Java’s Broken Booleans

[Daniele Futtorovic]

PS: What's yellow and equivalent to the Axiom of choice?

The bucket I threw up last time I drank too many cocktails and chose
never to do it again?

 

[Andreas Leitgeb]

The bucket I threw up last time I drank too many cocktails and chose
never to do it again?

No, that's just a corollary, but not equiv.

 

[Andreas Leitgeb]

Which ones are "natural"?

Of the total ones: none. There are some natural comparisons, which are
not mathematical orderings, for they fail on "a>=b && b>=a ==> a==b".

Nor very "natural".

Definite agree on this one.

Other than "naturalness".

I guess, we should just agree on that we disagree on that one.

 

[Andreas Leitgeb]

I guess, we should just agree on that we disagree on that one.

Oops, I was too fast on that. Of course, a total ordering on
logical values *can* be inconsistent with naturalness:
just define false >= true.
It just *doesn't need* to be, as with the other one.

 

[Lawrence D'Oliveiro]

Booleans with "and", "or" and "not" operations don't have field structure,
in the first place ...

Yes they do.

 

[Andreas Leitgeb]

Yes they do.

Either you are not familiar with what a "field" is mathematically,
or you missed the crucial difference between operation "or" and
addition in GF(2).

 

[Tim]

Either you are not familiar with what a "field" is mathematically,
or you missed the crucial difference between operation "or" and
addition in GF(2).

XOR is equivalent to addition in GF(2) and AND to addition; x XOR 1 is
NOT x, and NOT ((NOT x) AND (NOT y)) is x OR y, so it does seem that
from the field operations you can construct all three of the operations
you mentioned a couple of posts ago.

On the other hand, the field structure is specifically on AND and XOR,
not on AND, OR, and NOT.

So you're both half right.

 

[Tim]

XOR is equivalent to addition in GF(2) and AND to addition

Multiplication, of course.

Dammit, what the hell is wrong with this text editor?

 

[Andreas Leitgeb]

XOR is equivalent to addition in GF(2) and AND to multiplication(corr by tim);
x XOR 1 is NOT x, and NOT ((NOT x) AND (NOT y)) is x OR y, so it does seem that
from the field operations you can construct all three of the operations
you mentioned a couple of posts ago.

The more interesting part is that one can also construct the field-
operations from AND,OR,NOT. Maybe Lawrence meant that, but that's
no contradiction of my statement, just an added remark.