**Part ****12**:
Seldon’s* Insight*__s__
Series -- *The
Core of the** ‘*__CONTRA__-**Boolean**’
__Dialectical__ **Principle**: *‘‘‘***When a Something Becomes**
‘__OF__ Itself’, *It also becomes Something Else*,* Something
Other*,* Something *__More__
--* Something *__Q__*ual**itatively*,* Ontologically DIFFERENT!**’’’*

Dear *Readers*,

It is my pleasure, and my
honor, as an Officer of the **Foundation
**__Encyclopedia
Dialectica__ [**F**.__E__.__D__.]
Office of Public Liaison, to share with *you*, from time to time, as they are approved
for public release by the **F**.__E__.__D__. General Council, key
excerpts from the internal writings, and from the internal sayings, of **o**__ur__ *co**-***founder**,
Karl Seldon.

The *twelfth and final *such
release in this *new*
series is entered below [Some __E__.__D__. standard edits have been applied, in the version __present__ed below, to the direct
transcript of our co-founder’s discourse].

For *more information *__regarding__,
and for [*further*]
*instantiation*__s__
__of__,
these Seldonian *insight*__s__,
see --

ENJOY!

Regards,

Miguel Detonacciones,

Member, **Foundation**** **__Encyclopedia
Dialectica__ [**F**.__E__.__D__.],

Participant, **F**.__E__.__D__. Special Council for Public
Liaison,

Officer, **F**.__E__.__D__. Office of Public Liaison.

**“**... The *key* *insight* that the _{N}__Q_______ *‘*__contra__-**Boolean**
**arithmetic**’ -- **o**__ur__ *‘***first** __dialectical__ **arithmetic**’ -- was *engineered* to *capture* *can* *also* be *stated* as *follows* -- ‘*When an arithmos of monad*__s__ becomes* ‘*__OF__ Itself’, *It also becomes something*__s__ else,* something*__s__ other,* something*__s__ new and __un__precedented [*if* *this* is the *first* *occasion* of *its* *becoming* *‘*__OF__
Itself’];* something*__s__
__more__ --* something*__s__ __Q__*ual**itatively*,* ontologically DIFFERENT!*’.

*“***At**
**first**, I did *not* *grasp* the *mathematical* *modeling* *efficacy* of the *‘‘‘*__e__voluteness’’’ *product*__s__*-***principle**__s__. *At* *first*,
I *explored* *‘‘‘*__con__volute’’’ *product**-***rule**__s__ *and* *product* *axiom*__s__, *not* the *‘*__double__-**conservation**
«*aufheben*»*
*__e__volute **product** **rule**’, *not* the *‘***meta**-**catalysis**’ __e__volute **product** **rule**’, *not* the *‘*__triple__-**conservation**
‘**meta**-__gen__ealogical’
__e__volute **product** **rule**’.”

*“***Therefore**,
my *first* *formulation*__s__ of
the *‘*__contra__-**Boolean**
__dialectical__ **principle**’ took the form
--

__x__ **x**** **__x__ **=** __delta__*-*__x__

-- such that __delta__*-*__x__ **~=**
__x__ **&** __delta__*-*__x__ **~>**
__x__ **&** __delta__*-*__x__ **~<**
__x__.”

*“***Thus**,
__delta__*-*__x__ was __non__-__quant__itatively
__un__equal to __x__, *and* *therefore* *must* *be* __qual__itatively, *ontologically* __un__equal to __x__, while *also* *being* *still* *‘***meta**-__gen__ealogically’
__related__
__to__ the
__x__ «*arithmos*» *and*, *thus*, to __its__
«*monad*__s__».”

“This *contrasts*
*sharply* with
the *Boolean* *“***fundamental** **law**”, given by Boole as --

**x** **x**** ****x** **=** **x**, or **x**^{2} **=** **x**, which works for *an* **x** in the solution-set **{0**,**1}**

-- *and*
which Boole “factored-out” into --

**x** **x**** ****(1 ****-**** x)** **=** **0**, *and* *interpreted* as *an* *assertion* of *formal* *logic*’*s core* __non__*-***contradiction**
*principle*:

‘“**x**
**and** *not**-***x** is *nothing*”’.
”

“Nonetheless, the *idea* *all* *along* was that the *in*__ter__action of *an* «*arithmos*», i.e., of *a* *‘‘‘***number**’’’ [*of* «*monad*__s__» or of *unit*__s__ of a *given* *kind*, i.e., of a *given* *category*], __WITH__ __ITSELF__, ‘__x__ **x**** **__x__’, or ‘__x__^{2}’, __its__
*‘*__self__-**product**’,
*interpreted*
by **u**__s__
as *representing*
the *‘***in**__tra__-action’
of the *constituent*
«*monad*__s__»
that __it__
__im__plicitly *represents*, *produces* *an*__other__, *higher* *‘‘‘***number**’’’, *interpreted* by **u**__s__ as *constituting* *a* *new* «*arithmos*», a *‘***cumulum**’ of *‘‘‘***higher**’’’ «*monad*__s__», of «*monad*__s__» of *a* *new*, *‘‘‘***higher**’’’ *kind*.”

*“***This**
**idea** was *expressed* *analytical**-*__geometrically__
by *representing*
this *arithmetic*
*and* *its* *algebra* by *an* *abstract* *space* in which the __s__e__l__f*-***multiplication** of *any* *one* of the *‘*__meta__-**number**__s__’
*already* *constituting* *this* *space* *gives rise to* *a* *new* *axis*, *perpendicular* to *all* of the *previous* *ax*__es__ *extant* for *this* *abstract* *space*.”

“That is, *any*
__s__e__l__f*-***multiplication**
of *a* *‘*__meta__-**number**’
*already* in *this* *space* *gives rise to* *a* __new__ *‘*__meta__-**number**’, as *a* *new* *dimension*; *“***adds**” *a* *new* *orthogonal* *direction* [*in*]to that *space*, so that *the* *space* __expands__, as *a* *result*, *not* *just* __quant__itatively
*but* *dimensionally*. **W**__e__ *interpret* *this* as *defining* *a* *space* *that* *grows* __qual__itatively; *ontologically*, that *breaks*, *and* *breaks* *out* *of* -- __transcends__ -- *its* *“***closure**”, with *every* *new* *such* *arithmetical* *operation*.”

“Such __s__e__l__f*-***multiplication**
was to be *used*
to *model* *actualit*__ies__ in
which the *‘‘‘***singularity**’’’
*resulting* *from* the *crossing* of a *critical* *density*[/*‘‘‘***temperature**’’’] *threshold* *by* *and* *within* a *‘***cumulum**’ of «*monad*__s__» of a *given* «*arithmos*»/*kind*/«__gen__os» is *seen* to *give rise to* a *new* «*arithmos*», of a *new* *kind* of *unit*__s__.”

*“***If**
*we* *interpret* ‘__x__ **x**** **__x__’ after the manner of *classical* *function* *notation*, *then* ‘__x__ **x**** **__x__’ or ‘__x__^{2}’ *becomes* --

__x__**(**__x__)

-- which *can*
be read-off, *per*
*that* *function* *notation*, as ‘__x__ __OF__ __x__’, or as ‘__x__ __OF__ __itself__’. *Thus*, *per*
**o**__ur__ *‘‘‘*__con__volute’’’ *version* of **o**__ur__ *‘*__contra__-**Boolean**’
*fundamental* *‘‘‘***law**’’’: __x__ __OF__ __itself__ *yields* *‘*__delta__-__x__’: __which__
**w**__e__ *interpret* as *representing* *a* *new* «*arithmos*» *of *«*monad*__s__» *that* *are*, *precisely* -- ‘*something*__s__ else,* something*__s__
other,* something*__s__ new and __un__precedented [*if* *this* is the *first* *occasion* of *it*__s__ *becoming* *‘*__OF__ It__s__el__f__’];* something*__s__ __more__
--* something*__s__ __Q__*ual**itatively*,* ontologically DIFFERENT!*’’ -- ‘*something* *ontologically* __REVOLUTIONARY__.”

“If *one*
*looks* for *example*__s__ of ‘__x__s __OF__ __x__s’ in *‘***the **__dialectic__ of Nature’,
*one* *finds* *such* as the following --

‘...[__s__*ub**-***atomic**]
*particle*__s__
__of__ *particle*__s__ -- which
are no longer [__s__*ub**-***atomic**]
*particle*__s__,
but __a__*tomic nucle*__i__.’

‘...*atom*__s__
__of__ *atom*__s__ -- which are
no longer *atom*__s__,
but __m__*olecule*__s__.’

‘...__m__*olecule*__s__
__of__ __m__*olecule*__s__ -- which
are no longer __m__*olecule*__s__,
but [__poly__meric “macromolecules” *and*
__p__*re**-***eukaryotic**,
*or* __p__*rokaryotic*,] *cell*__s__.’

‘...[__p__*rokaryotic*]
*cell*__s__ __of__ *cell*__s__ -- which are no
longer [__p__*rokaryotic*] *cell*__s__, but __e__*ukaryotic* *cell*__s__.’

‘...[__e__*ukaryotic*]
*cell*__s__ __of__ *cell*__s__ -- which are
no longer [__e__*ukaryotic*]
*cell*__s__,
but *“*__multi__-**cellular organism**__s__”.’ ”

“Of course, a *key* *insight*
*along this way*
was to *see*
how *typically*
it was the case that *each*
of the *new* *unit*__s__ of *this* *new* «*arithmos*» *thus* *produced* were *some* *kind* of *‘‘‘***aggregate**’’’ of certain
of the *unit*__s__
*formerly* *inhering* *in* the *“***old**” «*arithmos*»; to *see* that __each__ of the *new* *unit*__s__ was a *‘***self**-**involution**’, a *‘***self**-**internalization**’, a *‘***self**-__meta__-**unit**-**ization**’,
or a *‘***self**-__meta__-**holon**-**ization**’ of *some* definite *‘*__sub__-«*arithmos*»’ of the *thus* *now* *former* *unit*__s__ of the *“***old**” «*arithmos*» -- *and* *seeing*
that *all* of *these* *description*__s__ of *such* *process*__es__ were, in
*their* *unity*, *description*__s__ of *an* «*aufheben*» *annulment*/*elevation*/*conservation* *process*, *and*, *hence*, of a *‘*__gen__e-**ric**’ __dialectic__.**”**