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Iconoclastic*thoughts*on*Spencer*Brown’s*Laws*of*Form*
*
Eric%Werner%
OARF.org%
ericwerner.com%
eric.werner@oarf.org%
%
Introduction:*
These%are%some%simple%first%impressions%of%Spencer%Brown’s%book%‘Laws%of%Form’(1).%
Brown’s%writing%style%is%so%obscure%that%it%has%more%the%flavor%of%a%religious%text%
rather%than%a%philosophical%tract.%%Indeed%some%of%my%friends%and%colleagues%seem%to%
worship%him%much%like%a%prophet.%%%And,%precisely%because%his%style%is%so%terse%and%
idiosyncratic%many%interpretations%of%his%work%are%possible.%%This%essay%is%just%one%
way%of%looking%at%this%curious%author.%%It%is%a%bit%iconoclastic%in%that%it%attempts%to%
break%the%aura%generated%by%Spencer’s%obscurantism.%%
%
This%essay%is%mostly%copied%from%an%entry%in%my%Journal%of%Research%Jan%19,%2005(2).%%
I%was%influenced%by%discussions%with%Dr.%Thomas%Hölscher%on%Spencer%Brown.%He%
later%published%an%introductory%work%on%Laws%of%Form%(3).%%These%early%discussions,%
which%occurred%years%prior%to%the%publication%of%his%book,%led%me%to%read%Spencer%
Brown%in%the%first%place.%%Since%my%Journal%entry(2)%much%has%been%written%about%
Spencer%Brown%that%I%have%not%had%the%time%to%read.%%My%apologies%to%those%many%
authors%for%the%lack%of%citations%acknowledging%their%difficult%efforts%in%clarifying%
Laws%of%Form.%%In%spite%of%its%naiveté,%hopefully%this%essay%will%be%of%interest%to%some%
of%the%philosophers%and%logicians%thinking%about%Spencer%Brown.%
*
Dimensions*and*Objects:%%
What%is%the%relationship%between%a%dimension%and%object%in%Spencer-Brown?%%Given%
that%a%distinction%is%needed%to%form%an%object%in%order%to%separate%it%from%its%
surrounding%space,%the%distinction%itself%would%not%provide%dimensional%
information.%%Or%it%need%not%do%so.%%Thus%we%can%have%a%one-dimensional%space.%%
%
Example%%1.%%%...........................................................................%
%
Now%we%make%a%distinction:%%
%
Ex%2.%%.........................*................................................%
%
The%distinction%just%separates%the%space%into%two.%%We%could%then%make%another%
distinction%or%mark%to%form%either%a%one-dimensional%object:%
%
Ex%3.%%%......*-------*..........%%
%
Or%a%space%between%two%spaces%%
%
Ex%4.%%%................*..............*....................%
%
or%two%(infinite%objects?)%separated%by%one%space%
%
Ex%5.%%%--------------*..............*----------------%
%
or%we%could%view%an%object%as%a%series%of%distinctions%or%marks%
%
Ex%6.%%%....................***********.......................................%
%
Rmk%1.%%Here%the%notion%of%a%space%already%has%a%direction,%an%ordering%of%
coordinates.%%It%implicitly%makes%possible%or%virtual%distinctions%at%each%coordinate.%%
If%the%space%is%finite%and%unbounded%e.g.,%a%circle%then%ex5%is%just%one%object.%%%
%
Rmk%2.%%Actually,%instead%of%three%marks%‘.’,%%‘*’%and%‘-‘,%we%just%need%two%marks,%say%
dash%‘-‘%for%space%and%star%‘*’%for%distinctions.%%%
%
Problem%1.%But%having%three%marks%allows%us%to%separate%distinctions%that%form%
boundaries%or%assign%places%to%space,%from%actual%objects%existing%in%space.%%Is%this%
necessary?%%%
%
Rmk%3.%%Observers.%In%making%distinctions%there%would%appear%to%be%an%observer%
who%makes%the%distinctions.%%
%
Rmk%4.%%Unique*IDs.%If%we%have%more%than%one%object%we%need%to%have%a%way%of%
separating%those%objects.%%Are%the%objects%impenetrable?%%Can%they%be%fused?%Do%the%
objects%have%unique%ID's%that%allow%them%to%identify%themselves%and%distinguish%
themselves%from%other%objects?%%This%is%the%way%living%systems%solve%the%problem.%%
They%have%identifiers%that%allow%the%cells%to%identify%foreign%cells%or%objects.%%%
%
Problem%2.%%%With%only%two%symbols%we%cannot%represent%two%objects%next%to%one%
another.%
%
Ex%7.%%%...................*-------**--------*..................%
%
%
%
Problem%3.%How%do%we%represent%an%object%inside%another?%
%
Ex%%8%%%..........*------*-----*--------*%
%%%
Problem%4.%%This%could%be%one%object%inside%another%or%three%objects%next%to%one%
another%or%three%objects%with%one%inside%one%of%the%other%ones.%%
%
Rmk%5.%IDs*and*Separation:%If%we%give%objects%unique%ID's%(using%numbers%for%
example)%then%we%can%separate%them.%
%
Ex%9.%%%...........*111*2222*11111*..........%%%%%%Object%2%inside%object%1.%%%
%
Ex%10.%%%............*111111.........11111111*......%%%%%Space%inside%object%1.%%
%
Is%this%the%same%as%the%following?%
%
Ex%11.%%%.........*11111*.........*11111111*.......%%%%%%Appears%to%be%two%objects%that%are%the%
same%yet%have%different%sizes.%Odd%indeed.%%
%
Concluding*thoughts:*
One%of%the%main%problems%with%Laws%of%Form%is%that%Brown%keeps%introducing%new%
concepts%without%motivation%or%logical%foundation.%%For%example,%he%introduces%the%
notion%of%a%boundary%as%that%which%cannot%be%crossed.%%However,%then%he%introduces%
the%notion%of%tunneling%as%a%way%to%get%around%boundaries.%This%is%done%without%the%
slightest%motivation.%%It%is%ad%hoc.%%He%also%introduces%concepts%that%make%significant%
psychological%assumptions%about%an%observer.%%To%draw%a%distinction%is%assumed%to%
be%the%most%primitive%act.%%However,%this%is%done%without%any%justification.%
*
What*is*most*disturbing*about*Spencer*Brown:%*
There%is%a%persistent%confusion%between%an%observer's%view%of%a%object%and%its%
surrounding%space%and%boundaries%with%the%object%itself.%%Spencer%Brown%implicitly%
assumes%an%observer%when%a%distinction%is%drawn.%%In%doing%that%he%draws%in%a%huge%
ontology%into%the%basis%of%his%theory%when%at%the%same%time%he%trying%to%start%with%no%
presuppositions.%%%%%
%
%
1.%G.%S.%Brown,%Laws(of(Form((Julian%Press,%New%York,%1972).%
2.%E.%Werner,%Journals%of%Research.%%(1971-2019).%
3.%T.%Schönwälder-Kuntze,%Wille,%K.%,%Hölscher,%T.%,%George(Spencer(Brown(-(Eine(
Einführung(in(die(„Laws(of(Form“.%%(Springer,%2009).%
%
