[plase use the BACK key to return to your previous pageLaws of Form
(iconosphere entry)

Refer to:  -[Laws of Form]- (in SCI: Maths-)

The so-called "Laws of Form" were the brain child of G. Spenser Brown
in attempting to resolve both the self-referential and Russell's paradoxes.

Following a brief review of these two topics, a discussiojn will
be *attempted* as to how the laws of form act and are used.

When Bertrand Russell and Alfred North WHitehead set out to completely
systemitise maths in the late 1800's, little did they realise how 
completely hopeless the whole problem would soon bcome.

In their monumental task of "starting from scratch" and then carefully
building theorem on theorem until (by #500 or so) they were finally
able to show that indeed 
                           1 + 1 = 2

In the meantime, a chap in Germany by the name of Otto Friche (?sp?) 
was doing the same thing for axiomatic set theory. He had finished
the first volume and sent it off to Russell for commenary. Russell
responded with a simple question which (so the story goes) drove
Friche to suicide.

This so-called "Russell's Paradox" goes something like this:

Consider two catalogs (sets), 

   the first catalog consists of all sets that CONTAIN THEMSELVES.

   the second catalog consists of all sets that do NOT contain 

All, fine and well, we take each set, look at it, and then place
it the correct catalog.

But, of course the two catalogs are themselves sets, so.....

If catalog one contains itself (which it may or may not) then
it is placed in its entries.

If catalog one does NOT contain itself, then it is placed in
catalog two.

Well, and good. Now, for catalog 2.

If catalog 2 DOES contain itself, then it gets listed in
catalog one.

But, wait, it can't contain itself, since it's the catalog that
contains sets that do NOT contain themselves.

Therefore, it must not contain itself.


By definition, catalog 2 contains all sets that do NOT 
contain themselves, so by its own definition, it MUST list

_-_-_- paradox _-_-_-_-_-

This was all (sort of) taken care of by [Goedel's Theorem]

But, still even introducing the "theory of types" as Russell
attempted to do, not much could be done with that nasty
paradox floating around like an albatros around the neck.

Enger, G. Specner Brown.

He postulated a new kind of meta-logic as well as classifying
self-referential problems as equivalently to the imaingary
number i. (The square root of -1).

This helped imensely, although the work still "has problems".
(THere's no escaping Goedel's Theorem).

The Laws of Form