This is the unedited version. The edited version appeared in Military Review in March-April 2002.
Abstract: The methods that the military currently uses to train and execute combat operations enable soldiers to kill the enemy effectively, but they leave the soldiers liable to post-combat psychological trauma caused by guilt. This is a leadership issue. I argue that combat training should be augmented by explaining to soldiers the moral justification for killing in combat, in order to reduce post-combat guilt. Soldiers deserve to understand whom they can kill morally and why those actions are indeed moral. I outline an explanation for that moral justification.
Military leaders are charged with two primary tasks—to train and lead units to fight effectively in combat in accordance with the war convention, and to care for the soldiers under their command. Military professionals generally hold these two tasks to be complementary, accepting General Rommel’s statement that “the best form of ‘welfare’ for troops is first class training.”
American military leaders have been very successful in their task to create combat-effective units. In response to the War Department’s World War II research that indicated that less than half of riflemen fired their weapons at the enemy in combat, the military instituted training techniques—such as fire commands, battle drills, and realistic marksmanship ranges—that resulted in much improved combat firing rates. 
Unfortunately, this improved combat effectiveness has come at a cost to soldiers’ welfare. The training techniques that leaders have employed to generate the advances in combat firing rates have resulted in increased rates of post-combat psychological trauma among combat veterans.
In this respect, “first class training” has actually been detrimental to soldiers’ welfare. Training which drills soldiers on how to kill without explaining to them why it is morally permissible for them to do so is harmful to them, yet that is the current norm. Modern combat training conditions soldiers to act reflexively to stimuli—such as fire commands, enemy contact, or the sudden appearance of a “target”—and this maximizes soldiers’ lethality, but it does so by bypassing their moral autonomy. Soldiers are conditioned to act without considering the moral repercussions of their actions; they are enabled to kill without making the conscious decision to do so. In and of itself, such training is appropriate and morally permissible. Battles are won by killing the enemy, so military leaders should strive to produce the most efficient killers. The problem, however, is that soldiers who kill reflexively in combat will likely one day reconsider their actions reflectively. If they are unable to justify to themselves the fact that they killed another human being, they will likely—and understandably—suffer enormous guilt. This guilt manifests itself as post-traumatic stress disorder (PTSD), and it has damaged the lives of thousands of men who performed their duty in combat.
In this article, I argue that military leaders’ important and legitimate role—that of transforming civilians into combat soldiers who are able to kill in defense of their country—carries with it the obligation to help their soldiers cope with the moral repercussions of their actions. Since military leaders train their soldiers in the skills required to kill others in combat, they owe it to them to educate them as well in the knowledge required to live with themselves in the years after combat. I contend that military leaders should augment current training by explaining to their soldiers the moral justification of killing in combat, and I outline such an explanation. I also suggest that this education would improve the Army’s mission effectiveness.
Section 1. Why Soldiers Deserve a Moral Justification for Killing
In this section, I offer a four-part argument that explains why military leaders should be concerned with the moral justification for killing in combat. It stems from their duty to care for their troops. First, their soldiers are human beings who naturally deem it morally wrong to kill other human beings who happen to be enemy soldiers. As a result, absent training that overcomes that moral aversion, most soldiers in combat would choose not to kill the enemy. Second, military leaders enable their soldiers to kill by utilizing training techniques—such as pop-up marksmanship ranges, fire commands, and battle drills—that emphasize reflexive (as opposed to reflective) action. Such techniques create a bypass around the normal moral decision-making process of an individual, so that soldiers act without first making the decision to do so. Third, while these techniques have greatly increased combat effectiveness, they have exacted a psychological cost on many of our soldiers. Many soldiers who have killed in combat—yet are unable to justify to themselves what they did—suffer from PTSD. Fourth, and finally, this problem can be solved by proactive leadership. Military leaders do not need to abandon proven training techniques. What they do have to do, however, is prepare their soldiers’ consciences for their post-battle reflections. They must help them understand that what they have taught them to do reflexively would be the same choice that they themselves would have made reflectively, because it is the morally right choice. They must also enable soldiers to make morally justified decisions in morally ambiguous circumstances. By doing so, military leaders can empower their soldiers to be able to live with clear consciences after they have justifiably killed for their country as their leaders expected them to do.
1.1 Most Soldiers Do Not Want to Kill the Enemy’s Soldiers
The starting point of my argument is an insight that should be banal, but it isn’t. It is that soldiers are people, too. And people are taught from their earliest days that it is wrong to kill another human being. “Thou Shalt Not Murder” is arguably the closest thing there is to a universally accepted moral norm. Yet, for some reason, military leaders expect those young men and women who become their soldiers to ignore their well-learned moral codes and to kill whenever they are ordered to. We should know better than that.
After all, research conducted on American soldiers in the Second World War suggested that most infantry soldiers chose not to engage the enemy, for primarily moral reasons. In Men Against Fire, Brigadier General S.L.A. Marshall, the official historian of the Central Pacific and European Theaters of Operations, described the problem in this way:
[The American soldier] is what his home, his religion, his schooling, and the moral code and ideals of his society have made him. The Army cannot unmake him. It must reckon with the fact that he comes from a civilization in which aggression, connected with the taking of life, is prohibited and unacceptable. The teaching and ideals of that civilization are against killing, against taking advantage. The fear of aggression has been expressed to him so strongly and absorbed by him so deeply and pervadingly—practically with his mother’s milk—that it is part of a normal man’s emotional make-up. This is his great handicap when he enters combat. It stays his finger even though he is hardly conscious that it is a constraint upon him.
Combat required a sharp break with many moral prescriptions of peacetime society. As easy as it seems to be for men to kill when their immediate group sanctions it, and as ambivalent as normal people often are about killing, it is still true that to kill another human being requires of most men from our culture an effort to overcome an initial moral repugnance. Under the requirements of the situation, men in combat were careful to hide this feeling, and it was not a subject of much discussion among soldiers. Killing is the business of the combat soldier, and if he is to function at all he must accept its necessity. Yet the acceptance of killing did not prevent the ambivalence revealed by such comments as that of a veteran rifleman who said, “I’ll tell you a man sure feels funny inside the first time he squeezes down on a Kraut.”
Lest we think that people are somehow fundamentally different today than they were in World War II, consider the experience of this Army officer in the 1991 Gulf War.
Well, later that evening, the battalion that I was supporting (as Engineers) hit four T-72s and a multitude of dismounts in trenches. The action lasted approximately ½ hour. Take note of this. The only soldiers who fired during that entire period were the tankers. They fired both main gun and coax. Not even [the engineer unit’s] .50 cals engaged the enemy. I have since often wondered what it would take to get a
While some may find the idea of military professionals being unwilling to kill in battle a bit embarrassing, we should instead think of it as encouraging. We want soldiers who choose to do only what is morally right, who kill enemy combatants yet protect all non-combatants, who can reintegrate into civil society after the war. What military leaders have to do, then, is explain to their soldiers why what they train them to do is the morally right thing to do.
1.2 Military Leaders Train Soldiers to Kill Reflexively
Still, despite this Gulf War platoon’s unwillingness to fire in combat, the military has made great strides in improving its soldiers’ firing rates since World War II. Whether or not
The modern day transitional (pop-up target) marksmanship ranges follow this advice. They enable soldiers to overcome their aversion to killing by conditioning them to act spontaneously to conditions that are combat-like yet morally benign. Retired infantry officer and psychologist Dave Grossman explains the process this way:
What is being taught in this environment is the ability to shoot reflexively and instantly and a precise mimicry of the act of killing on the modern battlefield. In behavioral terms, the man shape popping up [E-type silhouette] in the soldier’s field of fire is the “conditioned stimulus,” the immediate engaging of the target is the “target behavior.” “Positive reinforcement” is given in the form of immediate feedback when the target drops if it is hit. In the form of “token economy” these hits are then exchanged for marksmanship badges that usually have some form of privilege or reward (praise, public recognition, three-day passes, and so on) associated with them.
This conditioning, this training on pop-up marksmanship ranges, does enable soldiers to kill on the battlefield, and the 1993 Battle of Mogadishu provides great evidence of that. In that 17-hour fight, a few hundred soldiers from Task Force Ranger and the 10th Mountain Division battled thousands of Somalis in fierce, urban combat. The Americans suffered only eighteen dead, while they killed an estimated 300-1000 Somalis. They achieved this extraordinary casualty ratio by being well trained. Based on extensive interviews with the soldiers involved, journalist Mark Bowden wrote a best-selling account of the battle, Black Hawk Down, which includes these revealing comments:
[Ranger Sergeant Scott] Galentine just pointed his M16 at someone down the street, aimed at center mass, and squeezed off rounds. The man would drop.
Just like target practice, only cooler.
[Specialist John] Waddel shot the man. In books and movies when a soldier shot a man for the first time he went through a moment of soul searching. He didn’t give it a second thought. He just reacted.
In an interview with CNN/Frontline, Ranger Private First Class Jason Moore described his willingness to kill in these words:
I just started picking them out as they were running across the intersection two blocks away, and it was weird because it was so much easier than you would think. You hear all these stories about "the first time you kill somebody is very hard." And it was so much like basic training, they were just targets out there, and I don't know if it was the training that we had ingrained in us, but it seemed to me it was just like a moving target range, and you could just hit the target and watch it fall and hit the target and watch it fall, and it wasn't real. They were far enough away so that you didn't see, or I didn't see, all the guts and the gore and things like that, but you would just see this target running across in your sight picture, you pull the trigger and the target would fall, so it was a lot easier then than it is now, as far as that goes.
Clearly, modern military leaders are doing half of our duty—we are training our Soldiers to fight effectively on the battlefield. We are doing so by utilizing techniques that enable soldiers to fire their weapons at the enemy despite the natural moral reservations that they may harbor. By conditioning combat soldiers to reflexively engage targets and by giving them leaders who issue fire commands, military leaders greatly reduce moral deliberation for the soldier in combat.
At one level, this training accomplishes both aspects of military leaders’ duty—it accomplishes the mission, and it takes care of soldiers by keeping them alive. At a deeper level, however, this approach is inadequate. It makes soldiers able to kill, even if they are not willing to do so. It prepares soldiers to deal with the enemy, but it does not prepare them to deal with their own consciences. It keeps them alive, but it leaves them in a life that may be less worth living.
1.3 This Training Has Been Harmful to Combat-Veteran Soldiers’ Psyches
Training soldiers to kill efficiently is good for them because it helps them survive on the battlefield. However, training soldiers to kill without explaining to them why it is morally permissible to kill in combat is harmful to them because it can lead to psychological trauma. When soldiers kill reflexively—when soldiers kill because of military training that has effectively undermined their moral decision-making processes—they conduct their personal moral deliberation of their actions only after the fact. If they are unable to justify what they have done, they often suffer guilt and psychological trauma.
Many combat soldiers experience feelings of guilt in the months and years after their wartime actions. Listen to the words of some combat veterans who performed their wartime duties as their leaders had trained them to do.
First, reflections from a young soldier who fought in
Well, that day, I had absolutely no ethical or moral problems with pulling the trigger and taking out as many people as I could. And being back here, years later, I think that they had wives, children, mothers, sons, just like I have a mother and a dog, and all these things. Our government sent us there to do a mission, and I'm sure somebody was paying him to do a mission. [I just] reali[zed] that he was another human being, just like I am. And so that's hard to deal with, but that day it was too easy. That upsets me more than anything else, how easy it was to pull the trigger over and over again…It took a long time to wear off, a real long time, because we were still there for a little while, and then when we came back you were still sort of riding the waves of what happened. And I know for me, the hardest thing to live with is knowing that you took another human life, for no other reason than your government told you to. That's hard. I mean, I'm sure it's been said before but here I would have [gone] to jail for exactly what I did over there and got medals for.
At least one senior enlisted soldier who killed in the Gulf War may have found his actions to have been too much to live with. An officer in his unit described the situation:
Let me give you the results of one person who did kill. His name was 1SG
Doe. He was a 12B, combat engineer first sergeant. Known as hard charging and didn’t put up with much bullshit. While in Desert Storm, he was assigned to my unit. He volunteered for a bunker searching mission. Upon coming to one particular bunker, he heard movement inside. Without bothering to clear the bunker, he yelled at the people inside to come out. When they failed to respond, 1SG Doe fired three rounds from his .45 pistol into the bunker. The noises ceased. They then entered the bunker. 1SG Doe seemed okay with the fact that he had killed two Iraqis at the time. It was a very disturbing experience for everyone else. Note this. He is now at the psychiatric ward at Walter Reed. The pressures of his actions during Desert Storm and
I will address that rather disturbing final sentence in upcoming paragraphs, but first listen to one more recent example of a soldier who struggled to justify his combat actions.
Ray, a veteran of close combat in the 1989
These soldiers were “good” soldiers who effectively killed the enemy when their nation and its leaders asked them to do so, only to later suffer guilt. Their experiences are not exceptional. In fact, one non-commissioned officer who fought in the Battle of Mogadishu acknowledges that many of the veterans of
1.4 This is a Leadership Issue
We should not be surprised that soldiers—such as 1SG Doe—suffer debilitating guilt over killing in combat when even their own leaders believe that their actions were unjustified. Soldiers who perform their duty in combat deserve better from their leaders.
If killing another person were never morally justified, then the military profession would be an evil one. Because, however, at least some killing in war is morally justifiable, military leaders have a duty to understand that justification, to explain to their soldiers why it is justified, and to train their soldiers to kill only when it is justified.
Military leaders who train their soldiers to kill in combat without explaining to them the justification for that killing are treating their soldiers as commodities to be used, not as persons to be respected. A values-based Army can and must do better than that.
Section 2. A Proposed Justification for Killing in War.
In this section, I offer a moral justification for killing in combat that is based on the principle of self-defense. This justification is consistent both with legal judgments made in civilian society and with Judeo-Christian moral teaching, so it should be understandable and acceptable to the great majority of American military personnel.
2.1 Refuting a Concern about Offering a Moral Argument
Before explicating the justification, though, I will address the reasonable concern that teaching soldiers the morality of killing would actually harm them by fostering hesitancy on the battlefield. Soldiers who are morally aware of their actions, after all, may be less willing to respond immediately to orders to kill. Such delay could, in turn, cost them their lives and compromise the mission.
In fact, the opposite is more likely true. Soldiers who are confident that killing in war is justifiable and that their leaders are morally informed would be more likely to respond quickly to orders and combat stimuli. Akin to religious crusaders, they would fight with the assurance of moral rightness. Moreover, warfare is becoming increasingly decentralized and ambiguous, so military leaders must move beyond reflexive training. We require of our soldiers that they make life-or-death decisions in the absence of fire commands or obvious stimuli. In operations other than war, soldiers have to make judgment calls that cannot be “trained” in the traditional sense. If we want to maximize our military effectiveness, we must empower our soldiers to make morally informed decisions about when and whom to kill.
The words of an infantry battalion commander during OPERATION JUST CAUSE in
“Let me tell you the bottom line on our rules of engagement, your conscience…your moral conscience is going to carry it. I don’t want you shot; I don’t want your buddies shot…you don’t have time to call me to clear fires. Make your best call.” 
That was an enormous burden to place on soldiers whose “moral consciences” had not been prepared for the moral complexities of combat. It is, I think, soldiers who do not understand the justification of killing who would be more likely to hesitate on the modern, low-intensity, “make your best call” battlefield.
2.2 Justified Killing in Self-Defense
At long last, I will now offer an outline for a moral justification of killing in combat. I developed this by examining the elements that provide legal and moral justification to killing in self-defense in civilian circumstances. I do not have the space here to provide a theoretical discussion of what morality is, but my justification does presume a rights-based morality that is consistent with Judeo-Christian and Kantian moral thought.
Here is the bottom line. It is morally permissible to kill another person when these certain conditions are met: that other person has made a conscious decision to threaten your life or liberty; that person is imminently executing that threat; and you have no other reasonable way to avoid the threat. Moreover, it is morally obligatory to use the force necessary to protect an innocent person from such an attacker as long as you have the means to do so, and especially when you have voluntarily assumed the obligation of protecting that innocent person.
For example, if a person intentionally attacks you with a lethal weapon and you have no reasonable way to escape, then you are justified in using lethal force to protect yourself. Likewise, if you are a police officer, then you are morally obligated to use the force necessary to defend the life of an innocent person against an attacker.
All four conditions—a conscious choice, a threat to a value comparable to human life, an imminent threat, and no life-saving option—must be met to ensure that the killing is morally justified by self-defense.
For example, if the “attacker” were a two-year old child or a sleepwalker, then she probably would not have made the choice to cause the threat and thus would not be morally responsible for it, so killing her in self-defense would not be justified (although it might be excusable). The “conscious choice’ condition would not have been met.
If, likewise, the attacker were a robber who only wanted your or someone else’s wallet, then the value at stake would not justify killing him. The “value comparable to human life” condition would not have been met. We should not kill a human being to prevent mere monetary inconvenience and loss.
If, for example, someone threatened to kill you or someone else next week, then you would not be justified in killing him today. The threat must be imminent. The choice to kill in self-defense must be in response to the attacker’s intentional actions, not merely his intentions.
Lastly, if the attacker were a knife-wielding person confined to a wheelchair and you were fully mobile with access to a staircase, then you would not be justified in killing him. Instead, you should simply escape up the stairs. There must be a “forced choice” between fundamental values. If there is a way to escape the situation without compromising life or liberty, then you are obligated to choose that way and are thus prohibited from using lethal force in self-defense.
These examples illuminate the four necessary elements of justified killing in self-defense:
1) a morally responsible attacker;
2) a threat to a value worth killing for (life or liberty);
3) an imminent threat;
4) no other option to avoid the threat.
Significantly, these conditions also apply to justify killing an accomplice of an attacker. For example, if a gang member were chasing you with a knife with the intent to kill you, and you had to escape from the room, and another (unarmed) gang member were consciously blocking your escape, then you would be justified in using lethal force against your attacker’s unarmed accomplice. In legal terms, that person would be a conspirator to attempted murder. Morally, that accomplice would have made the choice to threaten your life, and you would have had no other way to avoid the imminent threat.
These conditions are more stringent than those required for legally justified homicide in self defense, yet they are met when soldiers kill enemy soldiers in combat.
2.3. Justified Killing Applied to War
When soldiers kill enemy soldiers in war, they meet the conditions of justified killing in self-defense.
The enemy soldiers are morally responsible for the threat that they pose. At some level, they chose to be soldiers, and they must know that they are at war against other people. Fully informed volunteers, of course, are more responsible than poorly informed conscripts, yet the fact remains that even conscripts chose to become soldiers. They had other options, however unpleasant they may have been. Human beings, after all, are not responsible for circumstances beyond their control, such as whether their nation goes to war. They are, however, responsible for the choices they make within those circumstances. People who make the choice to be soldiers in war are morally responsible for the threat they pose to their enemy’s soldiers.
Soldiers do fight to defend values that are worth killing and dying for. At least, they hope so. In a just war, that is the case. Because the moral responsibility for going to war lies with political authorities, and because the intentions of political authorities are often opaque, then soldiers should be largely immune from judgments about the just ends of a war. Therefore, unless soldiers have strong reason to be convinced that their war is being fought for values other than the defense of life and liberty, then they can justifiably assume that they are fighting in defense of those fundamental values.
Soldiers also do face an imminent threat from enemy soldiers. All enemy soldiers are either direct threats or accomplices to direct threats. They all act for the same end—to deny the soldier and/or those he is defending their rights to life and liberty. Soldiers have no recourse to a “higher authority” to defend them. They must fight, or they and other innocent persons will lose their cherished rights.
Finally, soldiers do not have a non-lethal option. If they flee before the enemy, the threat will follow them. Again, there is no “higher authority” to offer protection to them and to those who depend on them to defend their lives and freedom.
Therefore, not only is it morally permissible for soldiers to kill enemy soldiers in combat, but also it is morally obligatory for them to use the force necessary to defend the rights of those who depend on them. Soldiers are the last line of defense for the rights of life and liberty.
What I have proposed here is only a “user-level” justification for killing in combat. I realize that this argument is incomplete, but my goal is to spark institutional discussion on this important topic. I think that its further development and dissemination to the force would significantly enhance the moral standing of the military profession. The conditions that I have outlined are theoretically robust, and perhaps a more complete explanation of their foundation in rights theory could be offered as an element of officer and non-commissioned officer professional development.
Honest reflection on the moral demands of military service should play a part in the Army’s transformation. Soldiers who are empowered to make well-reasoned moral decisions would be more likely to exercise proper initiative and less likely to err by commission or omission. Rules of engagement are by nature static; the battlefields of the future will be fluid. The Army must grow soldiers who can think for themselves.
Not only should the Army include the moral justification for killing in combat in its training because it would enhance the Army’s effectiveness, but also because it is simply the right thing to do. The profession of arms is a noble calling, and military leaders perform their duties honorably. We devote their lives to preparing our soldiers—mentally, physically, materially—for the rigors of combat. We conduct demanding, realistic training; we keep them physically fit; we equip them with the best weapons. Unfortunately, we are unwittingly failing to prepare them morally, and in doing so we are failing in our duty to care for our soldiers’ welfare. Currently, military leaders are leaving our soldiers unprepared to deal with their post-combat consciences and unprepared to make morally right decisions about whom to kill in morally ambiguous circumstances. This is a leadership problem that is solvable, and it demands our attention and action.
References and footnotes
 LTC Dave Grossman, On Killing: The Psychological Cost of Learning to Kill in War and Society (New York: Little, Brown, and Company, 1995), 189.
 The prevalence and degree of PTSD among combat veterans is a disputed issue.
Dr. Jonathan Shay (Achilles in
 It goes without saying that military leaders must first understand the moral justification themselves before they can teach it to their subordinates. Therefore, military leaders have a duty to develop their own skills of moral discernment. I owe this good point to MAJ Tony Pfaff.
 Marshall, Men Against Fire, 78.
 Many military officers disputed
There are reasonable explanations for officers’ unwillingness to accept
Furthermore, some officers objected to
 Marshall, Men Against Fire, 78.
 See Roger Spiller, “S.L.A. Marshall and the Ratio of Fire,” Journal of the Royal United Service Institution 133 (December 1988) 63-71; and Russell W. Glenn’s Reading Athena’s Dance Card: Men Against Fire in
Naval Institure Press, 2000) 134-136.
 Samuel Stouffer, et al., The American Soldier: Combat and Its Aftermath,
vol. 1 (Princeton, NJ: Princeton University Press, 1949) 85-87.
 CPT John “Ike” Eisenhauer, personal email correspondence with author,
November 1997. CPT Eisenhauer is an outstanding officer whom I greatly respect.
His candor on this issue is admirable; others with whom I have spoken share his sentiments, but they are not willing to “be quoted.”
 The practice of employing psychologists to train men to kill in combat is not a post-WWII phenomenon. See Joanna Bourke’s An Intimate History of Killing (Great Britain: Basic Books, 1999) 57-90.
 These figures are from Grossman, 35, who references
 Marshall, Men Against Fire, 79.
 Marshall, Men Against Fire, 71, 81-82.
 This explains why nearly all of the officers that
 Marshall, Men Against Fire, 82.
Harper & Row, 1974) 186-189.
 Grossman, On Killing , 143. He identifies the researchers as Kranss, Kaplan, and Kranss.
 Marshall, Men Against Fire, 82.
 Grossman, On Killing, 254.
 Why did the Rangers and 10th Mountain infantry soldiers fire their weapons while the Gulf War engineer platoon did not? Perhaps it was their level of training, their level of conditioning.
 Mark Bowden, Black Hawk Down: A Story of Modern War (
Monthly Press, 1999).
 Bowden, Black Hawk Down, 64.
 Bowden, Black Hawk Down, 46.
 Not his real name.
 Eisenhauer correspondence.
 Grossman, On Killing, 240.
 Discussion with author, 20 November 1999,
 Discussion with author, 20 November 1999,
 Lieutenant Colonel Harry B. Axson, commander of the 2nd Battalion, 504th
Parachute Infantry Regiment during OPERATION JUST CAUSE, quoted in
Army Training and Doctrine Pamphlet 525-100-2, Leadership and Command on the
Battlefield (USA TRADOC, Ft. Monroe, VA:1993) 21-22.
 See the author’s M.A. thesis, “Soldiers, Self-Defense, and Killing in War,”
available at: http://scholar.lib.vt.edu/theses/public/etd-41998-18346/etd-title.html
 See Richard Norman, Ethics, Killing, and War (
 Whether or not it would be justified to threaten the robber with lethal force in order to prevent the robbery is another issue.
 Although my argument addresses what are traditionally considered jus in
bello concerns, I reject the absolute jus in bello/jus ad bellum distinction held by
 See the author’s M.A. thesis, “Soldiers, Self-Defense, and Killing in War,” available at: http://scholar.lib.vt.edu/theses/public/etd-41998-18346/etd-title.html
 I presented an earlier draft of this paper at the 2000 Joint Services Conference on Professional Ethics (JSCOPE). I want to thank all those who have provided encouragement and comments for my revisions, especially SAMS 2001/2 Seminar 2,