Fuzziness

[Guest guest]

" So far as the laws of mathematics refer to reality, they are not certain.

And so far as they are certain, they do not refer to reality. " -Albert

Einstein, Geometry and Experience

 

Dear List,

 

Those who are interested in Nag's dialectics may want to read the

following introduction.

 

~dave

 

300 years B.C., the Greek philosopher, Aristotle came up with binary

logic(0,1), which is now the principle foundation of Mathematics. It came

down to one law: A or not-A, either this or not this. For example, a typical

rose is either red or not red. It cannot be red and not red. Every statement

or sentence is true or false or has the truth value 1 or 0. This is

Aristotle's law of bivalence and was philosophically correct for over two

thousand years.

Two centuries before Aristotle, Buddha, had the belief which contradicted

the black-and-white world of worlds, which went beyond the bivalent cocoon

and see the world as it is, filled with contradictions, with things and not

things. He stated that a rose, could be to a certain degree completely red,

but at the same time could also be at a certain degree not red. Meaning that

it can be red and not red at the same time. Conventional(Boolean) logic

states that a glass can be full or not full of water. However, suppose one

were to fill the glass only halfway. Then the glass can be half-full and

half-not-full. Clearly, this disprove's Aristotle's law of bivalence. This

concept of certain degree or multivalence is the fundamental concept which

propelled Zader Lofti of University Berkely in the 1960's to introduce fuzzy

logic.

 

 

 

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[Guest guest]

i'm not a mathematician or a logician or a scientist but i think

aristotle was *also* right in his own way. our computers run on

binary system. they seem to work ok.

 

when we look at two identical objects, such as pentium 4 chips,

they're never identical at the quantum level. yet for practical

reasons we say " two chips " even though there is no such thing

as " two " chips in the physical world. numbers are ideals, invention

of the human mind to process information. with its limited

processing capacity there is no way the human mind can account for

all the possibilities. another example is a " car. " we cannot simply

list all the possible type of cars out there and name them as car

type 01, 02, 03...and so on. when we say a car, it's an abstract.

we recognize the abstract car as " one " car. also our minds become

emotionally attached to the idealization of ideas, ideal cars etc,

but that's a different topic. in the world of ideals, in the world

of aristotle, it's true that it's either one car or zero car. in

other words, aristotle's logic mimics how our mind works, observes at

the locomotive level.

 

as we move away from the world of ideal numbers into the " quantum "

world, things get complicated. instead of a simple 1 car we have

countless, *nearly* uncertain possibilities. that's one of the

reasons why i like nisargadatta's response when a seeker asked him

why his people (hindus) believed in karma, etc. maharaj said it's a

gross approximation. no matter how sophisticated they are, all models

of reality are built on gross approximations which depend on the fact

that the volitile quantum level won't seem to effect the observable

locomotive level that much.

 

this subject gets even more complicated at the qualitative level and

it's getting late to go there.

 

hur

 

 

 

Nisargadatta, " Dave Sirjue " <davesirjue@h...> wrote:

>

> " So far as the laws of mathematics refer to reality, they are not

certain.

> And so far as they are certain, they do not refer to reality. " -

Albert

> Einstein, Geometry and Experience

>

> Dear List,

>

> Those who are interested in Nag's dialectics may want to read the

> following introduction.

>

> ~dave

>

> 300 years B.C., the Greek philosopher, Aristotle came up with

binary

> logic(0,1), which is now the principle foundation of Mathematics.

It came

> down to one law: A or not-A, either this or not this. For example,

a typical

> rose is either red or not red. It cannot be red and not red. Every

statement

> or sentence is true or false or has the truth value 1 or 0. This is

> Aristotle's law of bivalence and was philosophically correct for

over two

> thousand years.

> Two centuries before Aristotle, Buddha, had the belief which

contradicted

> the black-and-white world of worlds, which went beyond the bivalent

cocoon

> and see the world as it is, filled with contradictions, with things

and not

> things. He stated that a rose, could be to a certain degree

completely red,

> but at the same time could also be at a certain degree not red.

Meaning that

> it can be red and not red at the same time. Conventional(Boolean)

logic

> states that a glass can be full or not full of water. However,

suppose one

> were to fill the glass only halfway. Then the glass can be half-

full and

> half-not-full. Clearly, this disprove's Aristotle's law of

bivalence. This

> concept of certain degree or multivalence is the fundamental

concept which

> propelled Zader Lofti of University Berkely in the 1960's to

introduce fuzzy

> logic.

>

>

>

> _______________

> MSN Photos is the easiest way to share and print your photos:

> http://photos.msn.com/support/worldwide.aspx