> Re: (1) What is identity?
>
> As we agree, the old absurd Aristotelian identity
> laws need to cite the holistic-identity structure
> in which A is A only relative to -A. As such, 1
> is 1, not due to its relation to itself, but 1
> is 1 fundamentally due to its relation to 0.
>
> Toward holistic revision, you have suggested
> that "with respect to 0" be added to the Three
> Laws of Thought in accord with zero mechanics.
>
> Having established that 1 is the 0/1 relation,
> we have 1, we've "achieved" identity, and this
> 0/1 relation is a holism, it is a whole set with
> subsets, or subfeatures dependent upon the whole.
>
> An issue we disagree on is does the addition of
> other identities relating to 0 into our universe
> of discourse change the identity of the first
> 0/1 relation that we had. You say no, I say yes.
>
> Our universe of discourse (U) contains the 0/1 relation:
>
> 0/1
>
> Now we add several more relations, none same as 0/1:
>
> 0/1 0/9
> 0/6 0/4
>
> In the first case, 0/1 was 100% of U, now the 0/1
> relation is only one-fourth of U, now it *is* LESS
> relative to the whole. We can now also say that the
> 0/1 relation is unique. When we say A is _____(fill
> in the blank), what it is is an attribute of its
> identity, and as we can see, adding new relations
> to U has added new identity attributes to 0/1,
> and as such, identity is a holistic function.
>
>
> Why Holism is Absolute
>
> 100% holism always wins, for even if we disagree
> with the above and instead believe that the 0/1
> relation has NOT changed, then this identified
> state of "not-change" (not-C) is "not-C" relative,
> and only relative, to C, and thus the non-changing
> of the initial 0/1 relation is a measure of holism.
> The change here being that of the contents of U.
>
> So the examples of the relations of relations
> cited have not identified any variety of free
> identity, and as such we always have 100% holism.
As I have constantly asserted, we OUGHT to get 100% holism: it's the same
theory with different definitions. In this case, I don't see that there's
any way that you could argue that I CANNOT define identity to refer only
to the A-0 partial difference. It's just a definition, after all: I can
define unicorns if I so wish. Within that context, identity is the
partial difference if you adopt the (my?) atomism set of definitions
and it is the net difference if you adopt the (your?) holism set of
definitions.
However, a thought occurred to me today which just might sink zero
mechanics as a theory. (Gasp!) As we both agree, zero mechanics is
completely compatible with Newtonian mechanics; indeed, this may be zero
mechanics's downfall.
Consider objects A and B, which comprise the entire universe. Imagine for
a moment that when they were at rest they measured each other's lengths
and found that both had the same length. So their identity chart for
length would look like:
A B
A 0 0
B 0 0
There is 0 difference between A's length and A's length; nor is there any
difference between A's length and B's length. The chart sums to zero.
So far, so good.
Now let us suppose that they change their speed relative to each other to
something quite large; 0.6c. The velocity of A->B is 0.6c, B->A is -0.6c.
A->A = B->B = 0. Sum them all, you get zero. Again, so far, so good.
But let's go back to observing their lengths again. According to special
relativity, A and B would EACH observe each other's lengths to have
contracted, while their own lengths remained the same (again, relative to
each). To be precise, A observes B's length to be 80% of what it
once was; B observes A's length to have contracted in the same way. Let's
call the magnitude of this change C. Now let's look at our identity
chart:
A B
A 0 -C
B -C 0
This chart sums to -2C, violating a principle of zero mechanics, and
ruining net identity's whole day.
Of course, so long as we take on an (my) atomistic definition, we're fine.
There is no principle of zero mechanics inherent in atomism, so we avoid
this problem entirely. Interesting, no?