Epistemic Status: I didn't think about this for that long, could be improved, but I still think it's a good first pass.
This post is was written as an answer to the "and how do we know that?" part of the question Space colonization: what can we definitely do and how do we know that?
Working on questions related to space colonization, I've formed a loose taxonomy of the kinds of arguments I've encountered - primarily those in Eternity in Six Hours, but also other sources and arguments I make myself.
A Taxonomy of Argument Types
1. Our understanding of the laws of physics says it should be possible. (Argument from Physics/Basic Science)
At the most basic, we have reason to believe doing something is possible when applying highly-confident models of physics say that it should be. For example, we have a lot of confidence in the laws of motion, general relativity, and chemistry. Related to these, we have (I believe) a lot of confidence in our models of astronomy and how far away different stars. These models state that with enough energy one can accelerate objects to fast enough speeds to reach remote celestial destinations.
At this level, we're dealing a lot with energy, distances, accelerations and things that resemble back of the envelope calculations.
Usually application of physical theory also requires use of empirically obtained data, such as calculations of interstellar dust densities. However, this data can often be generated from robust models and sensors that work off basic physical quantities. Plus one can explore the sensitivity of the models showing that even changing empirical parameters by an order of magnitude doesn't undermine the overall argument.
Note that the arguments in these models are both contingent and used to rule out of a lot of goals and scenarios. We could imagine worlds where everything is much further away and achievable speeds are much slower such that we could never reach anything. We also don't spend thought on things which seem ruled out, e.g. faster than light travel, or even levels of speed that would require exceedingly enormous quantities of energy.
2. Things nature has done, so reasonably we as intelligent beings in nature should eventually be able to too. (Argument from Nature)
Without elaboration, the authors of Eternity in Six Hours rely on this argument when making the assumption that humanity will eventually achieve atomically precise manufacturing (APM). I see the intuitive sense behind this argument. If the blind optimization process of evolution can accomplish something, why shouldn't an intelligence like us also be able to do it?
To borrow an example from the paper, nature is able to create an acorn which grows into a massive tree using local resources. Seemingly humans should be able to match that or do even better, e.g. how our flight is a lot better along many metrics than flight found in nature.
3. We have a proof of concept. (Argument from POC)
This builds on 1. Argument from Physics. With this kind of argument, we can point to both a theoretical understanding of why something should be doable together with a basic demonstration of the idea.
For example, we might propose that coilguns or laser propulsion might be feasible ways to accelerate probes to very fast speeds. In this case we have the physics models, but also basic "prototypes" of the ideas as smaller coilguns have been built (much, much, much smaller to be fair) and laser propulsion has been demonstrated in the lab.
At this point, the core physics mechanism has been proven and what remains is the engineering question about whether things can be scaled up sufficiently.
(We can actually say that 2. Argument from Nature is a form of 3. Argument from POC)
4. We've done it already. (Argument from Accomplishment)
Naturally, the strongest argument for our ability to do something is the fact that we've done it. For instance, we know definitely that we can rather large amounts of matter into orbit around the earth.
Limitations of These Arguments
The type arguments, from weakest to strongest, aren't conclusive. Just because the basic physics behind an idea checks out, doesn't mean that there aren't immense and overwhelming engineering challenges which would get in the way somewhere the in chain. Perhaps the energy efficiencies required can't be easily achieved, perhaps manufacturing tolerances can't be made precise enough, perhaps the cost is just too damn high. One can easily argue that theoretically doable and actually doable are not the same thing. Sheer scale can make things tough - consider that building ten fifty story buildings is probably much easier than building one five hundred story building.
Consider a practical example: despite our physics models describing nuclear fusion clearly and research having begun the 1920's, we do not yet have working nuclear fusion reactors.
Another argument I might make is that even if you can argue that all N technologies you think are necessary for some goal are physically feasible, until you have actually built it, there may remain plausible other further necessary technologies you failed to identify and which are impossible to produce.
When it comes to space colonization, we don't really have any cases of 4. "We've already done it" since in no case have we achieved the enormous scales required.
In the case of space colonization, however, and particularly the scenario described in Eternity in Six Hours, there is something of a rejoinder: It is okay if the engineering challenges are immensely difficult since it is okay if takes humanity thousands or even millions of years to overcome them. Here one might include an argument from analogy: in about the last hundred years, humanity gained the ability to construct building five times the height of the historical maximum; within fifty years we were able to make chips with a million times the transistor counts; and in less than a century of the field of microbiology coalescing, we are editing DNA. Perhaps these are reasons for optimism that with thousands or millions of years we could replicate anything nature does and build structures as vast as Dyson spheres.
Of course, as above, that still leaves the question of whether or not we're accounting for all the basic physical facts.