The "X is freer than Y" example is only superficially subjective. The issue at hand is that people disagree on what "free" means. This can be resolved in a mutually agreeable way by first clarifying the different possible aspects of freeness and clearly separating them out (in your example, one might state them as: BSD allows you to do more things than GPL with source code you receive under the respective license; GPL makes it likelier for you to receive more source code in the future, hence leading to a larger total number of potential actions you can do with source code over time (a point which requires a sub-tree of arguments)).
Then you further need to relate those back to the original statement by clarifying how different subjective target functions will have you come to a different final conclusion. (Not to mention that the "GPL is freer than BSD" or vice versa discussion is itself merely a sub-part of the larger "GPL is better than BSD (for my purpose)" or vice versa discussion.)
So my point is that it is possible in principle to provide a fully qualified link to a non-subjective presentation of arguments on that particular issue (and any other issue). I agree with you that the real challenge is UI, and probably moderation more than user education.
If you get the UI right and have reliably automated (even if user-sourced) tools for qualifying statements and disallowing (or rather, marking) logical fallacies, the users can educate themselves.
I've played around with UI ideas in the past. I think you need a nested structure, which can ideally be generated by the users (but would need to conform to the basic rules of logic [to whatever extent it has been defined]). Any argument will be in some knowledge domain, until you get to some "ultimate high level domain" (which probably doesn't exist -- not sure how you'd represent this in the UI; probably just the superset of all your as-yet-undomained arguments), so the nesting of domains should be reflected in the interface.
I think the UI problem is related to the data modeling problem. In my view, it seems like the UI should directly expose the data model. If that is the case, then the question is, "What is the right data model?".
For that, I think it's primarily directed graphs showing the relationship between the arguments. Of course there is more needed, as you'd need to annotate the arguments with various meta-arguments (eg. argument's conclusion is assumed as premise).
I do agree that one can probably come up with solutions for handling subjective arguments relatively well, I just think it might be difficult to come to a "this will handle all cases" solution. If someone says a particular argument is fallacious, why should we believe them? What happens when your database gets spammed with tons of bogus info? How do you make sure it stays out (or at least, can somehow be "excluded" from what you normally see)?
I don't see why it wouldn't be possible. If you could get arguments reduced to individual propositions, you could begin to run the resolution algorithm to find new conclusions.
Then you further need to relate those back to the original statement by clarifying how different subjective target functions will have you come to a different final conclusion. (Not to mention that the "GPL is freer than BSD" or vice versa discussion is itself merely a sub-part of the larger "GPL is better than BSD (for my purpose)" or vice versa discussion.)
So my point is that it is possible in principle to provide a fully qualified link to a non-subjective presentation of arguments on that particular issue (and any other issue). I agree with you that the real challenge is UI, and probably moderation more than user education.