Equality,” wrote Balzac, “may be a right, but no power on Earth can convert it into a fact.”

Just ask any schoolchild who has watched some classmates breeze four grades ahead in the maths curriculum as others struggle to complete their daily assignments. Life is rife with inequality: some people are good-looking and others plain, some clever and others slow, some soar to popularity while others long to be noticed.

No wonder we are so preoccupied with inequality, and no wonder our conversations about policy solutions leave off many of the inequalities that most worry us. The world is full of problems, but public policy recognises only those for which there’s a reasonable chance the Government might attempt a solution. Any other “problem” is simply a sad fact and will remain so.

If we want to have a public discussion about inequality, the first thing we have to do is define which sorts of inequality meet the definition of a “problem”. We then need to decide which of these problems should be solved. Not every problem qualifies.

The history of public policy is littered with “solutions” that turned out to be worse than the problem they were supposedly solving — the political equivalent of the proverbial fool who blows off his own head to cure his headache.

These steps are quite obvious and yet quite often forgotten. Some eye-popping figure about inequality is cited; anecdotes are sprinkled hither and thither; some dire predictions are made; and the whole thing closes with a moral exhortation to do something.

Over the next few months, Bloomberg View will be contributing to this conversation on inequality — how government policies contribute to it, whether government policies can and should reduce it. So let’s start at step one and proceed to step two.

We will begin by excluding the “sad facts”: the large swaths of inequality that the Government probably will not attempt to solve because the possible solutions would be politically impossible or morally abhorrent. The Government isn’t going to find you friends, nor can it get you a loving spouse or a better singing voice. On the other hand, the Government is pretty good at moving money around, so we tend to spend a lot of time talking about income inequality.

Yet even income inequality turns out to be surprisingly ill-defined. It is a melting pot into which we throw wealth inequality, wage inequality, inequality of opportunity, inequality of political power, and often rigidity of socioeconomic class. Frequently, we also toss in the absolute, rather than relative, difficulties of a life in poverty. Yet no matter how hard we stir, these things cannot all be made into a single issue called “inequality”. They do not arise from the same sources, nor would they be eliminated by the same solutions. Fixing one will not necessarily fix another, and there is no comprehensive solution that will fix them all.

So which ones should we try to fix, and how?

I would cross income inequality itself off the list of priorities. Far greater concerns include absolute suffering among those with low incomes; a socioeconomic structure that seems to be ossifying into a hierarchy of professional classes; and a decline in income mobility, which is to say, in equality of opportunity. It does not really matter whether Bill Gates has some incomprehensible sum of money at his disposal. It does matter a great deal whether there are Americans in desperate want. And, of course, it matters whether anyone with the aptitude and motivation can become the next Bill Gates, or only a handful of privileged people who are already well off.

I also submit that the importance of the issue is inversely proportionate to the ease of solution. The Government is very good at taxing income of some Americans and writing cheques to others. (Whether you think it should do this is, of course, a different question.) It is very bad at preparing someone to live a solid and fulfilling life of work and community, which is one reason we mostly leave that job to parents.

The Government is also not well suited to creating a lot of satisfying and remunerative jobs. It can contribute to productivity and help companies to flourish, for example through basic research and by maintaining a competent legal and regulatory system. And it can directly create a few jobs providing government services; these have been, for many communities at many times, a stepping stone to the middle class.

But there are limits to how many jobs the Government can create without choking off the productive economy that funds the Government — not least, the existing financial limits imposed by state budgets already deeply overstrained by financial promises made to previous generations of workers. For the most part, the best the Government can do is to avoid stepping on the creation of satisfying and remunerative jobs; no nation on Earth seems to have figured out how to generate “good jobs” for everyone.

All this means is that there is no silver bullet for the Government to guarantee full employment and to solve structural inequality. The Government can do something, but it remains to be seen exactly what, and how much.

Over the coming months, my colleagues and I at Bloomberg View, along with outside contributors and readers, will be exploring how the Government adds to inequality, and what it could do to reduce it. We’re not crazy enough to think that we’re going to solve all of America’s problems. But we may be able to identify some that are solvable, and avoid some “cures” that would be counterproductive.

• Megan McArdle, a Bloomberg View columnist, writes on economics, business and public policy