Charitable-R-Us

One of the central claims made by anti-tax opponents of welfare programs, social safety nets, and so on is that the necessary tax revenues erode the free generosity of charitable giving by grabbing up individual and corporate resources that might otherwise go towards helping the poor. (Not to mention the ultra-libertarian assertion that taxes are already a form of "forced labor," in Nozick's terms; but let's set this aspect aside here). So, carve carve away at social safety nets because decent caring wealthy people will carry the unfortunate and downtrodden in down-times through charitable giving. Is that so?