Aristotle remarked in his Nicomachean Ethics (I paraphrase) that we can expect of matters only the degree of certainty that they will bear. We can have absolute certainty in mathematics but in practical matters, this is not possible. Here’s the quote:
“Our discussion will be adequate if it has as much clearness as the subject-matter admits of, for precision is not to be sought for alike in all discussions, any more than in all the products of the crafts. Now fine and just actions, which political science investigates, admit of much variety and fluctuation of opinion, so that they may be thought to exist only by convention, and not by nature….We must be content, then, in speaking of such subjects and with such premisses to indicate the truth roughly and in outline, and in speaking about things which are only for the most part true and with premisses of the same kind to reach conclusions that are no better. In the same spirit, therefore, should each type of statement be received; for it is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs.”
Now, I would argue that the fundamental legal principle of libertarianism (the NAP) is absolutely clear and precise; it’s application, however, requires prudence, which is a form of practical judgement. After the passage I just cited from Aristotle, he goes on to say:
“Now each man judges well the things he knows, and of these he is a good judge. And so the man who has been educated in a subject is a good judge of that subject, and the man who has received an all-round education is a good judge in general. Hence a young man is not a proper hearer of lectures on political science; for he is inexperienced in the actions that occur in life, but its discussions start from these and are about these; and, further, since he tends to follow his passions, his study will be vain and unprofitable, because the end aimed at is not knowledge but action. And it makes no difference whether he is young in years or youthful in character; the defect does not depend on time, but on his living, and pursuing each successive object, as passion directs. For to such persons, as to the incontinent, knowledge brings no profit; but to those who desire and act in accordance with a rational principle knowledge about such matters will be of great benefit.”
Reasoning in politics and ethics is not a matter of applied mathematics and there is not escaping the need for prudential judgement. Everyone, no matter what his political beliefs, is in the same boat here. Libertarians, having a simple and clear fundamental principle, are better placed than most when it comes to argument.