advaita-siddhi 11 (Predicate logic formulation)

[Anand Hudli]

Vivek Anand Ganesan <v_ganesan at YAHOO.COM> wrote:

>  A small request.  Could you please frame this argument in
>terms of propositional logic ( as you had done before )?
>I have read it many times but I get lost as I approach the
>end.  I would surely appreciate a gist of this argument
>presented in familiar terms.


 The only reason why I did not attempt to formulate the definition
 in terms of predicate logic is because the logical expressions
 tend to get "unwieldy" quickly as the definition gets more
 and more refined. The first definition of mithyAtva (please see
 "advaita-siddhi - 6") is refined by the second definition. All that
 the first definition really says is that mithyA is something that is
 different from the absolutely real Brahman and from a fictitious entity.
 As per the first definition, the thing that is mithyA should be 1)
 cognized in some locus (substratum) and 2) be sublated (negated) at some
 time. The second definition refines the first by saying that the thing
 that is mithyA is 1) sublated in the very locus where it is cognized
 and 2) and it is sublated so for ALL times.

 At the risk of being unintelligible once again, I will attempt
 to formulate the second definition of mithyAtva in terms of
 predicate logic.

 To explain the second definition in terms of Western-style
 predicate logic, we need to introduce different time frames
 of reference. Also, we need to consider the second definition
 as a refinement of the first definition. The second definition
 comes from the VivaraNa on the PanchapAdikA which contains the
 first definition.

 The need for different time frames arises because of the
 following. In any case of illusion, there are two time frames.
 The first time frame, say T_A (time frame of avidyA), is that
 which holds when the illusion is in effect. During this phase,
 things are interpreted in terms of the illusion. For example,
 consider the illusion of the snake on the rope. When one
 is under the spell of this illusion, he/she thinks there is
 a snake. He/she may even interpret the movement of the rope due to
 wind, etc. as a movement of the snake! Note also that the second
 definition states that the thing that is mithyA is sublated in
 the same locus where it is cognized (pratipanna-upAdhau) and that it
 is sublated for all times (traikAlikanishhedha). Clearly, it is
 absurd to say that the illusion is sublated for all times DURING
 the illusion phase (avidyA) itself. This is akin to saying a dream
 is sublated during the dream. The dream is sublated only upon waking
 up, not while the dream is still occurring. Therefore, it is
 necessary to interpret traikAlikanishhedha as the sublation for
 all times in a time frame of reference that is different from the
 time frame during illusion. What is this other time frame?


 The other time frame is the time frame that holds AFTER the illusion
 ends. Call this time frame T_J (time frame after dawn of jnAna).
 Once the illusion ends, the previous time frame T_A no longer
 applies. There is no snake. One exclaims "there was no snake there,
 there is no snake now, and there won't be the snake in future!"

 What about the events of the old time frame T_A? These get
 re-interpreted or "mapped" into events in time frame T_J.
 For example, the movement of the snake in the illusory phase
 gets re-interpreted as "it must have been the wind that caused
 the rope to move in reality." In other words, the old events in
 time frame T_A that were in terms of "snake" get "mapped" into
 events in time frame T_J in terms of "rope". This is because
 there is NO "snake" in the time frame T_J. One may say that
 "history gets re-written" in time frame T_J!

 In the case of a dream-illusion, the dream events may generally
 be thought of as being mapped into "non-events" or a NULL event
 in the waking state.
 Sometimes it IS possible to "map" dream events into waking-state
 events. Have you dreamed of temple bells ringing only to wake up
 and find that in reality your alarm clock is ringing?! :-)

 Having defined the two time frames, the second definition of mithyAtva
 can now be described symbolically almost in the same way as the
 first definition. From now on, I follow the notation similar to that
 in the sixth part of this series ("advaita-siddhi - 6") with
 some additional notation.

 (Note: Sublated and negated mean the same.)

 Let us define a predicate S whereby S(X,L,t,T) means "X is sublated in
 substratum L for time t in time frame T"

  Also, let us say E(t) means the existential quantifier "there is
  a t", and U(t) means the universal quantifier "for all t." Let
  ~ stand for the negation operator.

  Then the definition of existence (sattva or simply sat) according
  to the first definition of mithyAtva is that thing, say X (Brahman),
  such that:

  ~ (E(t) such that S(X,L,t,T), for time t in some time frame T and
     for some substratum L) ................................... (A)

 or more concisely,

  ~ (E(T),E(t in T), E(L): S(X,L,t,T)) ....................... (A')

  Brahman is NOT something that can be sublated for some time in
  some time frame in some substratum.

  Next, MadhusUdana defines nonexistence (of something X) NOT as
  simply negating the expression (A) above which would just be

  (E(t) such that S(X,L,t,T), for time t in some time frame T, and for
   some substratum L)  .........................................  (B)
  this would mean "there is a time t in some time frame when X
  is sublated in substratum L"

  stated more concisely as:

  (E(T),E(t in T), E(L) : S(X,L,t,T)) ............................(B')

  (Note: The terms locus and substratum are used interchangeably.)

  Rather nonexistence (of something X) is defined  by MadhusUdana
  as "kvachidapyupAdhau sattvena pratIyamAnatva-anadhikaraNatvam.h"
  (please see advaita-siddhi - 6), "not being cognized in any locus
  at any time" which can be expressed as:

  (U(t): ~ C(X,L,t,T), for time t in all time frames, and for all
  loci)       ...........................................     (C)

  C(X,L,t,T)  means "X is cognized in a locus L for time t in
  time frame T." Something (X) is nonexistent if and only if
  "for all time t in all time frames, X is not cognized in any
  locus."

  Stated more concisely,

  (U(T),U(t in T ),U(L): ~ C(X,L,t,T)) ....................... (C')

  The negation of *this* type of nonexistence is:

  (E(t) such that C(X,L,t,T), for some time t in some time frame T, and
  for some locus L) ......................................   (D)

   or more concisely,

  (E(T), E(t in T), E(L): C(X,L,t,T)) .........................(D')

 which means "there is some time t in some time frame T during which X is
 cognized in a locus." And this is  the negation of nonexistence
 that is characteristic of illusions such as silver-in-nacre,
 snake-on-rope, and finally, the world-on-Brahman illusion.
 The illusory thing is cognized as existing in a locus
 (substratum) sometime (the period of illusion) and in the time
 frame T_A.

 The first definition of mithyAtva is : (B) AND (D).
 (please see advaita-siddhi - 6)

 Therefore, the first definition of mithyAtva is written:

 (E(t) such that S(X,L,t,T), for some time t in some time frame T, and
  for some locus L)
  AND
 (E(t): C(X,L',t,T), for some time t in some time frame T', and for some
  locus L')  ............................................. (E)

 or more concisely,

  (E(T),E(t in T), E(L) : S(X,L,t,T))
   AND
  (E(T'), E(t in T'), E(L'): C(X,L',t,T')) ..................(E')


 Now, what the second definition of the PanchapAdikA-vivaraNa does
 is to refine the first definition, make it more precise and less
 ambiguous. After all, the first definition comes from the Pancha-
 pAdikA and the second from the VivaraNa on the PanchapAdikA.

 What the second definition does is  1) fix the time frames in (E)
 above , 2) fix the loci in (E), and 3)  make the condition in the (B)
 part of the definition stronger by asserting that the sublation
 holds for all times.

 The second definition of mithyAtva may  be written first  by
 fixing the time frame in (B) as the time frame T_J (time frame
 after dawn of jnAna) and the time frame in (D) as the time frame
 T_A (time frame during the avidyA phase).

 (B with time frame T = T_J ) AND (D with time frame T = T_A)

 which is

 (E(t) such that S(X,L,t,T_J), for some time t in time frame T_J, for some
 locus L)
 AND
 (E(t): C(X,L',t,T_A), for some time t in time frame T_A, and for some
 locus L')

 The second definition of mithyAtva may next be written   by
 fixing the loci L and L' to be the SAME. The definition clearly states
 that the thing that is mithyA is sublated in the VERY LOCUS where
 it is cognized.

 This makes the definition:

(E(t) such that S(X,L,t,T_J), for some time t in time frame T_J, for
 locus L)
  AND
(E(t) such that C(X,L',t,T_A), for some time t in time frame T_A, and for
 locus L') AND (L = L')


 Next, making the condition in the (B) part of the definition
 stronger means the sublation should hold for all periods of
 time in time frame T_J.

(S(X,L,t,T_J), for ALL time t in time frame T_J, for locus L)
  AND
(E(t) such that C(X,L',t,T_A), for some time t in time frame T_A, and for
 locus L') AND (L = L') ....................................(F)

 or more concisely,

  E(L),E(L')((U(t in T_J): S(X,L,t,T_J)) AND (E(t in T_A): C(X,L',t,T_A))
             AND (L = L') ) ................................(F')

 Actually, if we wanted to be more picky and precise, we can say:

   E(L),E(L')((U(t in T_J): S(X,L,t,T_J)) AND (E(t in T_A): C(X,L',t,T_A))
         AND (L = L') )  AND (T_J != T_A)..........................(F'')

  to insist that the time frame T_A and T_J must not be the same.
  "!=" means "not equals".

 Introducing a predicate M(X) which means "X is mithyA", the
 predicate is defined as (using "<=>" to indicate equivalence):

 M(X) <=>
 E(L),E(L')((U(t in T_J): S(X,L,t,T_J)) AND (E(t in T_A): C(X,L',t,T_A))
  AND (L = L') )  AND (T_J != T_A)..........................(G)


 We have arrived at the final form of the second definition of mithyAtva:

 X is mithyA if it is sublated for ALL times in the very substratum
 where it is cognized.

 "pratipannopAdhau traikAlikanishhedhapratiyogitvaM vA mithyAtvam.h |"

 The second definition, if it has to be a refinement of the
 first definition, must imply the latter. ie.

  (F) -> (E)

 It is easy to see that this implication holds.

 Anand

--
bhava shankara deshikame sharaNam

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