Texte remanié de: Proefschrift--Letteren--Universiteit van Amsterdam, 1994. / résumé en anglais. Bibliogr. p. 391-408. Index.

Thesis (D. Litt. (English))--University of Pretoria, 2005. / Includes bibliographical references (leaves 240-257).

Proefschrift. / Bibliogr. p. 249-277.

This study furnishes some results of an investigation to ascertain whether the possibility of a Christian logic can be maintained as a meaningful question. This problem seems to be enmeshed in a complex encompassing the problem of Christian science* as such. Whether the possibility of a Christian logic is maintained or denied, at any rate this implies a positive standpoint towards the problem of a Christian logic. Some general remarks having been made in an introductory chapter, the main aspects bearing on the background of different points of view towards logic are presented in Chapter II. <1> The general philosophical conception adopted seems to be of importance with a view to the formation of a conception of logic in at least and especially two respects. <a> Philosophical trends have a marked influence on the view taken of logic. As far as modern philosophy is concerned, one can point to the differences appertaining to logic, its character, and the domain accorded to logic as science, its place in the cosmic reality, etc., differences which become evident in the conceptions of, for example, Descartes, Arnauld & Nicole, Kant, Opzoomer, Heymans, Bolland, Dewey, Bergson and Heidegger. Whereas Dewey, Bergson and Heidegger move in an irrationalistic direction, the first mentioned six philosophers bear evidence of a rationalistic point of view. The idealistic conception of Kant differs from the scientialism of a Descartes and the practicalism of the writers of The Port Ro*al Logic; the difference can be traced to the fact that Kant lends .the divergent solutions furnished by scientialism and practicalism to a unity, which ascribes to the ~ human perceptive faculty two functions, a theoretical and practical; theoretical reason and practical reason are autonomous, each in its particular sphere. The more recent rationalism of an Opzoomer, Heymans and Bolland, keeps to the rationalistic main lines but takes the a priori's of autonomous reason in a dynamic-active sense by laying stress on the scientific methods. Positivism advanced the first solution in this direction, overestimating scientific theory in a scientialistic spirit, with the result that the practical existence is viewed in the light of science. The positivism of a Comte and Opzoomer finds an antipode in the neo-positivism of, for instance, Dilthey, Wundt and Heymans, laying stress on the practical aspect. And then the neoidealism of Cassirer, Bosanquet, Bolland and others bridges the opposition between the positivistic and nee-positivistic conceptions. The far-reaching influence of rationalistic conceptions encountered a serious set-back on account of the increasing importance attached to the se-called critique of science and especially the rise of irrationalistic conceptions. Irrationalism accepts reason in a rationalistic sense, but limits its validity and importance to a specific sphere. The pragQatism of James and Dewey, for instance, supports science only in so far as it furthers practical purposes: one has to obey reason in order to experiment, but the important point is exactly the fact that one is busy experimenting on account of a need bearing on practical life. A second trend, the "philosophy of life" which had an eminent exponent in Bergson, emphasizes the importance of "life" (taken in an organicpsychovitalistic sense) instead of practical utility, and therefore accentuates intuition in contrast to the symbolic operational method of intelligence (which "belong to the domain of logic). And finally existentialistically-minded philosophers champion the cause of human existence, of the individual concrete situation. It is pointed out that these differences in philosophical conception result in different points of view taken of logic. <b> Secondly the specific type of philosophical point of view is an ontological factor of supreme importance in the realisation of a conception of logic. Kant and Hegel, for instance, both advance an idealistic conception, but differ as to the type of philosophical point of view; for Hegel attaches himself to a contradictory type whereas Kant propounds an "ennoetic" conception which regards the sensations as furnishing the material for the forms of the intellect, that is to say, the intellect has the sensations as contents of the mind. Moreover I may refer to the interaction-theory of a Descartes and the instrumentistic point of view of a Bergson or the psychomonistic type represented by a Heymans, etc. Each particular type of philosophical conception involves a specific cosmology and anthropology, and results in a particular conception of logic and the problems of this branch of science. <2> In addition to the above mentioned ontological matters, it is necessary to point separately to the importance of epistemological factors for one's conception of logic. This point is illustrated by enumerating some basic problems of a theory of knowledge and explaining a few points in greater detail, for instance, <a> the possibility and suppositions of knowledge; <b> the analysis of knowledge (including the essence, character and kinds of knowledge), the formation of knowledge, the purpose of knowledge and the unity of knowledge (including limits and scope of knowledge, the partial nature and coherence of knowledge); and <c> the validity of knowledge (including knowledge and law, knowledge and value, as well as the reliability of knowledge). <3> In yet another respect different points of view may arise, viz. according to the opinion held as to logic as science, its character and domain, and the investigation of the logical field. There is, for instance, a trend in logic which attempts to approach the field of logic from that of mathematics, and on the other hand some logicians undertake the task of studying the basic principles of mathematics with logic as the starting-point. Moreover, also the points of view of psychologism in logic (Sigwart) and Husserl’s reaction against this trend, tend to show that the scientific determination of the field of investigation bears testimony to the fact that the logician cannot afford to neglect matters which can be traced to <a> different attitudes in theory of science, and <b > different points of view in regard to the field of investigation. <4> Lastly the suggestion may be offered that one-sided stressing of one or more of the different factors of importance (mentioned above) as such, may also result in different conceptions of logic. * * * Up to this point no attention has been paid to the possibility of the Christian conviction, the Christian "life and world-view", etc., as an important factor in the formation of a conception of logic. Chapter III gives a general survey of the points of view taken on logic in a Christian atmosphere. <1> A Christian logic is an utter impossibility; this is the first standpoint taken as to this problem. This, point of view comprises, however, various subordinate solutions of the problem. <a> Some argue that as far as the importance and implications of Christianity are concerned, Christianity is confined to divine worship and this does not bear on logic in any way whatsoever. <b> Others acknowledge the importance of Christianity for divine worship, and add: for daily practical life too --- although in no wise for science and therefore not for logic. <c> A third solution accepts the significance of Christianity for a section of science, for instance <i> as far as theology is concerned, <ii> and also for philosophy, <iii> and perhaps in some respects for other branches of science (e.g. sociology, ethnology, the science of history, etc.) but at any rate not as far as logic is concerned. <2> On the other hand some scientists, inspired by the reformational concept of Calvin, maintain that Christianity, that the Christian view of cosmos and man, the Christian approach to scientific matters, etc., must be esteemed a factor of importance so far as the conception of science as such is concerned, and that moreover it is imperative that all scientific investigations be undertaken in the light of the revelation (in Holy Scripture); for this reason among others the idea of a Christian logic is not absurd. This thesis can be elucidated by mentioning some contributions to a Christian logic, for instance, <a> A. Kuyper's opinion that science is of two kinds because humanity is of two kinds, those regarding the cosmos as normal and those who take into account the reality of the fall of man in Adam, and therefore acknowledge the fact that an act of interference on the part of God is necessary to put the cosmos again in a correct relation to Him. On account of this difference Kuyper therefore maintains the existence of a Christian and non Christian science. As the fact of sin dit not affect the formal activity of thinking, according to Kuyper, he states that the palingenesis does not cause any difference in this respect; therefore only one kind of logic exists --- a Christian logic. <b> S.O. Los indicates the necessity of a Christian logic by stating that the Calvinistic principles ought to find application in every section of science, not excluding logic. A Christian logic takes into account the principles of Holy Scripture and brings them to bear upon scientific studies. <c> H.G. Stoker's conception of the cosmos as a created coherent diversity implies i n t era 1 i a that the field of logic has an irreducible, unique character of its own, but the logical sphere is part of a comprehensive totality in which all diversity is given in a coherent complex. Because it is a radical diversity, it is unlike the psychical, lingual or ethical sphere, and therefore the logical sphere may not be reduced to any other diversity nor isolated from the diversity with which it constitutes a totality. On account of the fact that cosmic reality is a created diversity, it is not autonomous nor self-sufficient; a Christian logic therefore naturally opposes the dogma of the autonomy of thought.<d> C. Van Til points out that whereas the facts and laws with which logic is concerned, are not detached from their being created, the facts and laws of logic too are not self-sufficient, but part of created reality; accordingly it is imperative that the Christian truths (of, for instance, creation, fall of man into sin, and redemption in Jesus Christ in the communion of the Holy Spirit) be acknowledged from the very beginning. Indeed, as Van Til explains in detail, no part of Christianity remains intact when once the Arminian logic is allowed to run its course. <e> K. Schilder puts forward various considerations bearing on the impossibility of a formal or neutral logic, and states that logic has a foundation in fundamental philosophical ideas, on account of which a Hegelian, Fiahtian and Calvinist have different conceptions of logic; moreover, logic is not detached from other sciences, and in no science can one find one's way without a standpoint in faith. <f> H. Dooyeweerd's "philosophy of the cosmonomic idea" states and illustrates in various respects both the possibility and necessity of a Christian logic. Especially his theory of the nodal spheres each subjected to its own law, discloses an insight of great depth concerning the logical sphere as a modal aspect of cosmic reality, having the numerical and spatial aspects, the aspect of mathematical movement, the aspect of physical energy, of organic life and of psychical feeling as substratum spheres and the historical and linguistic aspects, the aspect of social intercourse, the economic, the aesthetic, the jural, the moral aspects and the aspect of faith as superstratum spheres. In its modal nucleus each sphere enjoys a sovereignty in its own sphere and differs from every other modal aspect; on account of retrocipations each sphere coheres with every previous sphere in the cosmic order and by means of anticipations with the superstratum spheres, thus presenting also a universality in its own sphere. The variable phenomena of each sphere function subjected to a law of their own, for instance, in the logical sphere judgements are subjected to the logical (analytical) law; accordingly this subject is treated as the theory of the spheres of law --- a really important milestone on the way towards a Christian logic, particularly so, as it has proved to be exceptionally useful in determining the characteristic nature of the logical sphere. <g> D.H.Th. Vollenhoven has established the cardinal data of a Christian logic and acquired an insight into such various points of importance for the problem of a Christian logic, that it is considered necessary to treat thereof in a separate chapter. * * * The first section of chapter IV is given to a general survey of the more important writings of Vollenhoven in so far as they contributed towards his conception of a Christian logic. An attempt is made to show how Vollenhoven arrived at his final conception. This section is also intended to furnish the basis for an interpretation of his conception, which follows in the succeeding parts of chapter IV. <1 > <a> Ontology presents an insight into the difference in the being of God, law and cosmos. God is the Sovereign who created the cosmos and put his law to the cosmos. Only God is sovereign, i.e. not subjected to the law. It is only of the law that one can say that it obtains (for that which is subjected to the law); and the being of the cosmos exists in its being subjected to. the law. <b > The word "law" can be taken in three different senses: as structural (modal) law, as the commandment of love, and as positive law. <c> The being of the cosmos displays a diversity of created subjects, heavenly and earthly. <d> By temporarily disregarding the essentials in which man differs from other "things", it is possible to investigate the being of the thing. It is necessary to distinguish the being of the subject and the object, both being subjected to the law, but in different respects. Both have to be investigated as to the modal (universal) differences and to the individual differences, as well as their particular relations and the bonds between modal differences (retrocipations and anticipations) and between individual differences (coherences). An object is a complex having a subject as the bearer of object-functions, attributes such as colour, warmth, etc.; although being more complex than the subject, subject and object have this in common that they are both subjected to the law. <e> The structure of man is even more complex. Beside modal differences and individual differences (having this specific individual characteristic and not that, on account of which this judgement differs from that judgment --- although they do-not differ modally as both are logical), the difference in direction of his functions (good or bad) is of extreme importance as far as the being of man is concerned. For the different modal functions constitute the frame for the activities of man, and therefore the logical sphere is called the logical function. The activities of the heart of man (prefunctional) are, as it were, sent into a specific functional channel; and this activity is directed by the heart in a twofold exit, namely for better or worse. <f> The structure of the realms (man, animal, plant and mineral) brings us to the genetic bond; and <g> as to the structure of mankind two points are worth mentioning, viz. <i> the bonds of community (their character, diversity and mutual relation) and <ii> religion as the covenant between God, the Creator of heaven and earth, and man. <h > After the particular relation between heaven and earth has been treated, the bond between God, law and cosmos demands attention. <2> Theory of knowledge is distinct from ontology but nevertheless presupposes a close relation. <a> The theory of human knowledge is discussed in two main sections: <i> the structure of the non-scientific cognition (including its suppositions; the knowable; the activity of learning-to-know; the result of knowing; and the bond between the result of knowing and the activity of learning, the knowable, and the norm of learning-to-know! and secondly the development of the non-scientific cognition), and <ii> the structure of the scientific cognition (including firstly the cognition in particular scientists method and the diversity of scientific methods in particular science, the analysable for particular sciences, and the result of scientific cognition in particular sciences; and secondly the scientific cognition of nonparticular sciences as, for instance, philosophy); <b> the theory of science investigates particular sciences• and non-particular sciences; and c > methodology studies the problem of method as such, as well as in relation to the different sciences, not excluding logic. <3> Under logic is discussed <a> fundamental philosophical questions, including those of <i> philosophy of the logical field which discloses an insight into the logical sphere of law --- which logic has to investigate --( including in particular the question of what the logical modality is and how the logical aspect is present in that which subsists gnostically),and <ii> philosophy of logic (including, the problem of logic as a science and that of its relation to philosophy). <b> Under the general structure of the analytical (logical) sphere attention is paid to <i> the analytical law and <ii> the analytically subjected, viz. the analytical subjects (including the analytical activity, and the result of this activity: concept and judgment) and the analytical objects (i.e. the• analytical aspect of all the sub analytical); furthermore the bond between analytical subject and object, and lastly the bond between the analytical law and the analytically subjected, as well as the bond between God, analytical law and the analytically subjected. Under the concept is discussed the concept as such, the division of concepts and the particular relations of concepts. The theory of judgment likewise avails itself of these three themes for treating judgment. Chapter V investigates some problems of a more particular nature in the domain of logic; the investigation has had to be restricted to three subjects. <1> The analytical (logical) law. <a> Firstly the question is considered whether an analytical law exists, and it is pointed out that logicians who do give attention to this question usually stress one-sidedly the importance of either the analysable or the analytical activity or the result of thinking (the thought). <b > As far as the sense of the analytical law is concerned, a point of particular importance is Vollenhoven's insight that the analytical law is <i> specifically an analytical (and no nonanalytical, e.g. a mathematical) law, <ii> a structural law, 1. e. a modal law, and <iii> as law, the boundary between God and cosmos. <c> As to the contents of the analytical law, some critical remarks are made about the conception of e.g. Welton &Monahan, and reference is made to the importance and consequences of Vollenhoven's synopsis of the contents of the analytical law: "analyse well the analysable, whatever it may be". <d> The discussion of the question whether the analytical law can or must be considered as being formal, touches a few facets of the problem and gives some arguments for the supposition that it is not formal. <e> Ontology (stating the fundamental distinction between the being of God, law and cosmos) appears of cardinal importance also in respect to the question whether the analytical law be .considered a norm. <f> Finally attention is drawn to fallacies, And the supposition is advanced that one's conception of the analytical law determines in important respects one's view held as to fallacies. Fallacies seem to be due chiefly to the following three causes: <i> by disobeying the analytical norm, <ii > by reason of the fact that the substratum-functions of the logical function fail and <iii> on account of "wickedness of heart". <2> With reference to R. Robinson some points of importance concerning the problem of definition are discussed. The attitude is taken that definition is a specific kind of judgment, viz. a judgment in which the predicate does not analyse or evaluate the subject of the judgment, but delimits the sphere and scope of the subject, determines it, defines it, that is to say: attributes a predicate to the subject of a judgment with a scientific purpose. Definition can be given of concepts, or words, or the contents of words or of concepts, or the meaning of words. Especially important is the fact that the theory about definition presupposes a specific category theory; accordingly a Christian standpoint adopted in scientific study results in a different point of view taken towards definition. Lastly may be mentioned. that the difference between scientific and non-scientific definition ought not be neglected. <3> The comprehensive problem of the division of judgments likewise indicates that a Christian standpoint in science (logic) does not impede or hamper the investigation of the field of logic --- in this case the division of judgments ---- but on the contrary furthers scientific study and results in a new perspective, opening new fields leading to hitherto unexplored data. By comparing the divisions of judgments furnished by Welton & Monahan, Stebbing, De Vleeschauwer and Vollenhoven, the conclusion is reached that the point of view presupposed by each division determines the criteria employed in the division of judgments; the view is taken that a Christian point of view constitutes an exceptionally liberal and balanced conception of the subject, and in various respects avoids one-sidedness, partiality and the limitations inherent in some other points of view. From this it is apparent that the consequences and implications of the point of view taken in the study of logic Chapter VI gives a short conclusionary view in which some important consequences of the previous expositions are enumerated and a few critical remarks added to illuminate some aspects of the problem. <1> Christian logic furnishes a particularly penetrating insight into the philosophical basis of logic. Philosophical matters influence in fundamental respects the scientific investigation of the logical field and it appears imperative that logic be based on a philosophical conception (from whatever point of view adopted). Logic is different from philosophy but the scientific activity in the field of logic nevertheless presupposes a philosophical standpoint, as Chapter II has indicated. Particularly important is the fact that Vollenhoven could demonstrate the necessity for the logician to keep in mind both the modality (viz. logical) and the character (viz. as result of a previous analytical activity) of the concept and judgment, as well as to investigate the retrocipations and anticipations of the logical function on sub- and superstratum spheres respectively; logic derives from philosophy the insight that all of this, and the analytical activity too, belong to the logical sphere. The conception developed in logic cannot be considered to be detached from more fundamental philosophical matters nor to be formal nor neutral. A Christian philosophy is especially necessary with a view to keeping the spheres of ontology and epistemology distinct, as well as to determine the difference between and the relationship of logic and on the one hand cosmology and anthropology, and on the other hand epistemology. A Christian logic reaps the advantages of this distinction. Besides the option of e.g. either rationalism or irrationalism, a Christian standpoint in scientific matters is practicable. The results of Dooyeweerd, Vollenhoven, Stoker, Van Til and others have changed the possibility of a Christian point of view in science (including logic) into a reality. Chapter IV especially has indicated that and how a Christian logic presupposes a Christian philosophy and in Chapter V it has been possible to point out the importance of a Christian approach to logic, even in its details. <2> As regards the matter investigated by logic and its character, the point of view is taken that logic is a science and that no scientist can•accept his task of investigation or execute his analysis without a determination of his field of study and the nature of this field, as well as testing the results obtained with this determination; moreover continued reflection is necessary as to whether the. investigation has succeeded in complying with the determination of the field of investigation. The supposition is held that the determination of the field of investigation is a distinction according to modality, that is to say logic has to investigate the analytical (logical) sphere of law. A Christian logic opposes the various forms of reduction-logic which screen the logical field down to some of the most obvious phenomena of the logical sphere. A Christian logic results in various new finds, as well as a new. perspective of the whole domain of logic. <3> Logic according to a Christian point of view is not what it is often thought to be and moreover it is different from the traditional conception. Logic as science is not formal nor neutral. A Christian point of view accepts the relevance of religion and considers the Word of God to be the guiding principle for directing scientific cognition in its scientific investigation of the logical field. Christian logic is no logic of religion or vice versa, no logical creed, logical science of belief or a logic of divine worship, nor a compilation of texts from the Holy Scriptures bearing on the logical function, etc. A Christian logic does not investigate the logical field from or v 1 a the function of belief. have effects even in the most particular details of the field of logic. / Thesis (MA)--PU vir CHO, 1959.

This study furnishes some results of an investigation to ascertain whether the possibility of a Christian logic can be maintained as a meaningful question. This problem seems to be enmeshed in a complex encompassing the problem of Christian science* as such. Whether the possibility of a Christian logic is maintained or denied, at any rate this implies a positive standpoint towards the problem of a Christian logic. Some general remarks having been made in an introductory chapter, the main aspects bearing on the background of different points of view towards logic are presented in Chapter II. <1> The general philosophical conception adopted seems to be of importance with a view to the formation of a conception of logic in at least and especially two respects. <a> Philosophical trends have a marked influence on the view taken of logic. As far as modern philosophy is concerned, one can point to the differences appertaining to logic, its character, and the domain accorded to logic as science, its place in the cosmic reality, etc., differences which become evident in the conceptions of, for example, Descartes, Arnauld & Nicole, Kant, Opzoomer, Heymans, Bolland, Dewey, Bergson and Heidegger. Whereas Dewey, Bergson and Heidegger move in an irrationalistic direction, the first mentioned six philosophers bear evidence of a rationalistic point of view. The idealistic conception of Kant differs from the scientialism of a Descartes and the practicalism of the writers of The Port Ro*al Logic; the difference can be traced to the fact that Kant lends .the divergent solutions furnished by scientialism and practicalism to a unity, which ascribes to the ~ human perceptive faculty two functions, a theoretical and practical; theoretical reason and practical reason are autonomous, each in its particular sphere. The more recent rationalism of an Opzoomer, Heymans and Bolland, keeps to the rationalistic main lines but takes the a priori's of autonomous reason in a dynamic-active sense by laying stress on the scientific methods. Positivism advanced the first solution in this direction, overestimating scientific theory in a scientialistic spirit, with the result that the practical existence is viewed in the light of science. The positivism of a Comte and Opzoomer finds an antipode in the neo-positivism of, for instance, Dilthey, Wundt and Heymans, laying stress on the practical aspect. And then the neoidealism of Cassirer, Bosanquet, Bolland and others bridges the opposition between the positivistic and nee-positivistic conceptions. The far-reaching influence of rationalistic conceptions encountered a serious set-back on account of the increasing importance attached to the se-called critique of science and especially the rise of irrationalistic conceptions. Irrationalism accepts reason in a rationalistic sense, but limits its validity and importance to a specific sphere. The pragQatism of James and Dewey, for instance, supports science only in so far as it furthers practical purposes: one has to obey reason in order to experiment, but the important point is exactly the fact that one is busy experimenting on account of a need bearing on practical life. A second trend, the "philosophy of life" which had an eminent exponent in Bergson, emphasizes the importance of "life" (taken in an organicpsychovitalistic sense) instead of practical utility, and therefore accentuates intuition in contrast to the symbolic operational method of intelligence (which "belong to the domain of logic). And finally existentialistically-minded philosophers champion the cause of human existence, of the individual concrete situation. It is pointed out that these differences in philosophical conception result in different points of view taken of logic. <b> Secondly the specific type of philosophical point of view is an ontological factor of supreme importance in the realisation of a conception of logic. Kant and Hegel, for instance, both advance an idealistic conception, but differ as to the type of philosophical point of view; for Hegel attaches himself to a contradictory type whereas Kant propounds an "ennoetic" conception which regards the sensations as furnishing the material for the forms of the intellect, that is to say, the intellect has the sensations as contents of the mind. Moreover I may refer to the interaction-theory of a Descartes and the instrumentistic point of view of a Bergson or the psychomonistic type represented by a Heymans, etc. Each particular type of philosophical conception involves a specific cosmology and anthropology, and results in a particular conception of logic and the problems of this branch of science. <2> In addition to the above mentioned ontological matters, it is necessary to point separately to the importance of epistemological factors for one's conception of logic. This point is illustrated by enumerating some basic problems of a theory of knowledge and explaining a few points in greater detail, for instance, <a> the possibility and suppositions of knowledge; <b> the analysis of knowledge (including the essence, character and kinds of knowledge), the formation of knowledge, the purpose of knowledge and the unity of knowledge (including limits and scope of knowledge, the partial nature and coherence of knowledge); and <c> the validity of knowledge (including knowledge and law, knowledge and value, as well as the reliability of knowledge). <3> In yet another respect different points of view may arise, viz. according to the opinion held as to logic as science, its character and domain, and the investigation of the logical field. There is, for instance, a trend in logic which attempts to approach the field of logic from that of mathematics, and on the other hand some logicians undertake the task of studying the basic principles of mathematics with logic as the starting-point. Moreover, also the points of view of psychologism in logic (Sigwart) and Husserl’s reaction against this trend, tend to show that the scientific determination of the field of investigation bears testimony to the fact that the logician cannot afford to neglect matters which can be traced to <a> different attitudes in theory of science, and <b > different points of view in regard to the field of investigation. <4> Lastly the suggestion may be offered that one-sided stressing of one or more of the different factors of importance (mentioned above) as such, may also result in different conceptions of logic. * * * Up to this point no attention has been paid to the possibility of the Christian conviction, the Christian "life and world-view", etc., as an important factor in the formation of a conception of logic. Chapter III gives a general survey of the points of view taken on logic in a Christian atmosphere. <1> A Christian logic is an utter impossibility; this is the first standpoint taken as to this problem. This, point of view comprises, however, various subordinate solutions of the problem. <a> Some argue that as far as the importance and implications of Christianity are concerned, Christianity is confined to divine worship and this does not bear on logic in any way whatsoever. <b> Others acknowledge the importance of Christianity for divine worship, and add: for daily practical life too --- although in no wise for science and therefore not for logic. <c> A third solution accepts the significance of Christianity for a section of science, for instance <i> as far as theology is concerned, <ii> and also for philosophy, <iii> and perhaps in some respects for other branches of science (e.g. sociology, ethnology, the science of history, etc.) but at any rate not as far as logic is concerned. <2> On the other hand some scientists, inspired by the reformational concept of Calvin, maintain that Christianity, that the Christian view of cosmos and man, the Christian approach to scientific matters, etc., must be esteemed a factor of importance so far as the conception of science as such is concerned, and that moreover it is imperative that all scientific investigations be undertaken in the light of the revelation (in Holy Scripture); for this reason among others the idea of a Christian logic is not absurd. This thesis can be elucidated by mentioning some contributions to a Christian logic, for instance, <a> A. Kuyper's opinion that science is of two kinds because humanity is of two kinds, those regarding the cosmos as normal and those who take into account the reality of the fall of man in Adam, and therefore acknowledge the fact that an act of interference on the part of God is necessary to put the cosmos again in a correct relation to Him. On account of this difference Kuyper therefore maintains the existence of a Christian and non Christian science. As the fact of sin dit not affect the formal activity of thinking, according to Kuyper, he states that the palingenesis does not cause any difference in this respect; therefore only one kind of logic exists --- a Christian logic. <b> S.O. Los indicates the necessity of a Christian logic by stating that the Calvinistic principles ought to find application in every section of science, not excluding logic. A Christian logic takes into account the principles of Holy Scripture and brings them to bear upon scientific studies. <c> H.G. Stoker's conception of the cosmos as a created coherent diversity implies i n t era 1 i a that the field of logic has an irreducible, unique character of its own, but the logical sphere is part of a comprehensive totality in which all diversity is given in a coherent complex. Because it is a radical diversity, it is unlike the psychical, lingual or ethical sphere, and therefore the logical sphere may not be reduced to any other diversity nor isolated from the diversity with which it constitutes a totality. On account of the fact that cosmic reality is a created diversity, it is not autonomous nor self-sufficient; a Christian logic therefore naturally opposes the dogma of the autonomy of thought.<d> C. Van Til points out that whereas the facts and laws with which logic is concerned, are not detached from their being created, the facts and laws of logic too are not self-sufficient, but part of created reality; accordingly it is imperative that the Christian truths (of, for instance, creation, fall of man into sin, and redemption in Jesus Christ in the communion of the Holy Spirit) be acknowledged from the very beginning. Indeed, as Van Til explains in detail, no part of Christianity remains intact when once the Arminian logic is allowed to run its course. <e> K. Schilder puts forward various considerations bearing on the impossibility of a formal or neutral logic, and states that logic has a foundation in fundamental philosophical ideas, on account of which a Hegelian, Fiahtian and Calvinist have different conceptions of logic; moreover, logic is not detached from other sciences, and in no science can one find one's way without a standpoint in faith. <f> H. Dooyeweerd's "philosophy of the cosmonomic idea" states and illustrates in various respects both the possibility and necessity of a Christian logic. Especially his theory of the nodal spheres each subjected to its own law, discloses an insight of great depth concerning the logical sphere as a modal aspect of cosmic reality, having the numerical and spatial aspects, the aspect of mathematical movement, the aspect of physical energy, of organic life and of psychical feeling as substratum spheres and the historical and linguistic aspects, the aspect of social intercourse, the economic, the aesthetic, the jural, the moral aspects and the aspect of faith as superstratum spheres. In its modal nucleus each sphere enjoys a sovereignty in its own sphere and differs from every other modal aspect; on account of retrocipations each sphere coheres with every previous sphere in the cosmic order and by means of anticipations with the superstratum spheres, thus presenting also a universality in its own sphere. The variable phenomena of each sphere function subjected to a law of their own, for instance, in the logical sphere judgements are subjected to the logical (analytical) law; accordingly this subject is treated as the theory of the spheres of law --- a really important milestone on the way towards a Christian logic, particularly so, as it has proved to be exceptionally useful in determining the characteristic nature of the logical sphere. <g> D.H.Th. Vollenhoven has established the cardinal data of a Christian logic and acquired an insight into such various points of importance for the problem of a Christian logic, that it is considered necessary to treat thereof in a separate chapter. * * * The first section of chapter IV is given to a general survey of the more important writings of Vollenhoven in so far as they contributed towards his conception of a Christian logic. An attempt is made to show how Vollenhoven arrived at his final conception. This section is also intended to furnish the basis for an interpretation of his conception, which follows in the succeeding parts of chapter IV. <1 > <a> Ontology presents an insight into the difference in the being of God, law and cosmos. God is the Sovereign who created the cosmos and put his law to the cosmos. Only God is sovereign, i.e. not subjected to the law. It is only of the law that one can say that it obtains (for that which is subjected to the law); and the being of the cosmos exists in its being subjected to. the law. <b > The word "law" can be taken in three different senses: as structural (modal) law, as the commandment of love, and as positive law. <c> The being of the cosmos displays a diversity of created subjects, heavenly and earthly. <d> By temporarily disregarding the essentials in which man differs from other "things", it is possible to investigate the being of the thing. It is necessary to distinguish the being of the subject and the object, both being subjected to the law, but in different respects. Both have to be investigated as to the modal (universal) differences and to the individual differences, as well as their particular relations and the bonds between modal differences (retrocipations and anticipations) and between individual differences (coherences). An object is a complex having a subject as the bearer of object-functions, attributes such as colour, warmth, etc.; although being more complex than the subject, subject and object have this in common that they are both subjected to the law. <e> The structure of man is even more complex. Beside modal differences and individual differences (having this specific individual characteristic and not that, on account of which this judgement differs from that judgment --- although they do-not differ modally as both are logical), the difference in direction of his functions (good or bad) is of extreme importance as far as the being of man is concerned. For the different modal functions constitute the frame for the activities of man, and therefore the logical sphere is called the logical function. The activities of the heart of man (prefunctional) are, as it were, sent into a specific functional channel; and this activity is directed by the heart in a twofold exit, namely for better or worse. <f> The structure of the realms (man, animal, plant and mineral) brings us to the genetic bond; and <g> as to the structure of mankind two points are worth mentioning, viz. <i> the bonds of community (their character, diversity and mutual relation) and <ii> religion as the covenant between God, the Creator of heaven and earth, and man. <h > After the particular relation between heaven and earth has been treated, the bond between God, law and cosmos demands attention. <2> Theory of knowledge is distinct from ontology but nevertheless presupposes a close relation. <a> The theory of human knowledge is discussed in two main sections: <i> the structure of the non-scientific cognition (including its suppositions; the knowable; the activity of learning-to-know; the result of knowing; and the bond between the result of knowing and the activity of learning, the knowable, and the norm of learning-to-know! and secondly the development of the non-scientific cognition), and <ii> the structure of the scientific cognition (including firstly the cognition in particular scientists method and the diversity of scientific methods in particular science, the analysable for particular sciences, and the result of scientific cognition in particular sciences; and secondly the scientific cognition of nonparticular sciences as, for instance, philosophy); <b> the theory of science investigates particular sciences• and non-particular sciences; and c > methodology studies the problem of method as such, as well as in relation to the different sciences, not excluding logic. <3> Under logic is discussed <a> fundamental philosophical questions, including those of <i> philosophy of the logical field which discloses an insight into the logical sphere of law --- which logic has to investigate --( including in particular the question of what the logical modality is and how the logical aspect is present in that which subsists gnostically),and <ii> philosophy of logic (including, the problem of logic as a science and that of its relation to philosophy). <b> Under the general structure of the analytical (logical) sphere attention is paid to <i> the analytical law and <ii> the analytically subjected, viz. the analytical subjects (including the analytical activity, and the result of this activity: concept and judgment) and the analytical objects (i.e. the• analytical aspect of all the sub analytical); furthermore the bond between analytical subject and object, and lastly the bond between the analytical law and the analytically subjected, as well as the bond between God, analytical law and the analytically subjected. Under the concept is discussed the concept as such, the division of concepts and the particular relations of concepts. The theory of judgment likewise avails itself of these three themes for treating judgment. Chapter V investigates some problems of a more particular nature in the domain of logic; the investigation has had to be restricted to three subjects. <1> The analytical (logical) law. <a> Firstly the question is considered whether an analytical law exists, and it is pointed out that logicians who do give attention to this question usually stress one-sidedly the importance of either the analysable or the analytical activity or the result of thinking (the thought). <b > As far as the sense of the analytical law is concerned, a point of particular importance is Vollenhoven's insight that the analytical law is <i> specifically an analytical (and no nonanalytical, e.g. a mathematical) law, <ii> a structural law, 1. e. a modal law, and <iii> as law, the boundary between God and cosmos. <c> As to the contents of the analytical law, some critical remarks are made about the conception of e.g. Welton &Monahan, and reference is made to the importance and consequences of Vollenhoven's synopsis of the contents of the analytical law: "analyse well the analysable, whatever it may be". <d> The discussion of the question whether the analytical law can or must be considered as being formal, touches a few facets of the problem and gives some arguments for the supposition that it is not formal. <e> Ontology (stating the fundamental distinction between the being of God, law and cosmos) appears of cardinal importance also in respect to the question whether the analytical law be .considered a norm. <f> Finally attention is drawn to fallacies, And the supposition is advanced that one's conception of the analytical law determines in important respects one's view held as to fallacies. Fallacies seem to be due chiefly to the following three causes: <i> by disobeying the analytical norm, <ii > by reason of the fact that the substratum-functions of the logical function fail and <iii> on account of "wickedness of heart". <2> With reference to R. Robinson some points of importance concerning the problem of definition are discussed. The attitude is taken that definition is a specific kind of judgment, viz. a judgment in which the predicate does not analyse or evaluate the subject of the judgment, but delimits the sphere and scope of the subject, determines it, defines it, that is to say: attributes a predicate to the subject of a judgment with a scientific purpose. Definition can be given of concepts, or words, or the contents of words or of concepts, or the meaning of words. Especially important is the fact that the theory about definition presupposes a specific category theory; accordingly a Christian standpoint adopted in scientific study results in a different point of view taken towards definition. Lastly may be mentioned. that the difference between scientific and non-scientific definition ought not be neglected. <3> The comprehensive problem of the division of judgments likewise indicates that a Christian standpoint in science (logic) does not impede or hamper the investigation of the field of logic --- in this case the division of judgments ---- but on the contrary furthers scientific study and results in a new perspective, opening new fields leading to hitherto unexplored data. By comparing the divisions of judgments furnished by Welton & Monahan, Stebbing, De Vleeschauwer and Vollenhoven, the conclusion is reached that the point of view presupposed by each division determines the criteria employed in the division of judgments; the view is taken that a Christian point of view constitutes an exceptionally liberal and balanced conception of the subject, and in various respects avoids one-sidedness, partiality and the limitations inherent in some other points of view. From this it is apparent that the consequences and implications of the point of view taken in the study of logic Chapter VI gives a short conclusionary view in which some important consequences of the previous expositions are enumerated and a few critical remarks added to illuminate some aspects of the problem. <1> Christian logic furnishes a particularly penetrating insight into the philosophical basis of logic. Philosophical matters influence in fundamental respects the scientific investigation of the logical field and it appears imperative that logic be based on a philosophical conception (from whatever point of view adopted). Logic is different from philosophy but the scientific activity in the field of logic nevertheless presupposes a philosophical standpoint, as Chapter II has indicated. Particularly important is the fact that Vollenhoven could demonstrate the necessity for the logician to keep in mind both the modality (viz. logical) and the character (viz. as result of a previous analytical activity) of the concept and judgment, as well as to investigate the retrocipations and anticipations of the logical function on sub- and superstratum spheres respectively; logic derives from philosophy the insight that all of this, and the analytical activity too, belong to the logical sphere. The conception developed in logic cannot be considered to be detached from more fundamental philosophical matters nor to be formal nor neutral. A Christian philosophy is especially necessary with a view to keeping the spheres of ontology and epistemology distinct, as well as to determine the difference between and the relationship of logic and on the one hand cosmology and anthropology, and on the other hand epistemology. A Christian logic reaps the advantages of this distinction. Besides the option of e.g. either rationalism or irrationalism, a Christian standpoint in scientific matters is practicable. The results of Dooyeweerd, Vollenhoven, Stoker, Van Til and others have changed the possibility of a Christian point of view in science (including logic) into a reality. Chapter IV especially has indicated that and how a Christian logic presupposes a Christian philosophy and in Chapter V it has been possible to point out the importance of a Christian approach to logic, even in its details. <2> As regards the matter investigated by logic and its character, the point of view is taken that logic is a science and that no scientist can•accept his task of investigation or execute his analysis without a determination of his field of study and the nature of this field, as well as testing the results obtained with this determination; moreover continued reflection is necessary as to whether the. investigation has succeeded in complying with the determination of the field of investigation. The supposition is held that the determination of the field of investigation is a distinction according to modality, that is to say logic has to investigate the analytical (logical) sphere of law. A Christian logic opposes the various forms of reduction-logic which screen the logical field down to some of the most obvious phenomena of the logical sphere. A Christian logic results in various new finds, as well as a new. perspective of the whole domain of logic. <3> Logic according to a Christian point of view is not what it is often thought to be and moreover it is different from the traditional conception. Logic as science is not formal nor neutral. A Christian point of view accepts the relevance of religion and considers the Word of God to be the guiding principle for directing scientific cognition in its scientific investigation of the logical field. Christian logic is no logic of religion or vice versa, no logical creed, logical science of belief or a logic of divine worship, nor a compilation of texts from the Holy Scriptures bearing on the logical function, etc. A Christian logic does not investigate the logical field from or v 1 a the function of belief. have effects even in the most particular details of the field of logic. / Thesis (MA)--PU vir CHO, 1959.

The focus of this thesis is Pieter-Dirk Uys's use of the rhetorical trope chiasmus as a satirical tool, an aspect of his work that has, to date, received little attention. The multiple nuances of 'chiasmus' are examined, pointing to the performer/persona relationship in terms of ‘ “1" create Image; Image makes "I" , (Breytenbach, 1985) and the related 'semiotic richness of stage sign-vehicles' (Elam, 1980). The primarily semiotic analyses of chiastic configurations are supported by close textual analyses throughout. Pieter-Dirk Uys's chiastic admix of his satirical pleasure/pain principle (entertainment! censure) is analysed in one newspaper article, one prose work and two revues. Uys's satire is contextualised against the background of the development of satire. The inherently chiastic mode of satire and various techniques and writing styles are explored. Contemporary society lacks definitive moral, social and political norms, and the study attempts to show how Uys entertains by decoding 'the absurdities of contemporary reality' (Fletcher, 1987:ix) as a response to the amorphous experience of living in South African society from the early 1980s until 2001. Uys's use of female characters to articulate his dissatisfaction with South Africa's socio¬political climate during the last quarter of the twentieth century is explored in a selection of three plays, four prose works and ten revues. The focus falls on his creation of female personae, particularly the sustained portrayal of his popular persona, Evita Bezuidenhout. Uys's use of 'real' and 'false disguise' (Baker, 1994) is discussed. The transvestite persona's roles of both an 'intervener' who challenges thestatus quo and alerts the public to 'cultural, social or aesthetic dissonance' and an 'interventor' or 'enabling fantasy' (Garber, 1992:6) are considered. The focus then shifts to Uys's deployment of various non-verbal sign-vehicles in his dramatic productions. Non-verbal and verbal signs are jointly responsible for the production of meaning in the theatre. Because 'theatrical signs ... acquire qualities ... that they do not have in real life' (Bogatyrev, 1938:35-6), audiences must utilise 'theatrical competence' (Elam, 1980: 87). A study of electronic recordings of eight revues reveals that Uys's non-verbal signs are as chiastic as his verbal ones. Uys's perpetuation of the Evita 'myth' as/or 'legend' is traced from her beginnings as a newspaper 'voice', to popular theatre and television personality, to the recipient of prestigious awards. Evita's current and possible future roles are considered. Uys's fabrication of Evita's family and her 'biography' is also examined as contributory to the legend, exploring Evita's metamorphosis from a housewife to a political figurehead who conflates fictional and real life exploits with South African politicians - a strategy through which Uys appears to align himself with current feminist issues. The slippage between fact and fiction has interesting consequences for Uys's level of control over his Evita persona, who seems occasionally to control him. This thesis concludes with a review of the aims and rationale of the study, providing a broad synopsis of the main findings and looking at its limitations. Finally, it suggests possible areas for further research. / Thesis (DLitt (English))--University of Pretoria, 2001. / Modern European Languages / unrestricted

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Diese Masterarbeit diskutiert die philosophischen Grundlagen der Laws of Form von George Spencer-Brown, ihre Relevanz für die Systemtheorie sowie ihre Rezeption durch Niklas Luhmann. Dabei werden verschiedene Schlüsselfragen zu den Laws of Form beantwortet, einschließlich ihres Zwecks, ihrer Relevanz und ihrer Anwendbarkeit. Der Grundgedanke ist, dass die Laws of Form eine Sprachphilosophie sind, die in Struktur und Inhalt an Wittgensteins Werk angelehnt sind. Sie entwickeln ein Regelwerk für die Verwendung der Befehlssprache und behandeln die Entstehung der Objektivität als eine Konsequenz der Befolgung von Befehlen. Sie enthalten auch eine semiotische Komponente, indem sie die Trennung von Signifikat und Signifikant von einem Befehl abhängig machen. Aus dieser Semiotik leitet sich der mathematische Formalismus ab, welcher als das Indikationskalkül bezeichnet wird. Die Masterarbeit erklärt auch das Konzept des Re-entry sowie der Interpretation des Indikationskalkül. Darüber hinaus wird die Rezeption der Laws of Form in der Systemtheorie von Heinz von Foerster, Varela und Maturana kritisch diskutiert. Die These ist, dass Spencer-Brown mit dem Feld sowohl inhaltlich als auch historisch wenig zu tun hatte. Genauso wird kritisch auf die Missverständnisse in der Rezeption von Niklas Luhmann und Dirk Baecker eingegangen. Viel wichtiger klärt diese Masterarbeit darüber auf, welche Rolle Spencer-Brown in der soziologischen Systemtheorie spielte und spielen sollte. Darüber hinaus wird eine Grundlage für eine neue soziologische Leseart der Laws of Form gelegt und ein neuer Entwurf für eine soziologische Interpretation des Indikationskalküls vorgestellt.:Inhaltsverzeichnis Einleitung 1 1. Kontextualisierung der Laws of Form 8 1.1 Die Anfänge der Laws of Form 8 1.2 Die Entstehungsgeschichte der Laws of Form. Teil 1 10 1.2.1 Exkurs: Die logischen Grundlagen der Mathematik 10 1.2.2 Exkurs: Imaginäre und komplexe Zahlen 11 1.3 Die Entstehungsgeschichte der Laws of Form. Teil 2 13 1.4 Das „Mathematische“ der Laws of Form 14 1.4.1 Injunktive Sprache 14 1.4.2 Repräsentationslosigkeit 15 1.4.3 Injunktion und Wissen 17 1.4.4 De-Ontologisierung 18 1.4.5 Injunktion als Sprachspiel 20 1.4.6 Die Form 20 1.4.7 Die Unterscheidung 22 1.4.8 Die Form als Erkenntnismethode 24 1.4.9 Befehlsketten 25 1.4.10 Struktur injunktiver Sprache 27 1.4.11 Injunktion und Selbstreferenz 28 1.4.12 Paradoxie und Gedächtnis 31 1.4.13 Wahrheit und Realität 33 1.5 Zusammenfassung und Einordnung der Laws of Form 36 2. Die Laws of Form 39 2.1 Der Aufbau der Laws of Form 39 2.2 The Form 42 2.2.1 Definition 44 2.2.2 Axiome 47 2.3 Forms taken out of the form 48 2.3.1 Raum 48 2.3.2 Signifikationsprozess 50 2.3.3 Semiotik und Semiose 51 2.3.4 Ausdrücke und Wert 56 2.3.5 Von Namen zu Befehlen 59 2.4 Das Indikationskalkül 60 2.5 Primäre Algebra 63 2.6 Re-entry 66 2.7 Die logische Interpretation des Indikationskalküls 71 3. Systemtheoretische Rezeption der Laws of Form 75 3.1 Heinz von Foerster 75 3.1.1 Whole Earth Catalog 75 3.1.2 Die biologische Metapher 76 3.1.3 Biological Computer Laboratory (BCL) 77 3.1.4 Konstruktivismus 78 3.2 Humberto Maturana und Francisco Varela 81 3.2.1 Autopoesis 81 3.2.2 Autopoetische Systeme zweiter Ordnung 82 3.2.3 Varelas Calculus for Self-Reference 84 3.3 Rekapitulation der systemtheoretischen Rezeption der Laws of Form 86 4. Mathematische Rezeption der Laws of Form 87 5. Soziologische Rezeption der Laws of Form 89 5.1 Niklas Luhmann 89 5.1.1 Die Wichtigkeit des Missverständnisses 89 5.1.2 Die Form des Systems 90 5.1.2.1 Unmöglichkeit der Definition 90 5.1.2.2 Inkonsistenz des Konstruktivismus 92 5.1.2.3 Paradoxie der Systeme 93 5.1.3 Die Form der Systemtheorie 96 5.2 Dirk Baecker 98 6. Die soziologische Interpretation des Indikationskalküls 101 6.1 Der empirische Zugang 101 6.2 Notwendigkeit und Kontingenz als Zwischentheorie 102 6.3 Qualitative Forschungsmöglichkeit 104 6.3.1 Formalisierung 107 6.3.2 Berechenbarkeit 109 6.3.3 Beweisbarkeit 112 6.4 Quantitative Forschungsmöglichkeit 113 Fazit und Zusammenfassung 116 Literaturverzeichnis 121 Abbildungsverzeichnis 129 Anhänge 130 Anhang 1: Index of Forms 130 Anhang 2: Kreis auf einem Torus 135 Anhang 3: Berechnung Re-entry 136 Anhang 4: Beweis De-morgansche Gesetze 138 / This master thesis discusses the philosophical foundations of George Spencer-Brown's Laws of Form, their relevance for systems theory, and their reception by Niklas Luhmann. Several key questions about the Laws of Form are answered, including their purpose, relevance, and applicability. The basic idea is that the Laws of Form are a philosophy of language, modeled on Wittgenstein's work in structure and content. They develop a set of rules for the use of command language and treat the emergence of objectivity as a consequence of following commands. They also contain a semiotic component in that they make the separation of signifier and signified dependent on a command. From this semiotics derives the mathematical formalism which is called the calculus of indications. The master thesis also explains the concept of re-entry as well as the interpretation of the calculus of indications. In addition, the reception of the Laws of Form in the systems theory of Heinz von Foerster, Varela and Maturana is critically discussed. The thesis is that Spencer-Brown had little to do with the field both in content and history. Likewise, the misunderstandings in the reception of Niklas Luhmann and Dirk Baecker are critically addressed. More importantly, this master's thesis clarifies the role Spencer-Brown played and was supposed to play in sociological systems theory. Furthermore, it lays a foundation for a new sociological reading of the Laws of Form and presents a new outline for a sociological interpretation of the calculus of indication.:Inhaltsverzeichnis Einleitung 1 1. Kontextualisierung der Laws of Form 8 1.1 Die Anfänge der Laws of Form 8 1.2 Die Entstehungsgeschichte der Laws of Form. Teil 1 10 1.2.1 Exkurs: Die logischen Grundlagen der Mathematik 10 1.2.2 Exkurs: Imaginäre und komplexe Zahlen 11 1.3 Die Entstehungsgeschichte der Laws of Form. Teil 2 13 1.4 Das „Mathematische“ der Laws of Form 14 1.4.1 Injunktive Sprache 14 1.4.2 Repräsentationslosigkeit 15 1.4.3 Injunktion und Wissen 17 1.4.4 De-Ontologisierung 18 1.4.5 Injunktion als Sprachspiel 20 1.4.6 Die Form 20 1.4.7 Die Unterscheidung 22 1.4.8 Die Form als Erkenntnismethode 24 1.4.9 Befehlsketten 25 1.4.10 Struktur injunktiver Sprache 27 1.4.11 Injunktion und Selbstreferenz 28 1.4.12 Paradoxie und Gedächtnis 31 1.4.13 Wahrheit und Realität 33 1.5 Zusammenfassung und Einordnung der Laws of Form 36 2. Die Laws of Form 39 2.1 Der Aufbau der Laws of Form 39 2.2 The Form 42 2.2.1 Definition 44 2.2.2 Axiome 47 2.3 Forms taken out of the form 48 2.3.1 Raum 48 2.3.2 Signifikationsprozess 50 2.3.3 Semiotik und Semiose 51 2.3.4 Ausdrücke und Wert 56 2.3.5 Von Namen zu Befehlen 59 2.4 Das Indikationskalkül 60 2.5 Primäre Algebra 63 2.6 Re-entry 66 2.7 Die logische Interpretation des Indikationskalküls 71 3. Systemtheoretische Rezeption der Laws of Form 75 3.1 Heinz von Foerster 75 3.1.1 Whole Earth Catalog 75 3.1.2 Die biologische Metapher 76 3.1.3 Biological Computer Laboratory (BCL) 77 3.1.4 Konstruktivismus 78 3.2 Humberto Maturana und Francisco Varela 81 3.2.1 Autopoesis 81 3.2.2 Autopoetische Systeme zweiter Ordnung 82 3.2.3 Varelas Calculus for Self-Reference 84 3.3 Rekapitulation der systemtheoretischen Rezeption der Laws of Form 86 4. Mathematische Rezeption der Laws of Form 87 5. Soziologische Rezeption der Laws of Form 89 5.1 Niklas Luhmann 89 5.1.1 Die Wichtigkeit des Missverständnisses 89 5.1.2 Die Form des Systems 90 5.1.2.1 Unmöglichkeit der Definition 90 5.1.2.2 Inkonsistenz des Konstruktivismus 92 5.1.2.3 Paradoxie der Systeme 93 5.1.3 Die Form der Systemtheorie 96 5.2 Dirk Baecker 98 6. Die soziologische Interpretation des Indikationskalküls 101 6.1 Der empirische Zugang 101 6.2 Notwendigkeit und Kontingenz als Zwischentheorie 102 6.3 Qualitative Forschungsmöglichkeit 104 6.3.1 Formalisierung 107 6.3.2 Berechenbarkeit 109 6.3.3 Beweisbarkeit 112 6.4 Quantitative Forschungsmöglichkeit 113 Fazit und Zusammenfassung 116 Literaturverzeichnis 121 Abbildungsverzeichnis 129 Anhänge 130 Anhang 1: Index of Forms 130 Anhang 2: Kreis auf einem Torus 135 Anhang 3: Berechnung Re-entry 136 Anhang 4: Beweis De-morgansche Gesetze 138

A numerical method (SIMPLE DIRK Method) for unsteady incompressible viscous flow simulation is presented. The proposed method can be used to achieve arbitrarily high order of accuracy in time-discretization which is otherwise limited to second order in majority of the currently used simulation techniques. A special class of implicit Runge-Kutta methods is used for time discretization in conjunction with finite volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field in a lid-driven square cavity. In the test case calculations, power law scheme was used in spatial discretization and time discretization was performed using a second-order implicit Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was obtained from the proposed method and compared with that obtained from a commercial computational fluid dynamics software program, FLUENT 6.2.16. Also, steady state solution from the present method was compared with the numerical solution of Ghia, Ghia, and Shin and that of Erturk, Corke, and Goökçöl. Good agreement of the solution of the proposed method with the solutions of FLUENT; Ghia, Ghia, and Shin; and Erturk, Corke, and Goökçöl establishes the feasibility of the proposed method.

A numerical method (SIMPLE DIRK Method) for unsteady incompressible viscous flow simulation is presented. The proposed method can be used to achieve arbitrarily high order of accuracy in time-discretization which is otherwise limited to second order in majority of the currently used simulation techniques. A special class of implicit Runge-Kutta methods is used for time discretization in conjunction with finite volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field in a lid-driven square cavity. In the test case calculations, power law scheme was used in spatial discretization and time discretization was performed using a second-order implicit Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was obtained from the proposed method and compared with that obtained from a commercial computational fluid dynamics software program, FLUENT 6.2.16. Also, steady state solution from the present method was compared with the numerical solution of Ghia, Ghia, and Shin and that of Erturk, Corke, and Goökçöl. Good agreement of the solution of the proposed method with the solutions of FLUENT; Ghia, Ghia, and Shin; and Erturk, Corke, and Goökçöl establishes the feasibility of the proposed method.