Abstract
The Qur’an explains the philosophy of historicism in terms of purposeful conflict between Truth and falsehood, with the final prevalence of Truth in “everything.” Thereby, historicism comprises the positivistic combined with the normative explanation of historical events in the onticology of eventful narratives across time along the path of conscious continuum. Historicism, thereby, is established in the Qur’an as a philosophical study of purposeful events spanning the large and small cases spanning all the socio-scientific domain. The extensiveness of historical explanations of generalized events also establishes the fact of the Tawhidi principle of pervasive complementarities between the good and the goodly transformable entities. Thereby, the Tawhidi IIE(θ(ε))-model is shown to play its ontic role of translating normative principles derived from the Qur’an into positivistic onticology. Diverse topics are rigorously studied in the field of the philosophy of historicism in the light of the Tawhidi epistemic worldview represented in and through the Tawhidi IIE(θ(ε))-model. The Qur’an (8:17) states regarding the primal cause of all causations in the details of historical events to lie on the primacy of moral/ethical values that embody all events. The Qur’an narrates regarding historical event of the Battle of Oudh as lesson for believers: “It was not you who killed them, but it was God who killed them. And it was not you who launched when you did, but it was God who launched. And so that the believers would be tested well by God. God is Hearer, Knowledgeable.”
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Notes
- 1.
Qur’an (13:3): “And it is He who spread the earth and placed therein firmly set mountains and rivers; and from all of the fruits He made therein two mates; He causes the night to cover the day. Indeed in that are signs for a people who give thought.”
- 2.
Qur’an (3:190–191): “Behold! In the creation of the heavens and the earth and the alteration of Night and Day, − there are indeed Signs for men of understanding, − men who celebrate the praises of God, standing, sitting, and lying down on their sides, and contemplate the creation in the heavens and the earth, “Our Lord! Not for naught have You created this! Glory to Thee! Give us salvation from the Penalty of the Fire.”
- 3.
Qur’an (57:3): “He is the First and the Last, the Ascendant and the Intimate and He is of all things knowing.”
- 4.
Qur’an (45:24): “And they say: “What is there but our life in this world? We shall die and we live, and nothing but time can destroy us.” But of that they have no knowledge: they merely conjecture.”
- 5.
Qur’an 4:59): “O you who have believed, obey God and obey the Messenger and those in authority among you. And if you disagree over anything, refer it to God and the Messenger, if you should believe in God and the Last Day. That is the best [way] and best in result.”
- 6.
We state here a theorem on the compact topological space, X(θ(ε)): With X(θ(ε)) treated as an open cover of T(θ(ε)), it must have a finite subcover. X(θ(ε)) is then a neighborhood compact topological set. By the extension of ahkam on X(θ(ε)), every open sub-cover of X(θ(ε)) will show such extensions.
We have now fully established the two aspects of knowledge formation based on the aspect of fundamental knowledge and the aspect of details built upon this fundamental knowledge to gain insight in the divine law. These are the powerful conclusions grounded on the above verse (Qur’an 11:1).
- 7.
In reference to the formalization derivable from the previous verse (Qur’an 11:6), the tuple-vector, e(θ(ε)) = (y,t)(θ(ε)), where, y(θ(ε)) = (x,P)(θ(ε)), can represent the configuration of an event in knowledge, space, and time dimensions. But note that such an evolutionary equilibrium result is determined at a point in time as the conditions of stability of that point change from moment to moment of time as the discursive decision-making ensues according to the shura-tasbih practice. This was also shown earlier by means of the adaptive interrelationships between policy variables and socio-scientific variables. But such interactions, which are based on time-dependent decision-making events, influence the evolution of knowledge in the whole of the socio-scientific field of inquiry.
The underlying Tawhidi epistemic-induced geometry can now be formalized as follows: we will examine, firstly, how the values of {θ(ε)} over time, t(θ(ε)), and by discursive process denoted by say, {i}, relate to the formation of (y,P,t)(θ(ε))-tuple. It is, furthermore, noted from our treatment of the simulative nature of {θ(ε)it} that long-run adaptive nature of such random variables can be determined to make mappings between these variables and the socio-scientific variables meaningful. Hence, we have ordinal values of {θ(ε)it}. Now let the joint vector of {θ(ε)}-values and thereby (y,P,t)(θ(ε))-variables be defined by the bilinear form
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l1(θ1,θ2,...,θn; P1,P2,...,Pn)(θ(ε)) = bij...rs...AiBj...CrDs.... i,j,r,s,... = 1,2,...; “t” is assumed in all of these notations.
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(A1,A2,...,An1), (B1,B2,...,Bn2)….(C1,C2,...,Cn3) are values of (x,y,P)(θ(ε)). Corresponding to these values are the estimated values of (θ1,θ2,.,θn).
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B = [bij...rs...] is the matrix of the bilinear transformation relative to the basis vector of {θ(ε)it}.
A similar bilinear form can be defined in {θ(ε)it} vectors and {xktθ(ε)} vectors; i = 1,2,...,n; k = 1,2,...,m; m > n. Let the bilinear form be represented by
$$ {\mathrm{l}}_2\left({\uptheta}_1,{\uptheta}_2,\dots, {\uptheta}_{\mathrm{n}};{\mathrm{x}}_1,{\mathrm{x}}_2,\dots, {\mathrm{x}}_{\mathrm{n}1}\right)={\mathrm{c}}_{\mathrm{i}\mathrm{j}\dots \mathrm{kl}}\dots {\mathrm{A}}_{\mathrm{i}}^{\prime }{\mathrm{B}}_{\mathrm{j}}^{\prime}\dots {\mathrm{C}}_{\mathrm{k}}^{\prime }{\mathrm{D}}_{\mathrm{l}}^{\prime}\dots $$with similar definitions for the coordinates as before; t(θ(ε)) is assumed but suppressed in all of these notations.
Since there exist interrelationships (correspondences) between {θ(ε)it} variables and {x(θ(ε))kl} variables, therefore, the relationships x(P(θ(ε))) and P(x(θ(ε))) defined in the previous verse denote bilinear forms in {Pit(θ(ε))} and {xkt(θ(ε))} vectors. That is, there exists a symmetric bilinear form of the type, l1°l2 = l2°l1. Any element of this bilinear form is of the type that involves the transformation of one bilinear form into another, given values of θ(ε)-variables.
A theorem by Gel’fand can be further applied here:
If A* is the matrix of a bilinear form A(x,P)(θ(ε)) relative to the basis of {P(θ(ε))it} and B* is the matrix of A(x,P)(θ(ε)) relative to the basis of {x(θ(ε))kt}, then B* = C*'A*C*, where C* is the matrix of transformation of the basis of {P(θ(ε))it} to the basis of {x(θ(ε))kt}, and C*′ is the transpose matrix of C*. In the most general bilinear forms of l1 and l2, B* is an n-times covariant (contravariant) and m-times contravariant (covariant) tensor.
It is now obvious how given values of {θ(ε)} enter as primordially derived ontological values in the bilinear forms characterizing {P(θ(ε))it} and {x(θ(ε))kt} vectors. When the θ(ε)-values change, the tensor values also change, and these describe new points in the space of events denoted by the tensors themselves as coordinates of the above vectors. A tensor geometry of this type completely refines the static nature of tensor algebra and introduces a new theory of random fields into tensor calculus.
Certain forms of random fields have been studied in the literature. A random field is defined by joint variations in multiple variables qualifying a functional form. Such variations can be stochastically independent or correlated with each other. Thus, autocorrelations will arise in the second case. Furthermore, if such correlated variations are too extensive, then the estimation procedures applied to linear models in the random variables will be biased and inconsistent in the probabilistic sense, so that they cannot be relied upon to generate predictive properties for the dependent variables and the functions defined by them.
When sustenance is not defined in terms of such random fields, then neither the definitions of the socio-economic variables nor the estimation of the social objective function can be meaningfully obtained. Such a chaotic perspective of random fields is not the property of the Tawhidi IIE(θ(ε))-model of knowledge, which is seen to be primal in its state of stability. When chaotic random conditions do exist, then the existence of the shura-tasbih practice is proved to be void and ineffective.
However, two kinds of chaotic models of change can exist in respect of the topic of sustenance and sustainability in the context of the life-sustaining goods and services. Firstly, there is the trivial case of smooth knowledge-induced evolution and interaction between {(θ(ε))}-values and the (y,P,t)(θ(ε))-tuples. Secondly, there can be temporary chaotic random conditions, but soon transforming into orderliness (order out of chaos). This is the case mentioned in the Qur’an that God is forgiving to those who return to Truth.
There are two ways how such control of randomness can be actualized in the Tawhidi IIE((θ(ε))-model of change. We examine this issue, firstly, in regard to the sustenance problem; and secondly, in terms of the configuration of events explaining sustenance. When the random variations remain independent of each other, then there are no intersections between the {θ(ε)it} and {x(θ(ε))jt}. In such a case, the induction of the shura-tasbih practice is not fully effective. The second case happens when there are interactions between the variables as in the wellbeing function. Now the usual kinds of bilinear forms exist, determining tensors in the tensor transformation spaces.
In the general case with random elements in the variations, we can define the general bilinear form by
$$ \mathrm{l}\left(\mathbf{x},\mathrm{P};\uptheta \right)\left(\uptheta \left(\upvarepsilon \right)\right)={\mathrm{a}}_{\mathrm{i}\mathrm{j}\dots \mathrm{rs}\dots }{\mathrm{c}}^{\mathrm{i}}{\mathrm{c}}^{\mathrm{j}}\dots {\mathrm{d}}_{\mathrm{r}}{\mathrm{d}}_{\mathrm{s}}.\dots, $$where
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aij...rs...(θ(ε)) = l(x^,p^,θ̂)(θ(ε)),
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with x(θ(ε))^ being the basis vector of x(θ(ε)), P(θ(ε))^ being the basis vector of P(θ(ε)), and θ^ being the basis vector of θ.
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[ci] is the matrix defining the transformation of (x^,P^) basis;
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[dj] is the matrix defining the transformation of θ̂ basis.
Since randomness is introduced by variations in the simulated θ(ε)-values, therefore, probabilistic operations on l(x^,P^,θ^)(θ(ε)) must be transmitted to all spaces of transformations of the bilinear form l(x,P,θ)(θ(ε)).
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Choudhury, M.A. (2024). Historicism in Tawhidi Philosophy of Science. In: Handbook of Islamic Philosophy of Science. Springer, Singapore. https://doi.org/10.1007/978-981-99-5634-0_17
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DOI: https://doi.org/10.1007/978-981-99-5634-0_17
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