"the argument appears" is correct and usable in written English.
You can use it when you want to introduce a new argument or opinion. For example, "The argument appears to be that the current tax system is unfair to low-income earners."
The argument appears to have held sway.
Compare that number to UEFA's 31 members as recently as 1988 and the argument appears to have some traction.
The argument appears to have won over Riba at least; Pocket's Westminster development won one of the institute's awards.
As a result, the argument appears as the written equivalent of sound bites and is at times hard to follow.
The core of the argument appears to be that TED talks oversimplify and are intended to stimulate emotion rather than reveal the world's true complexity.
Much of the argument appears to rest on assumptions familiar from the rest of the EU referendum debate: that economic uncertainty would mean a falling pound and diminish purchasing power.
When Eisenhower accepted the consequences of the New Deal, the argument appeared to have been settled.
The argument appeared to have swayed voters, even those who did not oppose the practice on moral grounds.
The argument appeared settled last June when the five-member San Francisco Port Commission chose the Malrite proposal over that of the Bay Center.
The argument appeared aimed at limiting the damages that victims of abuse could recover by making parishes, rather than the diocese, liable.
The argument appeared to underscore the difficulty of drawing a firm line between religious worship and activities that are simply suffused with a religious point of view.
