Should the wealthier members of society be forced to pay through taxation, for the poorer members? If so, how much?

Uh, been that way for a very, very long time.

It's called a progressive tax system and that's what we have. In fact, once you factor in the Earned Income Credit, the poor get ' paid ' by the Rich in the sense that they get 15% more back in a ' refund ' than they paid in.

This already takes place.

They already do

The very basis of civilization, is for those that have, to take care of the have-nots! Taxation, or voluntary contributions, of enough to make it possible for the least of our citizens to live a safe, healthy, and comfortable life, should be a minimum. Any less, is to fail to meet your responsibility as a successful person. Any less is to hasten the end of civilization.

This is both a common belief and common practice. The debate is over how much more should they pay. Let's say both a rich and a poor person pays 10% taxes (makes the math easy); the rich person earns $200,000 / yr; poor person earns $20,000 / year. Each has a family of 4 and a $3000 / exemption or $12,000 of exemptions rendering the rich person's taxable income at 200,000 - 12,000 = $188,000 and the poor person's taxable income 20,000 - 12,000 = 8,000. The rich pays 0.1 x 188,000 or $18,800 taxes, the poor pays 0.1 x 8,000 = 800 in tax, making the rich pay 100(18800)/200000 = 9.4% and the poor pay 100(800)/20000 = 4% which means the rich pays 2.35 times more tax than the poor person under the same tax rate. Is this fair? I think so as the rich can handle more tax and maintain a higher living standard.

This doesn't even have to be seen from a moral standpoint.

Even the rich have a lot to lose when the people around them can't afford food and healthcare. If a poor man's mother is going to die of something that could be repaired by expensive surgery, is he morally obligated to steal to save her, or morally obligated to let her die? If he chooses to steal and innocent people die in the process, this becomes the rich man's problem. You can't pay to bring someone back to life.

Enough is the simple answer, but how that works out in practice is a loaded question.
Christianity has always recognized that the rich have an obligation to help the poor - it's called noblesse oblige. Jews and Muslims also recognize this principle. In our secular world, we might need another good reason to justify taxation and the distribution of wealth. And I have one: Fairness.

I see no logical reason why this should be the case , we have had charities for thousands of years and socialism for at least 100 and nothing has been cured or solved or improved just massive dependency and a sense of entitlement that defies belief