Is the flat earth cosmology scientifically justifiable today? With binoculars or telescopes you'd be able to see to other countries if the earth were flat. And looking out at the ocean we can see where the earth curves and things like the top of ships, not the whole ship. Unless those who think the earth is flat believe they are looking at the end of the world when looking out at the ocean? How do they arrive at this position?
I realize this queston might be closed, and perhaps this should've been a comment, but it got too long:
I was in a radio show last spring with a flat-earther. I really tried to understand him, rather than just ridicule him. We went to the beach with his 87x magnifying camera, to watch the coastline 19 km away. If my model of the geometry of Earth were right, we would be able to see the buildings on the other side of the belt, but not the shore. If his model were correct, I thought we would be able to see the shore, but it turns out they have an ad hoc explanation that has to do with the vanishing point on a flat Earth lying below the ground, thus making sufficiently distant objects disappear.
So, apparently this is their explanation.
When after five minutes I still didn't understand this, he told me it was no wonder that I didn't understand; it took him two  years to understand.
Well, big surprise, we couldn't see the shore. We could in fact see a bit more of the buildings than we should be able to if there were no atmosphere. I assigned this to refraction (which can actually move the horizon several tens of kilometers away, or even ~100 km over water in the springtime when the air is getting warm but the water is still cold), but since he didn't believe in refraction, that didn't convince him.
We then talked a bit about what mechanism might produce a flat Earth. The conversation sort of ended when I realized he didn't believe in gravity either…
Is a flat Earth scientifically justifiable today?
The question title has now been edited to a more easily answerable one. The answer is — unsurprisingly to most people on this site, I suppose — a big, resounding &quot;NO&quot;! The flat Earth theory is not a theory, in the scientific sense of the word. It's not even a hypothesis. You could call it a model, and in many cases, it's a fine model, namely on scales much smaller than the horizon distance. You may assume a flat Earth if you want to calculate the area of the parking lot. This is analogous to Newtonian dynamics being a fine model for small velocities and gravitational fields. It works fine if you want to calculate the force of an apple falling on Newton's head. But everybody knows it become less exact, the larger and faster the apple.
I suspect that the use of the word &quot;theory&quot; in everyday language influences how people think about science. &quot;It's just a theory&quot;, they say, without realizing the enormous amount of work, experiments, verifications, and falsifications that go into building a scientific theory.
Flat-Earthers in general don't realize, I think, that in science you can't just assume that something works in another way, without this assumption having severe consequences for many other theories.
Why not?
The list of reasons that a flat Earth is incompatible with a range of well-established theories is long. Here's a subset:

Gravity

Gravity explains why a large mass becomes round. FE'ers have no explanation of why it could be flat.


Electromagnetism

The Sun and Moon are circulating 5000 km over Earth, held up by electromagnetic forces. This is completely impossible within the frames of the accepted theory of electromagnetism, but they don't propose a new theory of EM.


Astronomical distances

Standard trigonometry reveals that in their model, the Moon would look different from different places of Earth. It does, but much, much less than if it were 5000 km away (because it is in fact 400,000 km away)


Meteorology

The guy I talked to had no explanation for why cyclones rotate clockwise and counter-clockwise in the Southern and Northen hemispheres, respectively. The Flat Earth Society explains this by &quot;The Wind Currents are put into gradual motion by the attraction of the Northern and Southern Celestial Systems, which are grinding against each other as gears at the equator line&quot;. I… I don't know what to say about this…


Constellations

The Southern Cross can be seen from Australia and South America. I'm in Oslo at the moment, which according to their world map is right in the middle between Australia and South America, yet I can't see the Southern Cross.


Satellites

FE'ers generally don't believe in Moon landings and space stations, but many satellites can be seen even with a relatively small telescope.


The disappearance of ships and other objects below the horizon.

Simple trigonometry shows that on a flat Earth, you should be able to see as far as the airmass allows you. On a round Earth, this is complicated by refraction, enabling us to see farther than if there were no atmosphere. But still, you can easily see how the Sun or Moon sets or rises partly below the horizon.


Lots of other inconsistencies

Stellar parallaxes.
The different weight of the same object at equator and the poles.
Eclipses (in particular the times at which they occur).
The movement of Jupiter's moons (which can be seen with a regular binocular).
Tides.



The problem is that there is no way to discuss these things with FE'ers. If you give an argument that they can't disprove, they will either claim that you're just wrong, or that &quot;you think so because that's how you were schooled&quot;, or that you're a part of the conspiracy.
In particular the last point is important. Since the FE model, were it right, would imply that most of all physics would be wrong, that means that either

all physicists in the world are stupid, which makes it pretty amazing that we've made planes fly, computers work, bridges hold up traffic, compasses show us the way, as well as predicted stuff like Venus transits and the weather tomorrow. Or

all physicists are a part of a conspiracy, which would be equally amazing how none of the millions of physicists through history has confessed. Where's my bribe?!


Why am I not just ignoring them?
You may say that by writing this, I am just feeding the trolls, and giving people the impression that flat-Earthers are a problem for science. But in my opinion, the attitude that they hold toward science is much larger than just a few crackpots claiming what is obviously false. It's a symptom of something sad in our society, namely that &quot;science is just one opinion, and my opinion is just a valid&quot;.
I acknowledge that scientists can tend to be cocky and should try to be more open to understanding why people don't believe us. But what makes a few people believe in a flat Earth is the same thing that
makes people deny that human activities affect the climate,
or makes them believe that vaccines are evil,
and makes some politicians get away with using a term like &quot;alternative facts&quot;.