The problem with arguing by analogy is that there are two possible cases:
1. Your analogy maps precisely, in which case it's no simpler than arguing about the original thing.
2. Your analogy is imperfect, in which case your conclusions are suspect.
Case #2 is most common, and the argument usually continues by proposing a different analogy. Now you're arguing about the merits of your analogies, rather than about the topic itself.
Analogy can be a good pedagogical tool, highlighting some aspects of the problem, and giving you an intuitive way to connect to them. But eventually the analogy always breaks, and now you've got to un-learn the analogy before re-learning the reality.
Formal systems aren't arguments, they're assumptions. As long as the assumptions hold, the formal systems are useful. If there's anything to argue about, that's a limitation of their utility.
1. Your analogy maps precisely, in which case it's no simpler than arguing about the original thing.
2. Your analogy is imperfect, in which case your conclusions are suspect.
Case #2 is most common, and the argument usually continues by proposing a different analogy. Now you're arguing about the merits of your analogies, rather than about the topic itself.
Analogy can be a good pedagogical tool, highlighting some aspects of the problem, and giving you an intuitive way to connect to them. But eventually the analogy always breaks, and now you've got to un-learn the analogy before re-learning the reality.
Formal systems aren't arguments, they're assumptions. As long as the assumptions hold, the formal systems are useful. If there's anything to argue about, that's a limitation of their utility.