[FOM] FOM Consequent Equivalence Theorems.

[John Corcoran]

- 

p-->q
(Ex) ....
(Ax)...
FOM Consequent Equivalence Theorems.

Theorem 1: In order for the consequent of a conditional to be logically
equivalent to the conditional itself it is necessary and sufficient for
the negation of the consequent to logically imply the antecedent.  

Q is logically equivalent to (P-->Q) iff not-Q implies P.


Q1.1. Where in the literature is this stated or discussed, even
implicitly?
Q1.2. Where in the literature is this proved or given as an exercise to
prove?
Q1.3. Who if anyone is credited for it?
Q1.4. What is this used for?
Q1.5. What is this called?

Theorem 2: In order for the closed consequent of a universalized
conditional to be logically equivalent to the universalized conditional
itself it is necessary and sufficient for the negation of the consequent
to imply the existentialization of the antecedent. 
 Q is logically equivalent to (Ax)(P(x)-->Q) iff not-Q implies (Ex)
P(x).

Q2.1. Where in the literature is this stated or discussed, even
implicitly?
Q2.2. Where in the literature is this proved or given as an exercise to
prove?
Q2.3. Who if anyone is credited for it?
Q2.4. What is this used for?
Q2.5. What is this called?

Many thanks,
John Corcoran
Philosophy
University of Buffalo
Buffalo, NY  14260-4150
http://www.acsu.buffalo.edu/~corcoran/
716.645.2444 X119 
corcoran at buffalo.edu
FAX 716.645.6139