History and Historicity in the Political Philosophy of Thomas Hobbes

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Hobbes’ early moral and political views may be traced back to the Aristotelian tradition. If this is the case, then it can be said that these views are definitely the materials for his political philosophy but not the seeds for his political philosophy. But his later views are in direct contrast to Aristotelianism. If it may be contended that Hobbes’ taking of considerable elements from Aristotle paved the way for a later break with Aristotle, then a sense of fundamental defect with the Aristotelian philosophy was a must for this break. Hobbes later elaborated these modifications and presented them as systematic objections. This deep dissatisfaction with traditional philosophy must have forced Hobbes for turning to history and thus citing his case in his humanist period. His turning to history is revealed in his revolutionary early thought. His turning to history was definitely intentional with philosophical contentions.

According to Hobbes, philosophy and history are fundamentally different. Philosophy lays down precepts for the right behaviour of men, but then again precepts don’t prove their practical aspects efficaciously. History, not philosophy, gives man prudence.

‘…the principal and proper work of history (is) to instruct and enable men, by the knowledge of actions past, to bear themselves prudently in the present and providently towards the future…’ ‘…the nature of history is merely narrative…look how much a man of understanding might have added to his experience, if he had then lived a beholder of their proceedings, and familiar with the men and business of the time: so much almost may he profit now, by attentive reading of the same here written. He may from the narrations draw out lessons to himself’.

History widens men’s experiences by making men capable of applying the precepts in the individual cases. Hobbes takes it for granted that this philosophy rightly lays down the norms for human actions. He asserts that practical wisdom is at least the sine qua non for moral virtue and this wisdom is gained only through experience. The study of history widens the experience from service to the acquisition of wisdom and thus from service to moral education. Aristotle believes in rational precepts having no influence on most men. But according to Aristotle’s view, what is true of most men is not by any means true of free and noble minded characters who love honour; they obey precepts. As Hobbes doubts the effects of precepts altogether, does he not assert the impotence of reason with reference to all men; can we not say that the dicta of impotence of reason was thoroughly established in his mind, before his engagement with natural science?

The question, by which history originally breaks with philosophy, is the question of effectiveness of rational precept. It purely becomes a matter of application of precepts. These precepts were handed down by Aristotelian ethics. Since Aristotle satisfactorily explicated these precepts, the fundamental problem of philosophy was solved; this gave Hobbes the leisure and ample opportunity to give thought to the secondary problem of the application of precepts. In reference to this application the assertion is made that the precepts are not effective in themselves that they are not followed for their own sake, but under all circumstances it may be made plausible by making use of other measures to ensure their being followed. Hobbes of course does not question the necessity and effectiveness of laws. But now the teachings to be drawn from history slip in as it were midway between the precepts of philosophy and the laws.

‘…(history) doth things with more grace and modestie then the civill lawes and ordinances do: because it is more grace for a man to teach and instruct, then to chastise or punish’.

The teaching to be drawn from history has from now on to fulfill the function for noble natures which, according to Aristotle, was the task of philosophical precepts. The teachings of history replace the precepts of philosophy in the education of the aristocracy.

The opposition of philosophical precept and the historical example based on the doubt of the efficacy of the precept is punctuated in the literature of the sixteenth century. It need only mean, we must attribute to a regrettable shortcoming on the part of the majority of men that they do not obey the precepts of philosophy, that they do not love virtue for itself, but for all its reward, which is praise. This doubt also means that the true motive of virtue is honour and glory. It essentially implies aristocratic virtue. As a result of the close connection between history and honour or glory, the more virtue is envisaged as aristocratic virtue, the keener will be the interest in history. Hobbes often quotes Lipsius as an authority for his views on history. Through Lipsius’ political philosophy, Hobbes successfully accomplished turning to history. What is felt as a lack is not so much the scientific writing of history; it is recognized that from all time histories have been written which are adequate for every possible demand; not even directions for the writing of history, but above all methodical readings of the histories already in existence. With a view to the teaching of history by methodically reading it is to be gained for the right ordering of human actions. The only clear knowledge of the application of the norms, which obtain for human actions, which have taken place in the past. History seeks the application and realization of precepts, the conditions and results of that realization. Unlike poetry, whose main objective is to give pleasure, history and philosophy derives its objectivity in seriousness. Hobbes names history and philosophy as the two fundamental branches of human knowledge.

If the main emphasis of history is to instruct and enable men, to bear themselves prudently in the present and providently in the future, undertaking a methodic utilization of history implies that a methodic education for prudence is aimed at. This education of prudence is to be sought by placing the whole available experience of mankind at our disposal, there has to be no room for any elements of chance. To the question, ‘How is one to behave in an individual case?’, one is no longer to receive the Aristotelian answer of how a sensible man would behave, but one receives for the particular case concrete maxims gained from the study of history. In this education, words and actions are important only in reference to aims. It is only through history that the reader is to be taught which kinds of aims are salutary and destructive. The systematic transformation to history, finds its most complete expression in Bacon’s philosophy.

According to Bacon, moral philosophy as the study of virtue and duty has been perfectly worked out in classical philosophy. But he opines that the fundamental shortcoming of ancient philosophy is the limiting factor that imposes itself on the description of nature of good versus the heroical descriptions of virtue, duty and felicity. As Bacon expressly says of a particular desideratum; a doctrine of the vices peculiar to the individual vocations; but as he thinks in all cases, they will seek what men sought to do, but what men really do. Traditional philosophy is blind to these materials; but the real solace comes about in the study of history. So if the neglect of history is surmounted, one of the weightiest reasons for the inadequacy and uselessness of scholasticism is given way to. Bacon makes a plea for history of literature; which he thinks has been neglected and going into this study makes him sure of making men wise.

‘History is natural, civil, ecclesiastical, and literary; whereof the first three I allow as extant, the fourth I note as deficient. For no man hath propounded to himself the general state of learning to be described and represented from age to age…without which the history of the world seemeth to me to be as the statua of Polyphemus with his eyes out; that part being wanting which doth most shew the spirit and life of the person…The use and end of which work I do not so much design for curiosity and satisfaction of those that are the lovers of learning, but chiefly for a more serious and grave purpose; which is this in few words, that it will make learned men wise in the use and administration of learning. For it is not St. Augustine’s not St. Ambrose’s works that will make so wise a divine, as ecclesiastical history, thoroughly read and observed; and the same reason is of learning’.

Bacon’s interest in history is its applicative tendencies. Bacon vehemently advocated the philosophy’s turning to history. But why? is the question? The primary reason for such a turn augments the most important material for philosophy because philosophic intent is shifting from physics and metaphysics to morals and politics.

According to Aristotle’s assertion, this change of interest takes place as soon as man becomes the consideration of being the highest being in the world. If, however, one looks back to Plato, to whom moral and political problems are of incomparably greater importance than to Aristotle, and who yet no less than Aristotle raised his gaze away from man to the eternal order, one must hold that it is not the conviction man’s superiority to all existing creatures but the conviction of the transcendence of good over all being, which is the reason why philosophic investigation begins with the ethical and political problems, with the question of the right life and the right society. This turn is caused not by the enhanced interest in the question of the good and the best form of State; but by the enhanced interest in man. The division of philosophy into natural philosophy and human philosophy is based on the systematic distinction between man and the world, which Bacon makes in express controversy against ancient philosophy.

‘…the works of God…show the omnipotency and the wisdom of the Maker, but not his image: and therefore therein the heathen opinion differeth from the sacred truth; for they supposed the world to be the image of God, and man to be exact or compendious image of the world, but the Scriptures never vouchsafe to attribute to the world that honour, as to be the image of God, but only the work of His hands; neither do they speak of any other image of God, but man…’

When the man is considered as the most excellent work of nature; then man instead of eternal order which transcends man becomes the central theme of philosophy. The ideal of contemplative life when substituted with moral virtues still ends up in a fiasco for explaining of the turn of philosophy to history. It is not the substitution of the contemplative ideal by moral virtue, in particular by the Biblical demands for justice and charity, but the systematic doubt of the efficacy of precept, which is added to this substitution, is the reason why philosophy turns to history. Bacon doubts the efficacy of rational precepts. The ancient philosophers, he says, ‘fortified and entrenched virtue and duty, as much as discourse can do, against popular and corrupt opinions’.

The reason for the turning of philosophy to history is thus the conviction of the impotence of reason, added to the enhanced interest in man. The impotence of reason is not the incapacity to establish or justify norms. It is not the way in which precepts are given to men, whether by reason or by revelation, the difficulty, which leads to the study of history, would still remain. The fact is that man does not obey the transcendent norm, whether it be rational or revealed, which is the reason of the study of history. History is studied to remedy man’s disobedience. In the sixteenth century, the reason why philosophy turned to history is the repression of the morality of obedience. As long as the distinction between philosophic knowledge on the one hand and the applicative techniques on the other hand is retained; there is at least implicitly and in principle a recognition of the pre-eminence of obedience over every other motive for action. Induction from history teaches one to distinguish between aims which justify themselves and lead to success, and aims which come to grief. The receipts to be gained from history bear only on success and failure. According to Bodin, he says in his Works, history is the easiest and the most obscure of sciences and is independent of every other science. Its subject is the study of aims and projects. By the distinction between good and bad aims, it makes possible knowledge of the norms for human actions.

Hobbes’ political philosophy, which from this time was gradually maturing precisely, had the function of replacing history, as history was understood in Bodin’s words. Hobbes’ political philosophy in its fundamental parts aimed at distinguishing between the good and the bad and thus leading to the discovery of the norms. Thus from the time of the formation of the new political philosophy, history sinks back into its philosophic insignificance; with the important difference being; in the new political philosophy, in contrast to the traditional, history is taken up and conserved. From this point of view one can appreciate the fact that Hobbes, who was particularly preoccupied with history up to the time of his return to philosophy, gives less and less thought to history as his political philosophy develops. As late as the Elements of Law, it is emphasized in a special paragraph that

‘belief…in many cases is no less free from doubt, than perfect and manifest knowledge…there be many things which we receive from report of others, of which it is impossible to imagine any cause of doubt: for what can be opposed against the consent of all men, in things they can know, and have no cause to report otherwise than they are, unless a man would say that all the world had conspired to deceive him’.

The more Hobbes learns to distinguish sharply between what is and what should be, the more the ideal character of the Leviathan becomes clear in his mind, the less significance has history for him. As a result, the distinctions between history, which is serious and seeks truth, and poetry, and the superiority of history over poetry, lose their former justification. History is thrust into the background in the measure that the new political philosophy gains clarity. For the new political philosophy fulfils the function, which had to be fulfilled by history, as, long as traditional political philosophy was acknowledged as valid. The necessity of political philosophy is shown because most men do not obey precepts. And the same presupposition, which caused the turn to history, is the basis of Hobbes’ political philosophy: the replacement of the morality of obedience by the morality of prudence.

‘All that is required, both in faith and manners, for man’s salvation, is, I confess, set down in Scriptures as plainly as can be. “Children, obey your parents in all things…Let all men be subject to the higher powers…” are words of the Scripture, which are well enough understood; but neither children, nor the greatest part of men, do understand why it is their duty to do so. They see not that the safety of the commonwealth, and consequently their own, depends upon their doing it. Every man by nature, without discipline, does in all his actions look upon, as far as he can see, the benefit that shall redound to himself from his obedience….the Scripture says one thing, and they think another, weighing the commodities or incommodities of this present life only, which are in their sight, never putting into the scales the good and evil of the life to come, which they see not’.

Bacon’s criticism of the Aristotelian morals that it does not teach the realization of virtues therefore becomes an element also in Hobbes’ criticism of Aristotle. For the turn to history had taken place precisely because traditional philosophy showed no way to the application of norms. This failure is remedied by the new political philosophy, whose boast it is, that it, in contrast to traditional philosophy, teaches an applicable morality. Hobbes allows the validity of the aristocratic virtue, completing it by a morality, which is systematically applicable and which appeals to the greatest part of men. Hobbes acknowledges the binding force of the Ten Commandments and only denies that they are applicable without more detailed interpretation by the secular power. In the same way, Hobbes admits the natural inequality, and only contests that this inequality is of any practical importance. Hobbes also concedes that the Civil Government be ordained as a means to bring us to a spiritual felicity, and thus that all earthly things are means to eternal bliss. But he denies that from this hierarchy of things earthly and things eternal, anything can be deduced as to the relative position of the holder of secular power and the holder of spiritual power. With this, Hobbes lets us see that even if there were an eternal order, he would take into consideration only the actual behaviour of men, and that his whole interest is centered on man, on application, on the use of means.

The shifting of interest from the eternal order to man found its expression in turning of philosophy to history. Hobbes doesn’t have the intention justifying the traditional norms in a way more practicable for application than was the way of traditional philosophy; he altogether denies the applicability of traditional morals; whether of ancient philosophy or of Biblical Christianity.  He not only showed that Aristotle did not show the way to a way of realization of the norms, but also that he did not even rightly define the norms. Hobbes wishes to play the passions one against the other, in order to show the way for the realization of already established norms, he wishes to draw up a political philosophy which will be in harmony with the passions from the outset. And after Hobbes found in the fear of the violent death, a truly applicable principle of political philosophy, it is again in accordance with the interest in the application that he progresses from this foundation to the establishment of the law of nature. The right to defend life, which man has from nature by the reason of the inescapable fear of death, becomes a right to all things and all actions; since a right to the end is invalid without a right to the necessary means. In order to avoid the arbitrariness, the uncertainty of what a wise man would decide under unforeseen circumstances, he rules that each man has a right to all things and all actions, since anyone under some circumstances may consider that anything or action is a necessary means for the defence of his life. The express premise of this finding is the equality of all men. Since there is no natural order, the difference between the wise minority and the unwise majority loses the fundamental importance it had for traditional political philosophy. Hobbes’ political philosophy first pushes history back into its old insignificance for philosophy. To this extent, it is true to say that Hobbes’ political philosophy is unhistorical. To make this judgment cognizant is however, not so much that Hobbes took no interest in history as that he made incorrect assertions as to history being the basis of his political philosophy. Hobbes’ fundamental error was his assumption that man’s primitive condition was the war of everyone against everyone. Hobbes cannot rest content with findings as to the historical origin States, for they give no answer to the only important question, which concerns the right order of society. So in the criticism that Hobbes’ political philosophy is ‘unhistorical’, the only statement that is justified is that Hobbes considered the philosophic grounding of the principles of all judgment on political subjects more fundamental, incomparably more important than the most thoroughly founded historical knowledge.

Hobbes considers the State of nature not as an historical fact, but a necessary construction. It is essential to his political philosophy that it should begin with the description of the State of nature, and that it should let the State emerge from the State of nature.  But he acknowledges that the subject of his political philosophy, is a history, a genesis, and not an order, which is static and perfect. To clarify this point, one has to compare Hobbes’ ‘compositive’ method with Aristotle’s ‘genetic’ method. When Aristotle depicts the genesis of the city as the perfect community out of primitive communities, the understanding of perfect organism is the main presupposition for the understanding of its constituent parts, the more primitive communities. For Hobbes, the imperfection of the primitive condition, or the State of nature, is perceived not by looking to the already, even if only cursorily clarified, idea of the State as the perfect community, but by fully understanding the experience of the State of nature. As for Hobbes the primitive condition is irrational, so for Hegel

‘knowing as it is found at the start, mind in its immediate and primitive stages, is without the essential nature of mind, is sense-conciousness’.

Hobbes has no intention of measuring the imperfect by a standard that transcends it, but as they simply look on, while the imperfect by its own movement annuls itself, tests itself. This is the meaning of Hobbes’ argument that the man who wishes to remain in the State of nature contradicts himself, that the mutual fear that characterizes the State of nature is the motive for abolishing the State of nature. The premise for an immanent testing, which necessarily finds its expression within the framework of a typical history is for Hobbes, the rejection for the morality of obedience. For Hobbes, at all events, history finally becomes superfluous, because for him political philosophy itself becomes a typical history. His political philosophy becomes historical because for him order is not immutable, eternal, in existence from the beginning, but is produced only at the end of a process; because for him order is not independent of human volition, but is borne up by a human volition alone. For this, political philosophy no longer has the function, as it had in classical antiquity, of reminding political life of the eternally immutable prototype of the perfect State, but the peculiarly modern task of delineating for the first time the programme of the essentially future perfect State. The repression of history in favour of philosophy means in reality the repression of the past; of the ancient, which is an image of the eternal; in favour of the future.

If the order of man’s world springs from man’s will alone, there is no philosophical or theological security for that order. Man then can convince himself of his capacity to order his world only by the fact of his ordering activity. Therefore according to Hobbes’ assumptions, one must turn to real history. Thus, the State of nature, which at first was intended as merely typical, again takes on an historical significance; not, indeed, as a condition of absolute lack of order, but as a condition of extremely defective order. The real history has as its function to vouch for the possibility of further progress by perception of progress already made. After that; historically, perhaps even earlier; its function is to free man from the might of the past, from the authority of antiquity, from prejudices. Authority loses its prestige when its historical origin and evolution are traced; as a result of historical criticism man’s limitations show themselves as limits set by himself, and therefore to be over passed. It is by the doubt of the transcendent eternal order by which man’s reason was assumed to be guided and hence by the conviction of the impotence of reason, that first of all the turning of philosophy to history is caused, and then the process of historicizing philosophy itself.

Role and Nature of Religion in Thomas Hobbes

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Hobbes’ three presentations of political philosophy may be with less justice called theological-political treatises. Hobbes with dual intentions becomes an interpreter of the Bible, in the first place in order to make use of the Scriptures for his own theory, and in the second place in order to shake the authority of the Scriptures. When Hobbes grants the theological motivation of political philosophy a last refuge in the discussion, which treats of the natural State, he indicates the connection between theology and the natural State in particular. As the natural State becomes less and less important to Hobbes, the theological arguments also become less and less important. Originally, when he had not yet conceived the idea of an artificial State, he was incomparably more under the spell of the theological tradition.

The space devoted to the criticism of religion increases considerably on the way from the Elements of Law to Leviathan and is accompanied by the deepening of the criticism. The fundamental question: On what authority does one believe that Scripture is the word of God? Is answered differently in different presentations. In the Elements of Law: On the authority of the Church, the successors of the Apostles. In De Cive: Not on the authority of the Church, but on that of Jesus. In the Leviathan: On the authority of the teachers whose teaching is permitted and organized by the sovereign power, i.e. one confesses verbally, for thoughts are free, that Scripture is the word of God, because secular authority commands this confession. But in all three presentations, Hobbes contends that all that is needed for salvation is the belief in Jesus as Christ. In earlier presentations, the belief in the immortality of soul belongs to these premises; whereas in the later works, the resurrection of the body is tacitly substituted for the immortality of the soul. The Leviathan finally openly opposes the resurrection of the body to the immortality of the soul and admits only the first as grounded in the Scriptures. Hobbes declares that unconditional obedience to the secular power is the bounden duty of every Christian. His question: is the Christian obliged to obey the secular power when that power forbids him the profession of his faith? is answered in the earlier presentations with the finding that the right and duty of the Christian in such a case is only passive resistance and martyrdom, while the Leviathan denies the obligation and even the right of martyrdom to the ordinary Christian who has not the special vocation of preaching the Gospel. In the De Cive it is a Christian dogma that Christ’s Kingdom is not of Earth but that of Heaven; in the Leviathan on the other hand, the Kingdom of God under the Old and also under the New Covenant is to be understood as a purely earthly Kingdom. In the Elements of Law, Hobbes defends the Episcopal constitution of the Church, whose rightness is proved by the fact that Christ in virtue of his sovereignty enthroned his Apostles. He also denies that in the Christian hierarchy there was a high priest to whom the individual bishops were subordinate. In the later presentations he rejects the Episcopal constitution, even the view that officials of the Church can be instituted by any ecclesiastical authority which is not in every respect dependent on the secular authority. The apparent contradiction of the general tendency of the Elements of Law on the one hand and of the later presentations on the other, is explicated by the fact that in the later writings, Hobbes attaches much less value to conformity with the teachings of the Scriptures. That Scripture vouches for priestly rule is from now on not an argument for priestly rule, but an argument against Scripture. Thus the single apparent exception is in reality the strongest corroboration of the assertion that on the path from the elements of Law via De Cive to the Leviathan Hobbes drew farther and farther away from the religious tradition. One may say, that Hobbes kept pace in his way, which was not very edifying, with the development from Anglican Episcopalianism to Independentism.

In the earlier presentation of his political philosophy, Hobbes is relatively close to Anglican Episcopalianism. Hobbes’ personal attitude to positive religion was at all times the same: religion must serve the Sate and is to be esteemed or despised according to the services or disservices rendered to the State. This view may be seen as early as the introduction to the translation of Thucydides where Hobbes defends his author:

In some places of his History he noteth the equivocation of the oracles; and yet he confirmeth an assertion of his own, touching the time this war lasted, by the oracle’s prediction. He taxeth Nicias for being too punctual in the observation of the ceremonies of their religion, when he overthrew himself and his army, and indeed the whole dominion and liberty of his country, by it. Yet he commandeth him in another place for his worshipping of the gods…So that in his writings, our author appeareth to be, on the one side not superstitious on the other side not an atheist’.

The fact that Hobbes accommodated utterances of his unbelief to what was permissible in a good, prudent subject justifies the assumption that in the decades before the Civil war, Hobbes for political reasons hid his true opinions and was mindful of the maintenance of theological convention. He says:

‘I long infinitely to see those books of the Sabbaoth, an am of your mind they will put such thoughts into the heads of the vulgar people, as will confer little to their good life. For when they see one of the Ten Commandments to be jus humanum merely, (as it must be if the Church can alter it), they will hope also that the other nine may be so too. For every man hitherto did believe that the Ten Commandments were the moral, that is, the eternal law’. It is noteworthy that Elements of Law defend a much more conservative ecclesiastical policy than do other writings.

As for the natural religion, he was skeptical originally and throughout which is more than the maintained its skeptical outlook. He considered any natural knowledge of God, which is more than the knowledge that a First Cause exists, completely impossible. Thus he systematically excluded revealed and natural theology from philosophy. To keep up an appearance that he attacked only scholastic theology and not the religion of the Scripture itself, Hobbes fought his battle against natural theology in the name of strict belief in the Scriptures and at the same time undermining that belief by his historical and philosophical criticism of the authority of the Scriptures. An apparent progress in his Biblicism indicated of his real progress in his criticism of natural theology, and thus was a proof that he originally judged natural theology more favourable than revealed theology. According to the Elements of Law, the binding force of natural law is based on natural knowledge of God; according to the later presentations it is based on revelation. The Elements of Law bring forward the proofs of the existence of God more emphatically and in more detail than does the Leviathan; for if one compares the formulation of these two works, one positively begins to suspect that in the Leviathan the argument is not seriously meant. The connecting link in this case as so often is in De Cive, where Hobbes says that without revelation atheism is almost inevitable. The traditional arguments for the supremacy of the monarchy, which are atleast mentioned in the earlier presentations, rest on assumptions of natural theology. Finally: in the elements of Law, there is a remark countering the ‘supernaturalists’ hostility to reason, to, which there is practically no parallel in the later works. Hobbes also fought his battle against supernaturalism with his weapons of materialism. At all events, as early as in 1641 in his correspondence with Descartes he defends the conclusions of his materialism with reference to God and the Soul. Before the complete elaboration of his materialism and particularly during his humanist period, when he had not yet freed himself from the authority of Aristotle, he in principle recognized natural theology.

Hedging. Part 1.

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Hedging a zero coupon bond denoted P(t,T) using other zero coupon bonds is accomplished by minimizing the residual variance of the hedged portfolio. The hedged portfolio Π(t) is represented as

Π(t) = P (t, T ) + ∑i=1NΔiP(t, Ti)

where ∆i denotes the amount of the ith bond P(t, Ti) included in the hedged portfolio. Notethe bonds P (t, T) and P (t, Ti) are determined by observing their market values at time t. It is the instantaneous change in the portfolio value that is stochastic. Therefore, the volatility of this change is computed to ascertain the efficacy of the hedge portfolio.

For starters, consider the variance of an individual bond in the field theory model. The definition P (t, T) = exp(-∫tT dxf(t, x)) for zero coupon bond prices implies that

dP(t, T)/P(t, T) = f(t, t)dt – ∫tTdxdf(t, x) = (r(t) – ∫tTdxα(t, x) – ∫tTdxσ(t, x)A(t, x))dt

and E[dP(t, T)/P(t, T) = r(t) – ∫tTdxα(t, x)dt since, E[A(t, x)] = 0. Therefore

dP(t, T)/P(t, T) – E[dP(t, T)/P(t, T) = – ∫tTdxσ(t, x)A(t, x))dt —– (1)

Squaring this expression and invoking the result that E[A(t, x)A(t, x′)] = δ(0)D(x, x′; t, TFR) = D(x, x′; t, TFR) /dt results in the instantaneous bond price variance

Var [dP(t, T)] = dt P2(t, T)∫tTdx ∫tT dx’σ(t, x) D(x, x′; t, TFR) σ(t, x’) —– (2)

As an intermediate step, the instantaneous variance of a bond portfolio is considered. For a portfolio of bonds, ∏ = ∑i=1NΔiP(t, Ti), the following results follow directly

d∏(t) – E[d∏(t)] = -dt ∑i=1NΔiP(t, Ti) ∫tTi dxσ(t, x)A(t, x) —– (3)

and

Var [d∏(t)] = dt ∑i=1Nj=1NΔiΔjP(t, Ti)P(t, Tj) ∫tTdx ∫tTj dx σ(t, x) D(x, x′; t, TFR) σ(t, x’) —– (4)

The (residual) variance of the hedged portfolio

Π(t) = P (t, T ) + ∑i=1NΔiP(t, Ti) ∫tTdx ∫tTdx’

may now be computed in a straightforward manner. For notational simplicity, the bonds P(t,Ti) (being used to hedge the original bond) and P(t,T) are denoted Pi and P respectively. Equation (4) implies the hedged portfolio’s variance equals the final result shown below

P2tTdx∫tT dx’ σ(t, x) σ(t, x’) D(x, x′; t, TFR) +2P ∑i=1NΔiPitTdx ∫tTdx’ + ∑i=1Nj=1NΔiΔjPiPjtTitTjdx’ σ(t, x) σ(t, x’) D(x, x′; t, TFR) —– (5)

Observe that the residual variance depends on the correlation between forward rates described by the propagator. Ultimately, the effectiveness of the hedge portfolio is an empirical question since perfect hedging is not possible without shorting the original bond. Minimizing the residual variance in equation (5) with respect to the hedge parameters Δi is an application of standard calculus.

Topology of Dark Networks

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Ecology is the study of the relationships between organisms and the biological and non-biological components of their natural environments. Ecologists consider natural systems to be organized in a nested structure. In a given locale, there are individual organisms, groups of organisms of the same species (populations), antagonistic or cooperative interactions among groups of species (communities), and interactions among communities and the non-biological environment (e.g., air, water, and sunlight). We refer to these latter units as biological ecosystems to distinguish them from human organizational structures, networks, and systems, which we refer to as organizational ecosystems. In biological ecosystems, nodes are different species (i.e., each node is a collective of individuals of the same species). Biological ecosystems can contain hundreds or even thousands of species, but certain species—keystone species—play outsized roles in structuring them. Generally speaking, keystone species are those whose removal can be expected to have exceptionally strong effects on other members of the community, and hence on the functioning of the ecosystem as a whole. Organizations increasingly belong to complex networks that enable them to work together in support of shared and complementary goals. To understand this trend, scholars, policy makers, and leaders regularly seek new viewpoints from which to explore the conditions and complexities associated with human networks and organizational systems. Sociologists have developed a range of analytical models for identifying actors and organizations within formal and informal systems, and for explaining the various relational ties that link these organizations together Social network analysis (SNA) has been used to describe the formation of and communication patterns within and between terrorist cells, as well as to predict the outcomes of particular cell activities. Many questions remain, however. Organizational scientists have begun to recognize the power of biological concepts to explain the dynamics that foster and sustain linkages between actors and organizations Here, we look to the field of ecosystem ecology for insights into the conditions, relational dynamics, and complexities that underpin and sustain violent non-state actor (VNSA) networks.

There are many potential applications of ecosystem models, but we are particularly excited about the potential for applying principles discovered by ecologists studying the effects of species extinction to develop testable hypotheses about the effects of eliminating particular militant groups within the VNSA organizational ecosystem. There are a number of crucial questions that could be explored using this framework. In the context of a region with multiple militant groups (pursuing a variety of goals, sometimes competing and sometimes cooperating, some more directly threatening to the United States than others, some using more brutal tactics than others), what traits identify groups that play a keystone role within the broader violent conflict ecosystem? How would eliminating a particular group affect the intensity of violence within the system as a whole? What are the effects—both beneficial and detrimental—on other VNSA nodes within the system and on the system as a whole? What other qualities of the broader environment condition the consequences of eliminating an actor within the system? There has been a tendency in both academic and policy circles to focus on the effectiveness of strategies designed to disrupt and destroy militant organizations while ignoring the wider system-level effects of eliminating any particular actor within the system. But counterterrorism strategists should be concerned with the potential unintended consequences of eliminating militant groups, as removing one node from a system clearly can have a wide range of effects…

Dark networks (such as those involving terrorists and criminal narcotics traffickers) are hidden from nonparticipants yet could have a devastating effect on our social order and economy. Understanding their topology yields greater insight into the nature of clandestine organizations and could help develop effective disruptive strategies. However, obtaining reliable data about dark networks is extremely difficult, so our understanding of them remains largely hypothetical. To the best of our knowledge, the data sets we explore here, though subject to limitations, are the rst to allow for statistical analysis of the topologies of dark networks.

We found that the covert networks we studied share many common topological properties with other types of networks. Their ef ciency in terms of communication and information ow and commands can be tied to their small-world structures, which are characterized by short average path length and a high clustering coefficient. In addition, we found that due to their small-world properties, dark networks are more vulnerable to attack on their bridges that connect different communities within them than to attacks on their hubs. This nding may give authorities insight for intelligence and security purposes.

Another interesting nding about the three elicited human networks we studied is that their substantially high clustering coefficients (not always present in other empirical networks) are dif cult to regenerate based on only known network effects (such as preferential attachment and small-world effects). Other mechanisms (such as recruitment) may also play an important role in network evolution. Other research has found that alter- native mechanisms (such as highly optimized tolerance) may govern the evolution of many complex systems in environments characterized by high risk and uncertainty……topology-of-dark-networks-xu-2007

Conjuncted: Quantum Field Theory and Evolution of Forward Rates in Quantitative Finance. Note Quote.

The propagator is an important quantity that accounts for the correlation between forward rates in a parsimonious manner. The propagator D(x, x′; t, TF R) corresponding to the Lagrangian in definition is given by the following lemma where θ(·) denotes a Heavyside function.

Lemma:

Evaluation of Propagator

The propagator equals

D(x, x′; t, TFR) = μTFR/sinh(μTFR) [sinhμ(TFR −τ) sinh(μτ′)θ(τ −τ′) +  sinhμ(TFR − τ′) sinh(μτ)θ(τ′ −τ) + 1/2cosh2(μTFR/2) {2coshμ (τ- TFR/2) coshμ (τ’- TFR/2) + sinh(μτ) sinh(μτ′) + sinhμ(TFR −τ) sinhμ(TFR −τ′)}] —– (1)

where τ = x − t and τ′ = x′ − t both represent time to maturities. Lemma is proved by evaluating the expectation E[A(t, x), A(t′, x′)]. The computations are tedious and contained in Baaquie but are well known in physics and described in common references such as Zinn-Justin. The propagator is seen as a special case of Lemma and is defined on the infinite domain −∞ < x, x′ < ∞ rather than the finite domain t ≤ x, x′ ≤ t + TFR. Hence, the propagator in Lemma converges to the propagator of as the time domain expands from a compact set to the real line. The effort in solving for the propagator on the finite domain is justified as it allows covariances near the spot rate f(t, t) to differ from those over longer maturities. Hence, a potentially important boundary condition defined by the spot rate is not ignored.

Observe that the propagator D(x, x′; t, TFR) in Lemma only depends on the variables τ and τ′ as well as the correlation parameter μ which implies that the propagator is time invariant. This important property facilitates empirical estimation when the propagator is calibrated to market data. To understand the significance of the propagator, note that the correlator of the field A(t, x) for t0 ≤ t, t′ ≤ t0 + TFR is given by

E[A(t, x)A(t′, x′)] = δ(t − t′)D(x, x′; t, TFR)

In other words, the propagator measures the effect the value of the field A(t, x) has on A(t′, x′); its value at another maturity x′ at another point in time. Although D(x, x′; t, TFR) is complicated in appearance, it collapses to one when μ equals zero as fluctuations in the x direction are constrained to be perfectly correlated. It is important to emphasize that μ does not measure the correlation between forward rates. Instead, the propagator solved for in terms of μ fulfills this role.

Remark: Propagator, Covariances, and Correlations

The propagator D(x, x′; t, TFR) serves as the covariance function for the field while σ(t, x) D(x, x′; t, TFR) σ(t, x′) serves as the covariance function for forward rates innovations. Hence, the above quantity is repeatedly found in hedging and pricing formulae presented in the next section. The correlation functions for the field and forward rate innovations are identical as the volatility functions σ(t,·) are eliminated after normalization.

As expected, the HJM drift restriction is generalized in the context of a field theory term struc- ture model. However, producing the drift restriction follows from the original HJM methodology as the discounted bond price evolves as a martingale under the risk neutral measure to ensure no arbitrage. Under the risk neutral measure, the bond price is written as

P(t0,T) = E[t0, t*] e−∫t0t r(t)dt P(t* ,T) = ∫ DA e-∫t0t dtf(t, t) e-∫t*Tdxf(t*, x) —– (2)

where DA represents an integral over all possible field paths in the domain t dt T dx. The t0 t notation E[t0,t][S] denotes the expected value under the risk neutral measure of the stochastic variable S over the time interval [t0,t].

Proposition: Drift Restriction

The field theory generalization of the HJM drift restriction equals

α (t, x) = σ (t, x) ∫tx dx’ D(x, x′; t, TFR) σ(t, x′) —– (3)

As expected, with μ equal to zero the result of Proposition reduces to

α (t, x) = σ (t, x) ∫tx dx’ σ(t, x′) —– (4)

and the one factor HJM drift restriction is recovered.

Quantum Field Theory and Evolution of Forward Rates in Quantitative Finance. Note Quote.

algoquant_macrossover_demo010

Applications of physics to finance are well known, and the application of quantum mechanics to the theory of option pricing is well known. Hence it is natural to utilize the formalism of quantum field theory to study the evolution of forward rates. Quantum field theory models of the term structure originated with Baaquie. The intuition behind quantum field theory models of the term structure stems from allowing each forward rate maturity to both evolve randomly and be imperfectly correlated with every other maturity. This may also be accomplished by increasing the number of random factors in the original HJM towards infinity. However, the infinite number of factors in a field theory model are linked via a single function that governs the correlation between forward rate maturities. Thus, instead of estimating additional volatility functions in a multifactor HJM framework, one additional parameter is sufficient for a field theory model to instill imperfect correlation between every forward rate maturity. As the correlation between forward rate maturities approaches unity, field theory models reduce to the standard one1 factor HJM model. Therefore, the fundamental difference between finite factor HJM and field theory models is the minimal structure the latter requires to instill imperfect correlation between forward rates. The Heath-Jarrow-Morton framework refers to a class of models that are derived by directly modeling the dynamics of instantaneous forward-rates. The central insight of this framework is to recognize that there is an explicit relationship between the drift and volatility parameters of the forward-rate dynamics in a no-arbitrage world. The familiar short-rate models can be derived in the HJM framework but in general, however, HJM models are non-Markovian. As a result, it is not possible to use the PDE-based computational approach for pricing derivatives. Instead, discrete-time HJM models and Monte-Carlo methods are often used in practice. Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. Their essential idea is using randomness to solve problems that might be deterministic in principle.

A Lagrangian is introduced to describe the field. The Lagrangian has the advantage over Brownian motion of being able to control fluctuations in the field, hence forward rates, with respect to maturity through the addition of a maturity dependent gradient as detailed in the definition below. The action of the field integrates the Lagrangian over time and when exponentiated and normalized serves as the probability distribution for forward rate curves. The propagator measures the correlation in the field and captures the effect the field at time t and maturity x has on maturity x′ at time t′. In the one factor HJM model, the propagator equals one which allows the quick recovery of one factor HJM results. Previous research has begun with the propagator or “correlation” function for the field instead of deriving this quantity from the Lagrangian. More importantly, the Lagrangian and its associated action generate a path integral that facilitates the solution of contingent claims and hedge parameters. However, previous term structure models have not defined the Lagrangian and are therefore unable to utilize the path integral in their applications. The Feynman path integral, path integral in short, is a fundamental quantity that provides a generating function for forward rate curves. Although crucial for pricing and hedging, the path integral has not appeared in previous term structure models with generalized continuous random processes.

Notation

Let t0 denote the current time and T the set of forward rate maturities with t0 ≤ T . The upper bound on the forward rate maturities is the constant TFR which constrains the forward rate maturities T to lie within the interval [t0, t0 + TFR].

To illustrate the field theory approach, the original finite factor HJM model is derived using field theory principles in appendix A. In the case of a one factor model, the derivation does not involve the propagator as the propagator is identically one when forward rates are perfectly correlated. However, the propagator is non trivial for field theory models as it governs the imperfect correlation between forward rate maturities. Let A(t,x) be a two dimensional field driving the evolution of forward rates f (t, x) through time. Following Baaquie, the Lagrangian of the field is defined as

Definition:

The Lagrangian of the field equals

L[A] = -1/2TFR  {A2(t, x) + 1/μ2(∂A(t,x)∂x)2} —– (1)

Definition is not unique, other Lagrangians exist and would imply different propagators. However, the Lagrangian in the definition is sufficient to explain the contribution of field theory ∂A(t,x)∂x  that controls field fluctuations in the direction of the forward rate maturity. The constant μ measures the strength of the fluctuations in the maturity direction. The Lagrangian in the definition implies the field is continuous, Gaussian, and Markovian. Forward rates involving the field are expressed below where the drift and volatility functions satisfy the usual regularity conditions.

∂f(t,x)/∂t = α (t, x) + σ (t, x)A(t, x) —– (2)

The forward rate process in equation (2) incorporates existing term structure research on Brown- ian sheets, stochastic strings, etc that have been used in previous continuous term structure models. Note that equation (2) is easily generalized to the K factor case by introducing K independent and identical fields Ai(t, x). Forward rates could then be defined as

∂f(t, x)/∂t = α (t, x) + ∑i=1K σi(t, x)Ai(t, x) —– (3)

However, a multifactor HJM model can be reproduced without introducing multiple fields. In fact, under specific correlation functions, the field theory model reduces to a multifactor HJM model without any additional fields to proxy for additional Brownian motions.

Proposition:

Lagrangian of Multifactor HJM

The Lagrangian describing the random process of a K-factor HJM model is given by

L[A] = −1/2 A(t, x)G−1(t, x, x′)A(t, x′) —– (4)

where

∂f(t, x)/∂t = α(t, x) + A(t, x)

and G−1(t, x, x′)A(t, x′) denotes the inverse of the function.

G(t, x, x′) = ∑i=1K σi(t, x) σi(t, x’) —– (5)

The above proposition is an interesting academic exercise to illustrate the parallel between field theory and traditional multifactor HJM models. However, multifactor HJM models have the disadvantages associated with a finite dimensional basis. Therefore, this approach is not pursued in later empirical work. In addition, it is possible for forward rates to be perfectly correlated within a segment of the forward rate curve but imperfectly correlated with forward rates in other segments. For example, one could designate short, medium, and long maturities of the forward rate curve. This situation is not identical to the multifactor HJM model but justifies certain market practices that distinguish between short, medium, and long term durations when hedging. However, more complicated correlation functions would be required; compromising model parsimony and reintroducing the same conceptual problems of finite factor models. Furthermore, there is little economic intuition to justify why the correlation between forward rates should be discontinuous.

Hobbesian Morality and State

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Political Philosophy, as that branch of knowledge which consists of moral philosophy on the one hand and, and politics on the other, was treated systematically and in details by Hobbes in three different pieces of work viz., Elements of Law (1640), in the second and third parts of the Elementa Philosophiae, and in the Leviathan (1651). In all of these three presentations, his political philosophy shows traces of Galilean science and more so of Galileo’s ‘resolutive – compositive’ method. Everyone who has written about Hobbes’ political philosophy has interpreted his treatises as heavily dependent upon natural science, either for his material or method, which he heavily incorporates through out his works. However, the recognition of this fact on closer and meticulous scrutiny proves to be extremely questionable.

The propensity of natural sciences in his political philosophy is questioned, because Hobbes very well knew the fundamental differences between the two disciplines in the contest of material and method. On this awareness lay his basic conviction that political philosophy is essentially independent of natural science. This independence is corroborated because the principles of political philosophy are not borrowed from natural science, and indeed not from any sciences, but borrowed from experience, which one has of him, or to put it more accurately, are discovered by the efforts of self-knowledge and self-examination of everyone. The evidence of political philosophy on the one hand, is much easier to understand: its subjects and its concepts are not so remote from the average man as are the subjects and concepts of Mathematics which form the basis of natural science. On the other hand, ‘the politiques are the harder study of the two’; by reason of their passions, men obscure the, in itself, clear and simple knowledge of the norms which political philosophy builds up. Moreover, man with his passions and his self-seeking is the particular subject of political philosophy, and man opposes by every kind of hypocrisy the self-knowledge on which the proof of these norms rests.

Hobbes considered both political philosophy and the natural sciences as the main components of human knowledge. It can be said that Hobbes’ classification of the sciences is based on a classification of existing things into natural and the artificial. It is not so much the artificially produced things that are basically different from all natural things as the production, the human activity itself, i.e. man as an essentially productive being, especially as the being who by his art produces from his own nature the citizen or the State, who, by working on himself, makes himself into a citizen. In so far as man works on himself, influencing and changing his nature, so that he becomes a citizen, a part of that artificial being called the State, he is not a natural being. ‘Manners of men’ are something different from ‘natural causes’. The basic classification of existing things which in truth underlies Hobbes’ classification of the sciences is classification under nature on the one side, and under man as productive and active being on the other.

The question whether his political philosophy is intended to be naturalistic or anthropological, bears not only on the method, but above all on the matter selected. The significance of the antithesis between naturalistic and anthropological political philosophy for the matter becomes fully apparent if one grasps that this antithesis is only the abstract form of a concrete antithesis in the interpretation of and judgment of human nature which extends throughout the whole of Hobbes’ work. Hobbes summed up his theory of human nature as it underlies his political philosophy in ‘two most certain postulates of human nature’. The first postulate being that of ‘natural appetite’. Eclectic as he was, this postulate takes its roots as rooted in man’s sensuousness, in his animal nature. Like that of all animals, his is constant movement. But, the specific difference between man and other animals is that of reason. Thus man is less at the mercy of momentary sense impressions, he can envisage the future much better than can animals; for this very reason he is not like animals hungry only with the hunger of the moment, but also with future hunger, and thus he is the most predatory, the most cunning, the strongest, and most dangerous animal. This view of human appetite is a specifically Hobbesian view, but then is contradicted in Hobbes’ writings by his repeated and emphatic statement that human appetite is infinite in itself and not as a result of the infinite number of external impressions. Seeing this, one can note that human appetite is essentially distinguished from animal appetite in that the latter is nothing but reaction to external impressions, and, therefore, the animal desires only finite objects as such, while man spontaneously desires infinitely and this corresponds to the intention of Hobbes’ political philosophy. The two conceptions viz., mechanistic and vitalistic conceptions differ not only in substance, but also in method. The mechanistic conception is based on the mechanistic explanation of perception and on the general theory of motion; on the other hand, the apparently vitalistic conception is based not on any general scientific theory, but on insight into human nature, deepened and substantiated by self-knowledge and self-examination. In spite of these differences, the two conceptions below the surface have something in common, which allows us to characterize them both  as naturalistic. 

The naturalistic conception of human appetite is clearly expressed in the proposition that man desires power and ever greater power, spontaneously and continuously, in one jet of appetite, and not by reason of a summation of innumerable isolated desires caused by innumerable isolated perceptions

‘…in the first place, I put for a generall inclination of all mankind, a perpetuall and restless desire of power after power, that ceaseth only in Death’. And the cause of this, is not alwayes that a man hopes for a more intensive delight, than he has already attained to; or that he cannot be content with a moderate power: but because he cannot assure the power and the means to live well, which he hath present, without the acquisition of more’.

According to him, only the irrational striving after power, which is found more frequently than the rational striving, is to be taken as the natural human appetite. The only natural striving after power, and thus man’s natural appetite, is described by Hobbes as follows: ‘men from their birth, and naturally, scramble for everything they covet, and would have all the world, if they could, to fear and obey them’.1 In the case of man, animal desire is taken up and transformed by a spontaneous infinite and absolute desire which arises out of the depths of the man himself.

We find a more detailed definition of the irrational striving after power:

‘because there be some, that taking pleasure in contemplating their own power in the acts of conquest, which they pursue farther than their security requires; if others, that otherwise would be glad to be at ease within modest bounds, should  not by invasion increase their power, they would not be able, long time, by standing only on their defence, to subsist. And by consequence, such augmentation of dominion over men, being necessary to a man’s conservation, it ought to be allowed him’.

It is clearly seen here that rational permissible striving after power is in itself finite. The man guided by it would remain ‘within modest bounds’, would ‘be content with a moderate power’. Only the impermissible, irrational, lustful striving after power is infinite.

In four different arguments, Hobbes designated the characteristics in the difference between man and animal as the striving after honour and positions of honour, after precedence over others and recognition of this precedence by others, ambition, pride, and the passion for fame. Since man’s natural appetite is a striving after precedence over others and recognition of this precedence by others, the particularities of natural appetite, the passions, are nothing other than particular ways of striving after precedence and recognition. Speaking about the cause of madness, Hobbes says: “The Passion, whose violence, or continuance maketh Madnesse, is either great vaine-glory; which is commonly called Pride, and selfe-conceipt; or great Dejection of mind”. All passions and all forms of madness are modifications of conceit or of a sense of inferiority, or in principle, of the striving after precedence and recognition of that precedence.

The same conclusion is reached if one compares the arguments by which Hobbes in the three presentations of his political philosophy proves his assertion that the war of everyone against everyone arises of necessity from man’s very nature. Every man for that reason is the enemy of every other man, because each desires to surpass every other and therefore offends every other. The discrepancies between the three presentations shows that Hobbes himself never completed the proofs of his fundamental assertion, and, as is seen on closer inspection, did not complete them simply because he could not make up his mind explicitly to take as his point of departure the reduction of man’s natural appetite to vanity. At the end of the most important part of his work, “Leviathan”, Hobbes says:

‘Hitherto I have set forth the nature of Man, (whose Pride and other passions have compelled him to submit himselfe to Government;) together with the great power of the Governour, whom I compared to Leviathan, taking that comparison out of the last two verses of the one and fortieth of Job; where God having set forth the great power of Leviathan, called him the King of the Proud’.

The state is compared to Leviathan, because it and it especially is the ‘King of all the children of pride’. Only the State is capable of keeping pride down in the long run, indeed it has no other raison d’etre except that man’s natural appetite is pride, ambition, and vanity. 

Why could not Hobbes take man’s natural appetite, which is vanity as the basis of his political philosophy?  If this conception of natural appetite is right, if man by nature finds his pleasure in triumphing over all others, then man is by nature evil. But he did not dare to hold this consequence of his theory. For this very reason, in the Leviathan, he puts vanity in the end. Because man is by nature animal, he is not by nature evil, therefore he is as innocent as the animals; thus vanity cannot characterize his natural appetite. Hobbes in defence against the reproach that according to his theory man is by nature evil does not mention vanity at all. In laying the foundations of his political philosophy, Hobbes puts vanity more and more into the background in favour of innocent competition, innocent striving after power, innocent animal appetite, because the definition of man’s natural appetite in terms of vanity is intended as a moral judgment. He is finally obliged to attribute to the judges the wickedness which he disallows in the case of the guilty, the criminals; he betrays particularly in his description of the striving after power itself, that the innocence, neutrality, and moral indifference of that striving is only apparent. The apparent moral indifference arises simply and solely through abstraction of the necessary moral difference. Hobbes’ political philosophy rests not on the illusion of an amoral morality, but on a new morality, or, so to speak according to Hobbes’ intention, on a new grounding of the one eternal morality.

The second of the ‘two most certain postulates of human nature’ is ‘the postulate of human reason’. In accordance with the naturalistic reasoning this postulate is reduced to the principle of self-preservation: since the preservation of life is the condition sine qua non for the satisfaction of any appetite, it is the ‘primary good’. As a logical conclusion of this thought, Hobbes attempts to deduce natural right, natural law, and all the virtues from the principle of self-preservation. It is noteworthy that Hobbes prefers the negative expression ‘avoiding death’ to the positive expression ‘preserving life’. That preservation of life is the primary good is affirmed by reason alone. On the other hand, that death is the primary evil is affirmed by passion, the passion of fear of death. And as reason itself is powerless, man would not mind to think of the preservation of life as the primary and the most urgent good, if the passion of fear of death did not compel him to do so. According to Hobbes, the preservation of life is the primary good, an unhindered progress to ever further goals, a ‘continuall prospering’, in a word, happiness is the greatest good, but there is no supreme good in the enjoyment of which the spirit might find repose. On the other hand, death is the primary as well as the greatest and the supreme evil. For death is not only the negation of the supreme good; but at the same time, it is the negation of all the goods. Only through death has man an aim, the aim that is forced upon him by the sight of death, the aim of avoiding death. For this reason, Hobbes uses the negative expression ‘avoiding death’ to the positive expression ‘preserving life’. This is also because we fear death infinitely more than we desire life. 

But Hobbes also does not adhere to the theory of death as the supreme evil, since for him the tortured life is a greater evil as compared to death. So for him, an agonizing death is much more evil than death. But in contradiction, if Hobbes had considered agonizing death as the supremest evil, he would have attributed an ever-greater importance on medicine, which he tends to forget. When he says of an agonizing death that it is the greatest evil, he thinks exclusively of violent death at the hands of other men. This fear of getting killed at the hands of other men, is a mutual fear, i.e. it is a fear each man has of every other man as his potential murderer. This fear of a violent death, pre-rational in its origin, but rational in its effect, and not the rational principle of self-preservation, is, according to Hobbes, the root of all right and of all morality. He finally denied the moral values of all virtues which do not contribute to the making of the State, to consolidating peace, to protecting man against the danger of violent death, or, more exactly expressed, of all virtues which do not proceed from the fear of violent death.

Since, Hobbes reduces man’s natural appetite to vanity, he cannot but recognize the fear of a violent death, not the fear of a painful death, and certainly not the principle of the preservation of life as the principle of morality. The ever-greater triumph over others, and not the ever-increasing, but rationally increasing, power is the aim and happiness of natural man. ‘Continually to out-go the next before is felicity’. Man’s life may be compared to a race: ‘but this race we must suppose to have no other goal, nor other garland, but being foremost’. Absorbed in the race after the happiness of triumph, man cannot be aware of his dependence on the insignificant primary good, the preservation of life and limb; failing to recognize his bodily needs, man experiences only joys and sorrows of the mind, i.e. imaginary joys and sorrows. Living in the world of his imagination, he need do nothing, in order to convince himself of his superiority to others, but simply think out his deeds for himself; in this world, in which indeed ‘the whole world obeys him’, everything is accomplished according to his wishes. He can awaken himself from this dream world only when he feels in his own person, by bodily hurt, the resistance of the real world. ‘Men have no other means to acknowledge their own Darknesse, but onely by reasoning from the unforeseen mischances, that befall them in their ways’. Because man by nature lives in the dream of the happiness and triumph, of a glittering, imposing, apparent good, he requires a no less imposing power to awaken him from his dream: this imposing power is the imperious majesty of death.

The ideal condition for self-knowledge is, therefore, unforeseen mortal danger. The vain man, who, in his imagination, believes himself superior to others, cannot convince himself of the rightness of his estimate of himself; he requires the recognition of hiss superiority by others. He therefore steps outside his imagination. Now, either the others take his claim seriously and feel themselves slighted, or they do not take his claim seriously and he feels himself slighted. In either case the making of the claims leads to contempt. The one slighted longs for revenge. In order to avenge him he attacks the other, indifferent whether he loses his life in so doing. Unconcerned as to the preservation of his own life, he desires, however, above all that the other should remain alive; for ‘revenge aimeth not at the death, but at the captivity and subjection of an enemy…revenge aimeth at triumph, which over the dead is not’. The struggle which thus breaks out, in which, according to the opinion of both opponents, the object is not the killing, but the subjection of the other, of necessity becomes serious, because it is a struggle between bodies, a real struggle. From the beginning of the conflict, the two opponents have, without realizing and foreseeing it, completely left the imaginary world. At some point in the conflict, actual injury, or, more accurately, physical pain, arouses a fear for life. Fear moderates anger, puts the sense of being slighted into the background, and transforms the desire for revenge into hatred. The aim of the hater is no longer triumph over the enemy, but his death. The struggle for pre-eminence, about ‘trifles’, has become a life and death struggle. In this way natural man happens unforeseen upon the danger of death; in this way he comes to know this primary and greatest and supreme evil for the first time, to recognize death as the greatest and supreme evil in the moment of being irresistibly driven to fall back before death in order to struggle for his life. Only for a moment can he free himself from the danger of death by killing his enemy, for since every man is his enemy, after killing of the first enemy he is ‘again in the like danger of another’, indeed of all others. The killing of the enemy is thus the least far-sighted consequence of the withdrawal from death. In order to safeguard his life, not only for the moment, but also in the long run, man needs companions, with whose help he can successfully defend his life against the others. Companions can be gained in two ways, by force or by agreement. The former appears as if it stands in the midway between the killing of the enemy and agreement with him; so it is natural enough for him to try out the latter. Since fear can hardly be made manifest, but by some action dishonourable, that betrayeth the conscience of one’s own weakness; all men in whom the passion of courage or magnanimity have been predominated, have abstained from cruelty…In one word, therefore, the only law of actions in war is honour. Thus arises the relationship of master and servant. The victor who has safeguarded his honour becomes the master. The vanquished, who ‘submitteth…for fear of death’, who admits his weakness and with that has forfeited his honour, becomes the servant. The dominion of the master over the servant, despotic rule, is one form of the natural State, and as the other part of the natural State, patriarchy, is construed by Hobbes entirely according to the pattern of despotic rule, we may even say: despotic rule is the natural State. The artificial State, which is as such more perfect, arises when the two opponents are both seized with fear for their lives, overcome their vanity and shame of confessing their fear, and recognize as their real enemy not the rival, but ‘that terrible enemy of nature, death’, who, as their common enemy, forces them to mutual understanding, trust, and union, and thus procures them the possibility of completing the founding of the State for the purpose of providing safeguards for the longest possible term, against the common enemy. And while in the unforeseen life-and-death struggle, in which vanity comes to grief, the futility of vanity is shown, it is revealed in the concord of living, and of living in common, to which their pre-rational fear of death leads them, that the fear of death is appropriate to human conditions, and that it is ‘rational’. It is even ostensibly shown that it is only on the basis of fear of death that life comes to concord and that the fear of death is the only ‘postulate of natural reason’.

Hobbes distinguishes no precisely than any other moralist between legality and morality. Not the legality of the action, but the morality of the purpose, makes the just man. That man is just who fulfils the law because it is law and not for fear of punishment or for the sake of reputation. Although Hobbes states that those are ‘too severe, both to themselves, and others, that maintain, that the First motions of the mind, be Sinnes’, he yet ‘confesses’ that ‘it is safer to erre on that hand, than on the other’. In believing that the moral attitude, conscience, intention, is of more importance than the action, Hobbes is at one with the Christian tradition. He differs from this tradition at first sight only by his denial of the possibility that just and unjust actions depend wholly on the judgment of the individual conscience. In the state of nature every action is in principle permitted which the conscience of the individual recognizes as necessary for self-preservation, and every action is in principle forbidden which according to the judgment of the individual conscience does not serve the purpose of self-preservation. If, then, in the state of nature, any and every action is permitted, even in the state of nature not every intention is permitted, but only the intention of self-preservation. Thus the unequivocal distinction between just and unjust intentions holds even for the state of nature and is, therefore, absolute.

Hobbes expressly denies the existence of a law, as if it were a natural law, which obliged man unconditionally, and therefore obliged him even in the state of nature. He says: ‘These dictates of Reason, men use to call by the names of Lawes; but improperly: for they are but Conclusions, or Theoremes concerning what conduceth to the conservation and defence of themselves; whereas Law, properly is the word of him, that by right hath command over others’. Law as an obligation is the basis of a covenant between formerly free and unbound men. Thus ‘where no Covenant hath preceded, there hath no Right been transferred, and every man has right to everything…But when a Covenant is made, then to break it unjust: And the definition of injustice, is no other than the not Performance of Covenant’. The just attitude cannot be anything but earnest striving to keep one’s given word; and is therefore far from being obedience that it is, on the contrary, nothing else but proud self-reliance. From the Leviathan, it is clearly noticeable that opinion, far from being the origin of just attitude, is rather the only origin of the unjust attitude. Not pride, and still less obedience, but fear of violent death, is according to him the origin of the just intention. It makes possible the distinction between the attitude of an unjust man who obeys the laws of the State for fear of punishment, and the attitude of the just man, who for fear of death, and therefore from inner conviction, as it were once more accomplishing in himself the founding of the State, obeys the laws of the State. 

Since man is by nature fast in his imaginary world, it is only by unforeseen mischance that he can attain to knowledge of his own darkness and at the same time a modest and circumspect knowledge of the real world. That is to say: the world is originally revealed to man not by detachedly and spontaneously seeing its form, but by involuntary experience of its resistance. The least discriminating and the detached sense is the sense of touch. This explains the place of honour which is tacitly granted to the sense of touch in Hobbes’ physiology and psychology of perception; all sense-perception, particularly that of the most discriminating and detached sense, the sense of sight, is interpreted by experience of the sense of touch.

Thus it can be seen, that the moral and humanist antithesis of fundamentally unjust vanity and fundamentally just fear of violent death is the basis Hobbes’ political philosophy. As an objection, it can be called to effect that this antithesis is to be found in Hobbes’ political philosophy only because Hobbes had not yet completely freed himself from the influence of the Christian Biblical tradition. This antithesis is the ‘secularized’ form of the traditional antithesis between spiritual pride and fear of God, a secularized form which results from the Almighty God having been replaced by the over-mighty State, ‘the Mortall God’. Is this affiliation to the antithesis in Hobbes’ moral work right by itself?

On the contrary, this antithesis is an essential indispensable element, or, more accurately, the essential basis of, Hobbes’ political philosophy. Political philosophy deprived of its moral foundations is, indeed, Spinoza’s political philosophy, but not Hobbes’. Spinoza made might equivalent to right. Thanks to the moral basis of his political philosophy, Hobbes kept the possibility of acknowledging justice as such and distinguishing between right and might. Hobbes’ political philosophy is really based on knowledge of men, which is deepened and corroborated, by the self-knowledge and self-examination of the individual, and not on a general scientific and metaphysical theory. And because it is based on experience of human life, it can never, in spite of all the temptations of natural science, fall completely into the danger of abstraction from moral life and neglect of moral difference.

The contention is that Hobbes’ humanist moral motivation of his political philosophy is more original than the naturalistic motivation. The important points of his moral motivation were firmly established well before he turned his attention to natural science and especially to Euclid’s Elements. This discovery of Euclid was an epoch in his life; everything he thought and wrote after that is modified by this happening. His discovery lent maturity to his later works and whether this is the case, can be decided only after the sparse remnants of his youthful philosophy is meticulously studied.