Defending a flat-earth

This is a sequel to my previous post:

http://triablogue.blogspot.com/2016/07/flat-earth-cartography.html

I'd like to revisit Dr. Byl's comment:

Sorry, Steve, but your arguments against a flat earth don’t work.

A flat earth model of the universe can easily be made empirically equivalent to a spherical earth model. Simply apply a mathematical transformation called a "geometric inversion". For each point in the universe, measure its distance R from, say, the earth’s South Pole, and move this point along the Pole-to-point half-line to a new distance 1/R. 

This transforms the spherical surface of the earth to a flat disk, centered on the North Pole, with the South Pole infinitely far away (i.e., this is the stereographic projection of geography). All points inside the Earth are transferred beneath the disk; all points in the sky are transferred above the disk. Galaxies that were infinitely far away end up a short distance above the new North Pole. 

The laws of physics are also transformed, with consequences that may seem strange for those accustomed to thinking in terms of the more conventional universe. For example, sunlight now travels in circular arcs, the sun and stars become much smaller than the (now infinite) earth, etc. See my post
Mathematical models and reality: http://reformation.edu/scripture-science-byl/pages/09-mathematical-models.htm
Terrestrial objects increase in size as they travel away from the North Pole, becoming infinitely large at the South Pole. However, since inversion is a conformal transformation, local shapes are preserved. Hence you won’t notice any changes as you travel. 

It is not my intent to defend a flat earth, but only to point out that, with some ingenuity, one can construct a mathematical model of the universe with almost any feature one wishes (the Duhem-Quine thesis), as long as one is willing to make adjustments elsewhere (e.g., sunrays become circular arcs, size is not preserved, etc.).

Since this flat-earth model is empirically equivalent to the spherical earth model, the choice between these models must be made on the basis of non-empirical factors, such as philosophical or theological considerations.

i) Several commenters, myself included, responded to Byl's argument. He never replied. That's his prerogative, but when you ignore objections, it weakens your case.

Now I'd like to discuss some additional problems. His defense has some paradoxical aspects. 

ii) When dealing with geocentric/flat-earth imagery in Scripture, mainstream inerrantists say the descriptions are poetic or phenomenological. In general, a round earth looks flat to an earthbound observer. Mind you, there's subtle evidence that that an optical illusion, even from the standpoint of an earthbound observer. 

Byl is making the same move in reverse: it's possible for a flat-earth to look round. What's paradoxical about this move is that Byl's own argument involves a phenomenological interpretation of the Biblical data or observational data. But in that event this comes down to a choice between two competing phenomenological interpretations: a spherical earth that has a flat appearance or a flat earth that has a spherical appearance. In that case, the flat-earther's appeal isn't any more straightforward than the alternative. Both positions save appearances. Both positions go behind naive realism. 

iii) Given, moreover, a choice between two phenomenologically equivalent interpretations, there may be other considerations that tilt the scales. Geometric inversion gives you mathematically equivalent descriptions, but they're hardly equivalent in other respects. The physics is different–as Byl concedes. And to my knowledge, flat-earthers haven't produced a detailed scientific alternative to standard astronomy in that regard. If one model has a lot of physics to back it up, whereas the physics hasn't been worked out for the other model, these aren't evidentially on a par. There's a difference between mathematical coherence and natural coherence. A scientific model has to balance out natural forces. I'm not saying modern astrophysics is complete. There are some well-known problems. But you can't beat something with nothing. 

iv) Another paradoxical aspect of Byl's argument depends on a mathematical model that would be incomprehensible to the original audience. Assuming ancient readers thought the earth was flat, did they think it was flat in that sense? Did they think the South Pole was infinitely large and infinitely far from the North pole? Did they think the flat earth was shaped in that way? 

The irony is to defend a flat earth by substituting a mathematical model that doesn't match the mental image which ancient readers (allegedly) entertained. It defends a particular interpretation of Scripture through a bait-n-switch. That's analogous to people who defend the historicity of Adam by combining theistic evolution with ensoulment. Although that maneuver can give you a "historical Adam", it's not the Adam of Gen 2. 

Typically, scholars who think the Bible reflects a flat-earth cosmography impute a three-story universe to Scripture. They do that by cobbling together scattered references in Scripture, without regard to genre, which they supplement with depictions from other ancient Near Eastern sources. That includes the solid dome, with the cosmic sea above the dome, and so on. Yet Byl pours scorn on that particular model:

http://bylogos.blogspot.com/2010/02/genesis-and-ancient-cosmology.html

If, however, we don't think Scripture reflects a flat-earth cosmography in that sense, then what's the evidence that it reflects a flat-earth cosmography in any sense? Surely the esoteric alternative that Byl proposes (for the sake of argument) would be inaccessible to ancient readers.