The Propositional Logic of Paraphastic Sets
 
 

Logic
Symantics            --------->          Expressions
Syntax
 

                                               Topology of Sentences
                                                Propositional Logic
                                                yields the topology
                                                of paraphrastic sets.
 

"Internal regions translate psychodynamically into the wholistic entity of personality."  ( p. 50) SW)

    1.)  Personality is a wholistic entity.

    2.)  Personality can be viewed as consisting of psychodynamic internal regions.

    3.)  Personality consists of internal regions that act as a psychodynamic system or whole.

    4.)  X consists of Y  that acts as Z  (X = personality; Y = internal regions; Z = Psychology whole)

    5.)  Y translates through Z into X
     (4ii)   (Good Nourishment)  Consists of (a raw food diet)  that acts as (a biochemical stabilizer to the body functions).
     (5ii)   (A raw food diet)  translates through  (a biochemical stabilizer to the b.j.)  into (Good n.).
 
 

PROPOSED EQUIANCE FRAME:  (i)  X consists of Y which acts as Z
                                                          (ii)  translates through Z into X

PROOF:

Eample 1:

Let     X = happiness
          Y = success and health
          Z = Ego boosting forces

Then i = (happiness)  consists of (success and health)  which acts as (ego bosting forces).

and ii = (Success and health) translates through (Ego boosting forces) into (happiness).
 



 
 

Example 2:

Let     X = electricity
          Y = moving electrons
          Z = a current or flow in a wire

Then i = (Electricity)  consists of  (moving electrons)  which act as (a current or flow in a wire).

and ii = (Moving electrons)  translate through  (a current or flow in a wire)  into  (electricity).
 

"The attribution of reward value to an attitude object (thing or person)  is expressed in a very large number of ways, and it helps to have a system for classifying them.  One method consists of..."  (SW, p. 56)

1.)  (Attitudes objects, things, or persons) (= X)  are entities to which ( reward value)  (= Y) may be attributed.  This process of attributing  (reward value)  (= Y)  to  (attribute objects)  (= X)  is (expressed in a very large number of ways)  (= Z),  These (ways of expressing)  (= Z)  can be classified by several methods of which the following is an instance.

2.)  X is an entity to which Y may be attributed.

3.)  (reward value)  (= Y)  may be attributed to such entities as (Attit. objects)  (= X)

4.)  Y may be attributed to entities such as X
 

PROPOSED EQUIVALENCE FRAME:

(i) = X is an entity to which Y may be attributed
(ii) = Y may be attributed to entities such as X
 

PROOF:

Example 1:

Let X= diamonds
      Y= hardness

Then (i) =  (Diamonds) are entities to which (hardness) may be attributed.
and   (ii) =  (Hardness)  may be attributed to entities such as (diamonds)
 


Example 2:

Let X= Citizen
      Y= Motives

Then  (i) =  ( A citizen)  is an entity to which (motives) may be attributed.
and    (ii) =  (Motives)  may be attributed to entities such as (citizens).
 
 
 

PROPOSED EQUIVALENCE FRAMES:

(i)  X belongs to Y but is excluded from Z
(ii)  X is excluded from Z though it belongs to Y
(iii)  Z includes Y but excludes X
 

PROOF:

Samples

(i)  Fingers (X) belong to hands (Y)  but are excluded from feet (Z).
(ii)  Fingers (X) are excluded from feet (Z)  though they belong to hands  (Y)
(iii)  Feet (Z)  include hands but(Y) exclude fingers(X).


(i)  Jane(X) belongs to the jetsetters(Y) but is excluded from the torpedoes(Z).
(ii)  Jane(X) is excluded from the torpedoes(Z) though she belongs to the jetsetters(Y).
(iii)  The torpedoes(Z) include the jetsetters(Y) but exclude Jane(X).



 

PEF

(i)  X appears as Y when Z
(ii) Y is X'sappearance during Z
(iii) Z is the condition for X to appear as Y

PROOF:

(i) The soldiers (X) appeared as phantoms(Y) when the curtain opened (Z).
(ii) Phantoms(Y) were the soldiers'(X) appearance during the curtain opening(Z).
(iii) The opening of the curtain(Z) is the condition for the soldiers(X) to appear as phantoms(Y).


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