Self-Referencing and Self-Reversing

In Möbius Logic: Puzzles that cannot reach binary resolutions, a post from 2007, Weekend Fisher writes:

The old logical puzzle

This sentence is false.

has a Möbius topography. Like the Möbius strip, it is self-referencing and self-reversing.

Because this is kind of an odd concept, let me repeat: Fisher establishes the definition of a Mobius loop as self-referencing and self-reversing. He offers examples, including Harry Potter's villain and Möbius logic in philosophical debates. Fisher provides a significant conclusion:

I would simply point out that when the debate is framed as a Möbius loop, it has been framed in a way that is entertaining but renders progress impossible. We have the tools to recognize such a logical structure. Once a presentation has been identified as a Möbius conundrum, we can know from the outset that no resolution can come from that particular way of framing the question.

Potential Output is a trend line connecting past, present, and future. If the present doesn't turn out to be as good as we expected while it was still the future, then our old estimate of Potential Output must have been wrong and it is okay to revise the past...

I have trouble with that logic. Even apart from the concept of changing the past (see yesterday's posts) I am troubled by the way Potential Output is used. I'm not sure, but maybe Weekend Fisher's analysis will be helpful. So let me just throw this out there.

Potential Output is "self-referencing". As William T. Gavin says, "the accuracy of our estimate [of potential GDP] depends on the accuracy of our long-term [GDP] forecast." Self-referencing. The best-case estimate of where GDP will go, depends on where GDP actually goes.

Potential Output is also "self-reversing". David Altig quotes The Washington Post's Neil Irwin:

What's amazing is that the Fed's newest projections, released in December of 2012, look like they could have been copy and pasted from 2009, just with the years changed

With every new estimate, the story is that GDP growth will be slow for the next year, and then things will pick up. Each year, the prior year's prediction of "good growth soon" is reversed. Self-reversing.

Potential Output, as used today, is self-referencing and self-reversing. Fisher says we "know from the outset that no resolution can come from that particular way of framing the question" and that it "renders progress impossible".