A Model of Generalized

This paper is intended to be a brief note on a mathematical formalization of the following methodology that we term as interactive, integrative and evolutionary in terms of its knowledge-centric order. We will then briefly indicate how such a complex model can be applied to specific problems of economics and social contract. Briefly we examine the chain:

Stock of Complete Knowledge (treated as primal topology), T. T is a universal topology in the sense that it is defined by the Completeness of knowledge called the Stock of Knowledge. Its cardinality, a concept required to generate explainable mappings, is called the supercardinality, SC(T), of T. T thus contains all classes of mathematical union and intersection of its subclasses which are indefinitely many sets. Thus T contains the sum-total in the supercardinal sense of all truth statements and its mathematical complementation comprising false statements. By this mathematical complementation property, T contains the null set and the universal set which is defined by the complementation of the null set. The null set is defined by f = {F }Ç {F '}, where, {F } denotes the complete class of all truth statements; {F '} denotes the complete class of all false statements. In terms of the uniquely universal laws, as of the Unity of God and the cosmic order, the world-systems, self and the other, abstract and experiential knowledge, {F } and {F '} would denote Divine Laws explaining the totality of Truth and the totality of Falsehood. We also call the latter disjoint categories as Knowledge Stock and De-Knowledge Stock, because of their completeness in the supercardinal sense corresponding to their own disjoint spaces. In the end we note that T is fully disjoint between {F } and {F '} while it remains unity in explaining both of these by a singular set of universal laws. {F } is explained by T by Divine Laws premised on Truth; {F '} is explained by the mathematical complementation of the set of same Divine Laws, which because of the universal topological property of T, is also contained in T. Hence, {F }Ì T; {F '}Ì T.

We also note that {F } and {F '} form topologies in their own: For any set of elementary knowledge encompassing the supercardinality, sc of {F }, denoted by {q }sc, sc' of {F '}, the usual properties of a topology are satisfied.

It remains to be explained that {q }scÇ {q '}sc' = f sc e {q }sc, for {q }sc e {F }; {q '}sc' e {F '}. Also, f sc' e {q '}sc'. Here the null sets, f sc and f sc' have been differentiated in order to show their candidacy in the corresponding sets as mentioned above. It is easy to note that if f scÏ {q }sc and if f sc'Ï {q '}sc', then some element of{q '}sc' would belong to{q }sc. Consequently, {q '}sc' e {F }, which would yield {F }Ç {F '}, a contradiction to the topological property of T, as mentioned earlier. The same inference holds if f sc' Ï {q '}sc'. We refer to {q }sc and {q '}sc' knowledge and de-kinowledge flows from the Stocks {F and{F '}, respectively, all emanating from T. Thus by virtue of its singularly complete nature with respect to the emanation of all flows including the Knowledge Stock and De-Knowledge Stock, T denotes the unity of knowledge in the sense of its completeness, uniqueness and thus absoluteness. The last attribute is established by noting that it would be tautology to have any other primordial inclusion of T in another similar set. If that were possible that T would acquire the position of {q }sc È {q '}sc', which would be a subset of T.

The same attributes of completeness, uniqueness and absoluteness of T are established by noting that for sequences if elements, say {q } e {q }sc, lim{q }e {q }sc e {F } (completeness of {F }). Likewise for {F '}. Hence the attribute of completeness of T is established from the property of topology of T in terms of {F } and {F '}. For reasons of integration and consensus in the system, for two sequential values, {q } and {q }*, |{q } - {q }*| < |({q } - lim{q }) - ( {q }* - lim{q }*)| < |({q } - lim{q })| + |{q }* - lim{q }*)| < indefinitely small value. This proves the uniqueness property of T through its topological property in terms of {F } and {F '}. For the absoluteness property of T we note that since T uniquely explains both {F } and {F '}, it is universal in the primordial sense of all sets of {q }sc and {q }sc'. Hence, if there exists T*Í T, then T assumes the role of {q }sc and {q }sc', and T* must become primal, etc. Thus, T*Í T is a tautology.

Construction of knowledge-centered unified world-system

Furthermore, the creative essence of T extends {F } and {F '} to the domain of objectification. Such a domain comprises the observed domain and the abstract domain. Hence, as much as the anthropic world-system is spanned by {F } so also is the relational order through its interactions with the anthropic order.

We will denote the spaces of cognitive entities by {X({q })} and {X'({q '})}. These have their topological properties as well, for {q } ® f X: X({q }) = f({q }). For the entire class of such functionals we obtain, {X({q })} as a monotonic transformation of {q }in real-world relations via a sequence of mappings {f}. But we note that by virtue of the topological property of {q } (hence of {q '}) and the monotonic transformation of X in terms of {q }, that {X{q }}also forms a topology. Likewise is the case of {X'{q '}}in the de-knowledge domain. Now all the properties relating to relationships between {X{q }} and {X'{q '}} will apply. We will not repeat the similar formalization here.

However, the distinction and characterization of the nature of f-functionals must be noted. There are two stages of such functionals here. First, the derivation of knowledge flows from the primal Knowledge Stock at the moment of establishing abiding moral laws is based on immutable attributes which we denote by the symbol A. Thus, ‘A' augments both {F } as well as {q } values as {F }[A] and {q }[A], respectively. We will thus denote the derivation, {F }[A] ® f*{F *[A]}: {F *[A]} = f*({F }[A]). Since f*({F }[A]) is a monotonic function of {F }, therefore, f*({F }) Ì {F }Ì T, after depressing A as being implied in these functionals. The nature of A is such that it remains immutable and primordial in the essence of T. Hence such an essence would not change in the induction of the world-system by the knowledge-flows, {q [A]}.

However, the second level of deduction from the primordial functional relationship via f* is characterized as follows: {F *[A]} ® f1 {q [A]}: f1{F *[A]}= {q [A]}. f1 denotes the mundane understanding and progressive mechanism of deriving worldly laws premised on the unity of knowledge T through the primal mapping, f*. f1 is thus the result of discourse, consensus and further evolution premised on the immutability of T in knowledge formation. Besides, since T establishes the unity of knowledge in the Stock, therefore, both f* and f1 are derivations that carry the same essence of unity in world-system. The nature of recreated unity in world-system is depicted by complementarity among the agents, variables and their relations in various sub-systems of the world-system. Among these sub-systems are society, economy, science, community, nations, subnations, the global order, self and the other. Broadly speaking the sub-systems along with their various elements are pervasively interactive within and across themselves. They thus form a cosmic order in the sense of the grand nexus of socio-scientific commons. The discourse that takes place in the essence of pervasive interactions leads to consensus in the sense of integration among the agents, variables and their relations. Systemic interactions leading to integration is the reflection of ‘unification' of knowledge flows in the light of unity of knowledge in the primal epistemology of T. We call this universal principle of unification premised on the fundamental unity of knowledge as the principle of universal complementarity.

Knowledge flows are pervasive inter-systemically and intra-systemically in order to carry the nature of unification across all changing nexuses of knowledge-induced systems. Hence an evolutionary phenomenon is intrinsic in the evolving world-system. But this stage of knowledge induction needs explanation.

Evolution from one level to another level of dynamic world-system comes about by a complementary combination of knowledge flows and their knowledge-induced forms. The latter are our X(q ) and the tuplet is (q ,X(q )). Evolution to higher levels of knowledge flows appears through post-evaluation and confirmation of certain well-defined criterion of well-being. One form of such a criterion is the social well-being function denoted by W(q ,X(q )). It is clear that each of the variables and hence the evaluation of this criterion takes place in terms of the immutable attributes, A.

We now have a chain of interactive, integrative and evolutionary stages that together define the process as follows:

T ® F {F } ® f* {F *} ® f1 {q } ® f2 {X({q })} ® ¯ ® f3 New {q } ® continuity ® T=H (1)

W(q ,X(q )) in repeated
processes

Primal ® Derivation® Process of ® Post-evaluation® Evolution® Continuity® Closure

Stock of of primal deriving of similar in the

Knowledge knowledge knowledge processes very

flows flows by large

discursion scale

universe

H here denotes the end of the cumulative process of all flows within and across nexuses of world-systems. The appearance of the attributes which is pervasive in all of the processes as the defining conditions of the nature of primal Stock of Knowledge and the derived knowledge flows has been suppressed.

The process of de-knowledge flows

Unlike the knowledge flows, de-knowledge claims a multitude of T to give rise to pluralistic knowledge flows with differentiated pre-conditions of such pluralistic orders. Consequently, although the nature of the evolutionary processes of de-knowledge flows is similar to knowledge flows, their interactive, integrative and evolutionary conditions are distinct. In de-knowledge flows these are defined by pluralism and dualism of interactions lading to individuation and differentiation, conflict and independence from each other. Thus, systemic interactions, integration and evolution devolve to individual sub-systems but do not interact across systems to gain integration, or unification of knowledge. Thus, universal complementarity is systematically replaced by marginalism, trade-off, conflict and substitution in the de-knowledge world-system. This is a pervasive fact of its socio-scientific perspective and explanation. Because of the random nature of its epistemological premise that remains disjointly distributed across sub-systems, their variables and relations, the essence of rationalism fully characterizes such sub-systems. Rationalism is defined as the epistemology of pluralism of thought without a premise that inter-systemically unifies knowledge according to certain unique laws. The premise of rationalism is sheer anthropic. The premise of unity of knowledge is the set of unique laws that remain immutable and that are then humanly comprehended and applied by reason to world-systems.

To formalize, let {T1,T2 ,…} denote the indefinitely large number of competing epistemes from which individually arise relational chains of the type shown by (1). Because of the axiom of systemic independence either of the following conditions will apply to {Ti}, i =1,2,….: (1) Ç i {Ti} = f (methodological individualism); (2) {Ti}=aj.{Tj}, i,j = 1,2,….

Consequently, each of the corresponding kinds of entities in the chains shown in (1) for the case of de-knowledge, remains mutually independent. Thereby, the beginning and endpoints of the chains in the very large scale universe are not unified across systems. In such universes equilibria can exist within the disjoint sub-systems but they do not exist across systems. The concept of interactions leading to integration is lost. Evolution of the disjoint systems result in infinitely many competing sub-systems. We refer to such individuated sub-systems as being characterized by endogeneity of de-knowledge flows within sub-systems but exogeneity of such flows across sub-systems. Contrarily, in the knowledge-induced world-system there is endogeneity of knowledge flows both across and within sub-systems of the world-system.

A generalized model of knowledge

Because of the pervasively relational essence of knowledge centered world system we will consider the following expression:

F1 Û F2 (2)

F1: T® F {F } ® f* {F *}® f11{q 1}® f21 {X1({q 1})}® ¯ ® f31 New {q 1} ® continuity ® T=H (3)

W(q 1,X1(q 1)) in repeated

processes

F2: T ® F {F } ® f* {F *}® f21{q 2}® f22{X2({q 2})} ® ¯ ® f32 New {q 2}® continuity ® T=H (4)

W(q 2,X2(q 2)) in repeated

processes

Between (2), (3) and (4) we obtain the following system of interrelationships:

® {q 1}® f21 {X1({q 1})}® ¯ ® f31 New {q 1} ® continuity ®

W(q 1,X1(q 1))

­ ¯

T ; ; ; ; ; T=H ….. (5)

¯ ­

® {q 2}® f22{X2({q 2})} ® ¯ ® f32 New {q 2} ® continuity ®

W(q 2,X2(q 2))

By an elementary disaggregation of relations we note that,

{q 1}® f21 {X1({q 1})}® f31New{q 1}

; X ; X ; X ; X ; … (6)

{q 2}® f22{X2({q 2})}® f32New{q 2}

where, X denotes cross-wise interactions. Such interactions are extensive as can be worked out even from this simple disaggregation when extended to second and higher number of processes (not shown). In terms of the functional mappings the extensive interactions cause compound functionals to arise.

The well-being criterion function resulting from the pervasive interactions across the interactive, integrative and evolutionary branches (3) and (4) is the non-linear aggregation of the separate well-being functions. One such non-linear form would be the product function with indexed coefficients of elasticities of the individual variables to the aggregate well-being function. The resulting non-linear aggregate well-being function is a cardinal measure of the complementarity among the various variables and their relations. Among the variables are also policy and institutional ones that imply the complementary role of agents in the underlying decision-making. Through the joint aspects of interactions that lead to the compound form of the branches, functionals and now well-being functions and the representation in the resulting well-being function of the complementary role of agents, variables and their relations, the essence of integration is introduced. Finally, because of the continuously dynamic nature of knowledge flows affecting decision-making, variables and their relations, evolutionary processes become the natural consequence.

The evolutionary nature of the interactive and integrative processes at each stage conveys the importance of simulative method of quantitative analysis in this interactive, integrative and evolutionary system (IIE). It also points to the replacement of all steady-state equilibrium points by a multiple evolutionary knowledge-induced equilibria. Optimization as a method is totally rejected as a method in the IIE system, as their cannot be any attained position of the system except in the instantaneous case of the variables, their relations and the underlying decision-making. The instantaneous case is not a sustainable perspective in knowledge-induced evolutionary models. Besides, the presence of unification of knowledge in the principle of universal complementarity by negating the contrary idea of marginal substitution, as in the case of neoclassical resource allocation, also rejects the idea of scarcity and constriction in resource supply. The circular causation and continuity model if unified reality in the IIE-system makes risk-diversification, product-diversification, institutional development and participation among the agents in the work place to constantly reduce the unit cost of production. The principle of universal complementarity and diversity of methods as signified by the branches of (5) followed by creative evolution are intrinsic in realizing reduction in unit cost due to risk and scarcity.

The systems methodology of de-knowledge

In the de-knowledge system there will be independent branches of the type shown in (1) with respect to each of the competing {Ti}, i = 1,2,… There will be a plethora of such emerging independent branches from any given branch in as far rationalism rules the individuating configuration of human thought and organization. Ultimately in such a process, all perspectives of convergence will be dispensed with giving way to utter randomness. Along each of these independent branches the condition of equilibrium is once again of the evolutionary type but optimality of the objective criterion is a precept independently of separate branches of the evolutionary process. Continuity and interrelationships across branches not being present, the optimal conditions of each of these branches are also unrelated to each other; so too are the equilibria of the evolutionary branches.

To formalize we let (xi*,Wi*(xi*)), i = 1,2,… denote the optimal values of the variable, xi and the objective criterion function, Wi(xi). From our formalization in (6) we note that in the generalized case a joint objective criterion function is given by,

W((q , x(q )) = S i Wi(q i, xi(q i)),

because of independence among the (q I, xi(q i))-tuplets, i = 1,2,…

The optimal value of W((q , x(q )) with respect to (q i, xi(q i))-tuplets, i = 1,2,…yields,

dW/dx = S i (¶ Wi/¶ xi).(dxi/dx)= 0 .. (7)

identically in the terms, because each ¶ Wi/¶ xi = 0,

i = 1,2,.. for reasons of optimality along the individual branches.

Likewise, dW/dq = S i [(¶ Wi/¶ q i).(dq i/dq ) + (¶ Wi/¶ xi).(¶ xi/¶ q i).(dq i/dq )] = 0 ..(8)

identically in the terms, because each ¶ Wi/¶ q i = 0, i = 1,2,… for the same reason.

These results clearly indicate that in a state of optimal trade-off must be maintained among at least two of the xi(q i)-variables, i = 1,2,… The determination of such variables by means of the trade-off is shown by dxi/dxj < 0 and dq i/dq j < 0. These results are consistent with the given optimal value of Wi(.), ii = 1,2,... along the independent branches. Aggregation of the knowledge flows and the variables being laterally additive implying independence among the variables, this aspect does not convey the meaning of interactions.

In the case of the IIE-system we would have the non-linear result corresponding to the expressions (7) and (8):

dW/dx = S i (¶ Wi/¶ xi).(dxi/dx)> 0 .. (9)

dW/dq = S i [(¶ Wi/¶ q i).(dq i/dq ) + (¶ Wi/¶ xi).(¶ xi/¶ q i).(dq i/dq )] > 0 .. (10)

corresponding to, dW/dq > 0, implying that dWi/dq I > 0, dWi/dxI > 0, dxi/dq i > 0, i = 1,2.., due to the positive induction of the complementary variables by knowledge flows in the IIE-system.These identically positive nature of the knowledge-induced variables and well-being function imply that optimization fails to be an acceptable method for use in the IIE-system, except in the instantaneous case of theq -value, when an attained consensus does not progress dynamically to higher levels. Consequently, the corresponding x-values and W-value also remain unchanging. We now relapse from the knowledge-induced forms to the neoclassical case of independence and inter-systemic exogeneity from interactions. This last case we will now prove.

Inter-systemic generalization of knowledge-induced model

Expressions (9) and (10) can be now extended to the inter-systemic case in accordance with expression (6). The evolution of the interactive and integrative sequences of knowledge flows and their knowledge-variables would now yield the following well-being system, where i denotes the number of interactions, k denotes a given numbered system; l denotes a numbered system, with k ¹ l (=1,2,…):

Simulate {q ikl}W(q ikl, xikl(q ikl)),

Subject to, } .. (11)

q ikl = f1(È i{q ik}Ç {q il}, x-ikl(q -ikl), W-(..)),

xikl(q ikl) = f2(È i{xik(q ik)}Ç {xil(q il)}, q ikl, W-(..))
symbol denoting recursively lagged values.
Underlying this simulation model is the IIE-epistemological circular causation and continuity chain,

T ® F {F } ® f* {F *} ® f1 [q ikl] ® [f(ikl)] [X ikl({q ikl})] ® ¯ ® [f ‘(ikl)] New[q ikl] ® T=H .. (12)

[W([q ikl],[X ikl(q ikl)]]

The square brackets indicate the matrix of variables, relations and well-being function corresponding to the ([q ikl],[X ikl(q ikl)])-entries across (k,l)-systems for given numbers of interactions (i). The same matrix meaning applies to the functionals.

The variables shown in (11) and (12) can be simplified by taking limiting values of the knowledge flows over given number of interactions, as was explained earlier. In this way the values of i would be assigned with respect to the number of interactions undergone to arrive at the limits of the ([q ikl],[X ikl(q ikl)])-values.

With such limit values of ([q ikl],[X ikl(q ikl)]), say ([q kl*],[X kl*(q kl*)]), the simulation path of the well-being function and variables in expression (12) can be depicted in figure 1.

Figure 1: Simulation path of the well-being function and variables



























The arrows in the diagram show the simulative direction of convergence of the knowledge flows, the knowledge-induced variables and the resulting simulated well-being function. This whole convergence marks one given process in the IIE-system. In the simplification of the expressions (11) and (12) we would substitute (q *1kl, X*1kl) for stage 1 in the interactions. The resulting simulated well-being function would be W*(q *1kl, X*1kl) for process 1 when the second process commences, and so on.

The expanding knowledge-inducing random field of interactive events, Ç kl(q *1kl, X*1kl) that can be made to converge into integration represents an aggregate topological domain. This is shown by,

W(q *1, X*1) = ò q *e {q *1kl} ò X*e {X*1kl} W(Ç kl(q *1kl, X*1kl)d X*1kldq *1kl. (13).

Furthermore, in the case of random field the variables are probabilistic. We then have to replace the integrand by the expected value of W(.). One is then led to determine the type of probability distribution of W(.) in the random field of (Ç kl(q *1kl, X*1kl). However, as knowledge flows and the knowledge-induced variables progress towards their limiting values greater certainty is gained. Consequently, it would be safe to assume a multivariate normal distribution in this random field.

In the complex case of conditional probabilities of a q occurring, subject Bayesian probability distribution of (Ç kl(q *1kl, X*1kl) needs to be used. That is, in terms of the inter-systemic interaction and integration of intra-systemic events during any given range of interactions denoted by 1, such as, Zk = (Ç k(q *1k, X*1k)) and Zl = (Ç l(q *1l, X*1l)), the Prob.(ZkÇ Zl) = Prob(Zk| Zl).Prob(Zl), where, Prob(Zk| Zl) denotes the conditional probability of Zl subject to the lagged occurrence of Zk. But since there exists causal interrelationship between the events of systems k and l, therefore, the simultaneous occurrence of these events will have a probability of Prob(Zl| Zk).Prob(Zk) or a linear function of this. But now, Prob(Zk| Zl).Prob(Zl) = Prob(Zl| Zk).Prob(Zk), or a linear relationship of the two. Hence the probabilistic condition for the simultaneous occurrence of events in knowledge-induced random fields under the principle of universal complementarity is given by the proportionality between the conditional probability of occurrence to the probabilities of actual occurrence of the events or a linear relationship thereof. That is,

Prob(Zk| Zl) / Prob(Zl| Zk) =.Prob(Zk) / Prob(Zl) (14)

Generalization to an expanding field of knowledge-induced random fields can be given by,

W(q *1, X*1) = Convolution of ò Ç kl(q *1kl, X*1kl)W(Ç kl(q *1kl, X*1kl)d(Ç kl(q *1kl, X*1kl) (15)

k,l = 1,2,…

P k,l=1N [Prob(Zk| Zl)].Prob(ZN) = P k,l=1N [Prob(Zl| Zk)].Prob(ZN') (16)

The proportionality condition as above is given by,

P k,l=1N [Prob(Zk| Zl)] / P k,l=1N [Prob(Zl| Zk)] = Prob(ZN') / Prob(ZN), (17)

where, k¹ l, N ¹ N', but, k,l = 1,..N.

Diagrammatic explanation of evolutionary knowledge and de-knowledge nexuses

The knowledge-induced nexus

In figure 1 we show the generalized region A as the intersection meaning interaction and integration of the three systems 1, 2 and 3. The region BBB shows the expansion or evolution of region A under the impact of knowledge flows. Consequently, the properties of the regions A and B under the impact of random field in which knowledge flows according to IIE are given by,

A = Ç k=13([q k*],[X k*(q k*)])

B = Ç k=13([q k**],[X k**(q k**)]),

with expanding limit values ([q k**],[X k**(q k**)]).

Aggregation of the well-being function is given by,

W(q **, X**(q **)) = ò Ç k(q **k, X**k)=B ò Ç k(q *k, X*k)=AE{W(Ç k(q *k,X*k)d(Ç k(q *k,X*k))} (18)

k = 1,2,3.

E{W(Ç k(q *k,X*k) is the expected value of W(Ç k(q *k,X*k) according to the conditional probabilities explained earlier, now taken for the three systems k = 1,2,3.

Expansion of the systems indicated by the arrows show the induction of these interactive and integrative systems by means of knowledge flows. If any of these three systems becomes disjoint with the other system, then interaction of the disjoint system with the remaining system cannot be maintained. The entire system then collapses into two competing system and disjointness continues between these competing systems. The extensive interactive nature of the systems on the other hand is the result of the complementarity between both {q *k} and {X*k(q *k)}, k = 1,2,3. Consequently, Ç k(q *k,X*k) ¹ f , Ç k(q *k,X*k) ¹ f . The systems can be of the most generalized kind ranging from scientific systems and global systems, to systems of variables and their relations in the socio-scientific order and between self and the other. We call any phase of such IIE-systems for a given range of interactions to be the nexus. Thus, (Ç k(q *k,X*k)) ¹ f , Ç k(q *k,X*k) ¹ f are nexuses corresponding to the range interactions given. The totality of such nexuses across various phases of interactions is given by, È i (Ç k(q *k,X*k) ¹ f , È i Ç k(q *k,X*k) ¹ f , i denotes sequences of interactions.

Figure 2: Generalized knowledge flows in random fields



























The nexus induced by de-knowledge

Figure 3 shows the methodological independence and disjointness of the three systems. The direction of the arrows indicate increasing disjointness of the systems as de-knowledge flows increase. The principle of complementarity is thus replaced increasingly by marginalist substitution or trade-off between alternatives. Contrary to the knowledge-induced generalized system, the generalized system of de-knowledge is shown by,

A = Ç k=13([q k*'],[X k*'(q k*')]) = f

B = Ç k=13([q k**',[X k**'(q k**')]) = f ,

across systems. Within such systems there are interactions.

The primed values stand for de-knowledge, with expanding limit values

([q k**'],[X k**'(q k**')]), independently across the three systems, k = 1,2,3.

Aggregation of the well-being function is given by,

W(q ', X'(q ')) = ò (q *'3, X*'3) ò (q *'2, X*'2) ò (q *'1, X*'1)E{W(q *'k,X'*k)d(q *'k,X*'k)} (19)

The probabilities are now additive indicating independence among the events ,

(q *'k,X*' k):

S k=13 Prob(q *'k,X*'k) = 1.

Figure 3: Systemic generalization in de-knowledge flows









Legacy of the knowledge and de-knowledge decision-making processes

Unity of knowledge has been the time honoured quest for scientific explanation of reality. Yet it is also the scientific project that remains the most evasive. This problem of lack of unity in knowledge across and within disciplines has posed the greatest problem of unification in theories of everything in present times. Yet this interdiscplinary insulation in the name of efficacy and scientific rigour within self-same disciplines has marked the nature of modern scientific inquiry. The post-modern inquiry into scientific inquiry remains unhappy within such a dichotomous perspective in the sciences by rejecting foundationalism, but at the same time a new barrier is raised by the utter randomness of pluralistic thinking in post-modernism. In the words of Foucault, "From one end of experience to the other, finitude answers itself; it is the identity and the difference of the positivities, and of their foundation …. "(Order of Things 315-16).

Yet unity of knowledge appears to be evasive because of its anthropomorphic origins primarily. The change of this anthropic primacy to the Unity of God returns the sciences and human designs to the axiomatic foundation of fundamental unity as the root of all world-systems. The world is then constructed on the basis of this singular, unique, complete and absolute primacy of unity. The world in its details is recreated by cause-effect relationalism in the midst of this fundamental Unity of God.

While all religions have shared in this primal contest of Divine Unity as a fundamental way to explain reality, yet the context of the emanating laws enabling the organization of various aspects of life and thought has not been uniform. In Islam this ordering of both the primal epistemology and ontology of Divine Unity and its expression in terms of Divine Laws in precise ways for externalizing to the world-system, is firmly established. The rumbling of fundamentalism in the Islamic scholarly legacy of all ages is precisely this causal relationship between the Divine Laws of Unity, their derivation, understanding and application to the world-system. In the Qur'an the fundamental Unity of God is termed as Tawhid. The Divine Laws emanating from this Divine episteme are termed as Sunnat al-Allah.The concrete way of deriving rules of life and thought from this epistemic origin is termed as Sunnat al-Rasul also called Sunnah, as the guidance of the Prophet Muhammad in their most authentic form. In the context of these fundamentals the epistemological domain of Divine Unity (Tawhid = T) interrelating Sunnat al-Allah with Sunnat al-Rasul, is given by the phase, T ® F {F } ® f* {F *}. This primal chain is further is further composed of T ® F {F } (Sunnat al-Allah) and {F } ® f* {F *}, which is Sunnat al-Rasul. The combination of these two sub-chains is the foundation of the ‘core' of Islamic Law (Shariah).

The derivation of rules (Ahkam) premised on the episteme of Tawhid is given by the extending mapping, ® f1 {q }. From the discourse or interactions (Ijtihad) arise the limiting values of {q } or consensus within and across the interactive systems (Ijma) that provide rules to guide the ordering of issues and problems of world-system. Hence arises the Qur'anic meaning of Signs of God (Ayath al-Allah) in the perceived world. This is signified by ® f2 {X({q })}. From a combination of knowledge flows (Ahkam) and the ordering of the world on the basis of these knowledge flows (Muamalat) is determined the post-evaluation of the applications of laws to issues of world-system and their reconstruction. This entire process is called the process of Islamic discursive institution (Shura) called the Shuratic Process. The Shuratic Process is pervasive and embryonic across and within world-systems in all its details. It is shown by the chain,

[T ® F {F } ® f* {F *}® f1]0 [{q } ® f2 {X({q })} ® ¯ ® f3 New {q }]1, (20) W(q ,X(q ))

where, the subscript 0 indicates the complete exogeneity and immanence of the episteme of Divine Unity in all matters. The worldly process of unification of knowledge premised on Divine Unity is shown by the endogenous knowledge-centered process subscripted by 1. The emergence of new knowledge flows through the interactive (Ijtihad) and integrative (Ijma) phases regenerates a new and similar Shuratic Process in which the exogeneity of the primal chain remains the cause and endogeneity of knowledge flows derived from the Unity episteme are regenerated. Such a discursive method of continuing the Islamic process of knowledge regeneration is the essence of the ever evolving nature of Islamic Laws (Shari'ah). The next round of the Shuratic Process is given by the chain,

[T ® F {F } ® f* {F *}® f1]0 [New{q } ® f2' New{X({q })} ® ¯ ® f3' Fresh{q }]2, (21) New[W(q ,X(q ))]

This kind of regeneration of the knowledge forming process in its cause and effect circular causation interrelationships in a knowledge-centered world-system is referred in the Qur'an as Khalq in-Jadid.

The attributes ‘A' that establish and sustain the uniqueness of the primal episteme are referred in the Qur'an as Asma al-Husna (the beautiful attributes of Allah). Because of the infinitely many diversity of the Asmas we reduce this to the enabling vector of attributes, {Justice (‘Adl), Purpose (Maqasid), Certainty (Haqq al-Yaqin), Well-Being (Falah & Tazkiyyah), Re-origination (Khalq in-Jadid}. Such a derivation and ordering of the attributes is not unique as many of the Asmas can be inducted into ‘A' in accordance to how we can comprehend and use them in systemic world-system studies.

Since (20) and (21) are uniquely premised on the same episteme of Unity, these must be diverse expressions of unity across and within systems in all matters of details. Hence we have the meaning of unification of knowledge by endogeneity within and across systems. We call such extended methodology of unification arising from Unity as the circular causation and continuity model of unified reality.

The endogenous knowledge inducing processual methodology just explained remains perpatually evolving and discourse oriented in the IIE perspective. However, in the very large scale perspective of the universal system, the cumulative supercardinality of T is attained. This can be the only point of Optimum and Final Equilibrium. Being so the End characterization of the topology of T, i.e. Hereafter H, is equivalent to the Beginning T in this supercardinal sense. In the Qur'an it is said that God will reveal Himself in Hereafter. This Qur'anic mention is equivalent to saying that the total Stock of Knowledge (Lauh Mahfuz) will be revealed.

Both the Islamic epistemologists and rationalists in different ways though, developed the epistemic worldview of Tawhid at great length. In the pure science of epistemology are the immortal works of Ibn al-Arabi, Imam Ghazzali, Shurawardi and Fakhruddin Razi. In the worldy matters applying the tenets Fakhruddin Razi was an original thinker on human fulfilment and social well-being and he made this idea epistemologically revolve around the precept of obedience to God. Thus he thought early in those years of the precept of self-actualization through a combination of self-reformation and appropriate socioeconomic choices. Ibn Taimiyyah and Imam Shatibi were great exponents of the social organization of well-being and market guidance. They considered issues such as of money, finance, preference formation under guidance of public policy, selection of means to attain public purpose, social contractarian and the market order, the proper structuring of social institutions and control of inflation. In recent years, Malik Ben Nabi wrote on the precept of Qur'anic historicism in scientific endeavour. He called upon Muslims to discover science in the Qur'an and take that scientific methodology to the highest level of analytical discourse and investigation. Thus in all we have amply significant historical legacy to confirm the place of the epistemology of Divine Unity that is at the same time backed up by pragmatism through the guidance of the Prophet Muhammad, what came to be known as the Sunnah.

Conclusion

The analytical and historical basis of the epistemological of Divine Unity and its crystallization in real world-system has left an abiding legacy for generations to look up to and discover new and fresh paths to the answer of unification of knowledge. Increasingly as the scientific endeavour marches on in answering the initial conditions of the universe, it has become inextricably gripped in the research project of theories of everything. In social theory as in scientific paradigm, the praxis of unifying the premise of markets with institutions or polity. The endogenous theory of institutions is notable in this area of economic research of institutionalism. However, to date the research has either taken up a purely historistic perspective or has been entrenched in neoclassical roots of new institutionalism and social choice theory. This has not helped in the critical study of discourse within market interactions. The invisible hands of the market order has remained hidden in explaining the preference formation of institutions, agents and markets.

The theory of unity of knowledge premised on the Unity of God and its externalization through concrete laws in the real world-system. This appears not to be a problem of religious fundamentalism. Rather it is a matter of deep analytical reasoning on which a substantive theory of science and society can be premised. Thus when we write on the need for unification of knowledge we treat the relevance of unity of knowledge on solid topological domains of functional relationism of Unity of Knowledge with unification of knowledge in endogenous world-systems. This precept of knowledge-induced endogenous world-system and its extensively complementary explanation holds a prospect of great significance in the scientific research program of theories of everything.