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When we think about the moral value of the story, I suppose we are talking about what morals or principles the story gives us in terms of how we should live our lives. If we think of this story, the obvious moral value seems to be that we should accept our lot in life and not try to change it or wish for anything different. The way in which the wishes of the White family all go horrendously awry points towards the way that we must be incredibly careful of what we wish for and recognise the dangers that are inherent in meddling with our fate. Let us remind ourselves of what the monkey's paw was created to demonstrate. The sergeant major tells the White family that it was made by a fakir with a specific purpose:
He wanted to show that fate ruled people's lives, and that those who interfered with it did so to their sorrow.
Of course, the Whites try to interfere with their fate, and they realise that such an attempt only brings them tragedy and sadness. Thus the moral value of this story seems to point toward an acceptance of our fate. We must not try to endlessly struggle against our destiny, but we must work with it.