Anatta a tool or reality?

No-self, good householder, is a tool, a tool (and as such, one toward real, also fine to call it real, at least where a non-liberated is) to gain "the real", the Unbound, and it's not a tool for intents in the world but used after First things are clear. Anatta is actually, as a path-tool also not used to struggle with questions whether there is a self or not, and actually there are many kinds of self, but to remind and encourage to investigate whether that of one just graspes is real, lasting, under ones controll, suitable to make or hold it as mine, me, myself. In this way it works as a tool for certain release, as one is already used in regard of outwardly things to take on or let go of this and that to be able to move on. In regard of the objects/phenomenas to be investigated it's, if one looks for himself, actually real so far, neither eye, it's object, touch at the eye, feeling, consciousness, will... are real, lasting, under ones controll, not fit to be regarded as me, mine, myself and therefore one is - if seeing clear, or reasons proper, or has faith that it is that way - able of letting go and release from it. Same holds for ears, nose, tongue, body and intellect, it's objects, touch...

As it is a tool to leave sensual world and even most refined spheres of experianses, it can be seen and used like late Mahathera Chan once gave in simple words (here used in regard of anicca, but also fit to use likewise anatta:

The Broken Glass

You may say, "Don't break my glass!" But you can't prevent something breakable from breaking. If it doesn't break now, it'll break later on. If you don't break it, someone else will. If someone else doesn't break it, one of the chickens will! The Buddha says to accept this. He penetrated all the way to seeing that this glass is already broken. This glass that isn't broken, he has us know as already broken. Whenever you pick up the glass, put water in it, drink from it, and put it down, he tells you to see that it's already broken. >Understand? The Buddha's understanding was like this. He saw the broken glass in the unbroken one. Whenever its conditions run out, it'll break. Develop this attitude. Use the glass; look after it. Then one day it slips out of your hand: "Smash!" No problem. Why no problem? Because you saw it as broken before it broke. See?

But usually people say, "I've taken such good care of this glass. Don't ever let it break." Later on the dog breaks it, and you hate the dog. If your child breaks it, you hate him, too. You hate whoever breaks it — because you've dammed yourself up so that the water can't flow. You've made a dam without a spillway. The only thing the dam can do is burst, right? When you make a dam, you have to make a spillway, too. When the water rises up to a certain level, it can flow off safely to the side. When it's full to the brim, it can flow out the spillway. You need to have a spillway like this. Seeing inconstancy is the Buddha's spillway. When you see things this way, you can be at peace. That's the practice of the Dhamma.

Once clear on the conventional truth of the path-tool, leading to the only real, having applying it already for all in the world of experiances, one, as sublime encouraged in the raft simile - actually dealing with anatta - has to give up the tools as well, having found a footing on the other shore, for who would carry on a raft, once having gained the secure. But to do not through out the baby with the bath-water, as many do, having got things wrong, not done, gained, the basics, "First things first!" as already linked above.

Liberated, done the task, all those questions are then total clear, and a little taste and release of doubt, will arise if good householder simply investigates one sense of the six after another, for this Dhamma is ehipassiko, not to be real gained in other ways aside of look, and see for oneself.

At least a certain promise of the Sublime Buddha as final encouragement to let go of the question as raised, on faith for now, and to get to the essence of the path: SN 25.1: Cakkhu Sutta — The Eye

(Possible extended or improved answer as well as space to get more active into the topic, can be found here)

[Note that this is not given for stacks, exchange, trades binding one here, but for release]

OP: However, is this reality or is it a tool?

It's both.

OP: Is there truly no self?

There is a self, but it is just a mental idea that appears when the five aggregates work together according to dependent origination. It is a mentally built up concept. There is no standalone indivisible object or thing called self anywhere.

It's like if you show me a chair - a chair is composed of its leg, seat, back etc. Is any one leg or seat or back by themselves the chair? No. Is the chair all the parts together? Also no - because if you remove a leg, it's still a chair, minus the leg. So, the chair is just a concept, an emergent phenomena. There is no standalone indivisible object called chair.

The Vina Sutta provides a nice analogy:

"Suppose there were a king or king's minister who had never heard the sound of a lute before. He might hear the sound of a lute and say, 'What, my good men, is that sound — so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling?' They would say, 'That, sire, is called a lute, whose sound is so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling.' Then he would say, 'Go & fetch me that lute.' They would fetch the lute and say, 'Here, sire, is the lute whose sound is so delightful, so tantalizing, so intoxicating, so ravishing, so enthralling.' He would say, 'Enough of your lute. Fetch me just the sound.' Then they would say, 'This lute, sire, is made of numerous components, a great many components. It's through the activity of numerous components that it sounds: that is, in dependence on the body, the skin, the neck, the frame, the strings, the bridge, and the appropriate human effort. Thus it is that this lute — made of numerous components, a great many components — sounds through the activity of numerous components.'

"Then the king would split the lute into ten pieces, a hundred pieces. Having split the lute into ten pieces, a hundred pieces, he would shave it to splinters. Having shaved it to splinters, he would burn it in a fire. Having burned it in a fire, he would reduce it to ashes. Having reduced it to ashes, he would winnow it before a high wind or let it be washed away by a swift-flowing stream. He would then say, 'A sorry thing, this lute — whatever a lute may be — by which people have been so thoroughly tricked & deceived.'

"In the same way, a monk investigates form, however far form may go. He investigates feeling... perception... fabrications... consciousness, however far consciousness may go. As he is investigating form... feeling... perception... fabrications... consciousness, however far consciousness may go, any thoughts of 'me' or 'mine' or 'I am' do not occur to him."

You can find more info in this answer.

OP: 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 & therefore there is actually a self? Or for another reason?

This comes from SN 44.10.

The ending is:

If I — being asked by Vacchagotta the wanderer if there is a self — were to answer that there is a self, would that be in keeping with the arising of knowledge that all phenomena are not-self?"

"No, lord."

"And if I — being asked by Vacchagotta the wanderer if there is no self — were to answer that there is no self, the bewildered Vacchagotta would become even more bewildered: 'Does the self I used to have now not exist?'"

The Buddha realized the truth that all phenomena is not self. So, he could not say: "yes, there is a self".

At the same time, Vacchagotta would be confused if the Buddha were to say that there is no self, because he does not understand anatta. Hence, the Buddha decided not to answer.

OP: 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.

The self is just a mental idea, a concept - that is conjured by the mind, concocted by the mind.

There is no soul in Buddhism.

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

Both - actually. The Noble Eightfold Path is an iterative process. Please find more details in this answer.

True Reality is : Sabbe Dhamma Anatta. All Dhammas are not me , mine or myself. Anatta is a concept not a tool. Tool is the practice and grasping of Dhamma to realize the true Reality. Dependent Origination is the Dhamma. Therefore you should practice Dhamma.

If you are asking whether Anatta is a useful fiction or a didactic simplification (an upaya) - the answer is no. It is the idea of Self that is actually a vast simplification, while Anatta is a characterization of the much more complex way things exist in reality, behind this convenient simplification (of Self).

It's like we can say: "see this cloud? Right now it looks like a distinct shape but in reality clouds are not static nor distinct, they are transient and amorphous. When we say "this cloud" that's just a simplification we use for convenience".

Similarly we can say: "see this universe? it doesn't actually have any entities, the notion of entities is a simplification we employ for convenience".

Similarly, we say: "sentient beings don't have a self, self is a simplification we use for convenience".

Anatta is a reality, as unambiguously explained in AN 3.136, which says all things are anatta regardless of whether or not Buddhas arise to explain anatta:

Whether Realized Ones arise or not, this law of nature persists, this regularity of natural principles, this invariance of natural principles: all things are not-self. A Realized One understands this and comprehends it, then he explains, teaches, asserts, establishes, clarifies, analyzes and reveals it: ‘All things are not-self.’ AN 3.136

The above said, the realisation of anatta is also a 'tool' that ends suffering, as follows:

Seeing [anatta] thus, the well-instructed noble disciple gets wearied of form, gets wearied of feeling, gets wearied of perception, gets wearied of mental formations, gets wearied of consciousness. Being wearied he becomes passion-free. In his freedom from passion, he is emancipated. Being emancipated, there is the knowledge he is emancipated.SN 22.59

I understand that realizing anatta reduces the suffering. You realize there is no "I" 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 & 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.