advaita-siddhi 11 (Predicate logic formulation)
Anand Hudli
anandhudli at HOTMAIL.COM
Wed Feb 9 12:44:58 CST 2000
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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