If we understand the word ’tradition’ to mean ‘a set of practices’, then the question is this: why continue a set of practices? When someone ‘justifies’ (I will soon explain why I use scare quotes for this) this by referring to the existence of a set of practices, what exactly is the person doing?
One way of looking at it is to say that the person ‘justifies’ his actions and understand justification to mean providing a logically derived conclusion from a set of premises. The validity of the reasoning would constitute the justification in this context. Quite obviously, because we are speaking of logical justification, we are inclined to formulate the premises, test the derivation and look at the truth value of the conclusion.
There is, however, another way of looking at the notion of ‘justification’. One justifies an action by pointing to some or another action. In this case, justification refers to some kind of a relation between actions, and not between beliefs. Even though it might not be clear at this moment what kind of a relation should exist between two actions such that one action justifies another, the point is that such a justification is also possible.
In the second case, what misleads the discussion is the use of the word ‘justification’ in one of its senses, the sense in which it is applicable only to beliefs. That is to say, the problem lies not in the fact that some person has to believe that he must continue the tradition; he is suggesting that the existence of a set of actions provides a justification (in the second sense of the word) for his actions.
Should it be possible to make sense of this construal philosophically, the answer is obvious: indeed one can justify the continuation of a tradition without having the belief that one must continue the tradition.