)


 

r

t

u

v

  t

v   (r    t)

  t

[v   (r    t)]    
(u    t)

1

T

T

T

T

 

T

 

 

T

 

 

T

 

 

 

T

 

 

2

T

T

T

F

 

T

 

 

T

 

 

T

 

 

 

T

 

 

3

T

T

F

T

 

T

 

 

T

 

 

F

 

 

 

F

 

 

4

T

T

F

F

 

T

 

 

T

 

 

F

 

 

 

F

 

 

5

T

F

T

T

 

F

 

 

T

 

 

F

 

 

 

F

 

 

6

T

F

T

F

 

F

 

 

F

 

 

F

 

 

 

T

 

 

7

T

F

F

T

 

F

 

 

T

 

 

F

 

 

 

T

 

 

8

T

F

F

F

 

F

 

 

F

 

 

F

 

 

 

T

 

 

9

F

T

T

T

 

F

 

 

T

 

 

T

 

 

 

T

 

 

10

F

T

T

F

 

F

 

 

F

 

 

T

 

 

 

T

 

 

11

F

T

F

T

 

F

 

 

T

 

 

F

 

 

 

F

 

 

12

F

T

F

F

 

F

 

 

F

 

 

F

 

 

 

T

 

 

13

F

F

T

T

 

F

 

 

T

 

 

F

 

 

 

F

 

 

14

F

F

T

F

 

F

 

 

F

 

 

F

 

 

 

T

 

 

15

F

F

F

T

 

F

 

 

T

 

 

F

 

 

 

F

 

 

16

F

F

F

F

 

F

 

 

F

 

 

F

 

 

 

T

 

 

Prof. Userer's second law is contingent.


Answer to Part III--C.

Prof. Userer's Third Law:

 

Form

(T  implies  notU)  implies  (P  implies  notQ)

(t  implies  notu)  implies  (p  implies  notq)


 

p

q

t

u

notu   notq

t implies notu

p implies notq

(t  implies notu)  implies
  (p implies notq)

1

T

T

T

T

 

F

 

  F

 

F

 

 

F

 

 

 

T

 

 

2

T

T

T

F

 

T

 

  F

 T

 

F

 

 

F

   

3

T

T

F

T

 

F

 

  F

 

T

 

 

F

 

 

 

F

 

 

4

T

T

F

F

 

T

 

  F

 

T

 

 

F

 

 

 

F

 

 

5

T

F

T

T

 

F

 

  T

 

F

 

 

T

 

 

 

T

 

 

6

T

F

T

F

 

T

 

  T

 

T

 

 

T

 

 

 

T

 

 

7

T

F

F

T

 

F

 

  T

 

T

 

 

T

 

 

 

T

 

 

8

T

F

F

F

 

T

 

  T

 

T

 

 

T

 

 

 

T

 

 

9

F

T

T

T

 

F

 

  F

 

F

 

 

T

 

 

 

T

 

 

10

F

T

T

F

 

T

 

  F

 

T

 

 

T

 

 

 

T

 

 

11

F

T

F

T

 

F

 

  F

 

T

 

 

T

 

 

 

T

 

 

12

F

T

F

F

 

T

 

  F

 

T

 

 

T

 

 

 

T

 

 

13

F

F

T

T

 

F

 

  T

 

F

 

 

T

 

 

 

T

 

 

14

F

F

T

F

 

T

 

  T

 

T

 

 

T

 

 

 

T

 

 

15

F

F

F

T

 

F

 

  T

 

T

 

 

T

 

 

 

T

 

 

16

F

F

F

F

 

T

 

  T

 

T

 

 

T

 

 

 

T

 

 

Prof. Userer's Third Law is contingent.


CONTINUE TO PART IV: FORMAL PROOFS

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