Is that the sound of the goalposts moving? You said “find me a mathematician
who statesâ€, and I did.
So you deny that he was using 1 and 0 to represent true and false?
You want some fries as well?
Why don't you try this? Why don't you just read "An
Investigation of the Laws of Thought"? Chapters II and III in particular
should set you straight. I recommend in particular reading the material
that leads up to logical Equation 2 in II.9, and then keep that in mind
(without skipping the good intervening stuff) for when you arrive at
Proposition II in III.13.
You'll see - assuming you bother reading any of this - that Boole refers
to 0 and 1 as _symbols_ in the system of _Logic_ (they are *not*
numbers), and both logical 0 and logical 1 represent *classes*. Logical
0 is Nothing, the empty or null set, and logical 1 is the Universe, the
set of all elements under discourse.
I made that reference to x and 1-x on purpose. For Boole, x is a class.
For example, x might be "all people who are programmers". In Boole's
terminology, 1-x (where '1' is very much the logical symbol 1, the
Universe) means the complement, i.e. all people who are not programmers,
where '1' would then represent the universe of discourse, "all people".
Furthermore, "true" and "false" only enter into the discussion, with
Boole, when he has already defined logical 0 and logical 1 and his signs
and his fundamental algebra. For example, the _expression_ 1-x contains
the logical symbol 1, but there is precisely zero notion of truth or
falsity implied by that expression, because there is as yet no
_proposition_. In fact it's nonsensical to associate 1 with True in that
context.
As an example, you might have it that x is one class, y is another
class, and z yet another, and express a positive proposition that all
elements which belong to x but not to y must be precisely those which
belong to z as
x(1-y)=z
or x(1-y)-z=0
But here 0 still does not mean False; it means the empty set.
Now, there is a very important statement by Boole, on page 70 of Chapter
V, which states that "We may in fact lay aside the logical
interpretation of the symbols in the given equation; convert them into
quantitative symbols, susceptible only of the values 0 and 1; perform
upon them as such all the requisite processes of solution; and finally
restore to them their logical interpretation".
That's all well and good if you actually even are aware of the logical
interpretation - everything I talked about prior. Everything you've said
indicates that you don't have a clue about anything that Boole developed
leading up to this statement. Your arithmetic tricks in various
programming languages demonstrate the shallowness of your understanding.
You're fixated on 0 and 1 as numbers, and incapable of getting that that
is a concrete representation.
Furthermore, you'd still be making a mistake if you thought of the
quantitative symbols 0 and 1 as identically True and False. After all,
True and False are _logical_ interpretations. Hie you forth and read
Chapter VI.
You should in fact read the cautions in Chapter V, after this above
statement of Boole's, to get a better grip.
AHS