VOLITION and Allied Causal Concepts
Chapter6.FURTHER ANALYSIS OF INFLUENCE
3.Instincts in relation to freewill
4.Liberation from unwanted influences
1.Some features of influence
We defined influenceas the relationship, to the action of a volitional agent, of contents of consciousness that make his exercise of willeasier or harder. To ‘make easier or harder’ means that: in the presence of these objects, provided one is minimally aware of them just before acting, the effort of will needed for some purpose is increased or decreasedby comparison tothat needed in their absence. If they are not contents of consciousness, they are effectively absent as influences, whether present or absent as facts.
The contents of consciousness involved may be experienced material, mental or even intuitive objects. That is, they may be concrete environmental or physiological factors or conditions, or phenomenal contents of mind (memories, imaginations, verbal thoughts, emotions, whatever), or again acts or attitudes within the agent himself. The operative contents of consciousness may also include abstractions from any such experiences (that is, concepts, inferences, any intellectual considerations). The degree of consciousness involved may be intense (‘conscious’), peripheral (‘subconscious’) or virtually nil (‘unconscious’); this may or not affect the degree of influence.
But in any case, the medium of consciousness is essential to characterization of something as an influence. If something has an effect on an agent’s actions independent of consciousness, i.e. (as we say) ‘objectively’, we may speak of ordinary conditioning, but not of influence. Thus, for instance, a person’s natural constitution (such as brain makeup or bodily structure, in comparison to other individuals of the same species or to other species) certainly affect his actions, but not in the way of influence. These may well yet be influences – if their apprehension plays a role in his actions. For example, if a man seeing his poor physical appearance in a mirror is discouraged from pursuing a woman – his ugliness ceases to be a mere condition and becomes an influence (on his own volition).
Influences are not sufficient conditions for will, but are ‘efficient’ in the sense that without them or others like them the willed act would be improbable, though still possible somehow. Positive influences make things more readily accessible (facilitate); negative influences make things more difficult (hinder). It depends which way one is headed.
A simple way to represent these tendencies is to visualize someone moving an object up or down a hill: the hillside (or the force of gravity) is analogous to a positive influence on a person moving the object down, but analogous to a negative influence on a person moving it up. The degree of influence may be illustrated by the inclination of the hillside. If it is steep, influence is great, pro or con. If it is not steep, the influence is small, pro or con. If the inclination is strong in a favorable direction (downhill), little effort is needed to achieve the desired end; but if it is unfavorably strong (uphill), much effort is required. If the inclination is not strong, comparatively more effort will be needed for positive goals (down) and comparatively less effort for negative ones (up) – comparatively to a stronger inclination, that is.
For this reason, we often speak of people’s proclivities or inclinations. The term inclination carries a useful image, suggesting a landscape with valleys or canals symbolizing the easy (more inertial) paths, and hills or other obstacles as requiring special (more volitional) effort to go over or overcome. We can imagine a marble (one’s will) traveling over such variable landscape, subject to alternative developments and the conditions of transition at different times from one to the other. The landscape idea allows us to view effort not merely in terms of modifying the paths of a marble (going with little effort on the easy courses, or with more effort on the harder ones), but also more radically in terms of remodeling the landscape itself.
To influence the course of events is to make themtendto go a certain way rather than any other. To clarify this, we might refer to effort, since effort is diminished or increased according as it goes with or against tendencies. But we should not confuse a heuristic formula with a description or an explanation. Our impression is that influences stimulate or stagnate our responses, i.e. increase or decrease our will. This aspect of influence can perhaps best be expressed with reference to thelikelihoodof a certain response.
It seems that themoreeffort an act of will requires, thelesslikely is the agent to provide it; thelesseffort it requires, themorelikely will he do so. The agent is naturally lazy or economical: if things are made easy for him, he will probably go for it; if difficult, probably not. This is said ‘all things considered’, i.e. taking into account all the influences involved, and not just focusing on some and ignoring others. It does not exclude that the agent may indeed invest more effort, and overcome some great resistance, especially if motivated accordingly by some other influence (for instance, a moral principle or a vain self-image).
A tendency may be viewed as a ‘force’, which goes in the same direction as the ‘force’ of one’s will, reducing the amount of effort needed and increasing the likelihood of such will, or in the opposite direction, making more effort necessary and the will less likely. The advantage of this concept of ‘force’ is to provide a common measure between tendencies and will, although they are very different in nature, making a calculus (additions and subtractions) possible.
Note that here, when we speak of probabilities (more or less likelihood), we mean something radically different from the statistics intended in causation, in that it doesnotsignify that, under certain unknown or unspecified conditions, the likelihood becomes a necessity. We here just report that that the greater the effort required the less likely it is to be provided; and the less effort required, the more likely provided. That effort and likelihood are thus inversely proportional may be viewed as a sort ofprinciple of inertiaobserved in the spiritual realm. But such analogy is not meant to imply inevitable behavior patterns.
As we have pointed out, the assumption of freedom of the will is that irrespective of all influences, where volition occurs it is nevertheless ‘freewill’. Perhaps an inner sense of freedom is involved, which allows us to think that, even if we have always behaved in a certain way in certain circumstances, we are still free to behave otherwise in similar circumstances. Nevertheless, we are inwardly aware that had the influential circumstance been different, we might well have behaved differently. In other words, the influential factor played a role in our decision, though not a determining one.
A person is said to have a (relatively) ‘strong will’, if over time his conduct is less readily influenced – especially by other people’s wills, but also more broadly by any circumstances. A person with ‘weak will’ is often (comparatively) driven or thwarted in his will, i.e. his effort is rarely equal to his intentions. Note that these two concepts are relative: they may compare different periods in the life of the same person, as well as the behavior patterns of different people.
The influence of something on one’s will is essentially subjective, since it depends on a cognitive act. Nevertheless, the influence as such is objective enough, in the sense that its increase or decrease of the effort requirement for a given volition in given circumstances may be considered as a ‘natural law’.
One’s cognitive assessment of a situation may be true or false, objectively justifiable or unjustifiable; the influence of something ‘perceived’, or assumed to be a fact, does not depend on its being a fact in fact. It suffices that onebelievesomething to be a fact, or to be likely enough, for it to have considerable influence. Whether such belief is based on experience, reason, emotion, wisdom, intelligence, stupidity, faith, guesswork, confusion or self-delusion is irrelevant, so long as it is operative.
It follows that a molehill may seem like a mountain, and vice versa. Thus, one man may be brought to a standstill by the prospect of resistances that were in fact minimal, while another may heroically overcome enormous odds because the challenge seemed puny to him. Neurotic doubts may ignore all evidence, and artificially inhibit volition, bringing on defeat. Shining faith may ignore all rational objections, and fire volition to triumph.
It should be made clear that influences on our actions are rarely singular and simple. Just as a mass of ordinary conditions underlie them, so influences are multiple and complicated.
To give an example: suppose I lift a heavy load. The lifting is objectively difficult because of the great weight of the load and the inadequacy of my muscles, or the wetness of my hands, or my having insufficiently eaten lately, or my feeling drowsy. But there are also mental factors, like my self-confidence, or my fear of dropping the load and making a noise, or my being in a hurry, which affect things more subtly and obliquely, in the way of influence. My considering myself strong encourages me, my fear of falling upsets my concentration, my feeling rushed spurs me. All these factors play a role in shaping my physical movements.
At any given moment, with regard to any pending act of will, there may be a multitude of influences. We may view them collectively as making one resultant influence. But it is more accurate to view them severally and analytically. Some point in one direction, others in the opposite direction; the resultant is the net influence, which may be positive, negative or balanced. Moreover, while volition is still undecided, there may be a range of options; each of these has its own resultant influences, so that the options may be ranked, ordered according to the degree and polarity of influence concerning them.
Furthermore, influences should not be considered as isolated forces, because they often mutually affect each other in some way. Causal chains and structures may interrelate them. This may mean ‘mutual reinforcement’, such that one gives rise to or increases another, and then the latter generating some more of the former, till both reach a certain stable level. Or it may mean ‘mutual counteraction’, such that one decreases or eliminates another or vice versa.
Thus, a detailed calculus of influences is theoretically possible, and needed to fully clarify each situation of will. In practice, such calculations are very tentative and approximate, since we do not have sure and precise data. We should also note the difference between identifying and estimating influences before the fact, i.e. as an aid to choice and decision, and doing so after the fact, i.e. as an aid to judgment about a completed volition. In the latter case, we are taking stock, to reward or punish ourselves by rating, or to learn lessons for the future.
2.Processes of influence
Natural objects or events influence an agent when appearing before him, as objects of consciousness (through his perceptual faculties, outer or inner, or, more broadly, through his conceptual faculties). Such cognitions may generate emotions, imaginations and deliberations in him, as well as consequent actions: these all involve or are influenced acts of will. Emotion involves evaluation, an act of will; imagination is largely willed projection of mental images; deliberation is thought, also largely willed; and of course, action means will.
Also, subjects normally influence other subjects via such natural objects or events. Thus, for instance, a woman may attract a man by walking or dancing in front of him (light), by speaking or singing (sound), by her odors or perfume (smell), by physical contact (touch), by her cooking (taste), or more abstractly by her beliefs and values made evident through the preceding sense data. These external items may generate emotions, imaginations and deliberations in the man, which eventually influence him into appropriate action.
Various subdivisions of influence need to be considered. One may be influenced byinformation, which may be perceptual givens or conceptual insights, whether in the material world or in the mental matrix, arising naturally or through research or by the suggestion of other people (through oral, written or visual means). The information need not be true; it suffices that it is believed. Our individual beliefs evidently influence our individual actions; moreover, our belief systems give rise to behavior patterns.
One may also or alternately be influenced byemotions: felt in the body or in the head, concretely or abstractly. Emotions, of course, often arise in the face of information (be it true or false). Though information may influence via emotions, it may also influence without intervening emotions. Some emotions are apparently ‘spontaneous’, arising without clear relation to any new information; we experience an emotional charge in us, but cannot offhand interpret its origin. This is quite normal; but if it happens too often without rational explanation, it may become a source of anxiety and pathology.
Some people believe, rightly or wrongly, in the possibility of direct ‘spiritual’ influence. In this view, one may transmit ideas to another by mysterious pathways, or even will one’s will on another’s will. In such cases, if influence need not happen through natural objects or events (i.e. mainly via matter), are the mechanics of influence more complicated than normally conceived? In the case of telepathy, this possibility changes nothing essentially; the label ‘influence’ remains accurate. In the case of takeover of will or domination, we may simply refer to an effective annulment of the power of will of one subject by another: such overpowering is not ‘influence’ in a strict sense, but more precisely a far-reaching volition, effectively a ‘conditioning’.
As earlier stated, information may influence actions in a roundabout way, as well as directly. The following is a more detailed analysis of such oblique influence in the case of emotions, for instance (similar analysis is possible for all information).
We can, by the way, distinguish three types of ‘emotions’ – visceral ‘feelings’ in the body, some of which are products of physical sensation (e.g. a pleasure during massage or a pain upon burning) and some of which seem of psychosomatic origin (e.g. a person wakes up in the morning with a cloud of anxiety in the stomach area or bubbles of joy in the upper chestor throat), and purely mental emotions whose phenomenal qualities are very subtle if at all discernable.
It should be stressed that an emotion may be present and felt – butunadmitted. In such case, it is said to be ‘subconsciously’ cognized, because one is aware of it with a low or minimal degree of consciousness. This is in contrast to ‘conscious’ emotion, which is more explicitly recognized, which means thatone identifies with itto some extent, at least enough to consider and deal with it. We may also distinguish between awarenessofan emotion, and awarenessthat it isemotion; the latter classifies the former, implying an additional cognitive act.
When an emotion occurs, our usual response is to try to explain it, so as to (a) quash it, or at least diminish it, if it is negative, or (b) continue it, if not intensify it, if it is positive. We naturally prefer the positive to the negative (unless we are masochistic, but then the desired positive emotion is further down the line, more tortuous), and cling to what we desire and escape from our objects of aversion.
This response of ‘trying to explain’, is a search for the cause(s) of the emotion or for its exact meaning (besides its being pleasant or unpleasant) – and the important thing to understand is that the interpretations we (or others) suggest are merely hypotheses, which may be right or wrong. In fact, they are very often mere conjectures, i.e. probably wrong, in that the more complex particular emotions usually have multiple causes, and it is hard to establish which of these are the dominant ones even when we manage to list them all.
Thus, emotions influence actions in two ways: simple/direct or complex/roundabout. First, the emotion itself may affect conduct, by easing or obstructing certain actions (e.g. a light-hearted child skips around; whereas a person with a headache avoids movement). Second, the emotion supplies the data around which we construct hypotheses about its causes, and these explanations in turn affect our actions (e.g. thinking I feel good or bad because someone said something to me, I pursue or avoid that person).
Psychologists studyspecificinfluences, which group together various combinations of the above-mentioned genera of influences. For example, the various categories of influence on one’s life might be listed, including one’s parents and other family members, one’s school teachers, other friends and acquaintances, certain books read (novels, religious documents, histories, philosophies, scientific treatises), the other media (movies, TV and radio programs, etc.), and so forth. Then for each category, the nature of the influence would be ascertained – e.g.whatdid one’s father or mother influence? Perhaps one’s moral inclinations, one’s manners, one’s choice of spouse, or one’s political beliefs. Andhowdid such transmission occur? Perhaps by example, by preaching, or through some shared experience. A nexus of information and emotions is involved.
3.Instincts in relation to freewill
With regard to the statement made that all volition is freewill, we have to answer a question concerninginstincts, i.e. seemingly inherited (or at least individually innate) environmental information and behavioral responses that are not mere reflexes. How are certain surprising observed behaviors to be explained? How come all members of a species behave in the same way in the same circumstances? Can some cognitive data be genetically stored and passed on? Can some volitions be controlled by genetic factors?
For a start, we should avoid confusion between intentional acts and acts with certain incidental consequences. In both cases, there is will, indeed free will – but the former are consciously aimed at some goal, whereas the latteronly seemto have a certain direction to an ex post facto observer. Theintentionof instinctive acts is obscure, vague and internal; it is not to be confused with the biologicalutilityof such acts identified by scientists. The instinctive act responds to an inner urge, in a way that calms or gains relief from that urge. The soul’s consciousness is focused on that urge, and the will’s aim is to answer that pressing demand anyway it can (whether the ‘how’ is immediately evident, or has to be discovered or learned). The soul is not told ‘why’ it has to do it, i.e. need not know what the life-sustaining value of its instinctive response might be. Theurgeto so act, on the other hand, may well be viewed as ‘programmed’ by nature (i.e. a product of evolutionary selection).
Consider for example a baby sucking at its mother’s bosom. The action as a set of mouth muscle movements is one we would consider volitional, yet we would not seriously suggest he has consciously directed his muscles for feeding purposes. The baby’s volition is surely influenced by hunger and perhaps by the smell of its mother’s milk. In such cognitive context, there may be a number of reactions the baby’s volition may choose from, including sucking, crying, waving arms, say. In this sense, the babyhas choice. But it just so happens that sucking movements are the primary choice, the most likely choice, i.e.the easiestoption in the range of available options.
Thus, the event involved is equivalent to trial and error learning, except thatthe first choice volition is influenced to takeis the ‘right’ one. The other options are therefore not tried.
Thus, ‘instinct’ is a legitimate and definable concept: it may be fully assimilated to our concept of influence. The volition involved in instinctive acts is not exempt from freedom and responsibility. We can therefore side with the proposition that genes do not transmit foreknowledge of the environment or complex living skills. Technically, the influence of instinct functions exactly like any other influential item.Simply, an instinct is an innate influence, which may or may not be partly affected by environmental circumstances or their cognition; and this influence happens to bethe most powerful of other innate or acquired influences.
Influences are not all equal: this is true in all contexts, as we have seen, and not just with reference to instinct. Influences are of varying effect on volition; some influences are strong, some are weak; they may be ranked. Influences are all operative simultaneously on the soul about to will; but the soul is most likely to will in the easiest direction, i.e. the one in favor of which the influence is strongest, loudest, most manifest. That this direction is consistently taken by a baby or a lower animal does not imply that other options are in fact absent; they are indeed present as potentials in the background of the volition, only being less influential they are less likely to be felt or acted upon.
For a more mature or more spiritually developed soul, the easiest option is not always the one taken; the soul has discovered its own volitional power, and can therefore choose less obvious directions. Note that even an animal may swerve (or be influenced to swerve) from its instinctive path; for example, a dog trainer can get a dog to resist its hunting instinct and obey the injunction to walk on when it comes across some prey.
In formal terms, we may refer to a disjunctive proposition, where “P or Q or R…” are the alternatives open to volition in given circumstances and influences. However, P may be more likely than Q, and Q more likely than R, etc. In such case, the agent will ‘instinctively’ opt for P, the most obvious and influential choice, although he may eventually discover his capacity to opt for Q or even R, notwithstanding their being less manifest and influential.
4.Liberation from unwanted influences
When we meditate on our internal workings, we can easily see the force of inertia existing in us. It is very evident that though we may to some extent have freewill, it is not always and everywhere immediately operative. Thoughts, imaginings, memories, emotions, faces, musical tunes, words – may go on and on for hours, without our being able to stop them or channel them for more than a few seconds, if that. It may however be possible to control such dull mental activity in the long run, thanks to disciplined spiritual exercises like meditation. Thus, freewill seems to exist, not in all things ‘at will’, but often only by ‘working on oneself’ over time, i.e. going through a time-consuming process.
This is how the yearning for innerliberationmay first arise. Once we have witnessed our own incapacity to concentrate our will over a period of time, we are appalled and become anxious to remedy this weakness of the will. Some philosophers think the solution to be asceticism, considering that most of the force that drags us down into such endless chatter of the mind is the body’s innate desire for food and drink, physical comfort, sex, and so forth. Others argue that more pondered methods must be used to overcome mental scattering and sluggishness.
Many people are not even at the level where they are concerned with the ongoing obsession and anarchy inside their minds, but are rather frightened by some of their compulsive external behavior patterns, such as anti-social anger and violence, or self-destructive and socially dangerous lust, for examples. Such actions may be viewed in religious terms as sins, and fought by prayer and other pious deeds; or they may be confronted in a more secular perspective. But what concerns us here is their relationship to freedom of the will.
Every punctual or sustained attempt to gain ascendancy over such subtle or coarse tendencies is an expression and affirmation of freewill. Self-mastery is possible, if we do not ‘identify with’ the influences on our will, i.e. if we do not say or think of them ‘this is me’ or ‘this is part of me’.
But in addition to the influences already within us, in the way of thoughts and feelings, we may need to look further out and consider the way nature and other people condition and influence our mental and physical actions. I will have different life-support issues to face if I live in a hot country or in a cold country. If someone imprisons me, or creates a totalitarian society around me, it affects the things I need to think about and what I may do or not do. The contents of my thoughts are affected by my environment.
Anything that affects our subjective world, or objectively broadens or narrows the choices open to us in our life, anything to be taken into consideration in the exercise of volition, is an influence. If it is considered good, if facilitates our pursuits; if bad, it makes things more difficult for us. We logically prefer the former, and so far as possible oppose the latter.
Volition is capable of being influenced, but is also capable of overcoming influences or diminishing their impact. This is made possible through a policy of awareness, or mindfulness – ‘working on oneself’.
5.Propositions about the future
Volition is expressed through propositions of the form “A wills W”, which may be called ‘volitional propositions’. Although the simple present tense is needed to discuss volition as it occurs (whether in categorical or conditional propositions), mostly we use such form in the past or future tenses. Usually, except for introspective reports, we only know after the fact that “A wills W” was true: i.e. such a proposition is derived from the past form “A willed W”. The future form “A will will W”has always been of especial interest to logicians and philosophers, because it seems to claim as a settled fact something that depends on free will and therefore cannot strictly be predicted with absolute certainty.
Many propositions less explicitly involve prediction of free will, yet depend for their truth on the will of someone or those of many people. For example: “the sea battle will take place tomorrow”. It should be noted thatsuch propositions about future will(s) are not only about volition, but also about the amount of influence on volition. In our example (it is actually Aristotle’s), the likelihood that the prediction come true is very high (though not absolute), because all the people involved are so entangled in their war that it would be very difficult (though not inconceivable) for them to make peace overnight. Thus, propositions about influences involved are tacitly implied.
All forms concerning the relation of influence may be called ‘influential propositions’. This includes positive forms, like “X influences A to will W”, and their negations, like “X does not influence A to will W”. Also, as we have seen, the extreme terms may be replaced by their negations – X by notX and W by notW. As for the middle term, A, there is no point considering its replacement by its negation, notA, since that would not refer to an agent; we can only substitute another agent, say B or C. A subspecies of influential forms are the forms of incitement, such as “X incites A to will W” and its derivatives.
One common form relating to both volition and influences thereon is “When/if X occurs, then A will do W” – where (i) X is any influential event, i.e. a natural (deterministic or otherwise) occurrence and/or a volition by self and/or other(s), which agent A is aware of or falsely believes to be true prior to acting, and (ii) agent A is any person or group of persons or other volitional entity or entities, and (iii) W refers to some act(s) of will by agent A (individually, in parallel or collectively), which act(s) of will may simply be a decision taken but not yet carried out, or a partly sustained process, or a process sustained to its conclusion, successfully or not.
Such forms may be referred to as ‘personal conditionals’ in that they resemble logical, natural and other types of conditional propositions. However, they are different in important respects. The antecedent here is an event that has not only to occur but be perceived to do so, or alternatively it may even just be wrongly thought to occur – by the agent(s) concerned. The consequent is connected to the antecedent not through some logical or natural necessity, but through the personalresolveof the agent(s) concerned, which may be of varying strength – which means that though the consequent uses the copula “will do” it is at best probable but never certain that the agent(s) will bring it about. The proposition as a whole can of course nevertheless be declared true or false, according as all its intended conditions are fulfilled or not.
Note that the proposition “When/if X occurs, then A will do W” does not strictly tell us what A will do when or if X does not occur; we should perhaps rather state more clearly “Only if X occurs, A will do W” to distinguish this from “Whether X occurs or not, A will do W”. We may classify personal conditionals as a category of de re propositions, different from natural, temporal and extensional conditionals; they are not, however, to be confused with logical conditionals, and in particular not with material implication (which is a subcategory of de dicta proposition, and not at all de re as its name might lead one to suppose).
Detailed formal study of these and other such forms is beyond the scope of this book, but the job needs eventually to be done by someone.
Of course, regarding the woman’s volition, it may be influenced by the man’s appearance in her sight, whether such appearance is a mere condition or an influence relative to his volition.
For example, in a physiological context, we might refer to the general health and tonus of one’s body as the underlying landscape. Every action occurring within a favorable bodily context is easier, so in the long run it is best to keep fit without having to predict what one will eventually undertake. Similarly, with regard to the mind and soul.
Influence may therefore be likened to natural spontaneity in that its results are only probabilistic, never determining. See chapter 1.3.
One might add that, conversely, our behavior patterns sometimes affect our belief systems.
If telepathy exists, it would mean that the thoughts of one person could receive information originating in the thoughts of another. The latter might be an already influential person (a guru, a parent, a teacher, a lover, a friend), but possibly even an unknown person. This could occur in waking hours, or equally well in the course of dreams. It is difficult to account for all dreams with reference only to subconscious volition of scenarios, coupled with ‘spontaneous’ eruptions of content from the brain. Dreams occasionally contain totally unexpected scenes, seeming beyond one’s usual creative abilities and too complex for chance. Is the explanation for them perhaps that they occurred by intermingling of two or more minds? Do all minds meet in some ‘collective unconscious’, maybe?
A sort of telekinesis of among spiritual entities. This would be another hard to prove thesis of ‘parapsychology’.
I suppose that until modern times people believed the seat of the soul to be in the heart due to the experience of certain feelings in that region.
Whether emotions are necessarily ‘intentional’, i.e. aim in the direction of some object, is an issue. I think some do and some do not. The latter may just be bodily or mental phenomena without significance. In that case, no interpretation will be found for them. Another question we might then ask is whether all emotions are perceived at some level or they can exist without being ever felt. Again, I suspect the latter may be true.
Similarly for animals. For instance, in the case of a baby turtle rushing to the sea before predators get it, after its egg hatches on the seashore. How did the poor beast know the danger and where and how to escape it? I have not studied the matter; but may suggest possibilities. It may well be born with a nervous urge to run immediately, a sort of angst it gains relief from by running; the issue is then what makes it run in the specific direction of the sea? Perhaps the smell of the sea, the breeze, the light or the temperature influence it. In any case, we need not assume some mysterious source of innate knowledge on its part. It suffices to say that the influences, whatever they be, are such as to favor that behavior rather than other possible alternatives.
Note that I use a similar schema of ordered disjuncts in my workFuture Logic, with regard to ‘factorial induction’ (see part VI).
It is no accident that the same word “will” is used both for volition and for the future tense. It has the same etymology in either sense [O.E.willa].
But seeAppendix 1for some additional comments on this topic.