An Introduction to Abhidharma Metaphysics

The Abhidharma school of Indian Buddhism represents one of the earliest attempts to form a complete, coherent philosophical system based on the teachings of the Buddha. Abhidharma metaphysics rests on mereological reductionism: the claim that wholes are reducible to their parts. On the Abhidharma view, a composite object like a table is nothing more than its parts arranged table-wise. The “table” is a convenient designator based on our shared interests and social conventions. Crucially, for Abhidharma Buddhists, this also extended to the self. The self, rather than being an enduring substance, is reducible to a bundle of momentary mental states (Carpenter, 2).

Based on this principle of reductionism, Abhidharma went on to develop the Doctrine of Two Truths. A statement is “conventionally true” is if it is based on our commonsense view of the world, and leads to successful practice in daily life. Thus, it is conventionally true that macro objects such as tables and chairs exist. A statement is “ultimately true” if it corresponds to the facts as they are, independent of any human conventions. According to the Abhidharma view, the only statements that can be considered ultimately true are statements about ontological simples: entities that cannot be further broken down into parts. The tendency to think that statements involving composite objects like tables are ultimately true arises when we project our interests and conventions on to the world.

The primary opponents of the Abhidharma Buddhists were philosophers of the Nyāya orthodox tradition, about which I have written before. Nyāya philosophers were unflinching commonsense realists. They held that wholes existed over and above their parts. The word “table” is not merely a convenient designator or a projection of our interests on to the world, it is a real object that cannot be reduced to its parts. Nyāya held that there are simple substances and composite substances. Simple substances are self-existent and eternal. Composite substances depend on simple substances for their existence, but cannot be reduced to them. They possess qualities that are numerically distinct from the qualities of their component parts.

There are some obvious difficulties with the view that wholes exist in addition to their parts, and Abhidharma philosophers were quick to point this out. If the table exists in addition to its parts, it would follow that whenever we look at a table, we are looking at two different entities – the component parts and the (whole) table. How can two different objects share the same location in space? Nyāya philosophers responded by stating that wholes are connected to parts by the relation of inherence. In Nyāya metaphysics, inherence is an ontological primitive, a category that cannot be further analyzed in terms of something else. To put it very crudely, inherence functioned as a kind of metaphysical glue in the Nyāya system. The inherence relation is what connects qualities to substances. The quality redness inheres in a red rose. Similarly, the inherence relation also connects wholes with their parts. In this case, the whole – the table – inheres in its component parts.

At this point in the debate, the standard Abhidharma move was to ask how exactly wholes are related to their parts. Do wholes inhere wholly or partially in their parts? If wholes are real and not reducible to their parts, but nonetheless inhere only partially in their parts, it would mean that there is a further ontological division at play. We now have three different kinds of entities. The parts of the table, the parts of the whole that inhere in the parts of the table, and the whole. Now, what is the relation between the whole and the parts of the whole that inhere in the parts of the table? Does the whole inhere wholly or partially in the second set of parts? If it is the former, then the second set of parts becomes redundant, for the whole could simply inhere wholly in the first set of parts (that is, the parts of the table). If the whole inheres partially in the second set of parts, then we will have to introduce yet another whole-part distinction, and there is an obvious infinite regress looming.

The Nyāya school held that wholes inhere wholly in their component parts. They drew an analogy with universals to make the illustration clear. Just as the universal cowness inheres in every individual cow, the table inheres wholly in every one of its individual parts. 

Abhidharma philosophers rasied a second set of difficulties for Nyāya. Consider a piece of cloth woven from different threads. According to the Nyāya view, the cloth is a substance that is not merely reducible to the threads. But now let us suppose I cannot see the whole cloth. Let us suppose most of the cloth is obscured from my view, and I only see a single thread. In this case, we would not say that I have seen the cloth. I am not even aware that there is a cloth – I think there is just a single thread. But if the Nyāya view is correct, then the cloth (the whole) inheres in every single thread, so when I see the thread, I should see the cloth as well. But since I don’t, it follows that the Nyāya view is incorrect.  

Now consider a piece cloth woven from both red and black threads. Since the cloth is a separate substance, and since composite substances possess qualities numerically distinct from their component parts, the cloth must have its own color. But is the color of the cloth red or black? Nyāya responded that the color of the cloth is neither red nor black, but a distinct “variegated” color (Siderits, 111). But this only multiplies difficulties. If the cloth is wholly present in its parts, and it possesses its own variegated color, why do I not see the variegated color when I look at its component parts? When I look at the red threads, all I see is red, and when I look at the black threads, all I see is black. I do not see the variegated color in the component parts and yet, if the whole inheres wholly in its parts, I should.

Finally, if the whole is a distinct substance over and above its parts, the weight of the whole must be greater than the sum of its parts. But we do not observe this when we weigh composite substances. This is highly mysterious on the Nyāya view. But these problems are all avoided if we simply accept that wholes are reducible to their parts.

Abhidharma is a broad tradition that encompasses numerous sub-schools. Two of the most prominent ones are Vaibhāṣika and Sautrāntika. While both sub-schools agree that everything is reducible to ontological simples, they disagree on the number and nature of these simples. The Vaibhāṣika school is fairly liberal in its postulation of simples, while Sautrāntika is conservative. Moreover, Vaibhāṣika treats simples as bearers of an intrinsic nature. According to Vaibhāṣika atomists, an earth atom, for instance, is a simple substance that possesses the intrinsic nature of solidity. The Sautrāntika school rejected the concept of “substance” entirely. There are numerous reasons for this (most of them epistemological, that I will cover in a subsequent essay), but roughly, it came down to this: We have no evidence of substances/bearers, only qualities. Further, there is no need to posit substances, because everything that needs to be explained can be explained without them. For Sautrāntika philosophers, an earth atom is not a substance that is the bearer of an intrinsic nature “solidity” – rather, it is simply a particular instance of solidity. Thus, in Sautrāntika metaphysics, there are no substances or inherence relations, there are simply quality-particulars. This position is similar to what contemporary metaphysicians call trope theory.

The term “reductionism” is often cause for confusion when used in relation to Abhidharma Buddhism. It must be emphasized that the kind of reductionism relevant here is mereological reductionism. Abhidharma Buddhists were not reductionists in the sense of believing that consciousness could be reduced to material states of the brain. All Abhidharma schools held that among the different kinds of ontological simples, some were irreducibly mental, as opposed to physical.   

Apart from mereological reductionism, the other key aspects of Abhidharma metaphysics are nominalism and atheism. I have covered the Buddhist approach to nominalism in a previous essay, so I will not go over it here. When it comes to atheism, it is important to recognize that Abhidharma Buddhists (like all Buddhists) were only atheistic in a narrow sense. They rejected the existence of an eternal, omnipotent creator of the universe. This did not mean that they were naturalists or that they rejected deities altogether. They believed in many gods, but these gods were not very different from human beings apart from being extraordinarily powerful. Venerating the gods was a means of obtaining temporary benefits in this life or a good rebirth, but the gods could offer no help with the ultimate goal of Buddhist practice: liberation from the cycle of birth and death. The gods themselves, being unenlightened beings, were stuck in the cycle of birth and death. To attain liberation one must seek refuge in the Buddha, the teacher of gods and men.

Works Cited:

Carpenter, Amber. Indian Buddhist Philosophy. Routledge, 2014. Print.  

Siderits, Mark. Buddhism as Philosophy: An Introduction. Ashgate, 2007. Print.

Śrīharṣa’s Master Argument Against Difference

The Advaita Vedānta tradition is one of the most popular and influential Indian philosophical systems. The best translation of the Sanskrit word advaita is “non-dual.” The thesis of Advaita is that reality is at bottom non-dual, that is, devoid of multiplicity. Advaita recognizes that our everyday experience presents us with of a plurality of objects, but maintains that the belief that plurality and difference are fundamental features of the world is mistaken. The ultimate nature of reality is undifferentiated Being. Not being something, but Being itself – Pure Being. The phenomenal world, in which we experience Being as separate beings is not ultimately real. It is constructed by avidya – ignorance of the true nature of reality. We are beings alienated from Being, and true liberation lies in ending this alienation.

One of the reasons offered by Advaitins for accepting these claims is that they form the most plausible and coherent interpretation of the Upaniṣads – scriptures accepted as being a reliable source of knowledge. But this will hardly convince someone who does not already acknowledge the authority of the Upaniṣad. Here, the strategy of Advaita philosophers has typically been to go on the offensive and argue that the very notion of “difference” or “separateness” is in some sense conceptually incoherent. The arguments for this claim were first formally compiled by the 5th century philosopher Maṇḍana Miśra. Subsequent philosophers in the Advaita tradition further developed, defended and extended these arguments. In this essay, I will briefly go over the master argument against difference presented by the twelfth century philosopher Śrīharṣa in his magnum opus, Khaṇḍanakhaṇḍakhādya (“The Sweets of Refutation”).

Śrīharṣa begins his inquiry by asking what “difference” really is. He identifies four possible answers to this question:

  1. Difference is the intrinsic nature of objects.
  2. Difference consists in the presence of distinct properties in objects.
  3. Difference consists in the mutual non-existence of properties in objects.
  4. Difference is a special property of objects.

Śrīharṣa considers each option in turn, and finds them all untenable.

The claim that difference is the intrinsic nature of objects is rejected because difference is necessarily relational. To state that bare difference is the nature of X is to utter something meaningless. At best, we can say that difference-from-Y is the intrinsic nature of X. However, this raises another problem. To describe the intrinsic nature of X is to describe what X is in and of itself, independent of anything else.  In contrast, the very notion “difference-from-Y” indicates a dependence on Y. We have arrived at a contradiction: if X has an intrinsic nature that is parasitic on the nature of Y, then it follows that X doesn’t really have an intrinsic nature.

Śrīharṣa offers a subsidiary argument to drive home the implausibility of the view that that difference is the intrinsic nature of an object. Consider a blue object and a yellow object. An object that is blue by its very nature does not depend on the yellowness of the other object. Even if all the yellow objects in the world were to disappear, the blue object would still be blue. But this could not be the case if difference-from-yellow-objects was the intrinsic nature of the blue object.

According to the second definition of difference, X is different Y if distinct properties are present in X and Y. X and Y can be any two objects, but we may use Śrīharṣa’s example: A pot is different from a cloth because the property potness is present in the pot, while the property clothness is present in the cloth. But this raises an obvious question: what makes potness different from clothness? The answer cannot be (1) – that is, that difference is the very nature of potness and clothness – because that view has already been refuted. If we answered the question with (2), then we would end up saying that what makes potness different from clothness is that potness is itself possesses a property that clothness does not. We would have to maintain that potness-ness is present in potness, and clothness-ness is present in cloth-ness. Even if we ignore the oddness of properties being present in other properties, we can raise another question: What makes potness-ness different from clothness-ness? This series of questions could go on indefinitely, generating an infinite regress. Hence, this option is unsatisfactory. 

Śrīharṣa considers the possibility that difference consists in the mutual non-existence of properties in objects. According to this view, what makes a pot different from a cloth is the absence of potness in the cloth, and the absence of clothness in the pot. But much like before, this raises the question of what makes potness different from clothness. It cannot be (1) or (2), because they have already been refuted. If we bring up (3) here, we would have to say that what makes potness different from clothness is the absence of potness-ness in clothness, and the absence of clothness-ness in potness. At this point, much like before, we could ask what makes potness-ness different from clothness-ness. Once again, we are left with an infinite regress.

This brings us to the final option: that difference is a special property of an object. According to this view, difference-from-Y is itself an attribute of X. But if difference-from-Y is an attribute of X, then difference-from-Y is not X itself, but something different from X. This entitles us to ask what makes the attribute difference-from-Y different from X. It cannot be (1), (2) or (3), so it must be (4). This would mean that it must be another attribute that makes difference-from-Y different from X. But then this attribute itself would be different from both X and difference-from-Y, which simply raises the same question. One more, we see an infinite regress looming.

Having rejected all four possibilities, Śrīharṣa concludes that the very notion of difference is incoherent, and so it cannot be a true feature of the world. A typical reaction to Śrīharṣa’s arguments is that there must be something wrong with them – indeed, something obviously wrong with them. But it isn’t necessarily straightforward to identify what exactly it is. One could question whether Śrīharṣa really has considered all the possible options, whether some of these options really lead to an infinite regress, and finally, whether an infinite regress is something to be worried about. Philosophers from rival traditions adopted all these approaches. Śrīharṣa and his successors anticipated and responded to a number of these objections. They also modified and extended the arguments against difference to more specific cases, to show that differentiating cause and effect, moments in time, and subject and object, were all impossible. For a thorough examination of Śrīharṣa’s critique of difference, Phyllis Granoff’s Philosophy and Argument in Late Vedānta is a good place to start.  

Why Verificationism isn't Self-Refuting

In the early to mid Twentieth Century, there was a philosophical movement stemming from Austria that aimed to do away with metaphysics. The movement has come to be called Logical Positivism or Logical Empiricism, and it is widely seen as a discredited research program in philosophy (among other fields). One of the often repeated reasons that Logical Empiricism is untenable is that the criterion the positivists employed to demarcate the meaningful from the meaningless, when applied to itself, is meaningless, and therefore it refutes itself. In this post, I aim to show that the positivists’ criterion does not result in self-refutation.

Doing away with metaphysics is a rather ambiguous aim. One can take it to mean that we ought to rid universities of metaphysicians, encourage people to cease writing and publishing books and papers on the topic, and adjust our natural language such that it does not commit us to metaphysical claims. Another method of doing away with metaphysics is by discrediting it as an area of study. Logical Positivists saw the former interpretation of their aim as an eventual outgrowth of the latter interpretation. The positivists generally took their immediate goal to be discrediting metaphysics as a field of study, and probably hoped that the latter goal of removing metaphysics from the academy would follow.

Discrediting metaphysics can be a difficult task. The positivists’ strategy was to target the language used in expressing metaphysical theses. If the language that metaphysicians employed was only apparently meaningful, but underneath the surface it was cognitively meaningless, then the language of metaphysics would consist of meaningless utterances. Cognitive meaning consists of a statement being truth-apt, or having truth conditions. If a statement isn’t truth-apt, then it is cognitively meaningless, but it can serve other linguistic functions besides assertion (e.g. ordering somebody to do something isn’t truth-apt, but it has a linguistic function).

If metaphysics is a discourse that purports to be in the business of assertion, yet it consists entirely of cognitively meaningless statements, then it is a failure as a field of study. But how did the positivists aim to demonstrate that metaphysics is a cognitively meaningless enterprise? The answer is by providing a criterion to demarcate cognitively meaningful statements from cognitively meaningless statements.

The positivists were enamored with Hume’s fork, which is the distinction between relations of ideas and matters of fact, or, in Kant’s terminology, the analytic and the synthetic. The distinction was applied to all cognitively meaningful statements. So, for any cognitively meaningful statement, it is necessarily the case that it is either analytic or synthetic (but not both). The positivists took the criterion of analyticity to be a statement’s negation entailing a contradiction. Anything whose negation does not entail a contradiction would be synthetic. Analytic statements, for the positivists, were not about extra-linguistic reality, but instead were about concepts and definitions (and maybe rules). Any claim about extra-linguistic reality was synthetic, and any synthetic claim was about extra-linguistic reality.

Synthetic statements were taken to be cognitively meaningful just if they could be empirically confirmed. The only other cognitively meaningful statements for the positivists were analytic statements and contradictions. This is an informal statement of the verificationist criterion for meaningfulness. Verificationism was the way that the positivists discredited metaphysics as a cognitively meaningless discipline. If metaphysics consisted of synthetic statements that could not be empirically confirmed (e.g. the nature of possible worlds), then metaphysics consisted of cognitively meaningless statements. In short, the positivists took a non-cognitivist interpretation of the language used in metaphysics.    

Conventional wisdom says that verificationism, when applied to itself, results in self-refutation, which means that the positivists’ project is an utter failure. But why does it result in self-refutation? One reason is that it is either analytic or synthetic, but it doesn’t appear to be analytic, so it must be synthetic. But if the verificationist criterion is synthetic, then it must be empirically confirmable. Unfortunately, verificationism is not empirically confirmable, so it is cognitively meaningless. Verificationism, then, is in the same boat with metaphysics.

Fortunately for the positivists, the argument above fails. First off, there are ways to interpret verificationism such that it is subject to empirical confirmation. Verificationism could express a thesis that aims to capture or explicate the ordinary concept of meaning (Surovell 2013). If it aims to capture the ordinary concept of meaning, then it could be confirmed by studying how users of the concept MEANING could employ it in discourse. If such concept users employ the concept in the way the verificationist criterion says it does, then it is confirmed. So, given that understanding of verificationism, it is cognitively meaningful. If verificationism aims to explicate the ordinary concept of meaning, then it would be allowed more leeway when it deviates from standard usage of ordinary concept in light of its advantages within a comprehensive theory (Surovell 2013). Verificationism construed as an explication of the ordinary concept of meaning, then, would be subject to empirical confirmation if the overall theory it contributes to is confirmed.

Secondly, if one takes the position traditionally attributed to Carnap, then one can say that the verificationist criterion is not internal to a language, but external. It is a recommendation to use language in a particular way that admits of only empirically confirmable, analytic, and contradictory statements. Recommendations are not truth-apt, yet they serve important linguistic functions. So, verificationism may be construed non-cognitively, as a recommendation motivated by pragmatic reasons. There’s nothing self-refuting about that.  

Lastly, one could take verificationism to be internal to a language, in Carnap’s sense, and analytic. However, the criterion would not aim to capture the ordinary notion of meaning, but instead it would be a replacement of that notion. Carnap appears to endorse this way of construing verificationism in the following passage,

“It would be advisable to avoid the terms ‘meaningful’ and ‘meaningless’ in this and in similar discussions . . . and to replace them with an expression of the form “a . . . sentence of L”; expressions of this form will then refer to a specified language and will contain at the place ‘. . .’ an adjective which indicates the methodological character of the sentence, e.g. whether or not that sentence (and its negation) is verifiable or completely or incompletely confirmable or completely or incompletely testable and the like, according to what is intended by ‘meaningful’” (Carnap 1936).

Rather than documenting the way ordinary users of language deploy the concept MEANING, Carnap appears to be proposing a replacement for the ordinary concept of meaning. The statement of verificationism is internal to the language in which expressions of meaning are replaced with “a . . . sentence of L” where ‘. . .’ is an adjective that indicates whether or not the sentence is verifiable, and thus is analytic in that language. The motivation for adopting verificationism thus construed would then be dependent on the theoretical and pragmatic advantages of using that language.

So, verificationism can be construed as synthetic, analytic, or cognitively meaningless. It could be considered a recommendation to use language in a certain way, and that recommendation is then motivated by pragmatic reasons (or other reasons), which makes it cognitively meaningless but linguistically useful, which does not result in self-refutation. Or, it could be considered a conventional definition aimed to capture or explicate the ordinary concept of meaning. It would then be verifiable because it could be confirmed by an empirical investigation into the way people use the ordinary notion of meaning, or by its overall theoretical merits. Lastly, it could be internal to a language, and thus analytic, but not an attempt at capturing the ordinary notion of meaning. Instead, it would be a replacement that served a particular function within a particular language that is itself chosen for pragmatic (non-cognitive) reasons. In any of these construals, verificationism is not self-refuting.

Works Cited:

Carnap, Rudolf. "Testability and Meaning - Continued." Philosophy of Science. 1936. Web.

Surovell, Jonathan. "Carnap’s Response to the Charge that Verificationism is Self-Undermining." 2013. Web.

 

Buddhist Apoha Nominalism

The Problem of Universals is one the oldest subjects of debate in Indian philosophy. Realists about universals believe that universals exist in addition to concrete particulars, while nominalists deny the existence of universals. The Nyāya and Mīmāṃsā schools were vocal defenders of realism. Nyāya philosophers believed in universals for a number of reasons:

  • Universals explain how different objects share common characteristics. Cow A and Cow B differ from each other in various ways, and yet we recognize that they’re both cows. The Nyāya explanation for this is that what Cow A and Cow B have in common is the universal “cowness” that inheres in both.
  • Universals fix the meanings of words. The word “cow” doesn’t just refer to a particular cow, but cows in general. How can a word refer to many different objects at once? The Nyāya solution is that the word “cow” refers to a particular qualified by the universal cowness, which is present in all individual cows.
  • Universals are a solution to the Problem of Induction, first raised by the Cārvāka empiricists. Nyāya philosophers viewed the laws of nature as relations between universals. Our knowledge of these universals and the relations between them justifies inductive generalizations, and consequently, inferences such as the presence of fire from the presence of smoke.

Buddhists were the best-known nominalists in the Indian philosophical tradition. The Buddhist hostility towards universals is perhaps best expressed by Paṇḍita Aśoka (9th century): “One can clearly see five fingers in one’s own hand. One who commits himself to a sixth general entity fingerhood, side by side with the five fingers, might as well postulate horns on top of his head.”¹

In this post, I will briefly go over how Buddhists responded to the first two reasons for believing in universals provided by the Nyāya school. The Buddhist defense of induction will have to be the subject of a separate essay.

The form of nominalism Buddhists advocated is called apoha, the Sanskrit word for “exclusion.” The first precise statement of apoha nominalism can be found in the works of Dignāga (6th century). Dignāga claimed that the word “cow” simply means “not non-cow.” Since there is obviously no universal “not cow-ness” present in every object that is not a cow, this semantic view doesn’t commit us to the existence of universals. Every cow is a unique particular distinct from all other objects. We simply overlook the mutual differences between cows and group them together based on how they’re different from non-cows.  Thus, it’s not because cows share something in common that we call them by the same name. Rather, we think all cows share something in common because we have learned to call them by the same name.

There are some objections that immediately spring to mind, and Nyāya and Mīmāṃsā philosophers brought them up repeatedly in their criticisms of apoha nominalism. First, how does saying that “cow” means “not non-cow” provide a solution to the problem of universals? “Not non-cow” involves a double negation, so to say “cow” means “not non-cow” is just to say “cow” means “cow.” This leads us right back to where we started, and just as before, it seems that we need to posit a universal cowness. Second, how can we focus on cows’ common differences from non-cows unless we already know how to tell what a cow is in the first place? Once again, we seem to have gone in a circle, and apoha seems to presuppose precisely what it was supposed to explain.

Dignāga’s successors responded to the first objection by drawing distinctions between different kinds of negation. Consider the statement: “This is not impolite.” Now, at first glance it might seem like this just translates to “This is polite,” because of the double negation involved in “not impolite.” But this is not necessarily the case. The statement could be about something to which the very category of politeness does not apply, in which case “not impolite” is distinct from “polite.” Thus, “not non-cow” can mean something genuinely different from “cow.”

To understand how Buddhists responded to the second charge of circularity, it helps to look at another Buddhist view. Buddhists were mereological reductionists: they did not believe that wholes were anything over and above their parts. So, a table, for instance, is nothing more than its parts arranged table-wise. The “table” is just a conceptual fiction: a convenient designator we use because of our shared interests and social conventions. It is conceivable, for instance, that someone who has never seen or heard of tables before will not see a table, just pieces of wood put together in seemingly random fashion. The idea that the table is ultimately real arises when we project our interests on to the world. How is any of this relevant to the question of universals? Buddhist philosophers argued that something similar goes on when we fall under the impression that all cows share a common cowness. We overlook the differences between individual cows because they satisfy some of our desires – for example, the desire for milk – that non-cows don’t. We then project our interests on to the world, mistakenly concluding that cowness is a real thing.

This may not seem like a very satisfactory response. It just pushes the problem back a step. How do all these particulars satisfy the same desire if they don’t share something in common? In this case, it seems like the cows really do share something: the ability to satisfy our desire for milk. Dharmakīrti (7th century) responded to this by using the example of fever-reducing herbs. He pointed out that there are many different herbs that reduce fevers. But it would be foolish to conclude from this that there exists a universal “fever-reducing-ness.” Each of these herbs is different, and they don’t reduce fevers in the same way, or use the same mechanisms to do so. We group them together under a single category only because of our subjective interest in reducing fevers. Dharmakīrti’s claim is that the same is true of everything. Each particular serves our interests in a manner that’s utterly distinct from everything else in the world. And so once again, there is no need to posit universals.

But there are still some lingering worries here. While we may accept that in the case of the herbs there is no universal fever-reducing-ness, does the same response work for simple substances such as elementary particles? Assuming for the sake of argument that an electron is an elementary particle, surely all electrons share something in common. Doesn’t the ability to bring about similar effects require a shared capacity – in this case, the same set of causal powers? One possible response to this line of argument, formulated by the philosopher Kamalaśīla (8th century), is to adopt what we would recognize as a Humean view of causation. Kamalaśīla rejected the notion of causal powers entirely, and like Hume, stated that there is nothing more to causation than constant conjunctions of events. Once again, talk of “causal powers” is just a convenient way of speaking about certain correlations that we never fail to observe.

This is obviously a very brief sketch of apoha nominalism. There is much more to say, particularly on the subtle differences between different versions of apoha defended by different Buddhist philosophers. This is a good place to start for further reading.

References

[1] From the translation in Apoha: Buddhist Nominalism and Human Cognition, edited by Mark Siderits, Tom Tillemans and Arindam Chakrabarti (2011).