Indian philosophy has 6 classical schools and 3 non classical ones. The 6 classical schools ( shatdarshan) are Nyaya, Vaisheshik, Sankhya, Yoga, Purva Mimansa and Uttar Mimansa ( Uttar Mimansa is also called Vedanta). The 3 non classical schools are Buddhism, Jainism and Charvak. It is said that the main difference between the classical and non classical schools is that the former rely on the authority of the Vedas, while the latter do not. This, however, is incorrect, as I will demonstrate.
The most popular of the 6 classical schools is the last i.e. Vedanta, which says that the world is unreal and Maya, while the reality is only one,Brahma.
I, however, believe in the first philosophy, Nyaya. This philosophy, according to the Nyaya Sutras written by its founder Gautam, states that nothing is acceptable unless it is in accordance with reason and experience, which is precisely the scientific approach. This is the age of science, and to progress we must adopt the scientific approach and develop the scientific outlook.
The second classical Indian philosophy, Vaisheshik, was the physics of ancient times. It propounded the atomic theory of its founder Kannada. At one time Vaisheshik was regarded as part of the Nyaya philosophy, since physics is part of science. But since physics is the most fundamental of all sciences, Vaisheshik was later separated from Nyaya and put forth as a separate philosophy. Sankhya philosophy provided the materialistic ontology for Nyaya and Vaisheshik, but there is very little original literature in Sankhya.There is nothing in the Nyaya, Vaisheshik or Sankhya philosophies that they rely on the authority of the Vedas.
The Nyaya philosophy is realistic and pluralistic. This is in sharp contrast to Vedanta. While Vedanta says that the world is unreal, Maya, Nyaya says that the world is real. While Vedanta is monistic, in other words, it says that there is only one reality, Brahman, Nyaya says that there are several real things in the world, and it is totally false to say that a tree, a table, an animal, a human body, a motor car, etc are really all one.
Nyaya philosophy relies on several pramanas i.e. means of obtaining true knowledge as its epistemology. But, according to it, the pradhan pramana or principal means of obtaining knowledge is pratyaksha pramana i.e. the knowledge obtained through the 5 senses, and this is also the approach of science. Of course there are other pramanas e.g. anumana i.e. inference, through which we can obtain true knowledge. Thus,when Rutherford propounded his atomic theory ( that there is a central nucleus, with protons, neutrons, etc around which electrons are orbiting, like the planets orbiting the sun) he had never actually seen an atom, but inferred his atomic theory from the scattering of alpha rays ( which are helium ions). Similarly, the existence of black holes has been inferred from the movements of neighbouring heavenly bodies, though no one has actually seen a black hole ( in fact one cannot see it because its material is so dense and compressed that due to its immense mass the gravitational pull is so strong that even light cannot escape from it ). Another pramana is shabda pramana, that is, a statement of an expert. Thus we accept that e=mc squared, which is the formula of Einstein, though we do not ourselves understand how Einstein derived this formula.. Yet we believe that it is true, because Einstein has an outstanding reputation as a theoretical physicist, and therefore we believe in what he says even without understanding it. Similarly, we believe in our doctor when he diagnoses some illness and prescribes some treatment, because a doctor is an authority in medicine.
For India to progress we must adopt the Nyaya philosophy, i.e. the scientific approach in everything. We must develop modern minds. To be modern, however, does not mean wearing a smart suit or a nice tie or a lovely sari or skirt. it means developing a rational mind, a scientific mind, a questioning mind. Our ancestors, like the ancient Greeks, had questioning minds, they questioned everything. There are records of hundreds of shastrarthas or debates in ancient India, and because of this we made tremendous progress in science in ancient times, e.g. in mathematics ( Aryabhat, Brahmagupta, Bhaskar, etc), in medicine ( Sushrut, Charak, etc), in astronomy ( Aryabhat, etc), in grammar ( Panini, Patanjali, etc), All this was possible because behind these sciences was the scientific philosophy of Nyaya which gave them great philosophical support.
Unfortunately, subsequently in our history we took to the unscientific path of superstitions and empty rituals, which has led us to disaster. The way out for our nation therefore is to go back again to the scientific path shown by our ancestors, the path of Aryabhat and Brahmagupta, Sushrut and Charak, Panini and Patanjali, Ramanujan and Raman, and of course the path of the Nyaya philosophy.
It must, however, be clarified that some subsequent philosophers who claimed to be Nyayiks, e.g. Vatsyayan (see his Nyaya Bhashya), Udayan (see his Kusumanjali) etc totally distorted the Nyaya philosophy by introducing theological elements in it, and the Navya Nyaya scholars like Gangesh who resorted to gymnasics in logic. I, however rely on the original Nyaya philosophy of Gautam, which I believe is the correct philosophy for our nation to progress