In the Buddhist view there can be no affirmation without negation and positive universals that in the Nyaya view are independent and eternal common characters shared by all members of a natural class should be replaced by difference from others that is a negative entity and a non-entity, e.g. what is meant by a cow is not that it is possessed of cow-ness but that it is not a non-cow. Udayana points out that cognition of a negative entity presupposes cognition (...) of what is negated, the negatum. Thus, cognition of cow if the same as not-not cow presupposes cognition of not-cow, but cognition of not-cow presupposes cognition of cow; hence the Buddhist view is open to the charge of mutual dependence. This difficulty does not arise in the Nyaya view. Even if there is no affirmation without negation, negation is not necessarily the content of affirmation. So far as common experience goes, cognition of positive entities does not always require cognition of negative entities, e.g. a cow may be recognized as a cow and possessed of cow-ness without reference to non-cows. (shrink)

As against the Buddhist view that everything is momentary Udayana argues that recognitive perception, such as that this is the same pot I saw before, provides evidence for permanence. Such recognitive perception is common experience and cannot be set aside without compelling evidence. The Buddhist objects that such experience is not reliable; even a burning flame is recognized to be the same, but it is clear from fuel consumption that it is not. Udayana agrees that in the case of a (...) burning flame it cannot be the same flame because then it would have to have opposed features (such as being fueled by more oil before and less oil now). But there is no compelling evidence for the claim that the pot or I would have to have opposed features if enduring. The Buddhist claim that anything enduring must have opposed features such as being both capable and incapable of being productive is groundless. Such features are not opposed and may be explained as being due to availability or non-availability of auxiliary causal conditions and so on. (shrink)

This paper is historical and is devoted to an old controversy in the Indian philosophical tradition with the Vedantins (and others) holding that cognitive states are self-revealing and the Nyaya taking the opposite position. I have summarized the major Vedantin arguments for their viewpoint and offered a critique from the Nyaya perspective. This throws light on a major philosophical controversy in the Indian tradition, a controversy that has not been studied in-depth in the Western tradition. Notably the problem of induction, (...) a major problem in contemporary epistemology, has been studied in-depth in the Western tradition since its introduction by David Hume in the 18th century but the said problem has been studied deeply in Indian tradition for centuries earlier. I have argued in my Classical Indian Philosophy of Induction (2010) that the older Indian contribution on this problem is fully relevant for the very best that contemporary philosophers have offered on this. I hope that this paper will draw the attention of contemporary Western epistemologists who would get involved in this critically important epistemological debate and address a lacuna in the Western tradition. (shrink)

Jnanasri, a famous 10th century Buddhist philosopher, holds that internal states like cognition alone are real and that there is no external, independent physical world. He argues that one may perceive something, say, a horse, irrespective of whether there is a horse or not. Accordingly, one cannot justifiably move from cognition to the external, independent existence of the object of cognition. Udayana points out that one misperceives only something that one in the ultimate analysis has perceived before. While the previous (...) perception may be false, it cannot be false always for then there is a vicious infinite regress. So true perceptions must also be admitted. The best explanation of true perception is that it is perceiving something where and when it is and that of false perception is that it is perception of something that is elsewhere or elsewhen or both. Thus, the Nyaya claims, the object of misperception too is external and independent of perception. Since the Nyaya position is not refuted, the above argument of Jnanasri suffers from assuming the bone of contention. (shrink)

Jnanasri argues: whatever does not reveal reliably presence or absence of something does not have that thing as the content. For example, perception of a cow does not reveal presence or absence of a horse and does not also have a horse as the content. The point is that perception does not provide reliable evidence for external objects for perception does not reveal reliably their presence or absence and does not have them as the content. Udayana claims that the general (...) premise is false. Something may be perceived and be the content even if it is not revealed where it is present or absent (as is the case in the Nyaya view in misperception). Further, it has been argued that a substance and its features are different and that a substance may be the content of perception or be perceived even if some or most of its features are not perceived. Since these positions are argued for and not refuted, Jnanasri has made gratuitous assumptions. (shrink)

Games and Decision Making, Second Edition, is a unique blend of decision theory and game theory. From classical optimization to modern game theory, authors Charalambos D. Aliprantis and Subir K. Chakrabarti show the importance of mathematical knowledge in understanding and analyzing issues in decision making. Through an imaginative selection of topics, Aliprantis and Chakrabarti treat decision and game theory as part of one body of knowledge. They move from problems involving the individual decision-maker to progressively more complex problems (...) such as sequential rationality, auctions, and bargaining. By building each chapter on material presented earlier, the authors offer a self-contained and comprehensive treatment of these topics. Successfully class-tested in an advanced undergraduate course at the Krannert School of Management and in a graduate course in economics at Indiana University, Games and Decision Making, Second Edition, is an essential text for advanced undergraduates and graduate students of decision theory and game theory. The book is accessible to students who have a good basic understanding of elementary calculus and probability theory. (shrink)

Although ancient Greek and Indian philosophers held remarkably similar philosophical positions, the possibility of these two traditions having developed independently cannot be discounted. However, in the fifth century BCE substantial parts of Greece and India were under the Persian rule and belonged to the same political entity. It is very likely that Greeks and Indians sat together in the Persian court where translation services were provided to mitigate the language barrier. In the fourth century BCE there were Greek kingdoms for (...) more than a century in and around northwest frontiers of India paving the way for substantial political and commercial contact. Greeks like Megasthenes, Diogenes Laertius, Suidas, Porphyry, etc. testify that eminent Greek thinkers like Democritus, Pyrrho, etc. visited India and/or that Plato, Plotinus, etc. knew about or admired Indian wisdom. Some of this evidence is relatively late but cannot be dismissed in the absence of specific rebuttal; thus, Indo-Greek scholarly exchange is likely. (shrink)

Indian logic is mainly devoted to the study of nyaya the logical structure of which is analogous to that of a categorical syllogism. In a nyaya it is inferred that since the probans (similar to the middle term) is pervaded by or never exists without the probandum (similar to the major term) and since the probans belongs to the inferential subject (similar to the minor term), the probandum belongs to the inferential subject. Many modern scholars hold that in early Indian (...) logic a nyaya was an analogical argument from particular to particular. We disagree. Early Nyaya works say explicitly that what deviates is a pseudo-probans; this implies that a probans is non-deviant or pervaded by the probandum and thus that a universal premise stating the pervasion of the probans by the probandum is needed. Such a universal premise is also found in articulated arguments. Further, a counterargument based on mere analogy to a nyaya based on a universal connection is viewed as a pseudo-refutation. (shrink)

Although ancient Greek and Indian philosophers held remarkably similar philosophical positions, the possibility of these two traditions having developed independently cannot be discounted. However, in the fifth century BCE substantial parts of Greece and India were under the Persian rule and belonged to the same political entity. It is very likely that Greeks and Indians sat together in the Persian court where translation services were provided to mitigate the language barrier. In the fourth century BCE there were Greek kingdoms for (...) more than a century in and around northwest frontiers of India paving the way for substantial political and commercial contact. Greeks like Megasthenes, Diogenes Laertius, Suidas, Porphyry, etc. testify that eminent Greek thinkers like Democritus, Pyrrho, etc. visited India and/or that Plato, Plotinus, etc. knew about or admired Indian wisdom. Some of this evidence is relatively late but cannot be dismissed in the absence of specific rebuttal; thus, Indo-Greek scholarly exchange is likely. (shrink)

Indian logic is mainly devoted to the study of nyaya the logical structure of which is analogous to that of a categorical syllogism. In a nyaya it is inferred that since the probans (similar to the middle term) is pervaded by or never exists without the probandum (similar to the major term) and since the probans belongs to the inferential subject (similar to the minor term), the probandum belongs to the inferential subject. Many modern scholars hold that in early Indian (...) logic a nyaya was an analogical argument from particular to particular. We disagree. Early Nyaya works say explicitly that what deviates is a pseudo-probans; this implies that a probans is non-deviant or pervaded by the probandum and thus that a universal premise stating the pervasion of the probans by the probandum is needed. Such a universal premise is also found in articulated arguments. Further, a counterargument based on mere analogy to a nyaya based on a universal connection is viewed as a pseudo-refutation. (shrink)

Indian logic is mainly devoted to the study of nyaya the logical structure of which is analogous to that of a categorical syllogism. In a nyaya it is inferred that since the probans (similar to the middle term) is pervaded by or never exists without the probandum (similar to the major term) and since the probans belongs to the inferential subject (similar to the minor term), the probandum belongs to the inferential subject. Many modern scholars hold that in early Indian (...) logic a nyaya was an analogical argument from particular to particular. We disagree. Early Nyaya works say explicitly that what deviates is a pseudo-probans; this implies that a probans is non-deviant or pervaded by the probandum and thus that a universal premise stating the pervasion of the probans by the probandum is needed. Such a universal premise is also found in articulated arguments. Further, a counterargument based on mere analogy to a nyaya based on a universal connection is viewed as a pseudo-refutation. (shrink)

The classical Indian school called Nyāya (literally “logic” or “right reasoning”), is arguably the leading anti-skeptical tradition within all of Indian philosophy. Defending a realist metaphysics and an epistemology of “knowledge sources” (pramāṇa), its responses to skepticism are often appropriated by other schools of thought. This paper examines its responses to skeptical arguments from dreams, from “the three times,” from justificatory regress, and over the problem of induction.

The Buddhist argues that when two cognitive states are different, their objects are also different. For example, awareness of a pot is different from awareness of a cloth and their objects are different as well. Based on the pervasion that no two different cognitive states have the same object the Buddhist claims that the objects of inference and testimony on the one hand are different from the objects of (indeterminate) perception on the other. That is, what is perceived is never (...) the same as what is inferred or learnt from testimony. This lends support to the Buddhist position that only unique particulars that are grasped in (indeterminate) perception are real; what are grasped in inference or testimony are not unique particulars and, accordingly, are not real. Udayana’s critique of the above position is explained and analyzed. (shrink)

One approaching a thing from a distance may perceive it as existent, then as a substance, then as a tree and, finally, as a fig tree. Thus, the same fig tree can be the object of all these different perceptions. This shows, Udayana argues, that difference in cognitive states does not necessarily prove that their objects are different. This argument is in response to the Buddhist claim that since perceptual cognitive states and non-perceptual cognitive states are different, their respective objects (...) are also different; unique particulars (svalakSaNa) that alone are real, are grasped in perception; general features (saamaanyalakSaNa) that are not real are grasped in non-perceptual cognitive states. The Buddhist objects: when the same thing appears to be the object of different cognitive states, only that cognitive state which leads to useful result is reliable. Udayana replies: More than one cognitive state in the above situation may lead to useful result; it is not justified to accept only one of them as reliable and reject the others. The Buddhist objects again: perceptual awareness is direct but non-perceptual awareness is indirect: hence their objects are different. Udayana replies: The same thing may be perceived when there is sensory connection with it and then inferred from an invariably connected sign when there is no sensory connection. Thus, the same thing may be the object of both direct and indirect cognitive states depending on different causal conditions. (shrink)

The Buddhist offers an inference from the Nyaya standpoint to prove that universals are not positive entities but are differences from others: Cow-ness is difference from non-cows because it has both positive and negative features. Whatever has both positive and negative features is nothing but difference from others. Thus, not being measurable has the positive feature of being related to time and the negative feature of not being prior absence and is nothing but difference from being measurable. Cow-ness too has (...) the positive feature (in the Nyaya view) of being, say, eternal and the negative feature, say, of not being horse-ness. So, cow-ness is nothing but difference from non-cows and so on, mutatis mutandis, for other universals. Udayana objects that this inference is unsound from the Buddhist standpoint: Self-differentiating unique particulars that alone are real for the Buddhists are not measurable; but these are not taken to be mere difference from others that is a non-entity for these are taken to be real. (shrink)

Counterinference is one of five kinds of pseudo-prover (similar to fallacy in Western logic) recognized in the Nyaaya school. Typically in counterinference while one side seeks to prove the thesis that a probandum belongs to an inferential subject because an inferential mark pervaded by the probandum belongs to that subject, an opponent challenges that by arguing that the probandum does not belong to the inferential subject because another inferential mark pervaded by absence (negation) of the probandum belongs to that subject. (...) A common example is: sound is eternal, since it is audible and audibility is pervaded by eternality (i.e. all that is audible is eternal, like sound-ness, the common property of all sound particulars); but sound is non-eternal, since it is originated (by clapping hands, etc.) and all that is originated is non-eternal, like a pot, etc. Critics from other philosophical schools have objected that counterinference is not an additional kind of pseudo-prover. Since it is impossible for an inferential subject both to have and not to have a probandum, either at least one of the inferential marks does not belong to the inferential subject (the fallacy of being unestablished) or at least one of the inferential marks lacks pervasion (the fallacy of deviation) and, accordingly, counterinference should be subsumed under those fallacies. Nyaaya philosophers have responded by pointing out that the formal structure of counterinference is different from that of the other fallacies: in counterinference we have two different inferential marks but not in the other candidates. The epistemic result of counterinference is also different from that of the other fallacies mentioned, it is argued further. Moreover, it is contended (against a Nyaaya faction) that the epistemic result is not doubt as specifically understood in Nyaaya but desire to know the truth about the chosen inferential mark and the probandum. Accordingly, counterinference may be explained as that which provides the ground for inquiring what is the truth about the original inferential mark and its probandum due to presentation of an inferential assimilation (paraamarsha) that contradicts the original inferential assimilation. The discussion yields also a broader normative principle that contradiction or counterproof provides the epistemic ground for further inquiry even if there is proof. The selection is from the Tattva-cintaa-maNi, the canonical Navya-Nyaaya work of GaMgesha (14th century CE?). The selection is from a large work and presupposes some things explained elsewhere in the text. Further, though written with great precision the work paradoxically belongs to the old Indian philosophical oral tradition in which a beginner is expected to read it with the help of additional information supplied by an expert. Hence paying close attention to what is implied in the context and supplementing certain ideas is necessary for interpretation and understanding. (shrink)

The problem of induction : East and West -- The later Nyaya solution -- The method of generalization : Vyaptigrahopayah -- Counterfactual reasoning : Tarkah -- Universal based extraordinary perception : Samanyalaksanapratyaksa -- Earlier views of adjuncts : Upadhivadah -- The accepted view of adjuncts : Upadhivadasiddhantah -- Classification of adjuncts : Upadhivibhagah -- Sriharsa's Khandanakhandakhadyam on pervasion -- Selected passages from Prabhacandra's Prameyakamalamartanda on critique of pervasion and inference -- Selections from Dharmakirti's Nyayabindu on non-perception as a probans.

Definition is an important scientific and philosophical method. In all kinds of scientific and philosophical inquiries definition is provided to make clear the characteristics of the things under investigation. Definition in this sense, sometimes called real definition, should state the essence of the thing defined, according to Aristotle. In another (currently popular) sense, sometimes called nominal definition, definition explicates the meaning of a term already in use in an ordinary language or the scientific discourse or specifies the meaning of a (...) new term introduced in an ordinary language of the scientific discourse. Definition combines the purposes of both real and nominal definition and is promoted by the Nyaya philosophers of India. Another important method of science and philosophy is induction. In a narrow sense induction is a method of generalization to all cases from the observation of particular cases. In a broad sense induction is a method for reasoning from some observed fact to a different fact not involved in the former. We understand induction in the broad sense though more often we shall actually be concerned with induction in the narrow sense. How can our limited experience of nature provide the rational basis for making knowlege claims about unobserved phenomena? (shrink)

Although ancient Greek and Indian philosophers held remarkably similar philosophical positions, the possibility of these two traditions having developed independently cannot be discounted. However, in the fifth century BCE substantial parts of Greece and India were under the Persian rule and belonged to the same political entity. It is very likely that Greeks and Indians sat together in the Persian court where translation services were provided to mitigate the language barrier. In the fourth century BCE there were Greek kingdoms for (...) more than a century in and around northwest frontiers of India paving the way for substantial political and commercial contact. Greeks like Megasthenes, Diogenes Laertius, Suidas, Porphyry, etc. testify that eminent Greek thinkers like Democritus, Pyrrho, etc. visited India and/or that Plato, Plotinus, etc. knew about or admired Indian wisdom. Some of this evidence is relatively late but cannot be dismissed in the absence of specific rebuttal; thus, Indo-Greek scholarly exchange is likely. (shrink)

Although ancient Greek and Indian philosophers held remarkably similar philosophical positions, the possibility of these two traditions having developed independently cannot be discounted. However, in the fifth century BCE substantial parts of Greece and India were under the Persian rule and belonged to the same political entity. It is very likely that Greeks and Indians sat together in the Persian court where translation services were provided to mitigate the language barrier. In the fourth century BCE there were Greek kingdoms for (...) more than a century in and around northwest frontiers of India paving the way for substantial political and commercial contact. Greeks like Megasthenes, Diogenes Laertius, Suidas, Porphyry, etc. testify that eminent Greek thinkers like Democritus, Pyrrho, etc. visited India and/or that Plato, Plotinus, etc. knew about or admired Indian wisdom. Some of this evidence is relatively late but cannot be dismissed in the absence of specific rebuttal; thus, Indo-Greek scholarly exchange is likely. (shrink)