The Heart Sūtra and the Problem of Grounding

Tesha Sengupta

Introduction

In this essay I will explore the doctrine of emptiness as presented in the Heart Sūtra. A common objection that is leveled against the doctrine is that it entails nihilism. In this essay I will argue against this objection. I will do this by proposing that though the doctrine of emptiness asserts that all concepts are empty of intrinsic nature, the concepts can still be grounded in the structure that they instantiate. In order to explain my proposal, I will provide two analogies. Lastly, I will consider an objection to my proposal and reply appropriately.   

Section 1: Preliminary Remarks about the Heart Sūtra

In this essay I will focus on the following verse from the Heart Sūtra: “Form is empty. Emptiness is form. Emptiness is not other than form. Form is not other than emptiness”. In this section, I shall provide a brief overview of Nāgārjuna’s doctrine of emptiness. By claiming that “form is empty”, Nāgārjuna argues that nothing has any intrinsic identity or essence; the essence of a particular object is determined by the relations that it holds to other objects. This is because all objects of reality are dependently originated. For example, take a table. Nāgārjuna would claim that the table has no intrinsic essence. Instead, its essence is dependent on its causes, the different parts of the table (i.e. the four legs), its color, its spatial relation with other objects, its dissimilarity to a chair etc. Therefore, there is no singular, intrinsic essence that identifies the table. Rather the table is identified by the set of relations it holds with other objects. Nāgārjuna thus argues that everything lacks intrinsic essence. 

Now note that the referents of “everything” are quite expansive. “Everything’ refers to physical objects of the external world, raw mental states (such as that of anxiety or happiness), abstract concepts (such as beauty), the products of language and more. Thus there is very little uniformity between these referents and it will be difficult to provide an account of the doctrine of emptiness that is sufficiently general but also takes into account all the differences between these referents. Therefore, for the purposes of this paper, I shall only focus on the concepts of reality. Hence, I will focus on the following types of claim: “the concept <table> has no intrinsic essence” rather than the claims of the form: “the object table has no intrinsic essence”.

I believe that this is justified because I claim that experiences are conceptual by nature. By this I mean that when one has any experience, they immediately self-reflect upon that experience in an attempt to characterize the contents of that experience through comparison with previous experiences. Take, for example, the experience of seeing a table. When I have this visual experience, I immediately form a mental picture of the table and compare said picture with other experiences that I have had (by noticing similarities and differences). This is done in an attempt to contextualize and situate the contents of my experience in the web of all other experiences. The resulting characterisation of the contents of my experience is what I am calling concepts of reality. Thus all the referents of “everything” do appear in experience as conceptual entities and hence will be accounted for indirectly in my narrowed-down analysis of the doctrine of emptiness. 

Section 2:The Problem of Grounding/ Nihilism

Having discussed Nāgārjuna’s position, I shall now discuss how the doctrine of emptiness could possibly lead to nihilism - the view that nothing exists. Nāgārjuna states that no object or concept has any intrinsic essence - each concept’s essence is constituted by the relation that it holds with other objects. However, these concepts’ essences are also constituted by relations that they hold to other concepts. Hence, there seems to arise an infinite regress. There seems to be nothing that grounds this whole process. In other words, there is nothing that everything else is defined by. Consequently, no concept has any identity. Therefore nothing exists. 

It is the goal of this paper to find some way to interpret Nāgārjuna such that the entailment of nihilism is avoided. In other words, I attempt to find some sort of grounding for the doctrine of emptiness. I will not attempt to provide a rigorous definition of grounding here as there is still an ongoing debate on what exactly is the nature of something that does ground. Instead, I shall appeal to the intuitive understanding of grounding - as something that provides some sort of meaning and determinate nature to the concepts of conventional reality.  

Section 3: My Proposal

In this section, I shall attempt to explain why the doctrine of emptiness does not entail nihilism. In other words, I will attempt to demonstrate that our concepts are grounded and that, though they might be empty of intrinsic nature, they do have some determinate nature. I claim that the structure which our concepts of conventional reality both instantiate and inhabit simultaneously grounds them and prevents the doctrine of emptiness from entailing nihilism. 

Section 3.1: Initial Concerns

However, before I begin, I want to provide the following caution. It is important to note that I can not provide a full and accurate description of the structure that does the grounding. I claim this because of the following reasons. 

Firstly, it is important to note that at all times we are functioning within the structure; any thought or concept that we form in our mind as an attempt to describe reality will occupy a specific position within the structure. In other words, any concept or label that we do employ in an attempt to describe this structure will be dependent on other concepts for its definition and nature. Therefore we can never fully characterize or conceptualize the entirety of the structure. Any concept that attempts to do so will be employing the structure to do so and hence there will be something which is missing from this conceptualisation. In fact the moment a thought <X-structure is doing the grounding> enters our conscious awareness, it no longer does the grounding because the very fact that this sentence makes sense to us is dependent on the actual structure that does the grounding. In summary, it is impossible for us to provide a complete and bird’s eye description of the structure when we are in the structure; what does the grounding can never be thought of completely or be a product of our thought. 

At this point one may have the following objection: if there is no way for us to provide or understand a description of said structure, what evidence do we have that it even exists? 

In response to this, I argue that the evidence of the structure’s existence is the very fact that we are able to operate within conventional reality and that we are able to use concepts to communicate effectively with one another meaningfully. The very fact that I am able to use concepts such as <cat>, <apple>, etc. in a conversation with other individuals in a meaningful manner is evidence that these concepts have determinate relationships with one another which give them meaning and identity. Therefore this is evidence that there is something which tethers each concept to one another such that when I do use it (either in thought or speech), it conveys some semantic content rather than meaning simply nothing. It is important to remember that I am not claiming that the structure is something different that is over and above the concepts of conventional reality. The structure is a part of conventional reality as it enables us to function within conventional reality. I am simply claiming that we can never characterize or conceptualize the entirety of the structure. 

Therefore, given our inability to directly describe or apprehend the structure, I will attempt to provide two analogies through which I will attempt to demonstrate how there is some structure and how it does ground the concepts of conventional reality and prevents the doctrine of emptiness from entailing nihilism. 

Section 3.2: The Analogy of the Reeds

The first analogy that I would like to introduce is to think of the concepts of conventional reality in the same way as a bundle of reeds. Through this analogy, I aim to provide an intuitive understanding of my position.

Imagine a bundle of reeds that support each other in a pyramid shape. I claim that each of our concepts of conventional reality (such as <this table>, <red>, <truth>, etc.) is like a reed in a bundle of reeds. In the bundle, the reeds mutually support one another by pushing against each other; each individual reed is standing up because it is both simultaneously pushing and is being pushed on by all the other reeds in the collection. Similarly, given that each concept is dependently originated, each concept both is defined by (i.e. “pushed”) and defines (i.e. “pushes”) other concepts. Take for example the concept <this fire>. This concept is dependent on the following concepts: <red > (by the relation “has color of”), <heat sensation> and <smoke> (by the relation “is the cause of”), <match> (by the relation “is the effect of”), etc. Yet at the same time, each of these concepts are in turn dependent on the concept <this fire>; the concept <red> is dependent on this concept by the relation “is the color of”, the concept <smoke> and <heat sensation> is dependent on this concept by the relation “is the effect of” , the concept <match> is dependent on this concept by the relation “is the cause of”, etc. Hence, just like the reed is standing up by simultaneously being pushed on and pushing other reeds, each concept conveys meaning to us by simultaneously being dependent on and supporting other concepts; we understand the concept <this fire> by grasping all the relations it holds with the other concepts of our conventional reality. 

Now let us consider what is supporting the collection of reeds as a whole (i.e. we are now considering what is supporting conventional reality as a whole). Notice there is not one single reed which supports the whole collection. Rather, the collection of reeds is supported (in that all the reeds stay standing) by the pyramid shape that all the reeds form. In other words, each reed is supported by the structure (i.e. the pyramid shape) that all the reeds collectively instantiate. Analogously, I do not claim that there is a single entity or concept that grounds all of the concepts of conventional reality. Rather, the concepts of conventional reality are grounded by the very structure that they collectively instantiate. However, unlike in the case of the bundle of reeds where we could understand the structure as the pyramid shape, in the case of conventional reality, it is impossible for us to conceive of the structure’s characterisation (what the structure ‘looks like’) for reasons that are stated above.¹ Despite this, there are still claims we can make about the structure of conventional reality by using this analogy. 

Firstly, note that we can infer that the bundle of reeds does instantiate some structure by virtue of knowing that each reed is standing up and is leaning on one another. Similarly, we can infer that the concepts of conventional reality do instantiate some structure in virtue of the fact that we can meaningfully use the concepts of conventional reality to communicate with one another and by being aware of their relational existence.  

Now that we can claim that the structure exists, let us focus on how this structure grounds conventional reality. In other words, how it prevents nihilism. Consider again the bundle of reeds. Notice that its pyramid shape supports the whole bundle by providing a specific role for each reed to play; each reed must be physically aligned in such a way (i.e. it must be slanted at a particular angle) for there to even be a pyramid shape and for it to be able to stand up. Paradoxically what determines this specific physical alignment of a singular reed is the pyramid shape (i.e, the structure) - the very thing that the singular reed partakes in creating. Therefore, what is interesting to note is that the pyramid structure is instantiated by the reeds but once it is instantiated, it switches roles and supports its own existence by providing each reed a role in the structure. Thus in virtue of instantiating and being part of the pyramid structure, each reed in a way determines a particular and abstract role that is to be played in the pyramid structure; namely whatever the role that particular reed is playing. I claim ‘abstract’ because once the role is determined, the particular that plays the role no longer matters - the reed could be replaced by a straw and the same role would be played. 

Analogously, I claim that the structure which the concepts of conventional reality instantiate provide the same supporting role that the pyramid structure does. By there being a structure that each concept is part of, these concepts define abstract, determinate roles that are to be played in the structure of conventional reality. Therefore, it is not the case that nothing exists in our conventional reality simply because the concepts have no intrinsic identity nor is it the case that these concepts all refer to nothing. Rather an abstract and determinate structure does exist with specific and determinate roles; what fills these roles (i.e. the particular concepts) are then empty of intrinsic essence. This avoids the problem of nihilism because we are claiming that conventional reality (i.e. the collection of ‘empty’ concepts) is not nothing but is something; this something is a determinate structure that is of pure form.² Consequently, concepts of conventional reality do not refer to nothing, rather they refer to the abstract roles of the structure. This is the way I interpreted the line “emptiness is not other than form”. 

Note that I am not claiming that this abstract structure is something over and above the concepts of conventional reality and has intrinsic essence. Just like how in the case of the bundle of reeds, the pyramid structure is solely dependent on the reeds, the structure that the concepts of conventional reality instantiate is dependent solely on the concepts of conventional reality themselves. In this way, the structure is conventionally real. However, this is not to say that the structure is a part of conventional reality. Note how the pyramid structure, once instantiated by reeds, then becomes a general, abstract structure which can be instantiated by any other materials (such as straws, pipes, logs, etc.). In this sense, the pyramid structure does not depend on the particulars that make it up. Similarly, the structure of conventional reality, once instantiated by the individual concepts, no longer depends on the particular concepts that make it up. It is this quality of the structure that allows it to play a grounding role for the concepts of conventional reality. This is the way I interpreted the line “form is not other than emptiness”.

Section 3.3: Analogy of Group Theory

The second analogy that I would like to use is one from mathematics, specifically from group theory. The aim of this analogy is to make more precise the conclusions of the previous section. 

I shall first provide a brief summary of what group theory is. Group theory is a branch of mathematics that studies different structures in mathematics. It takes specific sets (e.g. the set of integers or a set of functions) with certain operations that are defined on them (e.g. addition or multiplication) and extrapolates the general structure which they exhibit. By this I mean that group theory attempts to characterize the structure in such a way that does not make reference to the particular elements of the set or the particular mathematical operation; it aims to describe the structure in a way that only make reference to the form of the relations that any arbitrary elements must display if they were to be a part of the structure. Therefore two different and completely unrelated sets (with their respective operations) can instantiate the same group (i.e. the same structure).³ I have given a more detailed explanation of the specifics of group theory using an example in the Appendix. What is important for our purposes is that group theory allows us a way to think about the structures that systems of objects instantiate in an abstract and purely formal manner. In other words, group theory studies the form of the relationships that the entities can enter into with one another.  

Let us now consider our current conventional reality as a particular instantiation of some group (e.g. (Z/4, +) from the Appendix). Unlike the previous analogy, the “elements” of our conventional reality contain everything (including the relations that occur between different concepts). So our “set” (i.e. conventional reality) would look something like this: C = {<fire>, <cause>, <effect>, <smoke>, <cat>, <above>, <father>, …}. To stick with the analogy of a group, we do have some sort of operator on this set. Given any two concepts in the set, we would be able to find a third which connects those two in some way. For example, given the concepts <fire> and <cause>, the operator would perhaps output the third concept <match>. The very fact that conventionally real concepts are understood to be relationally existent ensures that this operator is well-defined (i.e. there does indeed exist a third concept for any given pair of concepts). However the technical details are not important. 

Now, understanding our current conventional reality as a particular instantiation of a group would entail that there is a group which provides a purely formal description of the bare bones structure that our conventional reality instantiates, devoid of any particular details about the elements and operation. (e.g. C₄ from the Appendix). Whatever structure our currency conventional reality (i.e. the particular instantiation of a group) instantiates is the structure which does the ground (i.e. the general, abstract group). This is just like the previous analogy; whatever structure the particular bundle of reeds instantiated is the general structure.   

Now how does this analogy answer the question of grounding? The following is my argument. 

I first argue that given any conventional reality, the general structure (or “group") that it instantiates will be the same. In other words, I claim that all conceivable variations of conventional realities are particular instantiations of the same general structure (or “group”, if we are to stick with the analogy). By this I mean the following. Assume that we were born on another planet where everything is different; the creatures are completely new and laws of physics are different. In this situation, the concepts of conventional reality will be completely different to those of current conventional reality. Let us call these concepts ‘alien’ concepts. I argue that, because of the way we experience, we would be able to map these ‘alien’ concepts back to our current conventional reality and we would observe that these ‘alien’ concepts would behave in the exact same way as the concepts of our current conventional reality. By this I mean the following: take whatever ‘alien’ concept that the concept <causation> is mapped to. If we look at all the concepts that this ‘alien’ concept is related to in the Martian conventional reality and map those ‘alien’ concepts back to our conventional reality, we would see that they are all the concepts that are related to the concept of <causation> in our current conventional reality. I argue that this isomorphism does exist in virtue of the way we have experiences. As mentioned in section 1, all our experiences are conceptual. Now given that this conceptualisation is a necessary part of experience, the type and nature of this conceptualisation will be the same regardless of its inputs (i.e. regardless of whatever experiences are about). Hence any conventional reality is an instantiation of the same general structure (i.e the same “group”).

Secondly, I claim that it is this existence of this singular general group which grounds the concepts of conventional reality and prevents the doctrine of emptiness from entailing nihilism. This is because it demonstrates that our conventional reality is not nothing rather it is something - it is a particular instantiation of a very specific structure. This specific structure is fixed and determinate, as demonstrated in the previous paragraph. Moreover its nature is not dependent on the particular concepts which instantiate it. In this way, the general structure can be said to ground the concepts of conventional reality.⁴ The concepts of conventional reality do not denote nothingness. Rather they do have determinate content, this content is just its pure form (i.e. the general position that they instantiate in the general structure). The doctrine of emptiness, therefore does not entail that nothing exists. Rather it states that everything has only structural existence; everything has determinate nature insofar as they are part of a structure. 

Section 4: A Potential Objection and Reply

However, one might have two principal objections to my proposal. First, an objector may claim that Nāgārjuna would reject my notion of a general structure. She may highlight that all I have succeeded in doing is positing an ontology of structures and that Nāgārjuna would argue that even this structure is empty (i.e. dependently originated from other concepts). Hence my claim that this general structure is fixed and determinate is erroneous as it asserts that this structure has intrinsic essence (i.e that it is not dependently originated). This would be a clear violation of Nāgārjuna’s doctrine. Secondly, my objector may claim that if I were to concede that my structure is dependently originated, then my proposal has clearly not achieved its objective. This is because if this grounding structure itself is dependent on other things, then clearly it does not ground the concepts of conventional reality.

To this I reply that I have not claimed that the structure is something that is not dependently originated - I have argued that it is dependently originated on the entities that make it up as seen in Section 3.2. Hence, I have not violated Nāgārjuna’s doctrine of emptiness by positing something that is not dependently originated (i.e. something that is not ‘empty’). I have clearly stated that the grounding structure depends on the concepts of conventional reality; without these concepts, there would be no grounding structure. By claiming that this grounding structure is fixed and determinante, I mean that given any conventional reality, the structure which its concepts instantiate will be the same. 

To address the second objection, I argue that this structure can still play a grounding role because its essence is not dependent on anything outside of it. By this I mean that the structure is dependently originated from the very entities that it provides the grounding for. This notion of simultaneous dependence prevents any sort of infinite regress to nothingness. Nihilism arises when there is an infinite regress of dependence relations between concepts. As there is nothing determinate ‘at the end’ of these dependent relations, it is claimed that none of these concepts have any determinate meaning - i.e. that they denote nothing. Consequently something is a ground for these concepts when there is something at the ‘end’ of the dependence relations; the concepts are then understood in terms of this ground. In my proposal, I have redefined the notion of grounding. Speaking metaphorically, rather than searching for something ‘at the end’ of the dependence relations, I have created a somewhat circular grounding. Hence the concepts get meaning from the form they embody. In other words, the concepts are grounded by the structure that they instantiate. Now since this structure is dependent only on these concepts for instantiation and its nature, there is no infinite regress that is entailed when I claim that the concepts are grounded by the structure. 

Conclusion

In conclusion, I have argued that Nāgārjuna’s doctrine of emptiness does not entail nihilism. This is because the concepts of conventional reality are grounded by the structure which they instantiate. I have provided two analogies in an attempt to demonstrate and motivate my position; the analogy of the reeds was aimed at providing an intuitive understanding of my position and the analogy of group theory was an attempt to formalize my position. I then considered a possible objection to my proposal and provided a reply. 

Appendix

Here I will give an example of two sets (along with their mathematical operation) that instantiate the same group. 

Consider the set X={0,1,2,3}. For this set, take the operation to be addition modulo 4. This simply means: take two numbers in the set, add them, divide them by four and take the remainder. Thus 3+2mod4=1. Notice that taking any two elements in the set X and performing the operation of addition modulo4 returns a number which is in the set X. 

Consider the set Y={1,-1,i,-i}, where i=√-1. For this set, take the operation to be multiplication. Note that i²= -1. Again notice that taking any two elements in the set Y and performing the operation of multiplication returns a number which is in the set Y.

In group theory, it is said that X and Y are particular examples of the same group. This group is called C₄. The group C₄ provides a general description of how particular representations of it behave. Hence, we say that X and Y are representations of the same group C₄. Thus, in group theory C₄ would be defined by some of the following statements:

• • It is a set with 4 elements.

  • It is a set where there is one element, which when added or multiplied to itself returns itself. In the case of X, this would be the element 0 (0+0mod4=0) and in the case of Y, it would be the element 1 (1  1=1). We call this element the identity element. 

  • It is a set where there is one element that is not the identity element, which when added or multiplied to itself returns the identity element. In the case of X, this would be the element 2 (2+2mod4=0) and in the case of Y, it would be the element -1 (-1  -1=1).

As it is demonstrated, the group C₄ attempts to provide a purely general description of the structure without making any reference to any particular set.