"Stoirm air Loch Gailili" le Rembrandt van Rijn (1633)
§ 2 - ÒRDAGH COSMACH NA TÌME SA CO-LEANAILT STRUCTAIREACH.
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§ 2 - THE COSMIC ORDER OF TIME IN THE STRUCTURAL COHERENCE.
De kosmische tijdsorde in den structuur-samenhang van zin-kern, modale analogieën en anticipaties.
The cosmonomic Idea directs and leads philosophical thought, and gives it the ὑπόθεσις without which it would be helplessly dispersed in the modal diversity of meaning. Our cosmonomic Idea postulates the cosmic time-order in the modal law-spheres.
But at what point is philosophic thought to make an entry into this cosmic temporal order, so that we are enabled to acquire theoretical knowledge of the place of the different modal law-spheres in it? Cosmic time appeared to be the pre-supposition of theoretical thought; the latter cannot transcend it; it has to abstract from the cosmic continuity in the temporal coherence of meaning in order to find its "Gegenstand" in the modal structure of the law-sphere that it sets out to investigate.
Consequently, only in the modal structures of the meaning-aspects themselves can theoretical thought enter into the cosmic order of time, though the latter itself can never be grasped in a concept. In the analysis of these modal structures the order of succession of the law-spheres, — be it in a discontinuous process of fixation by logical thought, — must be brought to light.
According to our cosmonomic Idea, each of the law-spheres is a temporal, modal refraction of the religious fulness of meaning. And as such every aspect expresses the whole of the temporal coherence of meaning in its own modal structure. If this is so, the temporal order of succession of the law-spheres must be expressed in this structure. Full justice ought to be done to the specific sphere-sovereignty of the modal law-spheres within their temporal coherence. Our cosmonomic Idea itself here provides philosophic thought with the hypothesis that must demonstrate its correctness in the analysis of the modal meaning-structures.
Nuclear meaning, modal retrocipations and anticipations.
Zin-kern, modale analogieën (retrocipaties) en anticipaties.
The modal sphere-sovereignty can only be maintained within the temporal inter-modal coherence of the different aspects, if the modal meaning of the law-spheres arranged between the initial and the final aspect has the following structure: it must have a nucleus guaranteeing the sphere-sovereignty of the entire aspect; and this kernel must be surrounded by a number of analogical modal moments which partly refer back to the meaning-kernels of all the earlier spheres, and partly refer forward to those of all the spheres that are later in the cosmic arrangement.
Let us represent this structure by a mathematical figure, viz. a circle divided into two equal halves. In the centre is the meaning-kernel; the radii drawn from the centre in the left hand half represent those modal moments of meaning that establish the coherence with the cosmically earlier spheres; and the radii in the right hand half stand for the modal meaning-moments maintaining the coherence with the law-spheres of a later position.
In future the anaphoric [terugwijzende] modal meaning-moments will be called the modal retrocipations; the modal moments referring forward will be styled the anticipations of the modal structure.
Modal retrocipations and anticipations remain qualifed
by the nucleus of the modal meaning.
Modale retrocipaties (analogieën) en anticipaties blijven
door de zin-kern van den wetskring bepaald.
Both the retrocipatory and the anticipatory moments remain qualified by the nucleus of the modal meaning. They do not adopt the nuclear meaning of the substratum-sphere or the superstratum-sphere respectively, to which they refer.
Since the modal structure of each aspect shows an indissoluble correlation between the law-side and the subject-side, this structure must manifest itself in its meaning-nucleus, its retrocipations and its anticipations, both on the law-side and on the subject-side.
Às an leabhar "An Introduction to Christian Philosophy" le J.M. Spier
The architectonic differentiation in the modal structure of the law-spheres.
De architectonische differentiatie in de modale zinstructuur der wetskringen.
If our Idea of the order of succession of the law-spheres is correct, an architectonic differentiation must be observable in their modal structure. The number of retrocipations must decrease, whereas the number of anticipations must increase in accordance with the number of law-spheres forming the substratum of a particular aspect, i.e. in proportion as its position in the cosmic order of time is earlier. And this again leads to the idea that there are two terminal spheres, the first of which has no retrocipatory moments and the second has no anticipations in its modal structure.
The purport of his hypothesis cannot yet be fully realized and will become clear only after further investigations. The fact that the first terminal sphere lacks retrocipatory moments can never be any reason to absolutize its structural meaning, although this aspect is the foundation of all the other law-spheres. Its lack of retrocipations does not render it independent and unconditioned, because the structure of this modality of meaning is not self-determined.
All the modal spheres are founded in the cosmic time-order and are determined and limited by it. The law-spheres do not determine each other; they are only related to one another by this order in the sense of a relation between foundation and superstructure. From this it follows, that only in the foundational direction of the time-order can we state that a law-sphere is more or less complicated than its predecessor. The degree of complication depends here on the position of the sphere in the retrocipatory structure of its meaning. But when the transcendental direction of time is also taken into account, there is no difference in structural complication. For, in proportion to the decrease of the number of retrocipations in the meaning-structure there is an increase of anticipatory moments, and vice versa.
Observation: Perhaps, in this connection the objection may be made that in our analysis of the modal structures of meaning there is a continual use made of quantitative concepts, and even of spatial analogies. Dialectical philosophy will find this a proof of the fact that the theory of the law-spheres has relapsed into the objectifying attitude of special science. On the dialectical standpoint our method should be "geisteswissenschaftlich", otherwise our philosophy has not yet attained to transcendental self-reflection.
How thoroughly unfounded this objection is, can only be shown in the course of our investigations. In the present context it should only be observed that in the theory of the law-spheres we are engaged in a theoretical analysis of the modal structures of meaning. It must be established that it appears to be impossible to do this without our relevant synthetic concepts of meaning containing analogies of number and space. This proves that the logical sphere has its foundation in the aspects of number and space. For the rest our transcendental basic-Idea is a sufficient guarantee that philosophic thought cannot lose its direction to the selfhood, not even in these theoretical analyses. [Overigens levert onze wetsidee afdoende waarborg, dat het wijsgeerig denken de richting op de zelf-heid ook bij deze theoretische analysen niet verliezen kan.]
The value of the analysis of modal meaning in tracing the original
and irreducible nuclei of its modal structure.
De waarde der modale zin-analyse in het opsporen
van de originaire modale zin-kernen.
The value of an analysis of the different modalities of meaning is this: it reveals the structure of a modality in cosmic time, and compels us to trace the original nuclear meaning-moment.
In its analytical abstraction this nucleus gives the fundamental analogical concepts a definitive modal qualification. It is true, the usual scientific terms for these concepts, examined in our introduction to this chapter, contain a general indication of the modal aspect in which the analogy presents itself. But we have noticed that these terms are handled without a closer analysis of the modal meaning-structures they refer to. The general adjectives giving these analogical terms their modal qualification, e.g. physical, psychical, logical, juridical, asthetical, etc. cannot prevent scientific thought from a false interpretation, so long as any insight into the modal structures of the aspects to which they refer is lacking. We have seen, for instance, how the analogical term 'juridical power' has been misunderstood even by famous scholars versed in legal thinking.
In the prevailing method of forming concepts the moments are unified in a relation of thought that has not been unequivocally qualified as to its modal meaning. Any one who has experienced the confusing equivocality of this procedure will at once admit the value of our analysis. Later on these unqualified general concepts will be discussed in greater detail. Logicism as a whole is essentially founded in the translation of the retrocipatory or the anticipatory moments in the structure of the analytical aspect into the original modal meaning-kernels they analogically refer to. [Het geheele logicisme steunt in wezen op de omduiding van analogische of anticipeerende momenten van den analytischen zin in originaire modale zin-kernen.] For instance, the logicistic concepts of number, of continuity, of dimension, of motion, of 'pure signification', of the fundamental jural relations and so on, are entirely based on these essential shiftings of the modal meaning.
The special theory of the modal law-spheres must start with a scrupulously accurate analysis of the modal nuclei of meaning and should point out the non-original character [niet-originaire karakter] of the modal analogies. This is still unbroken ground.
Merely by way of example I may refer to the dilemma in which modern mathematical thought is caught as regards its view of space.
IMMANUEL KANT's transcendentally psychologistic conception of pure space as an a priori 'intuitional form' of sensibility to which geometry is bound, as well as his conception of the exclusive a priori-synthetical character of the Euclidean axioms and theorems had proved to be untenable after the discovery of the non- Euclidean geometries in the 19th century. For mathematics there seemed henceforth to be no alternative but the following: Either pure geometry was to be reduced to the study of a so-called formal space (CARNAP) [1] in the logistical sense of a continuous series of propositional functions having two or more dimensions (RUSSELL) [2] without reference to any meta-logical aspect [3]; or its propositions were to be construed from the basal intuition of the bare two-one ness after the manner of the intuitionists (BROUWER), as the form of the conceived multiplicity of the intervals of time. The intuitionists confine themselves to a complete
arithmeticizing of geometry. But they hold to the quantitative nature of all mathematical entities, whose existence must be proved by the possibility of 'construction' from the basic quantitative intuition of time.
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[1] Cf. H. CARNAP, Der Raum (Berlin, 1922) p. 14.
[2] Cf. Principles of Mathematics, p. 372.
[3] MAX BLACK, The nature of Mathematics (London 1933) p. 158, also eliminates the term 'formal space' in his statement:
"the last reason for restricting geometry to the study of space has disappeared, and the following view of the nature of geometry is generally accepted: a geometry does not deal with space but consists of a series of formulae (a logistician would say: propositional functions) which are deduced from a number of initial formulae (axioms)... and any interpretation of the symbols mentioned in the axioms which converts the latter into true propositions, is an interpretation of the geometry."
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Logistic, on the other hand, reduces both pure arithmetic and pure geometry to logic. It speaks contemptuously of the 'exploded' view which supposed it had to bind arithmetic to the investigation of 'quantitative relations' (RUSSELL). On this point formalism must agree with logistic.
This dilemma has been removed in the philosophy of the cosmonomic Idea. It no longer considers space in its pure original sense as an unqualified a priori 'form' of the sensory contents of objective perception. Nor can it attach any meaning to a pretended 'logical origin' of the concepts of number, space, dimensionality, and continuity. It must also reject the intuitionist conception that the whole field of pure mathematical research is constructed from a basic intuition of the bare two-oneness in the intervals of time.
It raises the question about the original nuclear modal meaning of space and number in the cosmic coherence of the lawspheres. Through this also the confusing unqualified notion of so-called 'empirical space' becomes useless in science.
Herman Dooyeweerd, New Critique of Theoretical Thought, Vol II/ Part I/ Chapt 2/§2 pp 74-79)
