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The thought experiment that Bernard Williams mentioned in his work "A Critique of Utilitarianism" to establish that utilitarianism is an incoherent and unintelligible theory of morality and does not hold much ground, especially when it comes to decision making under pressure and in high risk situations. But it crumbles altogether when once integrity and moral compass is at stake.
This paper will explore some arguments related to the thought experiment that Bernard Williams has illustrated highlighting both the scenarios of George accepting and rejecting the job offer and how it affects his morality. It will also compare the utilitarian view point in the light of this thought experiment with other moral view points to establish that all theories do not fulfill all the criteria of a complete moral theory and does not fulfill our psychological and emotional needs.
Suppose if George accepts the job offer. By accepting the offer at the chemical and biological warfare lab, George will certainly provide economic prosperity to his family (as he going through tough time), additionally he will also once get the job will be able to better influence the work of the lab, by either slowing down the process and/or building up support at the lab to deliberately protract the process. All these actions of George will lead to a greater utility as he will become an instrument in increasing utility and decreasing harm by slowing down the process. He will also be able to provide a better future for his family thereby reducing suffering which could have been caused to him and his family should he not have accepted the job offer. It seems like that from a utilitarian point of view this is an ideal situation. However, Bernard Williams argues against this position. He says that even though it seems that everyone is benefiting from George's decision, for him it is not a good choice as it will alienate him from his projects that define him. In other words, as George is opposed to biological and chemical weapon, as he has to forsake his integrity in order to take a decision to accept the job offer. Bernard Williams call this as one's projects and argues that one must not forsake ones integrity and values which define us. George in this case has a deep rooted belief against biological and chemical weapons (their production and use) and should not forsake this. He sates:
"It is absurd to demand of such a man, when the sums come in from the utility network which the projects of others have in part determined, that he should just step aside from his own project and decision and acknowledge the decision which utilitarian calculation requires. It is to alienate him in a real sense from his actions and the source of his action in his own convictions. It is to make him into a channel between the input of everyone's projects, including his own, and an output of optimific decision; but this is to neglect the extent to which his actions and his decisions have to be seen as the actions and decisions which flow from the projects and attitudes with which he is most closely identified. It is thus, in the most literal sense, and attack on his integrity."
It is prudent at this stage to state a few points about the thought experiment itself, as a utilitarian could argue against their need. Thought experiments are a good way to provide us with a way of producing knowledge by stepping out of the domain of the real and day to day affairs. They can be seen as an instrument of judgment of possibility as well as consideration of conceivability. However, they are constrictive in nature, and arbitrarily cut off and restrict the range of choices available to decide on a course of action. This thought experiment, is reflective of all the constraints related to thought experiments in general but in particular it distances us from the consequences making it remote to the action that he will take, thereby it is difficult to assess from a practical point of view whether the thought experiment is of significance or not. The author has intentionally given little background as to how George has landed into this situation and thus has opened a wide array of generalization and universal applicability inhibiting the use of imagination and intuition.
Martin Bunzl provides an interesting viewpoint regarding thought experiments related to ethics and especially to consequentialist theories in general,
"...require a level of detail usually lacking in thought experiments. And it is the attempt to provide the missing detail (both consequentialist facts and the weightings on those facts) that yields the paradigm of a thought experiment that is out of control" 
This is an interesting take as the whole idea of providing missing information is to make us see a different paradigm not apparent in the thought experiment itself.
Now let's see the scenario from a different vintage point. Suppose George does not accept the job offer as he is an ardent believer in safeguarding the world from biological and chemical weapons. In this case he has listened to his moral voice. However, even in this case (when George is not taking an action by not accepting the position) he is responsible for action through the doctrine of negative responsibility. Consequentialism will not recognize the difference between George not taking the job offer and safeguarding his integrity on one hand but has allowed someone else to take up the job (who is for the use of biological and chemical weapons) thereby is equally responsible for the harm that may cause. It doesn't make any difference if the action is taken by George or the other person as he is the one who let it happen.
Looking at the broader picture keeping this thought experiment in perspective, John Rawls gives another viewpoint.
"The main concepts of ethics are those of right and the good. The structure of an ethical theory is, and then is largely determined by how it defines and connects these two basic notions." 
From a utilitarian perspective, the right and the good is of no importance to the decision making process. But from an deontological perspective it is not the badness or the goodness of the consequence that makes it wrong but the act itself is wrong. George is not permitted to act and take any decision if it violates the deontological constraint (certain things that we must not do, even if doing it produces overall better consequences, in this case George may slow the process of weapon production and/or make a substantial effort is convincing other people to support his viewpoint). If George thinks of his act as a right act then it has to derive from its motive and as per Kant the motive is to be found in the act of duty rather than the inclination (George's sense of duty will emerge from his strong belief against production of these weapons).
Even though the action George will take will devoid him of pain and will give him pleasure but it will not be a free action and will be subject to the laws of cause and effect. If he does not take the job and if he doesn't on the idea that because he respects the moral law of so many people dying he will be the one who will eventually be the participant in it. By following a utilitarian viewpoint George has retracted his autonomy to take action, as he is bounded by the effects of what will happen, and his own will be shattered. Thereby he is not being true to himself and is losing true freedom. George may go ahead with not accepting the job offer but his contemporary will; thereby it will not be a universal principle. George should not act only because he has a duty towards others, to act and safeguard their interest; self interest is not the reason why he should do the right thing.
One may also consider George's action not to be seen in the future consequences that it will bring, but in the past as well, how he landed in this situation, what are he motives which led to him being against the development of chemical and biological weapons. There are other considerations that need to be brought in than the consequences of the action in determining what he should do. These considerations other than the value of the consequence of the action that needs to be considered in determining what he should do. A consequentialist will say to George to let the idea go as it will prevent greater harm or will do greater good. Ross  suggests that there is no universal law in this. For him one value can be overriding by another value provided it relives the distress. George action of taking up the job will be an unethical kind of expediency and will put undue pressure on George to take up the burden of morality for the whole human kind on his shoulders.
Alternatively, George can see the whole issue from a different perspective altogether. He should not see the whole situation as being what is right or wrong but should focus on what is just, humane and generous. By doing this, he will not only see the moral dilemma as a focus but will be able to see his life as whole and his position in it. It will help him in acquiring a kind of a virtue and will take the stress of the moral burden of duty towards the whole mankind that he is trying to safeguard.
On the other hand this approach to decision making will be more introvert with the focus on fulfilling the demands of the "I" rather than the combined good of all. Furthermore, it abandons the moral universal principles and gives power to the individual (in this case George) to make his own judgement. It dodges the important moral issues without assuming a definite position.
Looking at this thought experiment and its conclusion, we reach a point where our approach to morality needs to be somewhere between this completely impartial and integrity-sacrificing mode and the danger of a completely subjective/relativist mode. The whole argument above clearly states that thought experiments can provide us with a way of thinking on issues but are limited in scope and should be used with caution.
"Thought experiments are profitably compared to compasses. A compass is a simple but useful device for determining direction. Nevertheless, it systematically errs in the presence of magnets ... it becomes unreliable near the North Pole, in mine shafts, when vibrated, in the presence of metal ... experts will wish to use the compass as one element in a wider portfolio of navigational techniques. Analogously, thought experiments are simple but useful devices for determining the status of propositions. Sadly, they systematically err under certain conditions and so are best used with sensitivity to their foibles and limited scope"