> This is blatantly false.
>
> So, assertion XX must be false.
It shouldn't have taken you a full page to disprove A = -A. Consider: A +
-A is zero, or should be. But if A = -A, then A + -A = A + A = 0. You
could do this for any number, including a constant; all numbers would
equal zero, including such important numbers as pi and e and 1 and
infinity, and the probability that anything exists at a given point. In
other words, you get a nonsense universe.
However, you have misunderstood Ian's holism. (He is often a little,
shall we say, synedochical?) A is not equal to not-A, but rather he makes
the point that you really have no idea what A is unless you define it in
terms of something that it isn't. To evince: if you came up to me and
asked me what A is, and I told you "A is A," while I would have said
something true, it would have been completely useless to you. On some
level, you really wanted to know something about what A is in relation to
something else; in other words, what A is not.
The bit about A = -A comes from the net identity charts. Basically, it
goes like this: take a universe consisting of only two things: A and B,
remembering that A is only defined in terms of its relationship to other
parts of the universe. Clearly, A is zero difference from itself, and it
has (let's say) a difference of 1 from B. (Units are deliberately left
out of this analysis: it doesn't matter what property you're referring
to.) Well, B has a zero difference from itself, and the difference from B
to A is -1. Ian points out that if you sum all of these relations, you
always get zero. He calls this the "net identity." It is always zero.
Here's where you make the dubious leap: if A is defined not by itself, but
by its relations to things which are not-A (in this case, B) then on some
level you could say that the identity of A is its net identity, which is
always zero. Repeat this for B, or -A, and you see that the net identity
of A is equal to the net identity of -A. A + -A = B + -B = 0.
This is really a trivial point, and doesn't really tell you anything about
anything that a properly defined atomism wouldn't. It is also not holism
in the way you'd probably define it (but which Ian would): note that for a
mysticist, because A = -A, (rather than the net identity of A = the net
identity of -A,) the sum of the net identity is 0, 1, 8, infinity, and all
other numbers simultaneously, because all numbers are equal to all other
numbers. Ian agrees that this is illogical, however: his identity charts
always sum to zero, and only zero. He WOULD argue that the net identity
of all numbers is equal to the net identity of 0, but as you can see, this
is a much weaker (and far more defensible!) claim.
I asserted that atomism = holism (IAN's holism, I mean!) because his
holism is saying much less than most holists. Meanwhile, he has held a
definition of atomism which basically states that things are defined in
terms of themselves; this is completely nonsensical, as you should be able
to see, because you have to have a frame of reference in order to define
anything. You can't say that A = A and then go on to say that you now
know what A is. Telling you A in relation to 0, however, may be more
useful, particularly if I give you a few other values in relation to zero.
This is what the atomists are really talking about: you won't find any
Newtonian physicist claiming that particles have a velocity independent of
their refrence frame, but they are atomists nonetheless, because they
believe that particles may have independent properties *within a single
reference frame*, ie in relation to zero.
To summarize: it's not that A=-A, it's that identity(A) = identity(-A) =
0. Whether you agree with this definition or not is your own lookout.