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The felicific calculus was an algorithm formulated by Jeremy Bentham for calculating the degree or amount of happiness that a specific action is likely to cause, and hence its degree of moral rightness. It is also known as the "Utility Calculus".
The calculus was proposed by Bentham as part of his project of making morals amenable to scientific treatment. Since classical utilitarians considered that the rightness of an action was a function of the goodness of its consequences, and that the goodness of a state of affairs was itself a function of the happiness it contained, the felicific calculus could, in principle at least, establish the moral status of any considered act.
Variables, or vectors of the pleasures and pains included in this calculation—which Bentham called "elements" or "dimensions"—were:
1. You help the young mother who's about to give birth
2. You help the young woman's husband.
3. You help the old man.
The possible outcomes are as follows:
1. Attending to the mother first is the primary concern of the doctor. The death of both mother and child is almost a certainty if he/she does not act now, where as the death of the men is uncertain. Plus, the pain of the mother is clearly greater than theirs at this moment in time. There is a greater richness and purity in saving the life of a young child who has, in all probability, a long happy life ahead. Therefore the extent and duration of the utility created by these two people is a clear likelihood.
2. Attending to the young husband is the next priority. The pleasures of a new family—its intensity, duration, extent, richness and purity—are all clear probabilites. If the doctor attend him first in all probability his wife and child would be dead. The mean would then experience pain (Pleasure Calculus). The pain experienced by the widowed husband is likely to outstrip any pleasure to be gained from continued life without his loved ones.
3. Attending to the old man is your last priority. The duration and certainty of his future pleasure are under question owing to his age. He has all but lived his life. This is sometimes known as the 'good innings' argument, according to this line of argument, the older you are the less claim you have to life.
Critics point that the happiness of different people is incommensurable, and thus a felicific calculus is impossible in practice.