Erez Elul’s «Pile System» ( http://iswith.info ) is a «new, radically relationist approach to data, structures and computing. Instead of representing and storing data, Pile registers only relations between data elements and stores relational patterns in a novel, non-hierarchic layered structure which can be fluidly traversed«.
Well, I had never heard of the «Pile System» till recently (May 2007). Then, one day I used the phrase «Multiple Form Logic» in Google search, just in case there exist web references to it that have escaped my attention.
Well, it appears that Mr. Ralf Barkow, who is a Pile System researcher, has been exploring intriguing new relationships between «Multiple Form Logic» and «Pile-Objects«, since about a year ago. E.g. in the following blog-posting Ralf deals with my «three axioms of Multiple Form Logic«, finding them compatible with Erez Elul’s «Pile»:
In another blog-post Ralf talks discusses my «First Axiom» (of Multiple Form Logic), re-expressing it in «Pile_objects» notation:
However, the most intriguing axiom of «Multiple Form Logic» is -undoubtedly- Axiom 3:
AXIOM 3: Perception is (reversible) internalisation
A , X # ( A, B) = A , X # B
In a (self-) Boundary of Perception X, any-thing A that exists outside the boundary, can also be brought inside the boundary. Conversely, any-thing A that exists inside a boundary of perception X can also be cancelled out iff (if and only if) it (or a “copy of itself”) also exists outside the boundary X.
I.e.: Any-thing we see outside ourselves, we may assume inside ourselves. Any-thing we assume inside ourselves, we need not assume (as something «imaginary«) iff we can also see it (as a «fact») outside ourselves.
This Third Axiom expresses a transcendence of both… Materialism and Idealism (If you can read Greek and are also… politically conscious read this post and my short comment here). Why? Because both Hegel and Marx had built their systems on the basis of (so-called) «identity of Reality and Reason», i.e. «What is Real is what is also rational» (logical and reason-able). The Third Axiom -on the contrary- very strongly suggests that Logic (and Reason etc.) is created ex-nihilo (which is a refutation of fundamentalist Christian flawed anti-nihilism – e.g. the Greek comment here); as an inescapable (non-nihilistic) formal consequence of the Relationship between Imagination ™ and Reality ™; more precisely as a consequence of multiple fundamental distinctions, between the Inner and The Outer World of Multiple Forms or… Beings!
These Inner and Outer worlds, are -nevertheless- initially indistinguishable or inseparable. As George Spencer-Brown said: A World that «seems initially like sifting sand between our feet, where initially boundaries may be drawn in any way we please».
UPDATE: Another post in this blog which is extremely relevant (to these radical ideas) is: » The CONSISTENCY of ODYSSEUS ELYTIS-”Genesis” with George SPENCER-BROWN’s ideas in “LAWS of FORM” (and the Greek version of the latter, «Η συνάφεια της «Γένεσης» του Ελύτη (Άξιον Εστί) με τις ιδέες του George Spencer-Brown στο βιβλίο του Laws of Form»).
Well, I still can’t understand very well Pile System Notation (although working on it) but I feel pleased that my «Multiple Form Logic» system is now -apparently- regarded as a respectable generalization of George Spencer Brown‘s «Laws of Form«, as well as formally compatible with «Pile», etc.
Recent extensions by «disciples»: Since 2003, a new web site (multiforms.netfirms.com, «Multiple Form Logic») claims to have «generalised Spencer-Brown‘s system into Multiple Truth Values» and to be «more consistent with Experience»; it uses the XOR operator and three «alternative axioms». The author is a member of the «Laws of Form Forum», where this theory (among others) was presented and discussed in recent years.
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