‘What is truth?” said jesting Pilate – in Bacon’s famous phrase. What is public and what is private? This is a question that people in higher education could well ask themselves in 2015.

They should ask not so much because of the scattering of private – some for-profit, some charitable – institutions that has been allowed into the (English) system either through the front door by being given degree-awarding powers or university titles or via the back door by being able to tap into student loans.

Most are small niche players. Their students are counted in the hundreds, not the thousands. They are no threat – yet – to the established universities. Maybe they never will be.

The question needs to be asked because the mainstream, still-just-about public, system is becoming increasingly “private”. Universities now conceive of themselves as corporate organisations driven by business plans.

We need to knock three myths on the head. The first is that the public-private distinction has something to do with legal status. All public universities, in effect, have been legally established as independent corporations.

The precise terms in which this independence is expressed differ – royal charters, statute-led instruments and articles of government, companies limited by guarantee. But the effects are the same – and not as different as we imagine from the governance of so-called private institutions.

The only substantial difference is that all public institutions are regarded as charities – and regulated accordingly. Only some of the new private institutions fall into the same category.

The second myth is that the distinction has something to do with receiving public money. Some private colleges that have attracted the beady attention of Margaret Hodge’s public accounts committee get more public money in proportion to their turnovers than the London School of Economics, one of our world-class universities.

The third myth is that private institutions are freer from state interference. They may not have to conform to the control exercised by the Higher Education Funding Council for England through its financial memorandum or may be more sheltered from the requirements imposed by freedom of information legislation. But private institutions owe their licence to operate to the state, by being given degree-awarding powers or university titles (which can be revoked). Private colleges are also far more likely to be exposed to censure by the Quality Assurance Agency. The more public money they receive, the more they will be bound by regulation.

None of this is surprising. Higher education is just playing catch-up. The Sercos and Capitas have long grown fat on public money. The line between public and private has also become hopelessly confused – as, for example, when the (French) state-owned EDF supplies privatised power to large swaths of the country.

No – the real problem is not the emergence of a puny private sector in higher education. Let the public accounts committee take care of rip-offs that are too blatant. Let the Department of Business, Innovation and Skills have to eat its free-market words by regulating the messy, inefficient and incoherent system it has created since 2010. The real problem is what is happening to public higher education. Put simply, we seem to be increasingly losing our sense of public responsibility and wider social purpose.

It is not just leftish, and therefore disposable, dreams of “widening participation” that are threatened by this loss. So, too, is the mainstream drive to include the “non-standard” majority in our universities. In its place is now a reputation game driven by the “satisfaction” of existing student customers, in other words the haves, not the have-nots.

Also threatened by the loss of this public ethos is the space that disinterested science and scholarship need in order to flourish. In its place is the inflationary gamesmanship of the Research Excellence Framework – “REF 2014 is dead, long live REF 2020!”

If public universities behave in ways that are increasingly entrepreneurial, how can they complain if private colleges bemoan the absence of a level playing field – for example, in terms of access to public money?

It would be naive to pretend it will be easy to reclaim that sense of public responsibility. The pressures on universities, and especially their leaders, to embrace corporate values and adopt quasi-business strategies are enormous. Nor in seeking to restore this public ethos can we place much trust in the quantifications of economists, and their reductionist attempts to define the public good as a residual when all possible private benefits have been calculated.

Ultimately, this is a moral issue that can only be addressed through courage and imagination – and politics. But the problem is not a few private colleges. The New Testament parable of (their) motes and (our) beams comes to mind.