[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 themselves. 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. But. By definition, catalog 2 contains all sets that do NOT contain themselves, so by its own definition, it MUST list itself. _-_-_- 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