Accepting? Was my bolding capitalisation still too subtle?

I meant you 'accepting

*for the sake of argument*'. I didn't mean you

*accepting genuinely as true*. You or anyone else won't win any debate with a FEer even by accepting their premises

*for the sake of argument *only to pinpoint logical errors in their thought process. Winning a FEer in a reasoned debate by coming across as the more logical and scientific party won't be winning them over. Full stop.

If you want to win a FEer purely in a reasoned debate, we've already done that adequately with the refraction argument head on irrespective of whether the FEer understands/accepts it. It's an easy win. But obviously it won't win 'hearts and minds'. To go anywhere else with the Quantum Eraser's modus tollens whilst ignoring refraction is tantamount to fruitless hairsplitting on delusional fancies.

I only think I may have found the actual premise.

And the mistake of the last few pages is just arguing about the wrong premise.

You may be right to some extent, and I may have added to the confusion.

Firstly, a premise can be wrong/right in at least two ways, (1)

*logically/mathematically* or (2)

*ontologically*. The first means that the premise at the start of a logical sequence is either self-contradictory or contradicts another proposition from which it is derived.* The second means that the premise doesn't correspond to reality (i.e. it doesn't tell us truths about the real world). It's either partially or fully an imaginary construct incompatible with reality.

I may have added to the confusion by not addressing QE's modus tollens precisely. For clarity, let's revisit it:

**"If the earth is a sphere with the radius 3,959 miles (***P*), then every horizon distance measurement must be no more than 1,225 x square foot of observer's height in feet (*Q*). *Not-Q*: The horizon distance is greater than 9,41 miles from a 1 foot observer. Therefore *not-P: Earth is not a sphere with a radius of 3,959 miles*."
Whilst the premise

*P* is both logically and ontologically (roughly)

*correct*, the implication

*Q* is

*neither*.

__The Logical Falsity of __*Q*:
If we are to be technically pedantic,

*Q* doesn't

*logically* follow

*P* because it doesn't

*preserve the truth* of

*P* but adds new truths to it.** Among other things,

*Q* adds new semantic components to the simple statement of a sphere with a certain radius (

*P*) such as an observer with a height observing the geometric horizon of

*P* on top of the

*P*.

*None* of these 'truths' are logical implications of

*P *but rather constitute

*additional* assumptions. A more logical formulation of the modus tollens is possible where the P explicitly includes these assumptions but still wouldn't escape the inherent ontological falsities.

__The Ontological Falsity of __*Q*:
*Q* is also

*ontologically* wrong by ignoring the effect of refraction on the observed horizon and, by extension, its distance from the observer. Due to refraction,

*every* actually observed horizon's distance measurement

*is* more than 1,225 X square foot of observer's height in feet which directly contradicts QE's articulation of

*Q*.

**Hence, QE's articulation of Q renders his modus tollens both illogical as well as divorced from reality. In other words, Q is the 'strawman' used by the FEer rather than P which we earlier mistakenly stated as the strawman. To 'win' the argument purely on the basis of reason, **__the glober needs only to highlight the strawman Q as incompatible with his actual position and as an illogical inference from P. The FEer misfires on both counts__.
*The premise could be a theorem (i.e. a proposition derived from another proposition) or an axiom (i.e. a proposition that is not derived from any other proposition).

**Truth preservation is a property of a valid deductive argument that ensures the truth in the premises is involved/transferred in/to the conclusion.

If you can't even appreciate the stunning beauty of refraction being the apparent premise then there really is no hope.

With or without refraction, every unobstructed sphere with an observer must show true horizons. Refraction doesn't change the truth of there appearing a horizon. Only the type of horizon being observed (apparent rather than geometric).

Also, horizons (whether geometric or apparent)

*have no existence independent of an observer*. Horizon is an optical appearance and changes as soon as the observer looks around or changes position. Like a rainbow, you can never walk to the horizon in order to 'find' it nor locate it on a map. In the case of a geometric horizon, it's purely a mathematical construct which is metaphorically visible to the metaphorical observer on a metaphorical refractionless sphere. It's never observed in the real world by real people.