*‘*

**Th**__e__**Ockhamian****Systematic**__Dialectic__of

*The Science*__s__*, c.*

**1323**C.E.,

__EXTENDED__*--*

*‘*:

**’**__Dialectogram__*‘*Seldon

__Dyad__ic

*Function*__Extended__Ockhamian__Dialectic__of**.**

*The Science*__s__
Dear

**,***Readers*
The

**of the***case**Philosophical*__D__*omain***the***of***,***late Medieval***,***Ockhamian*__Du__alistic__class__ification of**,***The*__S__cience__s__*propounded**circa***1323**C.E.,*may**also**count**as**yet*__an__other**of***case**possibly*__in__advertent__dialectic__al*‘*in the**content**-**structure**’**of***work**a***-- in***philosopher**this***, in the***case***of***work**a*__medieval__**whose***philosopher***the***view*__s____still__register within__modern__*“***Philosophy of Science**”.**of**

*This hypothesis*

__in__advertence**,**

*must***,**

*however***the**

*confront***of the widespread exposure of**

*fact***of Ockham’s**

*philosopher*__s__

*time*

*and***to**

*clime*

*ancient*

*philosophical***regarding**

*view*__s__**-- most prominently, to the**

__dialectic__

*view*__s__**of Plato**

*thereupon***,**

*and***, of Aristotle --**

*e*__speci__ally

*a***which**

*fact*

*may*

*cast*

*some*

*doubt*

*upon***, especially if, as in some still-extant tradition**

*this hypothesis*__s__, "dialectic" is restricted to the moment of opposition, or of antithesis, between two related term

__s__.

The medieval philosopher William of Ockham,

*circa***1323**C.E., developed a__bi__nary taxonomy of the science__s__, rooted ultimately in a__bi__nary ‘taxonomy of word__s__’, one that harks back to ancient Stoic philosoph__ies__of language.
The purpose of the ‘dialectogram’ below is to note how the
formulation of Ockham’s taxonom

__ies__in*a**‘*,**-**__meta__**equation**’*via***t**__h__**e**_{N}__Q__**,**__dialectic__al__ideo__graphy*as**a**systematic**-*__dialectic__al*‘***-**__ideo__**ontological**’*categorial***, when***progression***is iterated one**__i__t__s__tep beyond the**2**categor__ies__of science posited by Ockham, yields what**w****solve herein as a ‘**__e____pre__-construction’, or ‘‘‘prediction’’’, of the ‘__meta__-science’__speci__es of ‘‘‘Psychohistory’’’,**, via two**__Y____sub__-speci__es__of that__speci__es, a__speci__es of science that is still only nascent, and only ‘fractionally present’ today.
Regarding Ockham’s philosophical taxonomy of the science

__s__, W. L. Reese wrote as follows**: “Ockham makes an important distinction between**^{*}*categorematic*and*syncategorematic*terms. Most common nouns are*categorematic*, while words such as “not”, “all,” and “some” are*syn-categorematic*.”
“...Terms that refer to things are called terms of

*first intention*. Terms referring to terms of first intention are called terms of*second intention***.”**^{‡}
“In one sense the syncategorematic terms mentioned above are
second intentional; but, as Ockham wishes to use the distinction, categorematic
terms and syncategorematic terms, functioning together [

**F**.**.**__E__**.: i.e., forming sentence**__D____s__/proposition__s__], refer to things. “All men are mortal” is thus first intentional. But when we use terms such as “genus,” “species,” and “difference” we are using terms of second intention [**F**.**.**__E__**.: e.g., to form**__D__*proposition*of second intention]. Propositions utilizing such terms refer not to the world, but to terms [and to__s__*proposition*--__s__**F**.**.**__E__**.] of first intention.”**__D__
“...On the basis of the distinction just mentioned, Ockham
divides the sciences into two types.

*Scientia rationalis*, or rational science, is second intentional. Logic is a science of this type.*Scientia Realis*is first intentional. Physics is an example of a science of real things.**”****[W. L. Reese,**^{*}**, Humanities Press, NJ: 1980].**__Dictionary of Philosophy and Religion__**[cf. George Boole on “primary” vs. “secondary” proposition**^{‡}__s__, in George Boole, ...**..., NY: Dover Publications,**__Laws of Thought__**1958**, pp.**52**-**53**].
Suppose we denote the category for

*the world of*__r__*eal thing*by__s__**.**__r__
Suppose further that we solve for

__r__**as**^{2}__r__**+**, with__t__**denoting the category of “**__t__**erm**__t____s__”.
That is, assert [‘

**|-**’] the definition [‘__’] of the__**=**__q__**in --**_{rr}

__r__

^{2}**=**

__r__(__r__)**=**

__r__

*of*

__r__**=**

__r__

**+**

__Delta__**(**

__r__**)**

**=**

__r__

**+**

__q__**as connoting**

_{rr}**:**

__t__

*The*

__r__

*critique of*

__r__

__itself__

*as comprehending the entire known present*

__D__*omain of*

__r__*eal thing*__s__**=**

__r__

**+**

__Delta__**(**

__r__**)**

**=**

__r__

**+**

__q__

_{rr}

**|-**

**=**

__r__**+**.

__t__
If so, then

**implies the**__t__**of***presence***[**__h__*uman***],***oid*__self__-and-other-aware,*language**-*capable*“*--**thing**”__s__*“*that**thing**”__s__**,***have***, arisen***from long ago***via the****-localized ‘***brain*__s____self__-refl__e__xion’, the ‘self-involution’ [cf. Chardin],*the bending*[‘flex’]*back*[‘re’]*upon itself*[‘__self__’]*of the ‘*__pre__-self-aware*’ world of*__r__*eal*,**thing**__s__**, so that**__r__**of the thereby-resulting***part*__s__*‘***thing**-__s__**world**’*‘‘‘*, in however**’’’**__contain__**and***distorted***a way,***omissive**“*of**all**”**, if only via***it***erm**__t____s__**.***/language***What, then, happens if we, again,**

*¿**“*;

**square**”*if we, this time, square the result of our*

*earlier*

*squaring?***:**

__This__**(**

__r__**+**

__t__)^{2}=

*the***(**

__r__**+**

__t__)

*critique of***(**

__r__**+**

__t__)**=**

__r__**+**

__t__**+**

__q___{tr}**+**

**.**

__q___{tt}**What if we solve for**

*¿*

__q__

_{t}**in**

_{r}**(**

__r__**+**

__t__)^{2}=__r__**+**

__t__**+**

__q___{tr}**+**

**as connoting the comprehension, explanation, mental appropriation, or mental assimilation of the**

__q___{tt}*‘*by

**thing**-__s__**world**’**erm**

__t____s__-- by

**; by**

*language*

__h__*uman collective**“*

**universal**

*labor**”*; by

*the collective*

__h__*uman***, as merged into**

*mind**‘*

**t**__h__e

__h__*uman*

**’**__Phe__nome**?****the «**

__Then__*arithmos*» of all “true” [

*scientific consensus*] proposition

__s__

*/***erm**

__t____s__about

**eal**

__r__*forms the “*

**thing**__s____ex__ten

__s__ion” which represents the “

__in__ten

__s__ion” of

*the science*

__s__of**eal**

__r__*,*

**thing**__s__**»**Ockham’s ‘‘‘«

__S__*cientia*

*Rea***»’’’.**

__L__*is*
We may also denote this ‘‘‘«

__S__*cientia**Rea***»’’’ by**__L__*is***, such that**__L__**stands for the «**__L__*arithmos*»**category of the proposition***/*__s__“of first intention”, that constitute the ‘‘‘«__S__*cientia**Rea***»’’’.**__L__*is*
If we then decide to solve for

__q__**in**_{tt}**(**__r__**+**__t__)^{2}=__r__**+**__t__**+**__q___{tr}**+****as connoting the**__q___{tt}__self__-comprehension,

__self__-explanation,

*mental*__self__-appropriation, or

*mental*__self__-assimilation of the ‘

__t__*erm*__s__*-*

**world**’

*by*

__t__*erm*__s__**, i.e., by**

*themsel*__ves__**; by**

*language*

__h__*uman collective**“*; by

**universal labor**”

*the collective*

__h__*uman***, merged into**

*mind**‘*

**t**__h__e

__h__*uman**, what next results*

**’**__Phe__nome

*?***: The «**

__This__*arithmos*» of all “true” [

*scientific consensus*] proposition

__s__

*about*;

**proposition**__s__

__t__*erm*__s__about**, as found, e.g., in**

__t__*erm*__s__**and**

*logic***, forms the “**

*mathematics*__ex__ten

__s__ion” which represents the “

__in__ten

__s__ion” of the science

__s__

**“of second inten**

__t__ion”,

**»**Ockham’s ‘‘‘«

__S__*cientia*

*Ratio***»’’’.**

__N__*alis*
We may also denote this ‘‘‘«

__S__*cientia**Ratio***»’’’ by**__N__*alis***, standing for that**__N__**«***arithmos*»**category of such proposition***/*__s__as*i***unit**__t__*s*__s__.
In sum, we have thus solved as follows --

**(**

__r__**+**

__t__)^{2}=__r__**+**

__t__**+**

__q___{tr}**+**

__q___{tt}

**|-**

**=**

__r__**+**

__t__**+**

__L__

**+**

**.**

__N__In the first image pasted-in below, the

*‘*image,

**dialectogram**’**w**

__e__**Ockham’s**

__extend__**,**

__bi__nary**taxonomy of the science**

__du__alistic__s__, by ‘re-«

**»-izing on**

*arché*

__q__

_{t}**, solved-for as**

_{r}**, and by then**

__L__

*squaring***, thus generating**

__L__

*The*

__L__

*critique of*

__L__

__itself__

*as comprehending the entire known present*

__D__*omain of***--**

*the Science*__s__

__L__

^{2}

**=**

__L__**(**

__L__**)**

**=**

__L__

*of*

__L__

**=**

__L__

**+**

__Delta__**(**

__L__**)**

**=**

__L__

**+**

__q__

_{LL}

**|-**

**=**

__L__

**+**

__N__
-- i.e., so as to

__net__*-*generate__q__**, which**_{LL}**w****solve for**__e__**define as***/***, and which**__N__**w****identify with the fourth term,**__e____q__**, in**_{tt}**(**__r__**+**__t__)^{2}=__r__**+**__t__**+**__q___{tr}**+****.**__q___{tt}**W****then again**__e__**, but this time***square***w**__e__square**(**__L__**+****, to obtain --**__N__)**(**

__L__**+**

__N__)

^{2}

**|-**

**=**

__L__

**+**

__N__**+**

__N__**(**

__L__**)**

**+**

__N__**(**

__N__**)**

**|-**

**=**

__L__

**+**

__N__**+**

__q__

_{N}

_{L}**+**

__q__**.**

_{NN}
In the context of the foregoing

*‘*,**-**__meta__**equation**’**w****solve for the**__e__*net*result of__N__**(**__L__**)**, namely__q___{N}**-- the ratio**_{L}**al analysis**__N__**comprehension***/***assimilation of the system of proposition***/*__s__set forth by the science__s__of the ‘‘‘«__S__*cientia**Rea***»’’’ -- as connoting that portion of the still nascent ‘meta-science’ of**__L__*is**‘‘‘*,**Psychohistory**’’’**, whose proposition**__Y____s__seek, critically, to__explain__the difference__s__, the strife, the opposition__s__, including the*ideological***, among the theor***aspect*__s____ies__of the**science**__L____s__.**,**

*Likewise***w**

**solve for the**

__e__*net*result of

__N__**(**

__N__**)**, namely

__q__**, the ratio**

_{NN}**al analysis**

__N__**-comprehension**

*/***assimilation of the system of proposition**

*/*__s__set forth by the science

__s__of the ‘‘‘«

__S__*cientia*

*Ratio***»’’’, as connoting that portion of the ‘meta-science’ of**

__N__*alis**‘‘‘*,

**Psychohistory**’’’**, whose proposition**

__Y____s__seek, critically, to

__explain__the difference

__s__, the strife, the opposition

__s__, including the

*ideological***, among the theor**

*aspect*__s____ies__of the

**science**

__N____s__.

If we solve for

**define***/**‘‘‘*as a whole, denoted by**Psychohistory**’’’**, as the ‘‘‘sum’’’ of**__Y__*net*__N__**(**__L__**)**and*net*__N__**(**__N__**)**--**(**

__N__(__L__)**-**

__L__)**+**

**(**

__N__(__N__)**-**

__N__)**=**

**(**

__L__**+**

__q__

_{N}

_{L}

**-**

__L__)**+**

**(**

__N__**+**

__q__

_{NN}

**-**

__N__)**=**

__q__

_{N}

_{L}**+**

__q__

_{NN}**|-**

__=__

__Y__

_{1}**+**

__Y__

_{2}**|-**

**=**

__Y__

**Then what**

*--*

**comes to stand for includes**

__Y__**of**

*immanent critique*__s__**within the**

*ideology***science**

__s__

*in general*; within

*all*of the sciences

**--**an ‘ideo-ontological’ innovation that was pioneered by Karl Marx, in his four-volume treatise

__Capital____,__.

*A Critique of Political Economy*
In

**o**__ur__**, the meaning of***view*__q__**must extend beyond the nature of**_{LL}__formal__**, including***logic*__formal__*mathematical***, to include project***logic*__s__like that of Hegel’s**, whether or not**__Science of Logic__**holds that Hegel’s***one***succeeded in fulfilling such a project. Each**__Science of Logic__*proposition**-*in__unit__**that invokes a given universal category becomes a**__L____sub__*-*in that**unit****of***unit***that defines that universal category as the inten**__N____s__ion of the entire exten__s__ion of__L__**that invoke***proposition*__s__**use***/***refer to that universal category.***/***W**

**therefore adopt the word**

__e____s__of Tony Smith, and of Hegel, as quoted in the second image pasted-in below, to explicate why it is that

**w**

**assert [‘**

__e__**|-**’]

**to be the correct definition [‘**

__N____’] for__

**=**

__q__**in --**

_{LL}

__L__

^{2}

**=**

__L__**(**

__L__**)**

**=**

__L__

*of*

__L__

**=**

__L__

**+**

__Delta__**(**

__L__**)**

**=**

__L__

**+**

__q__

_{LL}

**|-**

**=**

__L__

**+**

**--**

__N__
with

__q__**connoting the [propositional] self-reflexion of the**_{LL}**science**__L____s__upon themsel__ves__.
If

**o****solution of**__ur__**(**__L__**+**__N__)^{2}**=**__L__**+**__N__**+**__q___{N}_{L}**+**__q__**is coherent, it should also suggest a meaningful solution for all of the term**_{NN}__s__in, including the new term__s__in --**(**

__r__**+**

__t__**+**

__L__

**+**

__N__**)**

^{2}=__r__**+**

__t__**+**

__L__

**+**

__N__

**+**

__q__

_{N}

_{r}**+**

__q__

_{N}

_{t}

**+**

__q__

_{N}

_{L}**+**

__q__**.**

_{NN}**W**

**will leave the explication of**

__e__**o**

**solution**

__ur____s__for those new terms,

__q__

_{N}**and**

_{r}

__q__

_{N}**, for**

_{t}**,**

*another***venue, leaving the problem, for now, in the hand**

*later*__s__of

**,**

*you***o**

__ur__**.**

*reader*__s__

*:*

__Hint__

__q__

_{N}**has something to do with the ratio**

_{t}**al, scientific analysis of, and “accounting for”, the**

__N__**erm**

__t____s__of “natural language

__s__”, and

__q__

_{N}**with the ratio**

_{r}**al, scientific analysis and explanation of**

__N__

*our***of “**

*perception*__s__**eal” [esp. of**

__r__**]**

__phys__ical**.**

*thing*__s__
FYI: Much of the work
of Karl Seldon, and of his collaborators, including work by “yours truly”, is
available for

**free-of-charge download via --***your*
Regards,

Miguel Detonacciones,

Member,

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

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