Like my fellow Muslims, I strenuously object to the lazy conjugation of the words Islamic and terrorism, for the rather obvious reason that there is nothing Islamic about the murder of innocent civilians. Unlike so many of them, however, I also take issue with the term “Islamic state”, and for the very same reason: there is nothing Islamic about a state. The two concepts have nothing in common.

Let’s take the word Islamic. The casual and careless application of this adjective to religious and cultural phenomena alike has blurred the all-important distinction between Islam, the divinely revealed, perfect and infallible faith, and Muslims, the rather flawed, imperfect and very human practitioners of that faith.

As the historian Marshall Hodgson pointed out: “One can speak of ‘Islamic literature’, of ‘Islamic architecture’, of ‘Islamic philosophy’, even of ‘Islamic despotism’, but in such a sequence one is speaking less and less of something that expresses Islam as a faith.”

To his list, I would add “Islamic state”, because, contrary to popular Muslim opinion, there is not a shred of theological, historical or empirical evidence to support the existence of such an entity. Its supporters tend to mumble vaguely about this or that verse from the Quran, or make vacuous references to the life example of the Prophet Muhammad. But the Quran prescribes no particular model of government, nor does it detail a specific political programme that Muslims must adopt. In fact, the concept of the state appears nowhere in the Quran.

And why would it? In his new book, Islam and the Secular State: Negotiating the Future of Sharia, the Sudanese-born academic Professor Abdullahi Ahmed An-Na’im points out: “You will not find any reference to an Islamic state or to state enforcement of sharia before the mid-20th century – it’s a post-colonial discourse based on a European-style state.”

Many Muslims fall back on a romanticised view of the very first community of believers in 7th-century Medina, ruled by the Prophet himself, and cite it admiringly as their precedent for an Islamic state, but this approach is flawed. First, any historical precedent that revolves around the presence of a divinely guided prophet-as-political-leader seems wholly irrelevant, in an era in which we have no divinely guided prophet to lead us.

Second, the Medina “state” should be seen as a purely political and pragmatic, rather than Islamic or religious, construct. The celebrated pact that the Prophet signed with the various tribes of Medina involved the non-Muslims of the city – chief among them the Jews, who were granted formal equality with the Muslims – recognising only his political and temporal, rather than his religious or spiritual, authority. As the historian Bernard Lewis puts it: “Muhammad became a statesman in order to accomplish his mission as a prophet, not vice versa.”

Third, Medina lacked fixed borders, a standing army, a police force, permanent civil servants, government ministries, foreign ambassadors and a public treasury. To pretend that it can serve as a practical model for the large, complex, post-industrial societies of the 21st century is fanciful.

Today it is difficult, if not impossible, to identify a Muslim-majority nation that could plausibly be identified as a modern, viable and legitimate “Islamic state”. Sunni Saudi Arabia and Shia Iran both loudly proclaim themselves to be such, but to each other they are heresies; they are also dictatorial regimes with terrible human-rights records. How about the Islamic Republic of Pakistan, blighted by military rule for much of its history? Or Sudan, accused of committing crimes against humanity among its own Muslim population in Darfur?

Not surprisingly, Professor An-Na’im concludes that “the Islamic state is a historical misconception, a logical fallacy and a practical impossibility”.

Mehdi Hasan is news and current affairs editor at Channel 4