What do the children "Want" and "Ignorance" symbolize in A Christmas Carol?

The children "Ignorance" and "Want" in A Christmas Carol symbolize the poor in Victorian society. Their inclusion in the story is meant to demonstrate how the poor have been forgotten and neglected by the middle and upper classes.

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Ignorance, the boy, can be interpreted as symbolizing the ignorance that keeps the poor, in Victorian England, poor. Without education, what chance can they have of bettering their situation? If people are ignorant, it is hard for them to know what to do to find a job, to know how...

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Ignorance, the boy, can be interpreted as symbolizing the ignorance that keeps the poor, in Victorian England, poor. Without education, what chance can they have of bettering their situation? If people are ignorant, it is hard for them to know what to do to find a job, to know how to keep a job, and so on. If, however, the poor are given a chance to be educated, and to feel the care of society at large, then they will be much better positioned to help themselves. Want, the girl, can be interpreted as symbolizing the sheer lack of resources and the need experienced by the poor. Although we often associate "want," in the twenty-first century, as a pure desire for something that we do not actually need, the word itself does mean to be needy or to have unmet needs. The Victorians would have understood want to signify these meanings.

However, I do think it is possible to interpret Ignorance in a different way: he could symbolize the ignorance of people like Scrooge who refuse to acknowledge the plight of the poor, who purposely remain ignorant of their needs and pain. Back in Stave 1, for example, when the gentlemen come collecting for the poor, they tell Scrooge that many of the poor would rather die than go to the prisons or workhouses. Scrooge responded, in part, "excuse me—I don't know that," and he claims that it is "not [his] business" to know of other people's problems and lives. The gentlemen tell him that he "might know it," essentially, if he cared to. Scrooge purposely remains ignorant, and this ignorance, if adopted by more and more people who could actually help those less fortunate, will lead to greater suffering for the poor and could spell the "Doom" that the Ghost of Christmas Present warns of.

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Confronted by the dirty, emaciated figures of Ignorance and Want, Scrooge suddenly realizes how "the other half" lives—what miserable, poverty-stricken lives they're forced to lead. Things were different at the start of the story: then, the miserly old skinflint sent a couple of charity collectors packing with a flea in their ear. He made it perfectly clear that he couldn't care less about the plight of the poor and underprivileged.

Unpleasant and mean-spirited though Scrooge's behavior may have been, it was by no means unusual at that time. Like many of his fellow countrymen in mid-19th-century England, Scrooge regards poverty as a sign of individual moral weakness. If people are poor, thinks Scrooge, then it's their own fault. But after seeing the allegorical figures of Ignorance and Want—the two great evils of Victorian society—he's forced to change his whole outlook on life.

It's instructive that Dickens uses two children to represent Ignorance and Want. They are wholly innocent, and so it would be ludicrous for Scrooge or anyone else to hold them personally responsible for their desperate plight. Dickens wants his readers to understand that poverty is generally not the result of individual bad choices, and that everyone, whatever their station in life, has a moral responsibility to help those less fortunate than themselves.

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In Stave Three, Scrooge encounters two children hiding beneath the skirt of the Ghost of Christmas Present. They are two children, called Ignorance and Want, whose appearance shocks Scrooge:

Where graceful youth should have filled their features out, and touched them with its freshest tints, a stale and shrivelled hand, like that of age, had pinched, and twisted them, and pulled them into shreds.

These children are symbolic of the poor in Victorian society, specifically the industrial poor who toil away in England's workshops and factories, struggling to make ends meet and, so very often, the victims of extreme deprivation.

Moreover, the placement of these children under the ghost's skirt is symbolic of how the poor have been largely forgotten by the Victorian middle classes. They are, quite literally, hidden from public view, forgotten and neglected by the wider society. 

By presenting the poor as two half-starved children, Dickens forces his readers to sit up and take note of the realities of industrial life, particularly those who become its victims.

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Ignorance and Want represent society’s abandonment of the poor and the consequences of that abandonment.

Above all else, A Christmas Carol is allegorical.  Dickens was a strong proponent of taking care of society’s poor and downtrodden, and this is why he chose to represent them in children.  Most people will have more sympathy for children than adults.  Dickens wanted to make the case that the adults we see as criminals started out as poor and abused children.

This boy is Ignorance. This girl is Want. Beware them both, and all of their degree; but most of all beware this boy, for on his brow I see that written which is Doom, unless the writing be erased. (Stave 3)

Ultimately, the little boys will turn into pickpockets and thieves (like Oliver Twist), and the girls will turn into prostitutes (like Nancy).  Unlike most high and might Christians of the Victorian era, Dickens did not look down on the poor.  He even started a charity house for prostitutes, because he recognized that these were the people that society threw away.

Dickens tells us to beware ignorance more than want.  This is telling, because it demonstrates the root of the problem.  If our poor are not educated, they have no chance to escape the cycle of poverty.  Want, or hunger and need, is important.  It comes from ignorance though.  We need to educate and take care of our young people so that they don't have children that are just as badly off as they are.

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The children represent those who were living in poverty, with no hope of improving their lot due to lack of education and lack of opportunity. The Ghost of Christmas Present was sheltering them as representatives of all those who were discounted and decried by Scrooge. Instead of contributing to charitable organizations that could help improve their lot, Scrooge's action was to ask "Are there no prisons?...Are there no workhouses?"

The Ghost reminds Scrooge of his unfeeling words after warning him of the consequences to all of Scrooge's society if the children, and the life conditions that they came from, continued to be unaddressed.

Beware of them both,...but most of all beware this boy (Ignorance), for on his brow I see that written which is Doom, unless the writing be erased.

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