Please Prove that Complementary Logic ( https://www.physicsforums.com/showpost.php?p=192318&postcount=25 ) can be reduced to a false/true logic.It seems that many valued logic must be formulated in terms of a stable 2-valued logic background.
Please look again at http://www.geocities.com/complementarytheory/BFC.pdf and see by your self that contradiction or excluded-middle reasoning are trivial private cases of Complementary Logic (which is a symmetrical logical system, unlike Boolean or Fuzzy Logics).Hurkyl said:I think the best demonstration of this fact can be seen by all of your posts about your theory. While your theory may be many-valued, all statements made about it have been decreed either true or false by you, thus reducing it to binary logic.
And you lose through this generalization (it is trivialization through my point of view) very interesting included-middle ordered Logical states.In general, any multi-valued logic can be reduced to binary logic by considering statements of the form "P has truth value S" (where P is a multi-valued proposition and S is one of the possible logic values)
Complementary Logic is a symmetrical logical system, therefore it includes Boolean or Fuzzy Logics as proper sub-systems (some broken-symmetry states) of it.In general, any multi-valued logic can be reduced to binary logic ...
I don't understand what do you want to say.(a xor b) and (a xor b) was the same as a and b, which it isn't,
b b
# #
a a
. .
| |
|&__|_
|
[B]a b
. .
| | <--- (Standard Math logical system fundamental building-block)
|#__|
|[/B]<--r--> ^
t t |
# # u
f f |
| | v
|&__|_
| a b
. .
| |
|#__|
|And you lose through this generalization (it is trivialization through my point of view) very interesting included-middle ordered Logical states.
(excluded-middle --> a binary fact) XOR (included-middle --> not a binary fact)No, you don't. Any statement is either in a given "included-middle ordered Logical state" or it is not; a binary fact.
<--r--> ^
t t |
# # u
f f |
| | v
|&__|_
|<--r--> ^
t t |
# # u
f f |
| | v
|&__|_
|So as we see, ((f # t)&(f # t)) is simultaneously (f & f)_(t & f)_(f & t)_(t & t), which is definitely not a Boolean Logic state.
WWW said:Please Prove that Complementary Logic ( https://www.physicsforums.com/showpost.php?p=192318&postcount=25 ) can be reduced to a false/true logic.
Hurkyl said:I said:
"((f # t)&(f # t)) is simultaneously (f & f)_(t & f)_(f & t)_(t & t)" is a boolean statement.
Are you saying that
"((f # t)&(f # t)) is simultaneously (f & f)_(t & f)_(f & t)_(t & t)" is simultaneously "(f & f)_(t & f)_(f & t)_(t & t)"?
And even if you are, isn't this new statement of yours true? (according to you)
<--r--> ^
t t |
# # u
f f |
| | v
|&__|_
|Yes, because it is consistent it is also incomplete and context depended, but unlike an excluded-middle logical system, it is not looking at vagueness as an enemy that we have to distinct by more and more accurate definitions.Russell E. Rierson said:If your complementary logic is context dependent, it still must have an invariant structure that gives a meaningful interpretation?
You are mixing between the existence of some system and it?s logical reasoning.
Please show us (t & f) as a valid(=1=existing) state in an excluded-middle system.
I used 'v' letter as an arrowhead in my diagram.what is u, what is r, and for that matter what is v?
and you can't have probabilties between 1 and 2 (unless it is 1).
AND and XOR connectives are independed and can be changed according to the "logical environment" that using them.Matt said:so the and and xor symbols you are using aren't the usual and and xor symbols. so you need to define them. (ie what they do)
My example of Mandelbrot set is this:Matt Grime said:don't understand how you can say that you can't describe QM with boolean logic seeing as without it you would never have learned about it in the first place. all the experiments you know of and theory is done in boolean logic.
AND and XOR connectives are independed and can be changed according to the "logical environment" that using them.Matt said:so the and and xor symbols you are using aren't the usual and and xor symbols. so you need to define them. (ie what they do)
<--[B]r[/B]--> ^
t t |
# # [B]u[/B]
f f |
| | v
|&__|_
| f t
| |
|#__|
| Uncertainty
<-Redundancy->^
d d d d |
# # # # |
c c c c |
# # # # |
b b b b |
# # # # |
{a, a, a, a} V
. . . .
| | | |
| | | |
| | | | <--(First 4-valued logical form)
| | | |
| | | |
|&_|&_|&_|_
|
={x,x,x,x}
{a, b, c, d}
. . . .
| | | |
|#_| | |
| | | <--(Last 4-valued logical form)
|#____| |
| |
|#_______|
|
={{{{x},x},x},x}
[b]
============>>>
Uncertainty
<-Redundancy->^
d d d d | d d d d
# # # # | # # # #
c c c c | c c c c
# # # # | # # # #
b b b b | b b b b b b b b b b
# # # # | # # # # # # # # # #
{a, a, a, a} V {a, a, a, a} {a, b, a, a} {a, a, a, a}
. . . . . . . . . . . . . . . .
| | | | | | | | | | | | | | | |
| | | | |&_|_ | | |#_| | | |&_|_ |&_|_
| | | | | | | | | | | |
| | | | | | | | | | | |
| | | | | | | | | | | |
|&_|&_|&_|_ |&____|&_|_ |&____|&_|_ |&____|____
| | | |
{x,x,x,x} {x,x},x,x} {{{x},x},x,x} {{x,x},{x,x}}
c c c
# # #
b b b b b b b
# # # # # # #
{a, b, a, a} {a, b, a, b} {a, a, a, d} {a, a, c, d}
. . . . . . . . . . . . . . . .
| | | | | | | | | | | | | | | |
|#_| |&_|_ |#_| |#_| | | | | |&_|_ | |
| | | | | | | | | | |
| | | | |&_|&_|_ | |#____| |
| | | | | | | |
|&____|____ |&____|____ |#_______| |#_______|
| | | |
{{{x},x},{x,x}} {{{x},x},{{x},x}} {{x,x,x},x} {{{x,x},x},x}
{a, b, c, d}
. . . .
| | | |
|#_| | |
| | |
|#____| |
| |
|#_______|
|
{{{{x},x},x},x}
[/b] b b
# #
a a
. .
| |
|&__|_
|
[b]
a b
. .
| | <--- (Standard Math logical system fundamental building-block)
|#__|
|
[/b]I know it, but in 1-dim all you can get is the shadow of what you can find between 1-dim and 2-dim, isn't it?mandelbrot's set doesn't have integer dimension...
Please explain Why do you think they are not defined?still not defined uncertainty and redundancy, non-standard terms.