At the second stage of talks about a possible new British-Irish agreement, John Hume of the nationalist SDLP will be there. So, too, will John Alderdice of the non-sectarian Alliance Party. But the main focus of attention will be the participation of the Unionist leaders, James Molyneaux and Ian Paisley.
Their domination of Unionist politics is complete. Over many years they ignored the call to negotiation, regarding talk of political solutions at best with very deep suspicion. So there is as much surprise as pleasure that they have talked themselves to this point.
'Breakthrough' is a term before which seasoned observers tremble. Northern Ireland has known many 'historic' moments in the past 23 years. The period is scarred with foul atrocities, thought at the time to provide 'a watershed'.
The same can be said of the current talks. Today's meeting represents the high point of a process initiated by Peter Brooke in January 1990. Despite abundant scepticism in Dublin (and London), the then Secretary of State for Northern Ireland detected among the Northern Ireland parties a desire for movement. For 18 months he laboured in 'talks about talks'. When press and public interest had just about died, he announced a breakthrough. The parties had finally agreed to negotiations addressing 'the three sets of relationships' - those within Northern Ireland, between North and South, and 'between the peoples of these islands'.
Enormous goodwill surrounded the talks that began on 30 April last year. However, they quickly degenerated into farce. A series of disputes - about agenda, venues, chairmanships, everything bar the size of the table - persuaded many people that the Unionists in particular were never serious.
Indeed, there was no further serious talk until the general election was out of the way. Although their leaders denied it, some Unionists were tantalised by the possibility of a hung parliament in which they would hold the balance of power. Likewise, Dublin and the SDLP held themselves in readiness for a Labour government which was committed to Irish unification.
The election result seems to have had a salutary effect all round. Following Mr Brooke's departure, and the appointment of the brusque Sir Patrick Mayhew, the parties returned to the table in a more sober mood.
Urged by Sir Patrick to proceed briskly to business, they did so. In doing so, they have considerably widened and deepened the talks process. They have also revealed the enormous gulf that separates them.
The Secretary of State last week said much progress had already been made in the internal 'Strand One' talks. He was equally right to warn that there is a long way still to go. Those discussions have yielded no agreement yet between the SDLP and the pro-Union parties on a structure of government for Northern Ireland. The Ulster Unionists, Democratic Unionists and the Alliance Party have developed a model for devolved government that the SDLP so far has declined to support.
This devolution plan, incorporating an assembly and the distribution of power in proportion to party strengths, presumes Northern Ireland will remain an integral part of the United Kingdom. Westminster would remain the sovereign power, and there would be a continuing role for a Secretary of State.
The SDLP alternative is for an 'executive commission' with altogether far more autonomy. The people of Northern Ireland would elect three commissioners. A further three would be appointed by the British government, the Irish government and the European Community.
Mr Hume's ultimate game plan is for a comprehensive settlement which would win endorsement in dual referendums north and south of the border. By this means, the SDLP leader would redefine 'self determination' for the Irish people and deny the IRA any lingering claim to act in their name.
The implication - never publicly confirmed by the SDLP - is that the dual referendums could leave the two parts of the island living constitutionally apart. However, Unionists believe Mr Hume has no such intention. They regard the SDLP's plan as an attempt to redefine the North's constitutional position.
Thus the traditional question - to which nation? - pervades the talks. And some Unionist purists, who think Northern Ireland should simply be integrated with the United Kingdom, content themselves that the talks will eventually fall apart under the weight of inherent contradictions.
Even so, for the next three days the parties will outline their thoughts on future institutional links between North and South. This will bring them face to face with the thorny question of articles two and three of the Irish Constitution, which lay claim to the territory of Northern Ireland. But that they have agreed to persist is potentially encouraging. Until last weekend, Dr Paisley was insisting that there could be substantive discussion with Dublin only if there was agreement first on the institutions of government for Northern Ireland.
To the outsider, the posturing and preconditions are tedious in the extreme. Yet for some of the participants, in personal terms, the pace of development has been significant and demanding.
Soon after his forceful repetition of the Unionist terms, Dr Paisley had a preliminary encounter with the Irish government in London. A huge symbolic barrier was thus broken. And few can doubt that for this lifelong scourge of compromisers it was a momentous step.
There are other signs, too, of a much altered mood. Next Monday the Orangemen will be on the march, celebrating King William's victory at the Battle of the Boyne. In the past, this fixation with the events of 1690 has demanded a near three-month break in political activity in the province.
Yet, barring collapse at the first hurdles, the Unionists contemplate the resumption of this week's talks on 15 July. This time they will be held at Stormont, home of the Unionist-controlled parliament abolished by Edward Heath in 1972.
Some sceptics of course maintain that it will amount to nothing in the end. Breakdown has seemed inevitable at various points. The formulae devised to keep the talks afloat have encouraged a widespread belief that nobody wants to take the blame for failure.
If that is the case, then the prospects are bleak - although that alone would point to some perceived public pressure not often acknowledged by the politicians. Certainly, if blame allocation is the name of the game, the parties have thus far found it difficult to extricate themselves from the process. Moreover, there plainly are people on all sides very serious about the talks, who believe the consequence of failure would be another prolonged period in the wilderness.
Arguably, this is a less troubling prospect for Dublin and the SDLP. In 1985 they secured from Margaret Thatcher the Anglo- Irish Agreement, which gave the Irish government the right to be consulted about the administration of the North. Combined with direct rule from London, this is an arrangement that well suits constitutional nationalists.
The current talks, at one level, are indeed borne of the Unionist desire to be rid of that agreement. However, there may be a confusion of purposes and designs at work. The Anglo-Irish Agreement itself foresaw devolution. Mrs Thatcher attempted to calm Unionists' fears, telling them they could dilute Irish influence in the inter-governmental conference by agreeing to share power in a devolved government.
In the seven years since, Dublin and SDLP thinking have moved significantly on, and their preference would be to use the current talks to gain a more radical arrangement in which Dublin's influence would be enhanced. This Conservative Government meanwhile appears attached to the original concept. And while this is not officially what the Unionists are about, they seem to have the assurance that London does not see these talks as an opportunity to further diminish their status.
Unionists have always argued that the 1985 Agreement gave Mr Hume an inbuilt advantage. For the time being at least they appear to have persuaded themselves that this need not be the case. As a result - whether or not they accurately read the Government's disposition - they have journeyed farther than seemed possible a year ago. All eyes will be on them as they ponder how much further they can travel, and calculate their losses if they get off the train.
The author is the London editor of the 'Irish Times'.
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