Anatta a tool or reality? I understand that realizing anatta reduces the suffering. You realize there is no &quot;I&quot; to suffer, to have anxiety, to be insulted etc. That is indisputable. However, is this reality or is it a tool? Is there truly no self? It is said that the Buddha remained silent upon the question of Am I? and Am I not?, was that because the answer to the question is irrelevant to the reduction of suffering &amp; therefore there is actually a self? Or for another reason?

'May my form be thus, may my form not be thus'; and indeed, O monks, since form is not-self, therefore form leads to affliction and it does not obtain regarding form: 'May my form be thus, may my form not be thus.'

After this is said about the 5 aggregates, and the saying there is no permanent soul/self, I understand that identifying with any of them only leads to suffering, due to their impermanence. But this doesn't mean the self cannot exist outside of it, right? What I mean by this is, not inside/outside/a combination/the collection of them all, but rather something else that we cannot even talk about.
Furthermore, is it wise to try to understand Anatta, or is it best to realize it?
I understand that realizing anatta reduces the suffering. You realize there is no &quot;I&quot; to suffer, to have anxiety, to be insulted etc. That is indisputable. However, is this reality or is it a tool? Is there truly no self?

Throughout history, many arahants from many traditions have attempted to describe the true nature of reality. You can see examples of this from diverging explanations of realizations between Buddhist traditions. Some traditions describe enlightenment from the perspective of “no self”. This perspective views the world as full of illusions, all empty, transient, and devoid of identity. This perspective can be said to be one of negation, where you realize there is no identity in what you once believed there to be. Others describe enlightenment through the perspective of “true self”. This perspective views the world as pervaded by an almost godlike entity, a being that can be seen as the source of all that arises. This perspective can be seen as one of addition, where you realize you are not only human, but also the totality of the universe, and become one with everything.
Whenever this conversation arises, I always am reminded of the Buddha’s parable about the blind men an the elephant. Each touching a different limb of the elephant, and endlessly arguing about who’s description is accurate. This situation is extremely similar. Neither the no self, nor true self perspectives are completely accurate. The truth lies somewhere in between.
The perspective of being an arahant is one that can only be experienced and is impossible to explain in its entirety. To the mind, it is logically paradoxical, and therefore can not be conveyed accurately. Experientially though, the paradoxes coexist easily and without effort.

It is said that the Buddha remained silent upon the question of Am I? and Am I not?, was that because the answer to the question is irrelevant to the reduction of suffering &amp; therefore there is actually a self? Or for another reason?

So, based off the above, hopefully you see why the Buddha avoided the questions. Describing the enlightened state is logically impossible. Anything that can be said about it can only be partially accurate. And people tend to get so caught up in the details, I think personally he was just trying to avoid blind men and the elephant situations in the hopes that people would make real progress as opposed to arguing about their belief systems.
I wouldn’t say the answer is irrelevant. The perspective you gain from becoming enlightened is what provides the understandings that ultimately ends suffering. It just can’t be accurately conveyed through language.

After this is said about the 5 aggregates, and the saying there is no permanent soul/self, I understand that identifying with any of them only leads to suffering, due to their impermanence. But this doesn't mean the self cannot exist outside of it, right? What I mean by this is, not inside/outside/a combination/the collection of them all, but rather something else that we cannot even talk about.

Those who describe true self understandings will tell you that what you really are is not a human being or body, but that indescribable thing that creates all that arises. That very same indescribable thing is what the Buddha describes as “empty” and “devoid of self”. Both perspectives are close, but again, not fully accurate.
So yes, one could say that a self exists outside of experience. But, thinking in this way will not help you become enlightened. Honestly I view it as a hinderance. In my experience, the illusory self likes to “jump” from one object to the next. For example if you believe you are the body, and then experience proof of the beliefs inaccuracy, the process of self identification tends to begin somewhere else. “I’m not the body, so I must be the mind! I’m not the mind I must be my thoughts!” Etc. My advice is to not think in this way. If you believe it’s possible that what you are something that exists outside of your experience, you put yourself in a bad situation. You are giving the illusory self a place it can nestle in, that is based on belief alone and can not be verified. If you wish to be free you must focus on investigating what you presently believe yourself to be, and constantly disprove places the self will try to hide.
Of course I’m speaking in metaphors here. The illusory self is not a thing that exists, but a process of identification that needs to come to a stop by observing that there is nothing permanent that can be claimed to be yourself.

Furthermore, is it wise to try to understand Anatta, or is it best to realize it?

Anatta can not be fully intellectually comprehended. Even those who are enlightened can not fully logically process the experience. They just experience life, as no one, someone, and the entire universe, at the same time. They accept the mind is of no help in the situation, and abandon any attempts to logically understand.
I would say it is not wise to investigate “what the enlightened experience is like”. One should work to become enlightened, and then once you get there yourself, you will fail too (as all others have before you) in explaining the experience to others. Even if you found an enlightened being that was willing to describe it for days on end to you, you would be no closer to the experiential understanding that is required to become free.
However, that being said, the Buddha’s no self teachings are filled with wisdom that should be used to guide you along your path. Enlightenment is inevitable if you can experience first hand how your current belief systems are incorrect. The first moment you truly break down the illusion of self and no one sees that the self doesn’t exist, from that moment on you will become free.