Gödel's version of the modal ontological argument for the existence of God has been criticized by J. Howard Sobel  and modified by C. Anthony Anderson . In the present paper we consider the extent to which Anderson's emendation is defeated by the type of objection first offered by the Monk Gaunilo to St. Anselm's original Ontological Argument. And we try to push the analysis of this Gödelian argument a bit further to bring it into closer agreement with the details of Gödel's own formulation. Finally, we indicate what seems to be the main weakness of this emendation of Gödel's attempted proof.
Gaunilo observed against St. Anselm that his form of argument, if cogent, could be used to “prove” all sorts of unwelcome conclusions - for example, that there is somewhere a perfect island. It would seem to even follow that there are near-perfect, but defective, demi-gods and all matter of other theologically repugnant entities. Gaunilo concluded, reasonably enough, that something must be wrong with the argument.
Kurt Gödel's modern version of the Ontological Argument  involves an attempt to complete the details of Leibniz's proof that it is possible that there is a perfect being or a being with all and only “positive” attributes. Given this conclusion, other assumptions about positive properties, and, well, a second-order extension of the modal logic S5, Gödel successfully deduced the actual existence, indeed the necessary existence, of the being having all and only positive attributes. Alas, or “Oh, joy!”, depending on ones’ theological prejudices, J. Howard Sobel showed that Gödel's assumptions lead also to the conclusion that whatever is true is necessarily true. Followers of Spinoza aside, this casts quite considerable doubt on the premisses of the argument. We shall consider here Anderson's emendation which does not suffer from the mentioned defect and which is still recognizably closely related to Gödel's argument.
Here are the assumptions and definitions -the notion of a positive attribute is taken as a primitive by Gödel and in the present version. We hasten to add that the idea is not crystal clear; Gödel's own explanations are extremely terse and somewhat cryptic. A property's being positive is supposed to be a good thing, such properties being characteristic of a completely and necessarily non-defective being.
When we describe the heart in this chapter, and in subsequent chapters, our account will be based on the organ as viewed in its anatomical position. Where appropriate, the heart will be illustrated as it would be viewed by the surgeon during an operative procedure, irrespective of whether the pictures are taken in the operating room, or are photographs of autopsied hearts. When we show an illustration in non-surgical orientation, this will be clearly stated.
In the normal individual, the heart lies in the mediastinum, with two-thirds of its bulk to the left of the midline (Figure 1.1). The surgeon can approach the heart, and the great vessels, either laterally through the thoracic cavity, or directly through the mediastinum anteriorly. To make such approaches safely, knowledge is required of the salient anatomical features of the chest wall, and of the vessels and the nerves that course through the mediastinum (Figure 1.2). The approach used most frequently is a complete median sternotomy, although increasingly the trend is to use more limited incisions. The incision in the soft tissues is made in the midline between the suprasternal notch and the xiphoid process. Inferiorly, the white line, or linea alba, is incised between the two rectus sheaths, taking care to avoid entry to the peritoneal cavity, or damage to an enlarged liver, if present. Reflection of the origin of the rectus muscles in this area reveals the xiphoid process, which is incised to provide inferior access to the anterior mediastinum. Superiorly, a vertical incision is made between the sternal insertions of the sternocleidomastoid muscles. This exposes the relatively bloodless midline raphe between the right and left sternohyoid and sternothyroid muscles. An incision through this raphe gives access to the superior aspect of the anterior mediastinum. The anterior mediastinum immediately behind the sternum is devoid of vital structures, so that the superior and inferior incisions into the mediastinum can safely be joined by blunt dissection in the retrosternal space.
Understanding the anatomy of septal defects is greatly facilitated if the heart is thought of as having three distinct septal structures: the atrial septum, the atrioventricular septum, and the ventricular septum (Figure 7.1). The normal atrial septum is relatively small. It is made up, for the most part, by the floor of the oval fossa. When viewed from the right atrial aspect, the fossa has a floor, surrounded by rims. The floor is derived from the primary atrial septum, or septum primum. Although often considered to represent a secondary septum, or septum secundum, the larger parts of the rims, specifically the superior, anterosuperior, and posterior components, are formed by infoldings of the adjacent right and left atrial walls. Inferoanteriorly, in contrast, the rim of the fossa is a true muscular septum (Figure 7.2). This part of the rim is contiguous with the atrioventricular septum, which is the superior component of the fibrous membranous septum. In the normal heart, this fibrous septum is also contiguous with the atrial wall of the triangle of Koch (Figure 7.3). In the past, we considered this component of the atrial wall, which overlaps the upper part of the ventricular musculature between the attachments of the leaflets of the tricuspid and mitral valves, as the muscular atrioventricular septum. As we discussed in Chapter 2, we now know that it is better viewed as a sandwich. This is because, throughout the floor of the triangle of Koch, the fibroadipose tissue of the inferior atrioventricular groove separates the layers of atrial and ventricular myocardium (Figure 7.4). From the stance of understanding septal defects, nonetheless, it is helpful to consider the entire area comprising the fibrous septum and the muscular sandwich as an atrioventricular separating structure, as it is absent in the hearts we describe as having atrioventricular septal defects.
ANOMALOUS SYSTEMIC VENOUS DRAINAGE
Abnormal systemic venous connections are usually of little surgical significance, as their clinical consequences are limited. The anomalies are apt to be encountered as the surgeon pursues a more complex associated intracardiac anomaly. They are of most significance in the setting of isomeric atrial appendages, which we discuss in Chapter 10, showing how so-called visceral heterotaxy is best considered in terms of right versus left isomerism. In this chapter, we consider the features of the anomalous systemic venous connections in their own right. They may be grouped into the categories of absence or abnormal drainage of the right superior caval vein, anomalies of the inferior caval vein, persistence or abnormal drainage of the left superior caval vein, and abnormal hepatic venous connections. Abnormalities of the coronary sinus usually fall into one of these groups, although unroofing, which produces an interatrial communication through the right atrial orifice of the sinus, has been discussed in Chapter 7.
Abnormalities of the right superior caval vein
These are extremely rare. The vein may be diminished in size. Alternatively, it may be completely absent when the venous return from the head, neck, and arms passes through a persistent left superior caval vein to the right atrium by way of the coronary sinus (Figure 9.1) or, rarely, directly into the left atrium. Only this last situation requires surgical intervention. The other conditions, if encountered during an open-heart operation, would require some adjustment from the usual technique used for cannulation. Although there is no definite evidence to this effect, we would not expect these abnormalities to affect the location of the sinus node.
The books and articles devoted to technique in cardiac surgery are legion. This is most appropriate, as the success of cardiac surgery is greatly dependent upon excellent operative technique. But excellence of technique can be dissipated without a firm knowledge of the underlying cardiac morphology. This is just as true for the normal heart as for those hearts with complex congenital lesions. It is the feasibility of operating upon such complex malformations that has highlighted the need for a more detailed understanding of the basic anatomy in itself. Thus, in recent years surgeons have come to appreciate the necessity of avoiding damage to the coronary vessels, often invisible when working within the cardiac chambers, and particularly to avoid the vital conduction tissues, invisible at all times. Although detailed and accurate descriptions of the conduction system have been available since the time of their discovery, only rarely has its position been described with the cardiac surgeon in mind. At the time the first edition of this volume was published, to the best of our knowledge there had been no other books that specifically displayed the anatomy of normal and abnormal hearts as perceived at the time of operation. We tried to satisfy this need in the first volume by combining the experience of a practising cardiac surgeon with that of a professional cardiac anatomist. We added significantly to the illustrations in the second edition, while seeking to retain the overall concept, as feedback from those who had used the first edition was very positive. In the third edition, we sought to expand and improve still further on the changes made in the second edition. In the second edition, we had added an entirely new chapter on cardiac valvar anatomy, and greatly expanded our treatment of coronary vascular anatomy. We retained this format in the third edition, as we were gratified that, as hoped, readers were able to find a particular subject more easily.
The surgical problems posed by cardiac malformations may be considerably increased when the heart itself is in an abnormal position. This is, in part, due to the unusual anatomical perspective presented to the surgeon because of the malposition, and also to the abnormal locations of the cardiac chambers, which may necessitate approaches other than those already discussed. Cardiac malposition itself, nonetheless, does not constitute a diagnosis. Any normal or abnormal segmental combination can be found in a heart that, itself, is abnormally located. The heart may be normal, despite its abnormal location, but extremely complex anomalies are frequently present. Consequently, the very presence of an abnormal cardiac position emphasises the need for a full and detailed segmental analysis of the heart. All the rules enunciated in Chapter 6 apply should the heart not be in its anticipated position. In this chapter, we confine ourselves to a description of abnormally positioned hearts, giving a more detailed discussion for specific types of malposition. We conclude with a review of the surgical significance of isomerism of the atrial appendages, which is generally agreed to be one of the major harbingers of abnormal cardiac position. We emphasise the need to segregate the syndromes, preferably into the subsets of right versus left isomerism, as the prognosis is markedly different for the two variants.
The coronary circulation consists of the coronary arteries and veins, together with the lymphatics of the heart. Because the lymphatics, apart from the thoracic duct, are of very limited significance to operative anatomy, they will not be discussed at any length in this chapter. The veins, relatively speaking, are similarly of less interest. In this chapter, therefore, we concentrate upon those anatomical aspects of arterial distribution that are pertinent to the surgeon, concluding with a brief discussion of the cardiac venous drainage and the cardiac lymphatics.
THE CORONARY ARTERIES
The coronary arteries are the first branches of the ascending portion of the aorta. They take their origin from the sinuses within the aortic root, immediately above its attachment to the heart (Figure 4.1). There are three sinuses within the aortic root, but only two coronary arteries. The sinuses can be named, therefore, according to whether they give rise to an artery, the normal arrangement being a right coronary, left coronary, and non-coronary aortic sinus (Figure 4.2). When described in this fashion, the terms ‘right’ and ‘left’ refer to the aortic sinuses giving rise to the right and left coronary arteries, rather than to the position of the sinuses relative to the right-to-left coordinates of the body (Figure 4.3). In the normal heart, the aortic root is situated obliquely, while in malformed hearts, the root is frequently positioned abnormally. Whatever the position of the aortic root, however, the two coronary arteries, when two are present, almost always take origin from those aortic sinuses that are adjacent to the sinuses of the pulmonary trunk.
Regardless of the surgical approach, once having entered the mediastinum, the surgeon will be confronted by the heart enclosed in its pericardial sac. In the strict anatomical sense, this sac has two layers, one fibrous and the other serous. From a practical point of view, the pericardium is essentially the tough fibrous layer; the serous component forms the lining of the fibrous sac, and is reflected back onto the surface of the heart as the epicardium. It is the fibrous sac, therefore, which encloses the mass of the heart. By virtue of its own attachments to the diaphragm, it helps support the heart within the mediastinum. Free-standing around the atrial chambers and the ventricles, the sac becomes adherent to the adventitial coverings of the great arteries and veins at their entrances to and exits from it, these attachments closing the pericardial cavity. The cavity of the pericardium is limited by the two layers of serous pericardium, which are folded on one another to produce a double-layered arrangement. The outer or parietal layer is densely adherent to the fibrous pericardium, while the inner layer is firmly attached to the myocardium, and is the epicardium (Figure 2.1). The pericardial cavity, therefore, is the space between the inner parietal serous lining of the fibrous pericardium and the surface of the heart (Figure 2.2). There are two recesses within the cavity that are lined by serous pericardium. The first is the transverse sinus, which occupies the inner curvature of the heart (Figure 2.3). Anteriorly, it is bounded by the posterior surface of the great arteries. Posteriorly, it is limited by the right pulmonary artery and the roof of the left atrium. There is a further recess from the transverse sinus that extends between the superior caval and the right upper pulmonary veins, with its right lateral border being a pericardial fold between these vessels (Figure 2.4). When exposing the mitral valve through a left atriotomy, incisions through this fold, along with mobilisation of the superior caval vein, provide excellent access to the superior aspect of the left atrium and the right pulmonary artery. This fold is also incised when a snare is placed around the superior caval vein. Laterally, on each side, the ends of the transverse sinus are in free communication with the remainder of the pericardial cavity.
The disposition of the conduction system in the normal heart has been emphasised already (see Chapter 2). In that earlier chapter, we pointed to the importance, during surgical procedures, of avoiding the cardiac nodes and ventricular bundle branches, and scrupulously protecting the vascular supply to these structures. In this chapter, we will consider the anatomy of these tissues relative to the treatment of intractable problems of cardiac rhythm. The abnormal dispositions of the conduction tissue to be found in congenitally malformed hearts, features of obvious significance to the congenital cardiac surgeon, will be discussed in the sections devoted to those lesions in the chapters that follow. In this chapter, nonetheless, we will discuss surgical procedures performed to treat arrhythmias that develop in the setting of the Fontan circulation.
LANDMARKS TO THE ATRIOVENTRICULAR CONDUCTION AXIS
In patients with intractable tachycardia, it may be necessary to ablate the atrioventricular bundle. Although this sometimes occurs inadvertently, it can be surprisingly difficult to divide this structure intentionally. The landmark to penetration of the atrioventricular conduction axis through the fibrous insulating plane is the apex of the triangle of Koch (Figure 5.1). The apex is marked by the point at which the tendon of Todaro inserts into the central fibrous body (Figure 5.2). Just inferior to the apex of this triangle, the components of the atrioventricular node gather themselves together, and enter the insulating tissues of the fibrous body (Figures 5.3, 5.4). Once insulated from the atrial myocardial mass, the conduction axis becomes the penetrating atrioventricular bundle, better known as the bundle of His. This part of the overall atrioventricular conduction axis is short, but extends leftwards as it pierces the fibrous body.
It is axiomatic that a thorough knowledge of valvar anatomy is a prerequisite for successful surgery, be it valvar replacement or reconstruction. The surgeon will also require a firm understanding of the arrangement of other aspects of cardiac anatomy to ensure safe access to a diseased valve or valves. These features were described in the previous chapter. Knowledge of the surgical anatomy of the valves themselves, however, must be founded on appreciation of their component parts, the relationships of the individual valves to each other, and their relationships to the chambers and arterial trunks within which they reside. This requires understanding of, firstly, the basic orientation of the cardiac valves, emphasising the intrinsic features that make each valve distinct from the others. This information must be supplemented by attention to their relationships with other structures that the surgeon must avoid, notably the conduction tissues and the major channels of the coronary circulation. For this chapter, throughout our narrative we will presume the presence of a normally structured heart, lying in its usual position, and without any coexisting congenital cardiac malformations.
THE VALVAR COMPLEXES
When considering the valves, we distinguish between the atrioventricular valves, which guard the atrioventricular junctions, and the arterial valves, which guard the ventriculoarterial junctions (Figure 3.1). The atrioventricular valves are best analysed in terms of the valvar complex, made up of the annulus, the leaflets, the tendinous cords, the papillary muscles, and the supporting ventricular musculature (Figure 3.2). All of these components must work in harmony so as to achieve valvar competence. The leaflets of the atrioventricular valves are supplied with a complex tension apparatus, as they must withstand the full force of ventricular systole, so as to retain their competence when in their closed position. The arterial valves are also a combination of complex anatomical parts.
In the previous chapter, we paid attention to those hearts in which the associated cardiac malformation existed in the setting of normal connections between the cardiac segments. All those associated lesions, of course, can also be found in hearts with abnormal segmental connections. It is these abnormal connections that will be our focus in this chapter, emphasising the associated anomalies that are particularly frequent with a given abnormal segmental arrangement. We conclude the chapter with a brief discussion of those hearts in which the relationships of the arterial trunks are abnormal in the setting of concordant ventriculoarterial connections, as these combinations still produce problems in understanding and description.
Over the years, hearts with a double-inlet ventricle have represented one of the greater challenges to surgical correction. They have also posed significant problems in adequate description and categorisation. Even these days, many continue to describe the lesions in terms of single ventricles, or univentricular hearts, despite the fact that almost all patients with a double-inlet atrioventricular connection have two chambers within their ventricular mass, one being large and the other small–. The semantic problems with description can now be resolved by the simple expedient of describing functionally univentricular hearts, this approach also accounting for the other lesions dominated by ventricular imbalance. At this point, we describe the relevant anatomical characteristics of all those hearts unified by the presence of the double-inlet atrioventricular connection, irrespective of whether they contain one or two ventricles, although almost all do have one big and one small ventricle. The previous problems with description centred on whether the small chamber in hearts with ventricular imbalance deserved ventricular status.
Systems for describing congenital cardiac malformations have frequently been based upon embryological concepts and theories. As useful as these systems have been, they have often had the effect of confusing the clinician, rather than clarifying the basic anatomy of a given lesion. As far as the surgeon is concerned, the essence of a particular malformation lies not in its presumed morphogenesis, but in the underlying anatomy. An effective system for describing this anatomy must be based upon the morphology as it is observed. At the same time, it must be capable of accounting for all congenital cardiac conditions, even those that, as yet, might not have been encountered. To be useful clinically, the system must be not only broad and accurate, but also clear and consistent. The terminology used, therefore, should be unambiguous. It should be as simple as possible. The sequential segmental approach provides such a system, particularly when the emphasis is placed on its surgical applications. The basis of the system is, in the first instance, to analyse individually the architectural make-up of the atrial chambers, the ventricular mass, and the arterial segment. Emphasis is thus given to the nature of the junctional arrangements (Figure 6.1). Still further attention is devoted to the interrelationships of the cardiac structures within each of the individual segments. This provides the basic framework within which all other associated malformations can be catalogued.
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