2Nyaya and VaisesikaThe Nyaya system is a philosophy of logic. Though it was first formally written down in the 3rd century B.C., its history extends over 20 centuries.The word Nyaya literally means that by which the mind is led to a conclusion. We are led to conclusions by reason and argument.The popular usage of nyaya is “right” or “just” and so Nyaya as a system has come to mean the science of correct reasoning.
3Four methods of knowledge(pramānas) According to Nyaya, there are four methods of gaining knowledge. They are direct perception (pratyaksa), inference (anumana), analogy or comparisons (upamana) and verbal knowledge or testimony (sabda).Not only are these methods of gaining knowledge but also methods for discovering new knowledge.
4The meaning of these methods The Nyāya Sutras define each of these methods as follows.“Perception is that knowledge which arises from the contact of a sense with its object, and which is determinate [well-defined], unnameable [not expressible in words], and non-erratic [unerring]. …Inference is knowledge which is preceded by perception, and is of three kinds, viz., a priori, a posteriori and “commonly seen.”…Comparison [analogy] is the knowledge of a thing through its similarity to another thing previously well-known. …Word (verbal testimony) is the instructive assertion of a reliable person.”
5Here is an exampleSuppose we see billowing smoke on the hill. This is visual perception and we know there is smoke on the hill.We infer that the smoke is caused by fire and conclude that there is a fire on the hill. This is knowledge by inference.The hill is shaped like a pyramid. This is knowledge of the shape of the hill through comparison or analogy.Historical texts say that the hill has been there for the last five centuries. This is knowledge of the age of the hill from reliable verbal testimony.By contrast, Vaisesika accepts only the first two methods of knowledge:perception and inference.
6Verbal knowledge (sabda) This refers to any method of transmitting knowledge, either by oral or written tradition.It is also a method for generating new knowledge. When we take up old writings and try to organize them, question them, analyze them, we are adding to knowledge.This is essentially the role of the scholar.A spectacular example of how organization of past knowledge leads to new knowledge is given by the discovery of the periodic table.
7The art of scientific research The art of research is really the art of asking good questions.How to generate good questions?These were: survey of relevant literature, observation of patterns, conjecturing theorems, re-interpretation of existing theorems, finding analogies, transferring ideas from one area to another, induction and checking converse propositions.
8Comparison with NyāyaIndeed, the method of survey is part of verbal knowledge.Observation is part of direct perception.Conjecture, induction, checking converse propositions are part of the process of inference.Finding analogies and transferring ideas are part of the process of analogy.Finally, re-interpretation is a combination of direct perception and inference.
9The periodic tableIn 1859, Dimitri Mendeleev was 25 and was a poor school teacher in Siberia. The knowledge of chemistry was meager at the time and the natural elements were slowly being classified. Mendeleev decided to organize the elements according to their properties and atomic number, that is, the number of protons in the nucleus.As he began to place the elements in the columns, he discovered a periodicity in their properties and could correlate them to their atomic number.Mendeleev had stumbled on a mathematical key to the chemical elements. It was a “Eureka” moment. Only 63 elements of the 92 natural elements were known at Mendeleev’s time.
11The survey methodMendeleev’s discovery organizes past knowledge by using analogies based on careful observations. Thus, direct perception (pratyaksa), analogy (upamana) and past knowledge (sabda) are all involved.What is brilliant about it is the “gaps” in the table that point to new elements. This is the method of inference (anumana).Thus, his work involves several methods of gaining knowledge: survey, observations, conjectures, and analogies.
12Observations and conjectures In the survey method, we make careful observations. This itself leads to new knowledge and suggests patterns.The patterns lead us to make conjectures and hypotheses to explain these patterns.All of these are involved in Mendeleev’s discovery of the periodic table.
13Analogy and transferThe method of analogy also suggests another method for generating knowledge and that is the method of transfer.What does this mean? A superb example is given by the Doppler effect.We all know that if we are standing on a railway platform, the sound pitch of an approaching train is different from the sound pitch of a departing train. This is because sound waves coming toward you are compressed and those moving away are stretched.Doppler had the idea to transfer this idea to astronomy. The color pitch of stars that are moving towards us should be different from the color pitch of those moving away from us. This is known as the Doppler effect.
14Inference and induction Inference as a method of discovering new knowledge can also be codified as the principle of induction in mathematics.If we have a sequence of dominoes, and the first one falls, and whenever a domino falls, its’ neighbor also falls, then we conclude that all of them fall.
15The converse questionIf A implies B, does B imply A? This is called the converse question.In 1813, Oersted observed that an electric current produces a magnetic field.This led Michael Faraday to ask if the converse is true. Does a magnetic field produce an electric current.He devised an experiment to show that this is the case and thus discovered electromagnetism.
16ReinterpretationThis is a way of gaining new knowledge where we re-interpret something that is well-known in a new way.An excellent example is gravitation.
17Newton’s view of gravity Newton viewed gravity as a force.
22Methods of knowledge SURVEY METHOD OBSERVATIONS CONJECTURES RE-INTERPRETATIONANALOGYTRANSFER OF IDEASINDUCTIONCONVERSE QUESTIONS
23VaisesikaVaisesika, created by Kanada (also referred to as Kashyapa), around 300 B.C. E.The system derives its name from visesa which means “particularity”.It can be viewed as a system of physics and metaphysics in that it tries to explain the fundamental nature of the world and being.It is non-theistic in that it does not mention God, but later commentators felt atoms by themselves could not have produced this universe and so there must have been a “first cause”.
24Vaisesika as an atomic theory This is an early attempt at the scientific method.The word “science” can be traced back to two Latin words, “scire”, meaning “to know” and “scindere”, meaning “to cut, to dissect, to analyze, to take apart.”By contrast, the word “religion” is derived from “religio” meaning “to bind, to unify, to put together.”Thus from an etymological perspective, religion and science seem to be opposites. However, on closer examination, we see that science refers to analysis and religion refers to synthesis.Both are needed for an understanding of ourselves and the world around us. This is the view of Vaisesika. We must examine the world by subdivision, refining the component parts but at the same time perceive the whole together with the components.
25Emil Artin on mathematics “We all believe mathematics is an art. The author of a book, the lecturer in the classroom tries to convey the structural beauty of mathematics, to his readers, to his listeners. In this attempt, he must always fail. Mathematics is logical, to be sure, each conclusion drawn from previously derived statements. Yet the whole of it, the real piece of art, is not linear; worse than that, its perceptions should be instantaneous. We all have experienced on some rare occasions the feeling of elation in realizing that we have enabled our listeners to see at a moment’s glance the whole architecture and all its ramifications.”In Vaisesika, the term samavaaya is used for coherence, or the instantaneous perceptions of the whole that Artin refers to in the above passage.
26Padarthas or categories There are six categories or padarthas: dravya (substance), guna (quality), karma (action), samanya (that which constitutes a genus), visesha (uniqueness or individuality), and finally, samavaaya (coherence).Each of these is again subdivided into further sub-categories. We indicate two such sub-divisions.Substance is divided into nine sub-categories: earth, water, light, air, ether, time, space, self and mind.The substances cannot exist without qualities of which there are 17: color, taste, smell, touch, number, extension, quantity, individuality, conjunction, priority, posteriority, thought, pleasure, pain, desire, aversion, and will.The substances are affected by 5 kinds of action: upward motion, downward motion, contraction, expansion and movement from one spot to another.The first four qualities, namely, color, taste, smell and touch are made up of invisible atoms which have no dimension.
27Six-fold view of perception Recall that the Nyaya school gave us a three-fold view of perception, namely, word, shape and genus. Vaisesika gives a six-fold view.This is best illustrated by an example. Consider Beatrice, the cow.When we see Beatrice, we see a cow (substance). We observe its color and shape (quality). We see it grazing (action). We are also aware that Beatrice is a member of a larger family (genus) of cows, at the same time, we are aware of Beatrice’s uniqueness (perhaps a beauty spot on its face) and finally, the unification of all these, or coherence..
28“Substance is not annihilated by effect or cause “Substance is not annihilated by effect or cause.” – Kanada’s VaisesikaHere, the point is that matter is indestructible at the atomic level.After expounding on the theory of cause and effect, Vaisesika proceeds to the manifold aspects of matter together with a detailed discussion of its qualities.From this, it deduces the existence of mind.“The appearance and non-appearance of knowledge, on contact with the senses and the objects are marks of the existence of the mind.”In a remarkable verse, it deduces there is only one mind. “From the non-simultaneity of volitions, and from the non-simultaneity of cognitions, it follows that there is only one mind in each organism.”After this, the treatise deduces the existence of the self or atman from the action of the life breath.
29The adrista, or the unseen “The circulation of water in trees is adrista. The sun’s rays and their action on convection of wind is adrista. The action of air and fire is explained by the action of the earth. The action of mind is explained by the action of the hand.”Finally, in verses that seem to echo the Gita, it says, “Pleasure and pain result from the contact of the self, senses, mind and object. Non-origination of that follows on the mind becoming steady in the self. After that, there is non-existence of pain in the embodied self. This is that yoga.”
30Difficulties in Vaisesika Even though everything has been reduced to atoms, the treatise finds itself in a quandary. Where does the knowledge of the combinations of atoms reside? This is its ultimate question.“Unique particularities reside in the ultimate substances. They are the factors that make for ultimate distinctions among these substances.”Another difficulty is that time, space, atman and manas are all classified under substance. Several chapters are devoted to discuss the nature of time and space. Finally, it presents the argument from design.“As from the motion of the chariot, we infer the existence of an intelligent guiding agent in the shape of the charioteer, so also we infer an intelligent guiding agent for the body … the agent is inferred from the action of breathing … from the fact that wounds of the body being healed up, we infer the existence of the agent who would be like the master of a house repairing it.”
31The important aspects of Vaisesika Minute detail is given to the working out of abstract concepts.A whole chapter is devoted to the concept of a number and how the mind apprehends such an idea. For example, 1017 occurs in the text.The number of stars in the observable universe is about 1022.It represents the beginning of the scientific method of analysis and synthesis.This attitude was expanded and amplified in later systems, as we shall see.