"A' Tarraing Làmhan" le M.C. ESCHER (1948)
§ 5 - AOGAS LOIDSIGEACH SLAT-TOMHAIS MODALACH NA CÈILLE AGUS SEÒL AN ANTÌNOMI.
§ 5 - THE LOGICAL ASPECT OF THE MODAL CRITERION OF MEANING AND THE METHOD OF ANTINOMY.
The principium exclusae antinomiae in its relation to the logical principle of contradiction.
In § 1 of this chapter the theoretical character of the criterion of a modal law-sphere was given prominence and reference was made to the logical side of this criterion.
The modal aspects are implicitly included in naive experience. Their "ex-plication", the theoretical unfolding of the functional modalities of meaning from what has been given in the naive attitude, is a task of philosophy, which has to make use of theoretical analysis and synthesis. Insight into a real synthesis of the logical function of thought with a non-logical aspect of experience can only be acquired on the condition of respecting the specific modal limits of the different law-spheres, including the logical one. Every attempt to erase these limits by a supposed autonomous theoretical thought results in theoretical antinomies. By laying bare such antinomies in immanence-philosophy, we apply a method of criticism whose efficiency can be denied only by those who employ a dialectical logic either to overcome the ultimate antithesis in their religious starting-point by a pseudo-theoretical synthesis, or to project this basic antinomy as an unconquerable contradiction into temporal reality itself.
The method of antinomy has continually been applied in our critical treatment of the development of the basic antinomy between 'nature' and 'freedom' in Humanistic philosophy; but the special use of this method in the theory of the modal law-spheres has not yet been brought to light.
The nature of the theoretical antinomy. The principium exclusae antinomiae.
What is the nature of a theoretical antinomy? Antinomy literally means a 'contradiction between laws'. PLUTARCH uses the term in a juridical sense to denote an inner conflict in positive law, revealing itself in the fact that two opposing parties can explain the law in their own favour.
It is especially the original relation of antinomy to law (of course in this case taken in its fundamental cosmological sense, and not in a modally jural application) that makes it necessary to give all the more prominence to its essentially subjective character of being opposed to law. It is not the law itself, in its basic meaning of the cosmic order of the modal law-spheres that can be antinomic, nor can the laws of the different modal aspects contradict one another. But all theoretical antinomies are caused by theoretical thought involving itself in self-contradiction in theoretical judgments, because it forms an erroneous conception of the coherence in the modal diversity of the laws thereby giving rise to a seeming mutual incompatibility of the latter.
Antinomy in its inter-modal character may not be identified with the intra-modal relation of contrariety.
Antinomy in this inter-modal theoretical sense ought to be sharply distinguished from the intra-modal relation of contrariety, including logical contradiction. Contraries like logical — illogical, polite — impolite, beautiful — ugly, lawful — unlawful, moral — immoral, belief — unbelief, and so on, present themselves within the same modal aspect of meaning. They do not contain a real antinomy between different modal law-spheres. In its theoretical character the latter implies a logical contradiction; but a logical contradiction as such is not an antinomy in the inter-modal sense here intended, referring as it does to the transcendental Idea concerning the mutual coherence of meaning between the different modal aspects of experience.
Antinomy in the sense of a seeming contradiction between the essential laws of different modal aspects of meaning is refuted by the Idea of cosmic order. Anyone who accepts the cosmic order of time regulating the coherence of meaning between the laws of different modal spheres, cannot acknowledge any theoretical justification for antinomy. The transcendental Idea of cosmic order implies the principium exclusae antinomiae.
The essentially antinomic character of all speculative thought. The antinomy of the sole causality of God in speculative theology.
If theoretical thought is indeed bound by the temporal coherence of meaning of the modal law-spheres, any attempt on the part of this thought to overstep the limit of the cosmic order of time must lead to antinomy. For this reason all speculative thought is necessarily antinomic.
Our thought cannot really exceed the cosmic limit of time. What actually takes place in speculative thought is not an antinomic conceptual comprehension of the supertemporal, but merely a theoretical eradication of the modal limits between the temporal law-spheres by making certain modal aspects absolute.
Take for instance the notorious antinomy of speculative natural theology with its notion of the 'unconditional ultimate causality of God' proceeding from the impossibility of a regressus in infinitum in the empirical causal relations. This notion lands us in an insoluble contradiction with man's personal accountability for his actions, since it makes God the ultimate term of a series of causes and effects which must be conceived as continuous and leaving no single hiatus in the causal chain.
For, if any hiatus would be allowed in the temporal chain of causes and effects, by the introduction of "free causes", in the sense of subjects of normative imputation, the whole argument would lose its foundation.
This argument starts from 'material' sensory perceivable effects and from these effects seeks to find the causes. It is impossible in this empirical way to find a free cause as the subject of normative imputation. The cause which can explain the effect must itself be the effect of another cause and so on.
It is not necessary that the causal relations found in this way are conceived of in a mechanical sense. But they cannot be of a normative character, because the normative imputation of an effect to a subject as its cause implies that the acting subject itself is a final point of reference in the normative aspects of the
causal relation .
 Cf. my treatise The modal structure of the juridical causal nexus, Mededeling Ned. Kon. Akademie van Wetenschappen (Nieuwe Reeks dl. 13, 2e ed. 1950).
The Thomistic proofs of the existence of God.
The first and second Thomistic-Aristotelian proofs of the existence of God as unmoved Mover handle the concept of causality in the metaphysical sense of the Greek form-matter scheme.
Causality is conceived here in the transcendental-analogical sense of the fundamental concept of being, with its general transcendental determinations of matter and form, actuality and potentiality. This implies that the causal relation is used without any synthetical determination of its modal meaning.
In the Aristotelian principle: Omne quod movetur ab alio movetur, 'movement' is meant in the analogical sense of a transition of matter to form, and of potentiality to actuality.
As long as this principle is handled in its purely metaphysical sense, the argument based on it cannot prove anything, because it contains only a theoretical logical explanation of the consequences implied in the religious pre-supposition of the form-matter motive in its Aristotelian conception .
 Cf. my treatise The Transcendental Critique of Theoretical Thought and the Thomistic Theologia Naturalis (Phil. Ref. 17 Year 1952, p. 151 ff).
As soon, however, as it is related to human experience of movements in the temporal world, it is no longer possible to use the concepts of movement and causality in an undetermined analogical sense.
In this case it becomes necessary to define the events arranged in the chain of causes and effects which are supposed to demand an unmoved Mover as the ultimate cause. And now theoretical thought cannot escape from defining the modal and typical sense of its concept of causality.
If it is possible to arrange a series of different natural events and human actions in the same chain of causes and effects which would be infinite without assuming God as the ultimate cause, the normative aspects of causality must be eliminated on the grounds explained before.
As to the remaining aspects it must be stated that — if they are irreducible to each other their inter-modal relation cannot be a causal one.
Consequently, it is necessary to define the modal aspect of causality meant in the empirical-theoretical argument. But, by making God the absolute or ultimate cause of a theoretically abstracted modal series of causes and effects, this modal aspect is absolutized because of its being related to the absolute Origin outside of its inter-modal coherence with the other aspects and outside of the religious centre of human existence. And so the antinomy between 'causality' and normative responsibility of man is inescapable.
It does not matter whether causality is conceived of in a metaphysical-mechanical sense, or in a metaphysical-biological or in a metaphysical-psychological one; in either case it is inevitably in conflict with the modal meaning of the normative aspects of human behaviour, as soon as it is brought to bear on the latter. If, for example, an instance of rational human behaviour were capable of an entirely mechanistic explanation, there would not be any foundation for normative juridical or moral accountability.
Human action, however, is incapable of being enclosed in certain aspects of reality in a purely functionalistic way, since insofar as it is human behaviour, it takes its origin in the religious root of human existence.
To the extent that a human ego is qualified as the super-modal cause of his actions, we speak about causality in the transcendental sense of the radical unity of all its temporal modalities, which refers to the religious concentration-point of human existence beyond all and any modal diversity of meaning. This human ego cannot be arranged in a mechanical or psychological causal series.
And insofar as we continue to speak of God being the ultimate cause, we can do so only in the sense of the transcendental Idea of the Origin of all meaning, if we want to avoid the errors of speculative immanence-philosophy. God can never be the ultimate cause in a mechanical or other modal series of causes and effects. Rather He is the Origin of causality in the temporal coherence and radical unity of all its modal aspects. A purely modal causality cannot refer to a real process, but only to a theoretical abstraction.
It has already been discussed in the Prolegomena that both Ideas (that of the radical unity and that of the Origin), contained in the transcendental basic Idea, are conclusive evidence of the fact that theoretical thought is not self-sufficient, not even in its own sphere, and that it is necessarily determined by the religious root of existence. Antinomy arises in the first place through ignoring this religious determination and dependence of theoretical thought, because this thought sets out to interpret God's causality or that of human volition in a functionalistic way. That which is one in the full sense of the word in the totality of meaning and in the Origin of all meaning respectively, turns into a contradiction between two modal functions of meaning, if interpreted functionalistically; the reason is that these two functions are made absolute in theoretical thought (e.g., mechanical causality and moral responsibility).
Any one who thinks he can solve such a speculative antinomy by granting man a certain measure of independence and freedom in his relation to God as 'prima causa' has not understood the true origin of this antinomy in speculative philosophy. For the speculative concept of cause (which implies an absolutization of a non-normative modal aspect of meaning as soon as it used in an argument which is based on a continuous series of causes) does not bear any limitation in its supposed applicability to the Absolute Origin of the cosmos.
If God, as a supposed unmoved Mover, is thought of as the ultimate cause in a purely mechanical series of causes and effects, His causal activity must be conceived in an absolute mechanical sense which has no room for any human responsibility. And the same consequence, viz. the exclusion of human responsibility, is implied in the absolutization of any other non-normative aspect of a causal process.
The source of the contradiction lies in this absolutizing itself. For human thought it is absolutely impossible to form a defined concept of causality in the supertemporal fulness of meaning or in the sense of God's creative act. Impossible, because human thought is bound within the limits of the temporal coherence of meaning.
Only in the transcendental Idea referring to the totality of meaning and to the Ἀρχή can human thought be concentrated towards that which passes beyond its immanent boundaries.
That's why St PAUL's words are full of wisdom when he answers those who speculate on causality with reference to the will of God. "Thou wilt say then unto me, why doth He yet find fault? For who hath resisted His will?" "Nay, but, O man, who art thou that repliest against God?" This answer is a direct dismissal of speculative thought and it does not enter into the false method of posing problems used by speculative philosophy.
To philosophical thought, concentrating on Christ and on God Who reveals Himself in Christ, this speculative way of posing the problem of causality is simply impossible. Only abstract speculative theoretical thought can take it seriously.
Thus the theoretical antinomies of speculative thought after all prove to be antinomies related to the transcendental Idea of the inter-modal coherence between the different law-spheres.
In the same way the basic antinomy in the Humanistic cosmonomic Idea between the ideals of science and of personality appeared again and again to lead to a theoretical antinomy between mechanical causality and moral freedom.
KANT's conception of the nature and the origin of the theoretical antinomies.
The problem concerning the origin of the specific theoretical antinomies has been raised also from the immanence-standpoint. KANT, the founder of the theory of the antinomies in modern thought, is of opinion that their origin lies in the abuse of the theoretical, cosmological Ideas of reason outside of the scope of all experience. The theoretical Idea of reason is nothing but a regulator for the use of our understanding, without having any constitutive function in human knowledge. It stimulates the understanding to carry thought beyond every condition discovered in an empirical phenomenon, and to refer it to the totality of conditions. This totality is never given in experience, since it is to be conceived of as absolute, self-sufficient, unconditioned.
The Idea of reason viewed thus, is nothing but the category of thought freed from the limits set to it by experience; it is the "bis zum Unbedingten erweiterte Kategorie" [the category that has been extended to the unconditional].
Only the "categories" in which the synthesis contained in them form a series, are alleged to be capable of such 'extension into the absolute'. And in this way KANT concludes that there are no more than four cosmological Ideas of reason (in accordance with the four points of view of KANT's table of categories).
These transcendental Ideas ought to be used theoretically only in such a way that they always urge the intellect, tied down to (sensory) experience, to add new determinations to those already found for some phenomenon. They are to be handled in such a way that they set an endless systematical task to theoretical knowledge.
If, however, the Idea is used as a metaphysical 'thing in itself' to which the categories of the understanding are applied as logical determinations without the aid of any sensory experience — as was done in rationalistic metaphysics — then reason inevitably gets involved in 'a dialectical illusion'. It sets up propositions that can neither be proved, nor be disproved by (sensory) experience. The remarkable thing in this "dialectical illusion" is that the thesis as well as the anti-thesis can be conceived without either of them being self-contradictory. They can both appeal to equally valid grounds of reason, but they contradict each other diametrically, notwithstanding. This is how in KANT the theoretical antinomies arise, whose number, according to him, is restricted to that of the cosmological Ideas. There are four of them, distinguished into two mathematical antinomies, relating to the limitedness or illimitableness of the world in time and space and to the infinite or the finite divisibility of matter; — and two dynamic antinomies, relating to the possibility or the impossibility of causality through freedom in the events of the world, and to the existence or the non-existence of the deity as the ens realissimum.
As appeared in the second part of the first volume, this Kantian conception of the nature and the origin of the theoretical antinomies is entirely dependent on the Kantian dualistic cosmonomic Idea with its isolating separation between the realm of experience (of nature) and that of super-sensory freedom.
In this dualism the fundamental antinomy between the ideal of science and that of personality is concealed. And this antinomy in KANT crystallized itself into the isolating separation between the theoretical realm of the understanding, restricted to the phenomenon, and the practical realm of reason, bearing on the super-sensory sphere of the absolute normative Ideas (noumena).
It is to be understood that KANT must find the origin of antinomy in the obliteration of the boundary lines between the transcendental Idea and the intellectual concept of a "Gegenstand". The theoretical Idea can only refer in a theoretically transcendental sense to the transcendent root of temporal reality. To KANT this root is the Idea of the "homo noumenon", the autarchic legislator of moral freedom. But the theoretical Idea may not itself pretend to be a "Ding an sich", as the metaphysics of the mathematical science-ideal before KANT wanted it to do.
The origin of the special theoretical antinomies in the light of our transcendental basic Idea.
Anyone who has understood the importance of the transcendental basic Idea will no longer hold that Christian philosophy can agree with this Kantian view of the nature and origin of antinomy. But this need in no way be an impediment for us to recognize the elements of truth implied in KANT's extremely penetrating doctrine of the dialectic of pure reason.
KANT's controversy with speculative metaphysics in general, and with speculative divinity in particular, retains its fundamental value, insofar as he had an insight into the fact that theoretical antinomies must be founded in a certain speculative overstepping of the limits of theoretical thought. Especially his criticism of the speculative use of what he styles the category of causality is in this respect a proof of his genius.
In a positive sense this doctrine of the antinomies, however, is useless to us, because of the conception of experience and the Idea of the transcendent root of temporal reality that forms its basis.
And precisely KANT's identification of the reality of temporal experience with its sensory and logical aspects is a source of inner antinomies, just as is his absolutizing of the moral aspect of meaning to the transcendent noumenon. It will appear that philosophical thought cannot avoid antinomies by simply separating the concepts of natural science from the normative ones.
It is not even possible to ward off antinomy by observing the modal limits between the various law-spheres without recognizing the mutual cosmic coherence of meaning between them.
We have discovered the true origin of the antinomies in a subjective turning away on the part of theoretical thought from the cosmic order of time. This order is the foundation of the inner sovereignty of the modal aspects within their own spheres, in their inter-modal coherence of meaning.
The special theoretical antinomy must consequently be due to a subjective violation of the modal sovereignty of the different law-spheres by theoretical thought.
Insofar as theoretical thought tries to avoid the antinomies that have arisen in this process, by separating and isolating a phenomenal and a noumenal world, embracing two different groups of mental functions ('nature' and 'normative freedom' in KANT), the antinomies are not really removed. The absolutized complexes of functions, dualistically separated from one another, cannot but cancel and exclude one another by this isolating separation.
In how far the antinomies are caused by a disregard of the meaning of the modal theoretical Ideas can appear only in a later part of our work, in which the relation of the concept of a meaning-modus to the modal Idea will be explained in the light of our transcendental basic Idea. It will then appear that there must be as many classes of theoretical Ideas as there are modal law-spheres in temporal reality.
In any case it ought to be clear that the number of possible theoretical antinomies is much larger than KANT assumed in his "Dialektik der reinen Vernunft", and that the first three of the four that KANT formulated and examined, can be entirely explained by the causes indicated by us. The fourth (oriented to the ontological proof of God's existence) cannot be recognized as a special kind of antinomy, because it touches on the Idea of the Origin in the foundation of all philosophy. On the basis of KANT's cosmonomic Idea it can be reduced to the specific antinomy between the causality of nature, on the one hand, and morality, on the other.
Antinomies are bound to ensue from the attempt to wipe out the limits of meaning between the mathematical aspects of number and space; hence by either assuming the actual continuity of the approximative functions of number (the infinitesimal and the infinitely large number resulting from the continuous series of real numbers), or by resolving space into a collection of points conceived of as real numbers. Antinomies are bound to ensue from the attempt to reduce the modal mathematical aspect of motion to that of the original spatiality, or to resolve the energy-aspect of matter into a spatial collection of points (the antinomies of ZENO; the race between ACHILLES and the tortoise, the flying arrow; KANT's second antinomy of the composition of matter). Antinomies must arise if we think the modal aspect of energy to be determined by the mathematical aspect of space (a more exact statement of KANT's first antinomy between the Ideas of finite and infinite 'worldspace'). There arise necessarily antinomies, when it is attempted to enclose human activity entirely in its physical aspect (the antinomy between mechanical causality and normative responsibility in the various normative aspects of meaning; a more exact statement of KANT's third antinomy). Antinomies must of necessity ensue from the attempt to reduce the original (mathematical) aspect of spatiality to the sensory (objective psychical) space of sight or touch (this antinomy has been examined in the first volume in our chapter on HUME's psychologizing of mathematics) .
 Vol. I, Part II, p. 238 ff.
By ignoring the modal limits marking off the aspect of sensory feeling from that of logical analysis, one ends in antinomies (we refer again to HUME's psychologizing of logical thought). The same result will follow from a logicizing of the jural aspect (cf. the antinomies of KELSEN's so-called "refine Rechtslehre", analysed in my Inaugural Address "De Betekenis der Wetsidee voor Rechtswetenschap en Rechtsphilosophie", 1926).
Theoretical thought is confronted with antinomies when it breaks through the boundaries between the juridical aspect of retributive justice and that of moral love, and so on.
In developing the special theory of the law-spheres, we shall systematically examine the antinomies arising from the theoretical violation of the modal boundaries of meaning. But in the general theory of the law-spheres we shall also have continually to apply the method of antinomy.
The cosmic order is maintained when theoretical thought, failing to recognize the modal sphere-sovereignty of the various aspects of reality, gets involved in inner contradictions, revealed as logical contradictions in the logical aspect of the theory. Every theoretical antinomy is at bottom founded in a subjective turning of theoretical thought against the cosmic order underlying also the laws of logical thinking.
The cosmological principium exclusae antinomiae is not identical with the logical principle of contradiction, but the former is the foundation of the latter.
The principium exclusae antinomiae is therefore by no means identical with the logical principium contradictionis, but rather its foundation.
Without the cosmic order of the law-spheres there is no possibility of logical thought, so that the logical principium contradictionis would be meaningless but for the cosmological principium exclusae antinomiae safeguarding the sphere-sovereignty of the modal aspects of reality within their inter-modal coherence of meaning. This especially distinguishes our theory of antinomy from that of the Kantian doctrine. According to KANT thesis and antithesis are separately conceivable without any inner contradiction. The antinomies, consequently, can in his view be reduced to merely logical contradictions, to a simple conflict between subjective thought and the logical principium contradictionis, which does not allow two contradictory logical judgments to be true at the same time and in the same respect.
From this logicizing of theoretic antinomy it appears most clearly that KANT tried to emancipate theoretical thought from the cosmic temporal order. This is why he has lost sight of the real states of affairs. The thesis about matter being limited by mathematical space (or vice versa the thesis of mathematical space being limited by matter); the thesis as to the infinite divisibility of matter; and that about the exclusively mechanical determination of human actions, are intrinsically antinomic in a cosmological sense. The immanence-standpoint itself is the origin of all cosmological antinomies ("cosmological" is here taken in the sense of our all-sided basic Idea of the cosmos, and not in the Kantian sense of the word).
Not before our analysis of the modal structures of the law-spheres can it be explained how immanence-philosophy is seemingly able to find a point of contact in these very structures for its theoretical violation of the boundaries between the modal aspects, from which the specific antinomies originate.
Antinomy plays havoc with the immanence-standpoint, affecting it in its very root, viz. in its dialectical religious basic motive. In the last instance it is due to the turning away of meaning from its true Origin, and to the emancipation of theoretical thought from the cosmic order of time in which the coherence of meaning is founded.
The method of antinomy tries to bring to light the consequences of this apostasy for theoretic thought. It is therefore pre-eminently a method of immanent criticism, because it tries to penetrate into other systems of philosophy along the lines of their own cosmonomic Idea. That is to say this method starts from their own pre-suppositions, and so lays bare the origin of the antinomy that has been brought to light.
The method of antinomy should consequently not be used exclusively from the viewpoint of the Christian cosmonomic Idea. As a method of criticism of immanence-philosophy it should enter into the transcendental basic idea that forms the foundation of the system whose inner antinomies are to be discovered.
The analytical criterion of a modal law-sphere.
The method of antinomy is, however, not only useful in the discussion with immanence-philosophy. As a critical method it is still more important in the positive development of our own philosophic thought.
On the basis of our transcendental Idea of the cosmic time-order this method postulates analytical purity in concept-formation, and thereby requires an analytical criterion for distinguishing the modalities of meaning.
This analytical criterion has no more than a dependent function in the theory of the law-spheres. It wards off impure analyses of meaning, and especially has the task to guard against any method which results in levelling the specific modal aspects by means of concepts that are supposed to possess generic universality of meaning (the method of finding a genus proximum and the differentia specifica).
The analytic impurity of such pseudo-generic and pseudo-specific concepts is to be demonstrated by showing their multiplicity of meanings. The concrete importance of this logical criterion cannot appear until we are acquainted with the method of analyzing the modal structures of the aspects. In the present context we are only concerned with the value of the method of antinomy with respect to the discovery of the material (synthetical) criterion of a modal law-sphere. Here this method acquires an heuristic function. If we are in doubt whether the fundamental concepts of jurisprudence, economics, historical science, and so
on, are related to specific modal aspects of human experience and empirical reality, we may try to reduce them to the fundamental concepts of other sciences whose modal fields of research have already been defined. When this attempt leads to specific insoluble antinomies, a negative proof has been given of a theoretical violation of the modal boundaries between irreducible law-spheres.
By applying this method to legal theory I was able to establish that the fundamental juridical concepts of causality, volition, power, interpretation etc. must have an irreducible modal juridical sense, since they do not permit themselves to be reduced to analogical concepts of other sciences without involving juridical thought in antinomies. But, because they are also used in other sciences — a state of affairs which refers to the inter-modal coherence of meaning between the different aspects — it is necessary to seek for the orginal juridical meaning-moment which alone can guarantee them their modal juridical sense. Here we are confronted with the modal structures of the aspects, which will be examined later on.
Herman Dooyeweerd, New Critique of Theoretical Thought, Vol II/ Part I/ Chapt 1/§ 5 pp 36-49)