One irony in Defence Minister Kevin Andrews' snafu in not being able to name the leader of the Islamic State is that his famously gaffe-prone predecessor would not have made the same mistake.

David Johnston was all over the detail of his portfolio. His trouble, according to critics, was that he couldn't put it together in a big picture way that could sway others towards a particular course of action.

Andrews by contrast, has impressed Defence with his ability to master a brief and get across the overarching issues of the portfolio in the four months he's been in the job.

Many will therefore put his failure to recall the name of Abu Bakr al-Baghdadi down to a mental blank. We've all been there.

Should we cut him some slack and move on? Not before pausing to recognise this: If our government believes Islamic State is a sufficiently threatening organisation that it is prepared to send Australian troops across the globe to help fight it, the prime decision-makers should have the essential facts about the terror group so readily at their fingertips that they do not have mental blanks.

The Defence Minister should be able to name the leader of the group with which Australia is at war, plain and simple.

His response both during and after the 7:30 interview was that Islamic State is an amorphous, shifting organisation – to focus on individuals neglects the complex and hydra-headed nature of modern, global terrorism.

True, the Islamic State has affiliations and rivalries that are subject to change. But Baghdadi is an immensely significant leader, without whom Islamic State would not be the organisation it is today.

He took it from a group that was seriously weakened after the death of its early leader Abu Musab al-Zarqawi and turned it into a jihadi powerhouse.

He has great symbolic importance. Military and terrorism experts have stressed the need to strip Islamic State of its aura of invincibility and inevitability. Much of its recruiting power comes from the millennial appeal to young and angry Muslims of joining an organisation that presents itself as the modern Caliphate, with Baghdadi as its undisputed Caliph, destined to bring together Muslims for an end-of-days battle against unbelievers.

Killing Baghdadi would put a major dent in that myth.

Furthermore, Islamic State is in fact a quite structured organisation. The understanding of its hierarchy is far from perfect and – to grant Andrews a point – it has elements of decentralisation. But it is widely believed to have an organisational nucleus with Baghdadi at the centre, directing his military leaders – many of whom are former commanders of Saddam Hussein's army – as well as influencing the group's territory as a quasi-state and of course acting as its theological head.

Islamic State's affiliates such as Nigeria's Boko Haram and Ansar Beit al-Maqdis on the Sinai Peninsula have declared "Bayat" or allegiance to Baghdadi personally, rather than to the Islamic State. Killing Baghdadi would arguably dissolve those allegiances.

A paper released last month by the venerable Brookings Institution argued that Baghdadi and his right hand man Abu Muhammad al-Adnani had "strategic acumen wholly lacking in their predecessors" and their deaths could "significantly weaken" their organisation.

Of Baghdadi, it concluded: "This man, one can be certain, is no mere actor."

Tony Abbott himself calls the group a "death cult". And cults always have leaders.

As the government prepared to commit more troops to confront the Islamic State, the precise nature of this complex organisation should have been foremost in the Defence Minister's mind. His mental blank suggests it was not.

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