Rich and Chris, (01)
RC> Actually, Nand and Nor logic is no more complex than And and Or
> logic, in my opinion. I used it extensively in digital circuit
> design once upon a time and never noticed any inconvenience or
> confusion at all. (02)
Yes, I said that it was useful for reducing the number of transistors
in logic circuits. For that purpose, it would indeed be "simpler". (03)
But several different choices of axioms and primitives would produce
identical theories of Boolean algebra. For applications, the choice
of primitives would be irrelevant, since all 16 Boolean operators
of two inputs would be definable in any of the theories (04)
CM> It is simply a greater conceptual challenge to master and work
> exclusively with Nand and Nor than with and, or, and not. (05)
I agree. There are good reasons why natural languages have
the equivalents of And, Or, Not, If-then, Some, & Every: (06)
1. Any observational statement can be expressed with just two
operators: And, Some. (07)
2. All other operators (Or, Not, If-then, Every, Nand, Nor)
can only be inferred, not observed directly. (08)
3. To deny something, you need Not. To state alternatives, you
need Or. For causality, you need If-then. For generality,
you need Every. (09)
4. But Nand & Nor are even farther removed from observation.
They require two steps: an inference plus a denial. (010)
RC> Why pick either one unless it's for a specific task, chosen
> for a specific person's utility in carrying out that task? (011)
I agree that different options may be useful for different
applications, and we should support as broad a range as
possible. Sometimes (as for Nand & Nor) those options come
"for free" with many different choices of primitives. (012)
In any case, I should have chosen Turing machines to illustrate
the point that simplicity in the primitives might not make the
complete system simpler. Very few people would be happy to
replace their programming languages with Turing machines. (013)
But all this discussion supports my main point: (014)
The question of what makes something simple is not simple. (015)
John (016)
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