Is the attainment of natural wisdom exclusive to Buddhism?

Nonduality is part of all religions and cultures, and exists back through time, as best I can tell, so it is "naturally" part of the human experience. It does not depend on a deity or scriptures or dogma, or any other artifact or particular: it depends only on increasing self-development and self-awareness.

That there are as many descriptions of it as describers, and differing opinions on how to achieve it, should not deter anyone. "You are unique, just like everyone else." Self Inquiry is the path to Nonduality (along with anything else that you personally find helpful), and is increasingly well-known and practiced by peer-led groups around the world. I co-lead one where I live.

Gone, Gone, Gone Beyond, Gone Completely Beyond, Wisdom, So Be It! (The Mantra of Prajnaparamita - Supreme Wisdom - from The Heart Sutra - which explicitly disavows and overturns all of the basic tenets of Buddhism.)

Is the attainment of natural wisdom exclusive to Buddhism? No.

Do you know other traditions, or religions or ways to attain wisdom? Yes.

Buddhist wisdom is not an enterprise owned by any cultural stream.

All spiritual attainments are beyond name and form.

Watching your mind (which includes the Four Foundations of Mindfulness) is recommended in almost every religious school and any self-developmental seminar worth a penny.

I could go into a long tirade as to why spiritual self-development is similar across all religions but there are a limitless explanation on the phenomena of shared experiences (kundalini, chi, visions, emptiness, heat, sweating, etc.).

I cannot do this topic justice though because there is a huge burden of proof that is already there.

So where do I recommend you look to get a detailed answer to both of your questions?

• Read Spiritual Paths and Their Meditation Techniques ($)
• Read How to Measure and Deepen Your Spiritual Realization - A Short Multi-disciplinary Course on Evaluating and Elevating Your Meditation Progress and Spiritual Experiences ($$$)
• Read all the articles here. There are many guidances of other non-Buddhist techniques you may apply to grow spiritually. (free)

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Now, I am assuming that you did look into explanations there above. Now are full of understanding of the 5 Stages of the Spiritual Path that are common to all cultivation schools. Now you know for sure that the spiritual path is something beyond any prayer to any deity... it is developing Pure Presence and cultivating other features of Being-As-Is.

Now, I would like to tell you that despite the fact that various cultural streams have many of the same features as Buddhism... and even similar or even equivalent practices... (Early) Buddhism is still better.

It is the most organized, systematic method available. Buddhism, especially Theravadin Buddhism, is the "only" direct path. It is what the Buddha first spoke after all...! It contains within it the bare essentials to practice -- the "extras" are supportive practices like to improve your morality practice Brahmavihara.

Although it may seem that some sects in some religions are exclusive, all the various methods within Buddhism and in all religions--fall under the 8/9 samadhi/dhyana/jhana that our Lord Buddha experimented with and shared.

"The Surangama Sutra" or the more adaptable "Twenty-Five Doors to Meditation - A Handbook to Entering Samadhi" both expand and explain this in a practical way.

A well known Vipassana meditation teacher, Mr. S.N. Goenka always refers to the Dharma (the truth or seeing things as they are) in a non denominational way.

Dharma is not Hindu nor Buddhist, not Sikh, Muslim, nor Jain; Dharma is purity of heart, peace, happiness, serenity. —Hindi doha of S. N. Goenka

Two thousand years ago in India, there were two distinct traditions. One tradition gave importance to the purity of Dharma. The other gave importance to sectarian rites, rituals, religious ceremonies, external appearances, and so on. In those days the tradition of pure Dharma was quite strong, but slowly it became weaker and weaker, and eventually vanished from India. What was left had no trace of pure Dharma. It is very unfortunate that we have lost Dharma. When one speaks of Dharma in today’s India, the question that arises in the audience’s mind is: "Which Dharma? Hindu-dharma, Buddhist-dharma, Jain-dharma, Christian-dharma, Muslim-dharma, Sikh-dharma, Parsi-dharma, or Jewish-dharma? Which Dharma?"

It is a great pity that we have totally forgotten pure Dharma. How can Dharma be Hindu, Muslim, Christian, Jain, Parsi, or Sikh? This is impossible. If Dharma is pure Dharma, it is universal. It cannot be sectarian. Sectarian rites and rituals differ from one sect to another. The so-called "Hindu-dharma" has its own rites, rituals and religious ceromonies; its own beliefs, dogmas, and philosophies; and its own external appearances, and disciplines, such as fasting. It is the same with the Muslim-dharma, Christian-dharma, Sikh-dharma, and so on. But Dharma has nothing to do with all these. Sectarianism is divisive. Dharma is universal: it unites. Source: The Gracious Flow of Dharma - by S.N.Goenka

Mr. Goenka's meditation centers around the world teach insight meditation in a completely non religious setting. Rules include not being able to bring religious items or continue with spiritual practices while you are there.

During the course it is absolutely essential that all forms of prayer, worship, or religious ceremony — fasting, burning incense, counting beads, reciting mantras, singing and dancing, etc. — be discontinued. All other meditation techniques and healing or spiritual practices should also be suspended. This is not to condemn any other technique or practice, but to give a fair trial to the technique of Vipassana in its purity.

I believe this to be an example of a practice of learning to attain wisdom, as it's known in the Buddhist tradition, outside of Buddhism.

Of course not!

In buddhism there are beings called paccekabuddhas, which are beings who attain enlightenment in a period where the dharma is not available in this world. Since this is possible, it's also possible that a practitioner of another tradition attains enlightenment, or at least some of the stages of enlightenment.

But when the Buddha said, in the Satipatthana Sutta that "This is the direct path", also translated as "This is the only path", he meant that any person who wants to attain enlightenment has to have direct knowledge of what he was teaching in that sutta. In short, that the body, sensations, mind states and mental objects are impermanent, unsatisfactory and are not-self.

What this means is that truth is truth, it's not buddhist truth. Whoever knows truth, he is enlightened. But he has to see the truth anyway, because there is no other way to liberation aside from directly knowing the truth.

Dhamma isn't exclusive to Buddhism. As the story goes, wherever there are apple trees, there are apples; but one can't expect to find apples where there aren't apple trees. Likewise, can't expect to find wisdom teaching where wisdom is not being properly taught.

While sitting on one side the wanderer Subhadda said this to the Gracious One: “Those ascetics and brahmins, dear Gotama, who have a community, a group, who teach a group, well-known, famous, religious founders, agreed upon as good for the people, such as: Pūraṇa Kassapa, Makkhali Gosāla, Ajita Kesakambala, Pakudha Kaccāyana, Sañjaya Belaṭṭhaputta, Nigaṇṭha Nāṭaputta, have they all understood, according to their own avowal? Have they all not understood? Or, have some understood? Or, have some not understood?”

“Enough, Subhadda, stop this: ‘Have they all understood, according to their own avowal? Have they all not understood? Or, have some understood? Or, have some not understood?’ I will teach the Teaching to you, Subhadda, listen to it, apply your mind well, and I will speak.”

“Very well, reverend Sir,” the wanderer Subhadda replied to the Gracious One, and the Gracious One said this: “Wherever, Subhadda, the Noble Eightfold Path is not found in a Teaching and Discipline there a true ascetic is not found, there a second true ascetic is not found, there a third true ascetic is not found, there a fourth true ascetic is not found.

But wherever, Subhadda, the Noble Eightfold Path is found in a Teaching and Discipline there a true ascetic is found, there a second true ascetic is found, there a third true ascetic is found, there a fourth true ascetic is found.

-- Mahāparinibbāna sutta, DN 16