Sanskrit language is very versatile language. A versatility of a language depends on its ability to offer flexibility to adapt to different functions & Etymology. Sanskrit is the only language, based solely on Etymology. Even today in English, we aren't able to find a synonym to 'Atman', we use soul or spirit. Although, soul or spirit isn't same as 'Atman.' Atman has multiple meanings in Sanskrit.
The Spirit means the non-physical part of a person which is the seat of emotions and character, the soul.
Atman is referred to as Jeeva or Chetana or the creatures. Atman also means - owner. This is the greatness of Sanskrit. Vedas are expressed in Sanskrit; this is the problem encountered in interpreting Vedas. If you interpret Vedas, based on the literal meaning, you won't be able to get its core meaning or you misunderstand it.
Context based understanding is critical to understand the core meaning of Vedas, then can only you get the whole crux of Vedas.
A person who's an expert in Vyakarana Shastra (Grammer of Sanskrit) may not understand Vedas. Without contextual analysis of the terms, you don't understand anything!
Sanatana Dharma as a whole, represent the heart of Vedic Philosophy. Hindu is wrong term; ours is not a religion. The dictionary definition of Religion - the belief in and worship of a superhuman power or powers, especially a God or gods. Every religion essentially encompasses one or more philosophies. Unlike Abrahamic religions, Sanatana Dharma doesn't impose beliefs, there's more freedom given to the follower. Sanatana Dharma don't impose the laws of blasphemy! It whole-heartedly embraces objectivity and subjective aspects of the philosopher & the philosophy; strives to give objectivity through philosophical debates through reasoning and with the help of Agamas or Veda Pramanas or Proof in Vedas.
There are many philosophies allied with this school of thought affiliated to Sanatana Dharma: - Charvaka, Jain, Nyayavaada, Sankhya Shastra, Meemamsakaaha, Advaita, Vishishta-Advaita, Dwaita, Goudiya Sri Vaishnava philosophies.
Philosophy is like science! The pioneers formulated or propounded certain philosophies, based on that, others improvised further. Until you find the correct one, keep looking! Don't settle!
Don't affiliate to any school of thought or philosophy or one religion, be free! Be open!
Affiliating to one school of thought or philosophy or religion, stops you from further learning other philosophies. You become a narrow-minded person! This alone stagnates your spiritual awakening! Your affiliation to one school of thought or a philosophy or religion is nothing but bodily affiliation. It's the reason, why you are here, trapped in this vicious cycle of birth-rebirth.
For a spiritual guy, truth alone should matter! It's only the truth that triumphs in the end!
We are taught to dim (or even hate) the beauty of other religions or school of philosophies, thoughts by glorifying ours!
When you blindly follow one religion or philosophy, you are blind to the negatives of the currently following philosophy, you magnify the negatives of other philosophies, or you may hate them for no or obvious reasons.
Approach any philosophy with the science (physics) approach. Classical scientists like Newton gave gravitation law, form then to now, here we are at the String theory level!
Having an open mind & the approach to philosophy are explained in the article in the related section. Here we are going to present each philosophy in an objective way (without being judgmental). We revere all philosophies or philosophers or Acharyas or Gurus.
For starters, only one philosophy of Vedanta, with due respect Kevala Advaita of Shri Aadi-Shankaracharya, considers the Jagat (Universe or chain of Universes.) to be Mithya or illusory, false. Acharya Shankara was not the first one to propose Advaita, Bhaskar Acharya proposed one version of Advaita, known as 'Bhaskara-Advaita.'
Kevala-Advaita is also known as Shankara-Advaita or Maya-Vada.
Shankara-Advaita recognized unity in multiplicity, a common identity between individual, pure consciousness, as having no existence apart from Brahman. It states that-
Brahma Satya: Jagan Mithya ||
Trans. - Brahman (God or Paramatma) is the only one, the Jagat (Universe) is all illusory or Mithya.
The major metaphysical concepts in Advaita Vedānta tradition, such as Māyā, Mithya (error in judgment), the belief in and worship of a superhuman power or powers, especially a God or gods. Vivarta (illusion/whirlpool).
The Brahman is the virtual simulator of the illusory universe, this is his greatness; you are trapped by Maya (illusion). Further there's introduction of Three Planes of Existence. According to classical Advaita Vedānta: the plane of absolute existence (Paramarthika Sathya), the plane of worldly existence (Vyavaharika sathya), which includes this world and the heavenly world, and the plane of illusory existence (Pratibhāsika Sathya or Pratibhāsika existence). The two latter planes of existence are a function of Māyā and are thus illusory to some extent, not completely.
A Pratibhāsika Existence, such as objects presented in a mirage, is less real than a worldly existence. Its corresponding unreality is, however, different from that which characterizes the absolutely nonexistent or the impossible, such as a sky-lotus or Akasha-Padma (a lotus that grows in the sky) or the son of a barren woman. The independent existence of a mirage and the world, both of which are due to a certain causal condition, ceases once the causal condition change. The causal condition is Avidya, or ignorance. The independent existence and experience of the world ceases to be with the gain of knowledge of Brahman.
Pratibhashika Sathya & Vyavaharika Sathya are illusory to some extent because Brahman is a virtually simulating both the planes of existence. That's why these two are referred to as Mithya or illusory to some extent.
Ex.- There's a rope laying on the floor at a far distance, you saw that and thought it's a snake. You by seeing the rope and thinking that it's a snake indicates you still have Avidya or Ajnana, you are still trapped by Maya. Shankara-Advaita propounds that there's some illusion associated or the plane of illusory existence surrounding the rope that's Pratibhāsika Sathya.
To conclude, Shankara-Advaita or Kevala-Advaita classifies Jagat into 3 planes of existence or categories, they are -
plane of absolute existence (Paramarthika Sathya),
the plane of worldly existence (Vyavaharika sathya),
the plane of illusory existence (Pratibhāsika Sathya).
On the contrary, Acharya Madhwa propounded that the Jagat is real, and Isha (Paramatma) is real. Illusion exists in human mind. You can observe that illusion is a product of 'Avidya' & 'Ajnana.' Coming back to the example, just because your bare feeble eyes thought that the rope is snake, doesn't mean the rope is snake or the snake can become rope. Both are different, they may resemble each other's physical structure, but they are completely different. Snake is a living creature; rope is a non-living object. This is Jeeva-Jada Bhedha: or there's difference between living or non-living creatures. It's all plane simple!
The plane of illusory existence is because of our defect to see the things. The world is objective. As per physics, humans aren't able to see 99% of the world around you, only 1% of the light spectrum is visible to human eyes. So, you can see only 1% of the world around you is visible, that's actually a biological flaw of the human body.
Coming to planes of existence, Acharya accepts that there are different planes of existence (plane of cosmic energy or Dhee: Shakti, as given in the Gayatri Mantra), but those are absolutely objective; what we think in our minds about the anything is subjective.
When the 3rd eye or the Ajna Chakra is opened or activated, you'll be able to access all the planes of existence, you'll see everything & everyone, most importantly, you'll see Brahman's presence everywhere & in everything.
Acharya Madhwa classifies the reality into 2 types -
Objective Reality (Sakshi)
Subjective Reality (Swabhava)
Sakshi or the objective reality is unaffected by our bias or prejudice, which is based on Jeeva Swabhava or nature of the creature.
Ex. In a class of 50, all the students have listened to the explanation of the teacher at the same time; still everyone has understood in their own unique way. This is reflected in the exam results, only one person gets the highest marks, others get different marks, but are not equal to the highest marks. Occasionally, one or two may get the get the same marks; not all students get the same marks.
This is supported by the following 'pramanas' or the 'agamica pramana' or the proofs from the Vedas -
यच्चि॒केत॑ स॒त्यमित्तन्न मोघं॒ वसु॑ स्पा॒र्हमु॒त जेतो॒त दाता॑ ॥
“The world which you have created is real indeed, for it is not empty.”
—Rigveda, Shaakala Samhita, Mandala 10, Sukta 55, Mantra 6
(Quoted by Shripaada Madhvacharya, in his Brahma Sutra Bhashya, Adhyaaya 2, Paada 1, Sutra 18)
ब्रह्म सत्यं तपः सत्यं सत्यं चैव प्रजापतिः । सत्याद्भूतानि जातानि भूतं सत्यमयं महत् ॥
“Brahman is real, Tapas is real, and Prajapati is also real. Because the various entities and the total material energy (of which this material world is a part) have taken birth from the supreme reality, they are also real.” -Mahabharata, Ashvamedha Parva, Adhyaya 35, Shloka 24
Brahman here refers to the one, who is responsible for creation, maintenance & the destruction of Metaverse. One or Eka: is the name of Vishnu. This is given in the 78th Shloka of Sri Vishnu Sahasranama.
Eko Naikah Sah: Kah Kim Yat Tat Padamanuttamam | Lokabandhur Lokanatho Madhavo Bhaktavatsalah ||78
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Bhagwan Sri Madhwantargata Shri Krshnaarpanamastu.