> > > Neither this, nor that, nor [neither this nor that], nor [both this and
> > > that].
> >
> > Not required. The Boolean transform of nor [both this and that] which
> > is equivalent to not[this and that] is [not-this or not-that]. But this
> > is the inclusive OR, so it includes as a true case [not-this AND not-that].
> > But this readily transforms into not[this OR that] or neither this nor that,
> > which was explicitly stated.
> >
> Not both/and is not equivalent to not neither/nor, any more than
> both/and is equivalent to neither/nor. The application of the same
> logical operation (in this case negation) to two nonequivalent terms
> results in the creation of two more nonequivalent terms. Q.E.D.
This is great fun, Joe. The linguistic expression was never meant to be formally rigorous. The Hindu "neti-neti" actually means, simply, not this, not that. My intention, when I wrote:
> What is Zen? Mu. What is not-Zen? Mu.
>
> Neither this, nor that, nor [neither this nor that]
was to suggest to the reader the need to eliminate all dualistic thinking, i.e. that any and all conceptual distinctions must collapse, and with them thinking itself, to experience the "meaning" of anything. The verbal statement taken literally is not even a logically correct rendering of "neti-neti".
My point was simply that the exclusiveNOR's in the original could be simplified to precisely the expression you suggested:
[- a . - b]
While I will admit to an equivocation in the original regarding the use of exclusiveOR and exclusiveNOR, I did so because "Mu" could never possibly be reduced to a verifiable proposition regardless of how many negations it contained. Any such expression would require both the Law of the Excluded Middle and the Law of Contradiction. If we succeeded at that, we would fail, because the resultant statement would have to be either true or false, another "discrimination" forbidden by Buddhism of any kind.
Do you suppose we have come up with a genuine Koan without a Roshi to clap us both about the ears?