Exegetical writing 5: Aristotle on the Order of Nature

May 28, 2023Michael LiuLeave a comment

In ‘Politics’, Aristotle makes a clear statement: “it is a mistake to believe that the statesman is the same as. the manager of the household.”^[1] This idea goes beyond a simple comparison; it points out key differences between the nature of individuals or households and that of the city. In this essay, I’ll examine and explain two of Aristotle’s arguments on why the individual or household and the city are different by nature.

The first argument is a phylogenetic argument, which states that human associations, or communities, first developed through a “conjugal union”^[2] of a male and a female to form a household, which then associated with more households to form a village, and eventually a number of villages joined together to form a city (or polis), which is the “final and perfect association”^[3] that has achieved the “height of full self-sufficiency.”^[4]The phylogenetic argument shows how a human association evolves from an individual to a city. However, if one only considers this argument, then one might think that the two only differ “according to the number”^[5] and that the city is simply an extension of the individual and the family.

Aristotle argues that the phylogenetic argument alone “cannot be accepted as correct,”^[6] and provides a second argument, a teleological argument, which states that “the city is prior in the order of nature to the family and the individual”^[7], even though it developed later in the process of human society. According to Aristotle, the reason why the city takes precedence over the family and the individual in the natural order of things is that “the whole is necessarily prior to the part.”^[8]

Aristotle’s teleological argument can be explained in the following way:

Firstly, Aristotle defines the nature of things as “what each thing is when its growth is complete.”^[9] Thus for Aristotle, the nature of a thing is not what the thing is but what it is capable of becoming. Its nature is not a static but a developing conception. For example, an acorn naturally grows into an oak tree, and the resulting tree exists by nature and not by craft. Likewise, in Politics the nature of a state can only be discovered by observation of its development and tendencies. Using this definition, Aristotle makes two assertions about human nature. In the first assertion, he argues that humans are naturally communal animals. In the second, he argues that “in a greater degree than bees or other gregarious animals,”^[10] human beings are political animals by nature.

Aristotle argues that humans are communal animals because they have an innate desire to live a social life, even when they do not require mutual support. Additionally, he argues that humans are political animals, not only because of their natural inclination to form partnerships with others but also because of their unique capacity for reason speech. This capacity allows humans to communicate and deliberate about what is “what is advantageous and what is the reverse”^[11] to each other, leading to the development and communication of moral concepts such as justice, goodness, and evil. This, in turn, leads to the formation of associations that are absent in other animals. For Aristotle, the “most sovereign and inclusive”^[12] form of such an association is the city or political association. Since the capacity for reason and speech eventually leads to the pursuit of the city, Aristotle believes that humans are political animals by nature.

Secondly, Aristotle argues that, according to his definition of nature, all associations, including individuals, families, villages, and cities, exist by nature. However, it is crucial to distinguish between the nature of the family/village and that of the city, as they possess different ends. The city differs from the other, more primitive and pre-political associations because it serves as the “consummation” of earlier associations, achieving full self-sufficiency, whereas the family and village exist by nature “for the satisfaction of daily recurrent need.”^[13] Aristotle claims that for any city, “it must devote itself to the end of encouraging goodness”^[14]. Thus, the distinction between the family and the city lies in the fact that while the purpose of the family is “merely to sustain life”, the purpose of the city is to enable citizens to “live a good life.” ^[15] In other words, while the end of the family corresponds to achieving the communal aspect of human nature, the end of the city corresponds to achieving both the communal and political aspects. Thus, one can say that the city is prior to the individual and family by order of nature because the city is aiming at achieving a higher moral end.

Aristotle asserts that the city, as the consummation of all associations, “includes all the rest,” “pursues this aim the most,” and is “directed to the most good.”^[16] Consequently, it is reasonable for him to claim that the city represents the whole, while other associations only represent parts of the ideal function of the city. The city achieves its end because it is composed of equal and free citizens, with political leadership exercised by the citizens themselves in rotation. The city provides opportunities for individuals to participate in politics and develop their moral character. Only within the city can individuals fully utilize their political nature, through activities such as deliberation and decision-making, which enable their moral character to be fully realized through rational communication.

Overall, Aristotle believed that humans are naturally social and political animals, distinguishing them from other creatures. However, individuals must reside in a city in order to develop and realize their natural capacities. Without the city, an individual is no more than a beast^[17], since they are not self-sufficient. This is similar to how a hand loses its ‘nature’ as a hand when the body is destroyed. Therefore, it can be argued that the city takes priority in the natural order over the family and the individual.

Works Cited

Cahn, S. M. (2015). Political philosophy : the essential texts . New York: Oxford University Press.

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Short Essay 4: Two Key Daoist Concepts

May 25, 2023May 26, 2023Michael LiuLeave a comment

The philosophical tradition of Daoism, as found in the Daodejing, centers on two key ideas: Dao (the Way) and wuwei (non-action). Dao, a complex and abstract idea, appears roughly 70 times in the Daodejing. Its interpretation varies greatly among scholars and readers, leading to significant debate. In this essay, I plan to delve into the meaning of Dao and wuwei in Daoist philosophy, discuss their importance, and share my views on these concepts.

After closely studying the texts, I suggest that there are three interconnected layers of meaning for Dao. These layers are: 1) Dao as a metaphysical concept, 2) Dao as objective laws and principles, and 3) Dao as practical and moral guidelines. I will detail each of these layers in the following sections.

Dao as a Metaphysical Concept

Laozi endows Dao with numerous metaphysical properties. A key feature of the Dao is its generative capacity, seen as the source of all existence. Laozi suggests that “Dao gave birth to One, which led to Two, then Three, and ultimately to the myriad of things.” This implies Dao as the progenitor of all things. In chapter 6, Laozi uses feminine imagery to characterize Dao, specifically its reproductive functions: firstly, he likens Dao to the “mother of the world,” emphasizing its nurturing essence; secondly, he equates Dao to a womb, the “root of heaven and earth”. This comparison highlights the Dao‘s generative and nurturing qualities, as it functions like a “womb” for the entire universe.

Moreover, Dao, while productive, is depicted as empty yet inexhaustible. Laozi compares Dao to an empty vessel that remains unfilled despite its use, yet is vast and deep. This emptiness, much like a womb, underlines Dao‘s nourishing and generative void, serving as the source of all life and matter in the universe. This nurturing capability of Dao is also symbolized as a valley, abundant with rivers and fertile soil that sustains various life forms, signifying its perpetual substance. As it embodies all things without being bound to any, Dao possesses an empty nature. Hence, if correctly interpreted, Laozi confers an ontological status to Dao as the basis of all existence.

Dao is also characterized by its consistency and eternity. Laozi underscores that the Dao, being soundless, formless, and independent, remains unaltered. In Chapter 22 of the Daodejing, Laozi states, “The myriad creatures are all in motion! I watch as they turn back. The teeming multitude of things, each returns home to its root.” This quote highlights the constancy and eternity of the Dao, as it not only gives rise to all things but also brings them back to their origins. The multitude of creatures act, interact, create, and transform within the natural world, engaging in a complex dance of existence. However, under the guidance of the Dao, they eventually return to their original position and form. The Dao‘s eternity and constancy arise from its all-inclusive nature, as it encompasses all things without limitations.

Given the attributes and characteristics of Dao, we can infer that it is the origin of all existence, transcending the dualities of being and non-being, substance and emptiness. This indicates that Dao is the metaphysical and ontological foundation of the universe, and its power and impact are beyond human comprehension

Dao as Objective Laws and Principles

Beyond its metaphysical implications, Dao may also be interpreted as a collection of natural principles or laws that are discernible and articulable by us. This interpretation of Dao, however, is inherently partial, bound by temporal and situational constraints, and relegated to particular descriptions. Essentially, this perspective of Dao mirrors nature, relying on our empirical observations, investigations, and applications to determine its patterns within nature and the universe.

Laozi elucidates, “Man follows Earth. Earth follows Heaven. Heaven follows Dao. Dao follows Nature.” Our ability to uncover principles and laws in nature stems from Dao‘s encompassing nature, pervading all things in the world, which underpins the spontaneity and naturalness of the world. Thus, what we observe are still aspects of the Dao, even though the totality of Dao remains beyond comprehension.

As an illustration, Laozi employs the metaphor of water, extrapolated from his observations of water’s conduct in nature, to propose that we should emulate water: non-contentious, humble, and lowly. This suggests that we can navigate the path of Dao, while acknowledging that its totality remains beyond our grasp. The Dao that can be verbalized is not the constant Dao, and as such, we must recognize the boundaries of our comprehension as we attempt to incorporate its principles into our lives. By observing and comprehending patterns, principles, and laws within the natural world, Laozi could unveil meaningful insights into the Dao and its applications.

Dao as Practical and Moral Guidelines

The third dimension of understanding views Dao not merely as an abstract philosophical notion, but also as a practical code of conduct for daily life. Laozi posits that ethics are predicated on the alignment of human behavior with Dao. This alignment is prescriptive, demanding adherence to Dao from all humans. Laozi asserts that an act is virtuous only if it aligns with the natural path of Dao. Morality involves emulating Dao, which surpasses human interpretations of good. When humans implement Dao in their actions, they achieve Virtue (De). Likewise, other creatures that manifest Dao in their existence exemplify Virtue (De). In this context, “Virtue” delineates the ideal state for all forms of existence.

Laozi’s teachings primarily emphasize the moral principle of non-action or inactivity (wuwei). It could be argued that the primary motivation behind Laozi’s Daodejing is the promotion of non-action. Non-action, as proposed by Laozi, is not tantamount to passivity or laziness but a purposeful pursuit aimed at accomplishing more than what excessive effort could achieve. For instance, in chapter 38, Laozi states, “Those of highest Virtue do not strive for Virtue and so they have it. Those of lowest Virtue never stray from Virtue and so they lack it.” In chapter 22, he notes, “Because they do not contend, no one in the world can contend with them.”

Moreover, Laozi employs various metaphors to elucidate non-action, such as those of the female and valleys. In chapters 6 and 28, he likens “the role of the female” to “the spirit of the valley” and “the ravine of the empire.” These metaphors resonate with the water metaphor, a recurring theme in the Daodejing. Valleys and ravines, being low-lying land areas usually with a stream, embody and reflect water’s attributes such as receptivity, passivity, softness, yielding, humility, and harmony with all things in nature. These qualities align with the principle of non-action. Laozi also underscores how the female (symbolizing non-action) overcomes the male (symbolizing power and dominance). In chapter 28, he advises to “keep to the role of the female,” and in chapter 61, he claims that “the female always gets the better of the male.” This suggests the triumph of the feminine over the masculine akin to the soft overcoming the hard, the weak overcoming the strong, the yielding overcoming the dominating, and so forth.

On a political level, non-action is the ideal method of ruling. For instance, in chapter 61, Laozi takes the diplomacy between a large state and a small state as an example: “The large state, by taking the lower position, annexes the small state.” Laozi insists that when the large state is tolerant and submissive instead of aggressive and militant, it can secure the goodwill and trust of the smaller state. Therefore, those who act in accordance with principles of non-contending and non-acting put themselves in a more advantageous position.

However, it’s important to note that, unlike Confucius, Laozi’s principle of non-action isn’t designed to “rectify” the world, nor does it provide practical guidance for restoring order in a corrupt world. Instead, he presents an ideal suited for a primitive society with basic natural needs. Laozi held that all unnatural desires stem from societal conditioning. In his perspective, human nature is inherently good, and the natural world is harmonious. Thus, the less human interference, the more harmonious human society becomes.

In conclusion, following the exploration of the tri-layered interpretation of Dao and the concepts of wuwei as a moral and political paradigm, I wish to put forth personal insights and assessments.

Although this essay has delved into numerous metaphysical and ontological facets of Dao, my personal viewpoint is that these are not the primary concerns or objectives of Laozi in composing this text. Instead, I propose that Laozi’s intention was to establish a philosophical basis for his moral and political philosophies. According to my interpretation and assessment, roughly 80% of Dao‘s usage centers on the second and third layers of meaning. Another indication supporting my conjecture is the frequent usage of the term “sage,” referring to an ideal ruler, which features 32 times across 23 chapters in the text. This implies that Laozi dedicated approximately one-third of the entire text to discussing the nature of ideal governance and the potential pitfalls rulers should avoid. Consequently, I put forth that Laozi is more of a pragmatic problem-solver than a theoretical philosopher or mystic practitioner. The emphasis on practicality and real-world applicability is more apparent when assessing the moral and political dimensions of his teachings.

However, I concede that more evidence and corroboration are needed to fortify my argument, and alternate viewpoints are plausible. It is vital to persist in probing Laozi’s philosophy from diverse perspectives to attain a holistic understanding of his teachings and intents. Like any philosophical text, interpretations and evaluations may diverge, yet the depth of Laozi’s thought offers abundant scope for continued discourse and analysis.

Note:

The principal translations consulted for this essay were those by Philip J. Ivanhoe and D.C. Lau.
Due to constraints in time and space, I did not delve into why Laozi proposed non-action as superior to taking action. However, his argument supporting this viewpoint can be traced to chapter 40.

Argumentative Writing 4: Mencius vs Xunzi on Human Nature

May 23, 2023May 23, 2023Michael LiuLeave a comment

Mencius and Xunzi were prominent Confucian philosophers who lived during the Warring States period in ancient China. Despite their common interest in Confucian virtues, moral cultivation, and rulership, their views on human nature diverged significantly. Mencius believed in the inherent goodness of human nature, which he argued could be developed through the cultivation of innate moral virtues. In contrast, Xunzi asserted that human nature was inherently bad and required strict moral education and regulations to improve. This essay aims to analyze the philosophical arguments of Mencius and Xunzi, explore the similarities and differences in their views on human nature, and evaluate the significance of their ideas in the context of Confucian thought and beyond.

I will first examine Mencius’ views on human nature and compare them with Xunzi’s perspective. In his work, Mengzi, Mencius employed a series of analogies to illustrate his argument for human nature. Following his approach, I will provide a thorough explication of the logics of his analogical reasoning.

To begin, I will delve into Mencius’ assumptions regarding human nature. Firstly, Mencius asserts that human nature is universal to all human beings. To support this claim, he uses an analogy of barley, which is a kind of plant that inherently develops into grain, regardless of the various environmental conditions that affect its growth^[1]. This, he argues, is indicative of a broader phenomenon – natural kinds^[2]. From this analogy, Mencius argues that human beings are also a natural kind and share similar characteristics by nature. Although humans may differ in their tastes, preferences, and abilities, these differences are shaped by external environments and experiences, and do not reflect the essential nature of human beings.

Secondly, Mencius argues that human nature is unique to humans, as it distinguishes them from all other animals. He states that “the nature of a dog cannot be the same as the nature of a cow, just as the nature of a cow cannot be the same as the nature of a human^[3].” Based on this assumption, he rejected the idea that the desire for food and sex is part of human nature, for the reason that these are not unique to humans. He further argued that humans are different from other animals because of their pursuit of humanity and righteousness, which origins from their innate potential for moral virtues, a capacity of the human heart/mind^[4]. Since the heart/mind is a biological organ that comes with birth and possessed by all humankinds, its capacity must be part of the human nature. Thus, to Mencius, the innate potential of morality is a universal nature of all human beings. This leads to his claim that “there is no man who is not good; there is no water that does not flow downward^[5].” Just as water has a natural inclination to flow downward, humans also possess an innate tendency that guides their actions and decisions toward goodness.

To substantiate his claim of inherent human goodness, Mencius further explores the connection between the heart/mind and morality. He asserts that the capacity of moral virtues origins from the innate feelings of our heart/mind. Mencius argues that suppose when someone witnesses a young child in danger of falling into a deep well, they experience a natural sense of anxiety and concern for the child. This response is not driven by a desire to win favor from the child’s parents, gain recognition from others, or an aversion to hearing the child’s cries, but by a feeling of compassion and empathy, which makes humans intolerable to the suffering of others^[6]. This shows that human heart/mind is naturally a “heart of compassion^[7],” which is, as Mencius claims, the beginning of a fundamental moral virtue – humanity.

Thus, according to Mencius, human beings are believed to be inherently good due to their possession of unique moral sprouts that are not found in other animals. These moral sprouts are primarily generated from the innate feelings of empathy and compassion within our mind and heart. This implies that humans are born with a natural inclination towards morality, leading Mencius to conclude that they are naturally good.

However, a question arises: if humans have a natural tendency towards goodness and if all individuals possess the seeds of morality within them, then why aren’t sages abundant everywhere? While Mencius advocates for the existence of moral sprouts, he does not hold a naive view of the moral reality of humans. Just like a sprout, there are two possibilities: it can either bear abundant fruit when carefully nurtured by humans or it may wither away, unable to withstand the adversities of a harsh environment.

Mencius acknowledges the potential for moral failures. To explain these failures, he specifically argues that our mind and heart serve as the sources of our moral virtues, while our sensory organs such as our ears, eyes, and mouth act as sources of our sensory desires. Mencius refers to our mind and heart as the “major part^[8]” of our being, while considering the sensory organs as the “minor part^[9].” Since the “minor part” lacks the ability to think and reflect like the “major part,” it can influence us to deviate from the moral path. Mencius attributes most cases of moral failure to excessive attention given to our sensory desires, neglecting the functions of our mind.

To address this moral failure, Mencius proposes that the goal of moral education is to focus on reducing the influence of our sensory desires and cultivating our mind. By doing so, we develop the right “qi^[10],” a form of moral spirit that will be manifested in our appearance and daily actions.

On the surface, Xunzi seems to hold a directly opposite view of Mencius, as he says: ” People’s nature is bad. Their goodness is a matter of deliberate effort.^[11]” However, upon closer examination of Xunzi’s overall moral theory, one might realize that it could be difficult to pinpoint their exact points of disagreement. Since Mencius views our mind/heart as the foundation of morality, let’s first examine how Xunzi views it.

Xunzi believes that our body is composed of two parts: “the heavenly faculties^[12],” which consist of our sensory organs, such as eyes, ears, nose, mouth, and body. The function of our heavenly faculties is to detect and observe the properties of natural objects and the outside world. Apart from our sensory organs, Xunzi argues that another part of our body is our mind/heart, which he calls “the heavenly ruler^[13].” The mind/heart is a ruler because it “controls^[14]” our sensory organs in two ways: first, our mind processes all of our sensory data and forms overall conceptions of the objects we perceive; secondly, our mind/heart is able to be “rid of” the biases and desires that arise from our senses and guide us towards moral composure^[15].

By examining Xunzi’s construction of the mind and body, it appears that Xunzi and Mencius share a similar view on this subject. They both agree that our mind/heart is the superior faculty to our senses, and it is able to regulate our sensory desires and enable us to make moral judgments. While they may differ in their views of human nature, both philosophers recognize the importance of the mind/heart in developing morality. This shared understanding suggests that the differences in their moral theories may not be as stark as they initially seem, opening up further avenues for comparative analysis.

Next, let’s look at how Xunzi defines human nature: “Human nature is what is accomplished by heaven. It is something which cannot be learned and to which one cannot apply oneself^[16].” What one has at birth are basically one’s biological characteristics, such as our sensory organs, which are not so different from those of other animals. The direct contrast to this definition of human nature is wei^[17], which is defined as “That in man of which he can become capable through learning.^[18]”

Thus, at this point in his argument, Xunzi has not yet said that human nature is bad, but he is saying that human nature is amoral since morality is not what we are born with. However, even Mencius would somehow agree with this point since, as I have pointed out, Mencius claims that humans are merely born with a moral tendency. To fully realize our moral potential, one has to constantly cultivate one’s mind/heart. However, Xunzi argues that “emotions are the content of human nature” because “love, hate, joy, anger, sorrow, or happiness^[19]” are the responses of our mind/heart to the sensory data we receive through our biological organs.

Based on this definition of human nature, Xunzi claims that the following argument can be made: in response to our emotions, our desires develop. As our desires grow and since there isn’t any part of our nature that can constrain it (although our mind/heart is capable of exercising control, such ability is not part of our nature since it requires conscious efforts), it grows endlessly. The amount of resources presented in a society is limited. If everyone indulges in their material desires, they will soon be fighting each other for things, which will lead society into chaos and ruins. Since following our nature will lead to chaos and disorder, human nature is naturally bad.

We have now arrived at the end of Xunzi’s argument about human nature. To avoid the disastrous consequences of our unrestrained nature requires the deliberate efforts (wei) of our mind to control our desires. Among human beings’ deliberate efforts, Xunzi lists rites and rituals, moral principles and moral teachings, laws, and regulations, etc. What deliberate effort accomplishes are all forms of moral conduct and moral sentiments. The whole process of human civilization acts against man’s innate desire to aggrandize his possession and gratify his senses. Therefore, Xunzi declares, the goodness of human beings is the result of their deliberate effort.

Therefore, as I argue that Xunzi and Mencius in fact agree with each other in many aspects. First, both Xunzi and Mencius agree that our mind/heart is able to control our inborn desires and is the basis for morality. Secondly, both Xunzi and Mencius agree that although humans have the capability to be morally good, such capability is not realized at birth. Thirdly, they agree that morality cannot be fully developed without the help of conscious moral cultivation.

The main points of disagreement are that Xunzi rejects that we have innate moral sprouts since, to him, our nature is what we are born with, which refers to our physical and biological characteristics. If we are inherently good as Mencius said, then everyone should be born as a sage. Based on the definition of human nature, Mencius considers moral education as a deliberate effort, and the consequence of that will not be part of our nature.

Based on the comparisons, I argue that the differences between Xunzi and Mencius primarily stem from their distinct definitions of human nature, rather than genuine disagreements on the overall moral theory. As a result, despite their theoretical divergence, Mencius and Xunzi share many commonalities in practice, and both are considered inheritors of Confucianism.

Having established a comparison between Mencius and Xunzi, I would like to offer some personal thoughts and reflections on the philosophical debates between the two, particularly regarding human nature.

Firstly, it is important to note that Mencius did not blindly argue for innate human goodness but instead emphasized the potential for goodness within each individual. This perspective, in essence, is not too far from Xunzi’s argument, which also acknowledges the possibility of cultivating morality through deliberate effort.

Secondly, I think Xunzi’s argument is somewhat limited in its scope. By focusing primarily on what we are born with, it leaves little room for discussion on the development of human potential beyond our innate characteristics. This narrow focus may hinder a more comprehensive understanding of human nature and morality.

Third, the notion of human nature being solely defined by what we are born with could be challenged. For example, as children, most of us are not yet capable of complex logical reasoning. However, some modern cognitive scientists have discovered brain networks that endow humans with superior reasoning skills. These skills may not be readily apparent at birth but could emerge as we grow and develop. In light of this, should we not consider the capacity for logical reasoning as part of our human nature, even if it is not fully manifested at birth?

This observation presents a significant challenge to Xunzi’s theory, which posits that human nature is limited to our innate characteristics. By reevaluating the concept of human nature to include not only what we are born with but also our potential for growth and development, we may arrive at a more nuanced understanding of both Mencius and Xunzi’s arguments.

References:

Legge, James, “孟子 – Mengzi.” Chinese Text Project, Simplified Chinese version, ctext.org/mengzi/ens.

Hutton, Eric L. Xunzi: The Complete Text. Princeton University Press, 2014. JSTOR, https://doi.org/10.2307/j.ctt6wq19b. Accessed 1 May 2023.

Mencius, 11A:7 ↑
lei/类 ↑
Mencius, 11A:3 ↑
Xin/心 ↑
Mencius, 11A:2 ↑
Mencius, 3A:6 ↑
恻隐之心, ibid. ↑
大体, Mencius, 11A:14 ↑
小体,ibid. ↑
浩然之气, Mencius, 3A:2 ↑
Xunzi, chapter 23; Hutton, p. 248 ↑
天官; Xunzi, chapter 17; Hutton, p. 176 ↑
天君; Xunzi, chapter 17; ibid. ↑
Xunzi, chapter 17; ibid. ↑
This is interpreted from the phrase “虛壹而靜”; Mencius, chapter 21 ↑
Xunzi, chapter 23; Hutton, p. 249 ↑
伪, ibid. ↑
ibid. ↑
Xunzi, chapter 23; Hutton, p. 248 ↑

Argumentative Writing 3: Reconciliating Feminism and Confucianism – Is Confucian Feminism Possible?

May 23, 2023Michael LiuLeave a comment

This essay has been edited and improved from a coursework paper.

INTRODUCTION

In the pursuit of gender equality and women’s emancipation, the challenge of reconciling traditional cultural values with modern feminist ideas has sparked considerable debate. Confucianism, a predominant ethical and philosophical system in East Asia, has faced criticism for perpetuating patriarchal norms and impeding women’s rights progress. Yet, is the complete abandonment of Confucianism truly the key to women’s liberation, or can this ancient tradition be reformed and integrated into feminist thought? I argue that Confucian feminism is not only feasible but also possesses the potential to offer valuable insights and contributions to the global feminist discourse. Through this paper, my aim is to demonstrate that Confucian feminism presents a unique and powerful perspective capable of addressing complex issues surrounding gender equality and enriching the ongoing global conversation on feminism.

This paper will be divided into two parts to thoroughly investigate the potential of Confucian feminism. The first part will discuss the limitations of completely discarding Confucian values and traditions for achieving gender equality. This section will emphasize the importance of understanding the cultural and historical context of Confucianism, particularly in China and Korea. The second part will concentrate on rectification, reinterpretation, and the integration of Confucianism and feminism. I will explore key tenets through the original Confucian classics to identify areas of common ground. I will also explore the potential of merging the Confucian concept of Ren with care ethic as an example of how Confucian feminism can contribute to and expand upon existing feminist ethical theories.

By structuring the paper in this manner, I aim to provide a comprehensive and nuanced analysis of the relationship between Confucianism and feminism, highlighting the potential of a Confucian feminist perspective to make valuable contributions to the global feminist discourse.

ABOLISHING CONFUCIANISM? A REFUTATION OF THREE SCHOLARS

In this section, I will examine the views that primarily call for the abolishment of Confucianism in order to achieve gender equality. I will discuss the arguments presented by He-Yin Zhen, Yun Chi Ho, and Julia Kristeva, and analyze their critiques of Confucianism in relation to women’s liberation.

In her work “On the Revenge of Women,” He critiques Confucianism as an instrument of male tyrannical rule, enabling men to uphold a hierarchy of superior men and inferior women (He 146). She argues that the “rites and propriety” promoted by Confucian scholars serve to subjugate women, concluding that a complete abandonment of Confucianism is necessary for women’s liberation (He 135). Similarly, Korean feminist Yun Chi Ho attributes the crisis in Korea to Confucian philosophy, which he believes contains the seeds of corruption and perpetuates oppressive gender relations (Choi 38). Julia Kristeva, in “About Chinese Women,” contends that feudalism and Confucianism were used to impose maximum patriarchal authority in China, with the traditional Confucian family structure being one of the chief obstacles to women’s liberation (Kristeva 80).

While these critics present compelling arguments for the rejection of Confucianism, I contend that their approaches are flawed as they commit two crucial mistakes. The first mistake is that by making Confucianism the sole culprit for all problems related to gender inequality, they ignore other significant economic, social, and cultural factors beyond the tenets of Confucianism.

For example, in the context of China’s feminist movement in the early 20th century, Henrik Ibsen’s play A Doll’s House had a significant impact, with Nora’s escape from the house being treated by Chinese feminists as a symbol of rebellion against the patriarchal clan system prescribed by Confucianism (Yan 356). Many feminist scholars at that time considered Nora’s walking out a success in achieving women’s liberation. However, Lu Xun, a scholar contemporary to He, offers a different interpretation of the play’s ending. Lu questions what happens after Nora leaves her home, suggesting that she has only two options: to fall into degradation (prostitution) or to return home (Lu, 257). Lu emphasizes the importance of economic and material factors, arguing that a liberated mind alone cannot overcome the challenges Nora would face after leaving her home. While women escape from home with hope and belief, they find that these hopes cannot be realized in a society where feudalism still exists but capitalism is not fully developed.

Drawing on this analysis, I argue that while Confucianism has indeed been criticized for its patriarchal aspects, simply rejecting it does not automatically guarantee women’s liberation. Other cultural, economic, and political factors can also contribute to the oppression of women. Therefore, a more comprehensive approach is needed that takes into account multiple factors that impact women’s rights and freedoms, rather than solely focusing on the rejection of Confucianism.

The second mistake that critics like He, Yun, and Kristeva make is advocating for the complete abandonment of Confucianism as a solution to gender inequality. Yun views Christianity as the replacement for Confucianism, stating that “Christianity is the salvation and hope of Korea “(Choi 36). Meanwhile, in her work “On the Question of Women’s Liberation,” He presents an anarcha-feminist solution, which calls for the abolition of all Confucian and capitalist systems. This approach, which follows their initial mistake of attributing all gender inequality issues to Confucianism, is neither meaningful nor practical. To support my argument, I will provide a historical analysis, focusing on the example of the Cultural Revolution in China and the removal of the “four olds.”

The Cultural Revolution (1966-1976) aimed to eliminate feudal and bourgeois influences, including Confucianism, by destroying the “four olds” — customs, cultures, habits, and ideas. Although intended to create a more egalitarian society, the outcome was far from its original goal, leading to the decay of public morality in contemporary China. According to Chu and Ju, the Cultural Revolution uniquely contributed to the decay of social trust, as friends and family members betrayed each other (Chu and Ju 283). They argue that growing up in a cultural vacuum, with neither traditional nor new values to guide them, may have done more damage to young Chinese than the impact of value denunciation their parents endured (Chu and Ju 300). This moral decay might have been mitigated if Confucian rituals and teachings were still in place to guide interpersonal relationships and social behavior.

Thus, I argue that the abolishment of Confucianism would lead to the loss of the moral foundation and cultural roots that have shaped societal values, customs, traditions, social interactions, and interpersonal relationships in countries like China and Korea. With Confucianism deeply ingrained in their culture and history, disregarding it could result in a loss of self-identity, as it would disconnect people from their shared cultural heritage. This loss can manifest on national, social, and personal levels, as individuals grapple with the disintegration of the values and traditions that once defined their identity and provided a sense of belonging and purpose.

Therefore, for countries like China and Korea, where Confucianism is deeply rooted, the importance and necessity of a reconciling approach become apparent. Instead of entirely discarding Confucianism, these countries could benefit from reinterpreting and adapting certain aspects of Confucianism to align with contemporary values such as gender equality and individual freedom. By doing so, they can preserve the positive aspects of their cultural heritage while addressing the issues of gender inequality that stem from traditional Confucian teachings. In the next part of this paper, I will discuss the strategy that can be applied to address the issues of feminism and gender equality.

RECTIFICATION, REINTERPRETATION, AND INTEGRATION: AN APPROACH TO RECONCILIATION

In the previous section, I argued that a reconciling approach between Confucianism and feminism is necessary, as a complete abandonment of Confucianism is not practical. To facilitate this reconciliation, I propose a three-stage approach: rectification, reinterpretation, and integration. However, before embarking on these processes, we must address two critical inquiries: to what extent is Confucianism inherently sexist? How can we account for the presence of sexist passages or concepts within certain Confucian texts?

Cheng Yang Li, in his book “The Sage and Second Sex,” contends that sexism became characteristic of Confucianism sometime after Confucius and Mencius died. The Han Confucian master Dong Zhongshu maintained that, between the two principles governing the universe, yang and yin, yang is superior, and yin is inferior. Dong’s views were later developed and amplified by Song-Ming Neo-Confucians like Zhu Xi, who advocated the “Three Bonds,” asserting the ruler’s authority over the minister, the father’s over the son, and the husband’s over the wife. These views then became institutionalized, leading to oppressive practices like foot binding and chaste widowhood, which placed significant pressure on women (Li, 4).

Thus, it is important to note that these sexist interpretations of Confucianism do not necessarily reflect the original teachings of Confucius and Mencius. According to Li, Confucianism without later modifications deserves the name of Confucianism, and oppressing women is not an essential characteristic of the philosophy founded by Confucius and Mencius (Li 34). This distinction highlights that Neo-Confucianism is just one branch of Confucian development, and other interpretations are possible. For example, the Qing Confucian scholar Wang Chuanshan developed a Yin-Yang cosmology that emphasized the relative opposition and complementary nature of yin and yang in the universe (Liu 325). While Wang did not explicitly make a gender equality argument, by applying his ideas, we can envision a form of Yin-Yang cosmology that promotes balance and harmony between the genders. This interpretation demonstrates that alternative, non-sexist interpretations of Confucianism exist and can be further explored.

Rectification

By examining the development of Confucianism and identifying when and how sexist ideas were introduced or became more prominent, we arrive at the first stage, rectification. Rectification involves distinguishing between the original teachings of Confucianism and the later sexist interpretations. It also requires focusing primarily on the original texts and teachings of pre-Qin scholars such as Confucius and Mencius, as well as their works, the Analects and Mencius, for their ungendered approaches towards virtue, ethics, and values. The process of rectification is essential to pave the way for reinterpretation and integration with feminist ideas. By carefully examining the historical development of Confucian thought and identifying instances where sexist interpretations were introduced or amplified, we can work towards a more inclusive understanding of Confucianism that aligns with feminist values.

Reinterpretation

Having demonstrated that Confucianism is not a monolithic and static philosophical tradition, but rather one open to various interpretations throughout its development, we can explore different adaptations of Confucianism. Some scholars argue that it can be reinterpreted to be more compatible with modern feminist values.

For instance, Li seeks to establish a connection between humaneness^[1] and the ethics of care. To do so, he emphasizes the love and care aspects of humaneness, arguing that both humaneness and care focus on the tender aspects of human relatedness (Li 24). While this interpretation holds some truth, Li does not extensively emphasize the connection between humaneness and ritual^[2], opting instead for an interpretation that highlights certain aspects of Confucian concepts to establish a stronger connection with feminist philosophy. This approach suggests that Li prioritizes exploring the nuanced and relational aspects of humaneness, focusing less on the more rigid and formal dimension associated with ritual. By doing so, Li aims to bridge Confucian thought with feminist philosophy, emphasizing values such as empathy and care. Li’s treatment of humaneness can be viewed as a form of reinterpretation. As the discussion of humaneness and care ethics will be explored in greater detail in the next stage, let us consider another example of reinterpretation.

Another well-known and controversial passage on women in the Analects is the following: ” It is the women and the inferior men that are difficult to deal with. If you let them get too close, they become insolent. If you keep them at a distance, they complain.”^[3]

Although this passage has traditionally been interpreted as evidence for Confucius holding sexist views, I argue that an alternative interpretation is possible, one that does not degrade women. According to the passage, Confucius encountered difficulties in managing relationships with both groups. Nevertheless, the causes of these difficulties could be entirely distinct for each group. Confucius’ struggle with inferior individuals might originate from their hypocrisy and arrogance, which could provoke conflicts when he becomes too close to them, as demonstrated on numerous occasions in the Analects. Conversely, the rationale behind Confucius’ perception of women as difficult to interact with remains ambiguous, as he did not explicitly elaborate on this matter in the Analects. Consequently, it would be unwarranted to assume that the reasons are identical to those of inferior individuals.

The possibility arises that Confucius found it difficult to understand women because they possess greater emotional complexity than men. This stronger emotional intricacy and capability, however, can be seen as the foundation for care ethics, which emphasizes the significance of relational and emotional connections. Therefore, this passage might be seen as a starting point leading to feminist ethics of care.

All in all, the reinterpretation stage is instrumental in reconciling Confucianism and feminism by facilitating a reevaluation of traditional Confucian concepts. The next stage follows closely, which involves the synthesis of these reinterpreted concepts with contemporary feminist theories, further bridging the gap between Confucianism and feminism.

Integration

While the reinterpretation and integration stages are structurally separated in my essay, they often function as a coherent process and should be treated as such. Integration pertains to the amalgamation of Confucian and feminist philosophies, with the objective of elevating both to more advanced levels of understanding. This is achieved by broadening the scope of each philosophy to encompass a more diverse range of situations and perspectives, ultimately creating a more comprehensive and inclusive ethical framework.

For example, when examining the Confucian concept of humaneness through the lens of care ethics, the importance of emotional connections in discerning the needs of others is emphasized. Mencius posits that witnessing a child in peril evokes feelings of alarm and compassion, which stem from our capacity to empathize with the emotions of others. These feelings serve as the foundation of humaneness. While some scholars, such as Daniel Star, contend that care ethics are more flexible and contextual in comparison to the Confucian ethics of humaneness (Star 85), the fundamental care-oriented components of both philosophies exhibit striking similarities.

However, Nel Noddings, a prominent American philosopher who developed the theory of care ethics, articulates that care ethics suggest a limitation on our obligations (Noddings 107); we cannot extend care to everyone, which implies that our obligations are more significant towards those with whom we have a connection. Noddings accentuates the relational nature of care ethics, concentrating on individuals with whom we have formed close relationships. Critics have raised concerns that, in the absence of a broader sense of justice, care ethics might foster cronyism and favoritism (Friedman 61-67). However, through integration with Confucianism, care ethics can potentially address these criticisms and evolve into a universal moral theory that transcends intimate relationships and gender distinctions. Building on the ideas of Confucius, Mencius argues that promoting humanity does not require the denial of our natural inclinations or the pursuit of impartiality. Rather, we must extend our natural preferences to others, empathizing with individuals who harbor similar feelings towards their family members. Thus, it merely necessitates that we progress one step further, expanding respect and tenderness to not only our own kin but also to elders and young individuals in other families. ^[4] By connecting care ethics and Confucianism in this manner, we can create a more comprehensive ethical framework that addresses the limitations of both philosophies while providing a broader foundation for moral action. The culmination of this synthesis results in a universal socio-political theory that envelops various aspects of social life. Consequently, care is not solely an individual or gender-specific matter, but rather an all-encompassing ethical ideal and institutional arrangement that engages the nation, society, and individuals.

It is important to note that the analysis provided above offers a simplified version of the integration between care ethics and Confucianism. Humaneness, as a central concept in Confucianism, is broad and intricate, and the comparison with care ethics only captures a small portion of its complexity. Consequently, a more in-depth analysis would be necessary to fully understand the potential integration between these two ethical theories.

Moreover, the integration of care ethics and humaneness is just one example of reinterpretation and integration. Numerous other approaches exist that utilize this process. For instance, Rosenlee, her essay “Confucian friendship (You 友) as spousal relationship: a feminist imagination”, draws a connection between Confucian friendship and modern-day marriage, while Ivanhoe, in his essay “Mengzi, Xunzi, and Modem Feminist Ethics”, identifies Mencius’s and Xun Zi’s ethical theories with two variations of contemporary feminist ethical theory. Both Confucianism and feminism are broad, rich, and intricate disciplines, and there is no one-size-fits-all solution that can settle the disputes and connections between them. Exploring various aspects of reinterpretation and integration can further our understanding of these disciplines and enable the development of more comprehensive ethical frameworks that draw upon the strengths of both philosophies.

CONCLUSION

It has been shown that the development of Confucian feminism holds significant potential, particularly in countries like China and Korea where Confucian traditions have had a profound impact on social and ethical norms. Through a process of rectification, reinterpretation, and integration, Confucian feminism can emerge as a powerful force that enriches feminist ethical theories and provides unique insights grounded in the rich history of Confucian philosophy. Humaneness and care ethics serves as an example of how these two ethical frameworks can be synthesized, but it is important to remember that this is just one of many possible approaches. Confucian feminism offers a valuable perspective that can contribute to addressing complex issues related to gender equality and help advance the global conversation on feminism. By engaging in this dialogue and exploring the interplay between Confucian and feminist thought, we can work towards a more inclusive and comprehensive understanding of both philosophies that can guide us in addressing the challenges of the modern world.

REFERENCES

Zhen, He-Yin. “On the Revenge of Women.” The Birth of Chinese Feminism: Essential Texts in Transnational Theory, edited by Lydia H. Liu, Rebecca E. Karl, and Dorothy Ko, Columbia University Press, 2013, pp. 105-146.

Choi, Hyaeweol. “Gender Equality, a New Moral Order.” Gender and Mission Encounters in Korea: New Women, Old Ways, University of California Press, 2009, pp. 21-44.

Kristeva, Julia. “Confucius – An Eater of Woman.” About Chinese Women. Marion Boyars Publishers Ltd, 1986, pp. 66-99.

Yan, Yuheng. “A Study of the Influence of a Doll’s House on Chinese ‘Women walk out’ Literature.” Advances in Social Science, Education and Humanities Research, vol. 594, 2021, pp. 354-357.

Lu, Xun. “What Happens after Nora Walks Out 娜拉走後怎樣.” Jottings under Lamplight, edited by Eileen J. Cheng and Kirk Denton, Harvard University Press, 2017, pp. 256-261.

Chu, Godwin C., and Yanan Ju. The Great Wall in Ruins: Communication and Cultural Change in China. State University of New York Press, 1993.

Li, Chenyang. The Sage and the Second Sex: Confucianism, Ethics, and Gender. Open Court, 2000.

Li, Chenyang. “Jen and the Feminist Ethics of Care.” The Sage and the Second Sex: Confucianism, Ethics, and Gender, Open Court, 2000, pp. 23-42.

Liu, Jeeloo. “Is Human History Predestined in Wang Fuzhi’s Cosmology?” Journal of Chinese Philosophy, vol. 28, no. 3, September 2001, pp. 321-337.

Confucius. The Analects (Lun yü). Translated with an introduction by D.C. Lau. Penguin Books, 1979.

Star, Daniel. “Do Confucians Really Care? A Defense of the Distinctiveness of Care Ethics: A Reply to Chenyang Li.” Hypatia, vol. 17, no. 1, Winter 2002, pp. 77-106. Published by Wiley on behalf of Hypatia, Inc.

Noddings, Nel. Caring: A Feminine Approach to Ethics & Moral Education. University of California Press, 1984.

Friedman, Marilyn. “Beyond Caring: The De-Moralization of Gender.” Justice and Care: Essential Readings in Feminist Ethics, edited by Virginia Held, Westview Press, 2006, pp. 61-77.

Mencius. Translated by D.C. Lau. Mencius. Penguin Classics, 1970.

This word is translated from the Chinese character ren 仁. ↑
This word is translated from the Chinese character Li 禮. ↑
‘唯女子與小人爲難養也。近之則不孫、遠之則怨’, Analect, 17.25; Lau, p. 253. ↑
This interpretation is based on Mencius 1A:7, where the phrase “老吾老、以及人之老幼吾幼。以及人之幼天下可運於掌” is particularly relevant; Lau, p. 53. ↑

PDE notes: Method of Characteristic

August 16, 2022Michael LiuLeave a comment

1. Introduction

The method of characteristics is a general technique for solving first-order equations. The basic idea is to reduce the determination of explicit solutions to solving ODE.

Initial value problem in one space variable ${x}$ and time ${t}$ take the form

$\displaystyle u_t+cu_x=0, t>0 \ \ \ \ \ (1)$

$\displaystyle u(x,0)=f(x) \ \ \ \ \ (2)$

We solve (1) using the method of characteristics, which reduces the initial value problem to an initial value problem for a system of ODE. In this method, we depend on the observation that if ${\{(x(t),t):t\geq 0\}}$ is smooth curve, then along the curve, ${u(x(t),t)}$ has rate of change

$\displaystyle \frac{d}{dt} u(x(t),t) = u_t+\frac{dx(t)}{dt}u_x \ \ \ \ \ (3)$

given by the chain rule. Comparing (3) with (1), we see that the expressions are identical if we set

$\displaystyle \frac{dx(t)}{dt}=c \ \ \ \ \ (4)$

and interpret ${c}$ as speed. The left-hand side of the PDE can also be interpreted as the derivative of ${u(x,t)}$ , in the direction ${(c,1)}$ in ${x-t}$ space.

Now the PDE in (1) can be replaced by the ODE system,

$\displaystyle \frac{dx(t)}{dt}=c \ \ \ \ \ (5)$

$\displaystyle \frac{d}{dt}[u(x(t),t)]=0 \ \ \ \ \ (6)$

These ODEs are called the characteristic equations. Take note that ${u(x(t),t)}$ is constant along the curve ${x=x(t)}$ . We solve (5) to get

$\displaystyle x(t)=ct+a \ \ \ \ \ (7)$

where ${a}$ is an unknown constant. Equation (7) is the equation for the family of parallel characteristic curves of (1). We observe that at ${t=0}$ , we have ${x(0)=a}$ , and hence this constant ${a}$ is the point where the characteristic curve starts. We call it the anchor point. If a point ${(x,t)}$ is given, we can always find the corresponding anchor point as

$\displaystyle a=x-ct \ \ \ \ \ (8)$

Now we solve the second characteristic ODE to get

$\displaystyle u(x(t),t)=k \ \ \ \ \ (9)$

where ${k}$ is an arbitrary constant.

Initial conditions for the ODE system are derived from the initial condition ${u(x,0)=f(x)}$ for the PDE problem (1). We already know that the initial condition for ODE (5) is ${x(0)=a}$ . We write ${u(t)}$ in place of ${u(x(t),t)}$ , then the initial condition for ODE (6) is

$\displaystyle u(0)=f(x(0))=f(a)=f(x(t)-ct) \ \ \ \ \ (10)$

Since u is constant along the characteristic curve,

$\displaystyle u(x(t),t)=f(x(0),0)=f(a) \ \ \ \ \ (11)$

Thus, given a point ${(x,t)}$ , there is a unique characteristic curve passing through ${(x,t)}$ , with anchor point at ${a=x-ct}$ , and the general solution at ${(x,t)}$ is

$\displaystyle u(x,t)=f(x-ct) \ \ \ \ \ (12)$

Next we extend the method to allow for linear forcing terms. We try to solve the following PDE for ${u(x,t)}$ on ${-\infty < x < \infty}$

$\displaystyle u_t+\alpha u_x+\gamma u=0 \ \ \ \ \ (13)$

$\displaystyle u(x,0)=f(x) \ \ \ \ \ (14)$

Solution From the chain rule we have

$\displaystyle \frac{du}{dt}= u_t+\frac{du}{dx}u_x \ \ \ \ \ (15)$

Hence the characteristic equation becomes

$\displaystyle \frac{dx}{dt}=\alpha \ \ \ \ \ (16)$

$\displaystyle \frac{du}{dt}=-\gamma u \ \ \ \ \ (17)$

The initial conditions are

$\displaystyle x(0)=a \ \ \ \ \ (18)$

$\displaystyle u(0)=f(a) \ \ \ \ \ (19)$

The solution for the first characteristic equation is

$\displaystyle x=\alpha t + a \ \ \ \ \ (20)$

Thus, the anchor point for the characteristic passing through the point ${(x,t)}$ is

$\displaystyle a=x-\alpha t \ \ \ \ \ (21)$

The solution for the second characteristic equation is

$\displaystyle u= u(x(0),0)e^{-\gamma t} \ \ \ \ \ (22)$

and the solution along the characteristic ${x=x(t)}$ is

$\displaystyle u=u(a,0)=f(x-\alpha t)e^{-\gamma t} \ \ \ \ \ (23)$

${\square}$

For this kind of initial value problem, the method of characteristic is summarized as:

Rewrite the initial value problem (13) as a system of ODE consisting of the characteristic equations (16) and (17) with initial conditions (18) and (19).
Solve the ODE and initial condition for ${x(t)}$ and ${u(t)}$ , with the anchor point ${x(0)=a}$ to get the solution along the characteristic.
Solve for ${a}$ as a function of ${x,t}$ . This effectively changes variables from ${t,a}$ to ${x,t}$ .
Write the solution ${u=u(x,t)}$ .

We can extend our concepts to first-order equations with non-constant coefficients in the form

$\displaystyle A(x,y)u_x+B(x,y)u_y=C(x,y,u) \ \ \ \ \ (24)$

In applications, this PDE is usually accompanied by a side condition of the form

$\displaystyle u(x,y)=f(x,y) \ \ \ \ \ (25)$

for ${(x,y) \in \Gamma_a}$ , where ${\Gamma_a}$ is a curve of anchor points and ${f}$ is a given function. Suppose that ${u(x,y)}$ is the solution to (24) subject to the side condition (25). We can think of ${z=u(x,y)}$ as a two-dimensional surface in the ${x-y-z}$ space. Denote by ${\Gamma}$ the curve on the surface ${z=u(x,y)}$ whose projection onto the ${xy-}$ plane is ${\Gamma_a}$ . The curve ${\Gamma}$ is called the initial curve. We parameterize the initial curve ${\Gamma}$ using the anchor points to get

$\displaystyle \Gamma: \left\{ \begin{array}{lr} x=x_0(a) \\ y=y_0(a) \\ z=z_0(a)=f(x_0(z),y_0(a)) \end{array} \right. \ \ \ \ \ (26)$

Equation (24) states that the vector field ${\textbf{F}=(A(x,y),B(x,y),C(x,y,u))}$ is tangent to the solution surface ${z=u(x,y)}$ , since the solution surface has normal

$\displaystyle \nabla(u(x,y)-z)=(u_x,u_y,-1) \ \ \ \ \ (27)$

The solution surface can therefore be generated by integrating along the vector field, starting at each point of the curve ${\Gamma}$ .

Integral curves

$\displaystyle \textbf{r}(s)=(x(s),y(s),z(s)) \ \ \ \ \ (28)$

of the vector field ${\textbf{F}}$ which starts from the initial curve ${\Gamma}$ satisfy the following vector ODE:

$\displaystyle \frac{d\textbf{r}}{ds}=\textbf{F} \ \ \ \ \ (29)$

$\displaystyle \textbf{r}(0)=(x_0(a),y_0(a),z_0(a)) \ \ \ \ \ (30)$

or, in component form, the system of ODEs:

$\displaystyle \left\{ \begin{array}{lr} \frac{dx}{ds}=A(x,y) \\ x(0)=x_0(a) \\ \end{array} \right. \ \ \ \ \ (31)$

$\displaystyle \left\{ \begin{array}{lr} \frac{dy}{ds}=B(x,y) \\ y(0)=y_0(a) \\ \end{array} \right. \ \ \ \ \ (32)$

$\displaystyle \left\{ \begin{array}{lr} \frac{dz}{ds}=Z(x,y) \\ z(0)=z_0(a) \\ \end{array} \right. \ \ \ \ \ (33)$

The system of ODEs (31), (32), (33) are called the characteristic equations for the PDE (24). The solutions to the characteristic equations are called the characteristic curves for the PDE.

The procedure to solve the PDE (24) and (25) is as follows:

Solve the first two characteristic equations (31) and (32)to get ${x}$ and ${y}$ in terms of the characteristic variable ${s}$ and the anchor point ${a}$ :
$\displaystyle x=X(s,a), y=Y(s,a) \ \ \ \ \ (34)$
Insert the solution from the previous step into equation (33) and solve the resulting equation for ${z}$ :
$\displaystyle z=Z(s,a) \ \ \ \ \ (35)$
Apply the Inverse Function Theorem. In this step we solve the equations

$\displaystyle x=X(s,a), y=Y(s,a) \ \ \ \ \ (36)$

for

$\displaystyle s=S(x,y), a=\wedge(x,y) \ \ \ \ \ (37)$

The solution is guaranteed by the Inverse function theorem.
Write the solution for ${z}$ in terms of ${x}$ and ${y}$ to get the solution to the original PDE:
$\displaystyle u(x,y)=Z(S(x,y),\wedge(x,y)) \ \ \ \ \ (38)$

This procedure will work as long as the transformation in (36) and (37) is invertible. We can guarantee this locally by appealing to the Inverse Function Theorem.

Short Essay 3: A study of the word “female” in Daodejing

May 19, 2022May 23, 2023Michael LiuLeave a comment

“雄兔脚扑朔，雌兔眼迷离。” A depiction of female (ci) and male (xiong) rabbits in the Ballad of Mulan.

The objective of this essay is to conduct an in-depth study of the term “female” as it appears in the Daodejing, with a particular focus on two specific characters – ci 雌 and pin 牝 – that are intrinsically associated with femininity in the text. Although typically used to describe female animals, plants, or feminine objects, an interpretation grounded in Daoist cosmology allows for the extension of the meaning of ci and pin to encompass the human female, in line with the Daoist view of a unitary whole, where humans and other species are contiguous. This usage is consistent with the fundamental Daoist principle that posits humans are not superior to other forms of life. The study will take a three-pronged approach: (1) a review of occurrences of ci and pin in Daodejing; (2) an interpretation of their meaning(s) based on the context of the chapters where they are found; and (3) an exploration of their broader significance within the text.

To initiate the study, I will examine the instances of ci and pin in Daodejing. Primarily, I will rely on D.C. Lau’s translation. ci appeared twice in chapters 10 and 28, respectively: “When the gates of heaven open and shut, are you capable of keeping to the role of the female (ci)?” and “Know the male (xiong 雄), but keep to the role of the female (ci), and be a ravine to the empire.” pin appeared five times in chapters 6, 55, and 61: “The spirit of the valley never dies. This is called the mysterious female (pin). The gateway of the mysterious female (pin) is called the root of heaven and earth”; “It does not know the union of male and female (pin), yet its male member will stir. This is because its virility is at its height”; “A large state is the lower reaches of a river: the place where all the streams of the world unite. In the union of the world, the female (pin) always gets the better of the male (xiong) by stillness. Being still, she takes the lower position”.

Drawing upon the selected passages, it emerges that Laozi’s portrayal of femininity can be categorized into the following dimensions:

1. The Female embodies qualities such as softness, passiveness, yieldingness, humility etc.

In Chapters 6 and 28, Laozi equates “the role of the female” with “the spirit of the valley” and “the ravine of the empire.” The metaphors of the valley and the ravine have a strong connection with the metaphor of water, a prominent motif in Daodejing. Valleys and ravines, being low-lying areas of land often traversed by streams, are embodiments of water, reflecting its inherent “qualities.” As per Laozi, water refrains from entering into contention^[1] (buzheng 不争) with other things and is compatible with all things (wanwu 万物) in nature, which signifies its receptiveness and passivity. In addition, Needham ascribes softness and yieldingness to water, as he points out that water is “yielding and assumes the shape of whatever vessel it is placed in^[2]“ (Needham, 1956). Laozi also asserts that humans, akin to water’s natural inclination to flow from higher to lower regions, should strive to maintain a “low” stance, implying the virtues of humility and discretion. This is exemplified in Chapter 61, where the act of assuming a lower position is associated with both water and pin. Consequently, one might argue that water, ravine, the spirit of the valley, and the female form all metaphorically epitomize attributes such as softness, yieldingness, receptiveness, passivity, humility, etc., which to a certain degree are traits commonly associated with the female gender.

2. The female overcomes the male

In chapter 28, Laozi urges one to “keep to the role of female”; in chapter 61, Laozi asserts that “the female always gets the better of the male.” It is clear that, in Laozi’s perception, the female overcomes the male. By corollary, this also implies that the feminine overcomes the masculine in such a way that: soft overcomes hard, weak overcomes strong^[3], and yieldingness to triumph over dominance. In chapter 61, Laozi takes the diplomacy between a large state and a small state as an example: “the large state, by taking the lower position, annexes the small state.” Laozi underscores that it is only when the larger state exhibits tolerance and submission, as opposed to aggression and militancy, can it garner the goodwill and trust of the smaller state. Hence, those who align their actions with these feminine principles place themselves in a more advantageous position.

3. Associating Female Sexual and Reproductive Functions with Dao

Laozi depicts Dao as the “mother of the world.” In chapter 6, Laozi attributes various characteristics of female, especially the female sexual and reproductive functions, to Dao: “The spirit of the valley never dies. This is called the mysterious female. The gateway of the mysterious female is called the root of heaven and earth. Dimly visible, it seems as if it were there, Yet use will never drain it”.The valley is connected to the mysterious female in two ways: firstly, valleys, brimming with rivers and fertile soils, foster and nourish diverse life forms, such as plants, animals, and trees. This is symbolically akin to the role of the female womb that provides nutrients to the embryo. Secondly, the overall structure of a valley – a moist, concave, and open ‘container’ – bears resemblance to the form of female reproductive organs. Consequently, when Laozi refers to the mysterious female, he may specifically be indicating the female womb. The “gateway” may symbolize the opening of the womb during childbirth, a process through which new life emerges. At a more profound level, Laozi suggests that Dao functions akin to a “womb.” The Dao, the principal concept of Daodejing, embodies these characteristics: (1) Dao is empty^[4] and inexhaustible^[5]; (2) Dao generates the world^[6] (dao-sheng-wan-wu 道生万物). Dao, with its generative emptiness and nourishing capabilities, is the source of all beings. For this reason, Dao is equated with the infinite maternal force accountable for the nourishment and sustenance of all entities. Therefore, it would be justified to perceive the female as an anthropomorphic representation of Dao.

Two additional points of note include the comparative reading of A. Charles Muller’s translation, which offers minor variances that do not significantly impact text interpretation, and the literal interpretation of the “union of male and female (pin)” in chapter 55 as sexual intercourse, which does not necessitate further explanation.

Works Cited

Lao Tzu, Trans. by D.C. Lau (1963). The Tao Te Ching.

Laozi, Trans. by A. Charles Muller (1991). Daode Jing.

Needham, J. (1956). The Water Symbol and the Feminine Symbol . In J. Needham, Science and Civilization in China (pp. 57-61). Cambridge: Cambridge University Press.

Daodejing, chapter 8. ↑
Science and Civilization in China, p.77. ↑
Daodejing, chapters 36 and 78. ↑
Ibid. chapter 4. ↑
Ibid. chapter 5. ↑
Ibid. chapter 42. ↑

[Upcoming] Exegetical Writing 4: Daodejing – chapter 40; Argumentative Writing 1: Is Mencius right to claim that emotions are the origin of morality? Why or why not? What is the role of reason?

October 1, 2021May 19, 2022Michael LiuLeave a comment

Argumentative Writing 2: Emptiness, Dependent Arising, and the Cosmology of Tiantai School

October 1, 2021January 21, 2022Michael LiuLeave a comment

Emptiness (Śūnyatā, 空) and Dependent Arising (Pratītyasamutpāda, 緣起) are common tenets in all Buddhist schools, but different schools give the terms different interpretations. In this essay, I will examine the philosophical development of the concepts of Emptiness and Dependent Arising in the Tiantai school, and discuss how they have influenced the cosmology of Mahayana Buddhism in East Asia.

The Tiantai school of Buddhism was founded in six century China. The major theses of Tiantai school are established by the fourth patriarch Zhiyi, who regards the Lotus Sutra as having the highest status of all Buddhist doctrines. Zhiyi takes Emptiness and Dependent Arising to be the core concepts of his defining argument – the Threefold Truth (三諦), which includes the truth of Emptiness, the truth of Temporariness, and the truth of the Middle Way. The truth of Emptiness states that all dharmas are empty in the sense that they do not have inherent self-nature. The truth of Temporariness states that all dharmas depend on many causal factors to exist. Without these factors, things would not have come into being. Therefore, dharmas exist, but they exist provisionally, temporally, and dependently. I argue that the first two truths proposed by Zhiyi are similar to Nagarjuna’s theory of Twofold Truths: on the level of the phenomenal world, all things exist independently and provisionally; on the level of ultimate reality (Nirvana), however, things are all empty in nature. (Mitchell and Jacoby, p. 160) Nevertheless, Zhiyi makes an explicit integration of the truth of Emptiness and the truth of Temporariness by constructing a third truth: the truth of the Middle Way. In Fahua xuanyi (法華玄義), Zhiyi explains the notion of Middle as “The reality of non-duality is called the Middle.” The “Way” is translated from the Chinese word “Dao (道)”, which means “the ultimate reality of the universe”. Thus, the truth of the Middle Way simply states that the ultimate reality of the world is that all dharmas are both provisionally existent and empty. Finally, Zhiyi completes his argument by saying, in Fahua xuanyi, “Though these are an integrated unity, they are called threefold; though they are threefold, they are called a unity.” Therefore, the Threefold Truths can be seen as three aspects of one thing – the real nature of our world. In other words, Emptiness, Dependent arising, and the Middle Way are ultimately identical. Standing alone, each of them represents a partial truth; taken together, they jointly depict the one reality.

Zhiyi’s notion of Threefold Truths reveals a fundamental distinction between the cosmology of early Buddhist traditions and Tiantai Buddhism (as well as other major Mahayana schools). Early Buddhism sees the phenomenal world and nirvana as two separate realms of existence. The ordinary sentient beings who live in the phenomenal world go through the endless cycles of life in the six dharma realms. When one is enlightened, he/she will exit the six dharma realms and be completely free from the cycles of life and death. The phenomenal world is not real, since all things are devoid of inherent self-nature and independent existence. The realm of nirvana is the ultimate reality – it is real, unconditioned, and empty. (Mitchell and Jacoby, p. 62)

Figure 1. A painting showing the Cyclic Existence, or Saṃsāra, in early Buddhism

On the other hand, the Tiantai school rejects the duality of this worldview by claiming that there is no other realm outside the provisionally existent phenomenal world as shown in the Threefold Truths. In other words, the phenomenal world is nirvana and nirvana is the phenomenal world, as Zhiyi puts it in Mohe Zhiguan (摩訶止観), “A single, unalloyed reality is all there is.” Zhiyi describes the worldview of Tiantai as having ten dharmas realms. Besides the previous six mundane realms, there is also four holy realms: the realm of Śrāvaka (Hearers of Buddha, 緣覺乘), the realm of Pratyekabuddhayāna (Solitary Buddha, 辟支佛), the realm of bodhisattva (菩薩), and the realm of Buddha. One notable characteristic of this worldview is that the ten dharma realms are mutually contained, meaning that they are all part of the whole world. Thus, all ten dharma realms are at the same time empty, provisionally and dependently existing, and manifesting the Middle Way.

Figure 2. A painting showing the Ten Dharma Realms

Base on this worldview, Zhiyi puts forward another important thesis for the Tantai school:

“One mind contains ten dharma-realms, but each of these dharma-realms contains ten dharma-realms, resulting in 100 dharma-realms. One realm contains 30 kinds of worlds, hence 100 dharma-realms contain 3,000 worlds. These 3,000 worlds are contained in a fleeting moment of thought.” (Mitchell and Jacoby, p.235)

The assumption of this argument is that all of us have Buddha nature – the potential to become a Buddha. Indeed, the Lotus Sutra says that “the Buddhas of the present and future, whose numbers are beyond calculations”. Base on the Tiantai worldview, those Buddhas reside in the same reality as we do. The moment they gain true enlightenment, they turn the phenomenal world into Nirvana. Thus, entering Nirvana depends on nothing more than our own mind’s ability to perceive and understand the reality. The minds of sentient beings conceive all dharmas to be full of defilements and attachments; they are thus stuck in the cycles of life and death and can never be totally free from Duḥkha (suffering). The minds of Śrāvaka, Pratyekabuddhayāna, and bodhisattva are able to conceive all dharmas to be dependently arisen, thus they separate the phenomenal world and Nirvana into two distinct realms. Finally, the minds of Buddha conceive all three thousand worlds to realize their true nature – all things in the world are provisionally and dependently existent, empty in nature, and manifest the Middle Way. Thus, he/she is able to understand Cosmo as one unified reality. Therefore, one can conclude that the creation of three thousand worlds in one thought depends on one’s own mental power – one thought can bring one down to the realm of hell; the other can raise one up to the realm of Buddha.

All in all, the Tiantai school developed a new cosmology for Mahayana Buddhism in East Asia based on the concepts of Emptiness, Dependent Arising, and the Middle Way. By eliminating the barrier between the phenomenal world and the realm of Nirvana, Tiantai Buddhism offers all sentient beings a chance to be free from suffering and become enlightened. Personally, I appreciate the Tiantai tradition for making the very first attempt to transform early Indian Buddhism into a more accessible and inclusive religion. I also found the major arguments made by the Tiantai scholars logical and rigorous, so I am convinced (and impressed) by this development.

Works Cited

Donald W. Mitchell, S. H. (2013). Buddhism: Introducing the Buddhist Experience. Oxford: Oxford University Press.

Argumentative Writing 1: “Gradual enlightenment” vs “Sudden enlightenment” in Chan(Zen) Buddhism

September 28, 2021January 21, 2022Michael LiuLeave a comment

There is a major distinction between the Northern School of Chan and the Southern School of Chan – the Northern School taught gradual enlightenment; The Southern School taught sudden enlightenment. In this essay, I will begin by analyzing the two poems written by Shenxiu and Huineng, to see how the two schools diverge theoretically.

Shenxiu’s poem says (Mou-Lam and Price, p. 72):

Our body is the bodhi tree,

And our mind a mirror bright.

Carefully we wipe them hour by hour,

And let no dust alight.

Shenxiu’s verse starts with an assumption that we have an originally pure mind, which, I argue, is the theoretical foundation of the Northern School. Shenxiu further explores the properties of the mind in his work Guan Xin Lun, “Of the myriad dharmas, the mind is the most basic…There are two different minds…The first is the pure mind. The second is the defiled mind.” The two states of mind can be explained in the following ways: Our mind is initially pure and clean, but it is venerable to the distortions by defilements (dust) caused by “Three Poisons,” namely greed, anger, and ignorance. The purpose of Buddhist practice is thus to purify our mind and get rid of all defilements. In particular, Shenxiu’s teaching focuses on “beholding the mind (guanxin),” which means to keep a vigilant watch over the mind through solitary meditation. By keeping our mind and our initial purity in view, one can identify and avoid all sorts of defilements, and thus “let no dust alight”. Moreover, since our mind is being constantly defiled, one cannot preserve the initial purity without the assiduous and continuous efforts of the watchful mind. We have to “wipe hour and hour” until our mind is cleansed of all defilements to reach Nirvana. Therefore, it is a tireless process to attain enlightenment, and this is why Shenxiu’s verse supports the claim that the Northern School teaches gradual enlightenment.

Huineng’s poem says (Mou-Lam and Price, p.74):

There is no bodhi tree,

Nor stand of a mirror bright.

Since all is void,

Where can the dust alight?

Huineng’s verse, on the other hand, contradicts sharply with Shenxiu’s teaching of the mind. Huineng believes that there is no duality between the pure mind and the defiled mind. By taking “All is void” as the fundamental assumption of their teaching, the Southern School rejects the existence of a mind as an entity that needs to be preserved. Since there is no mirror to be attached to, how can any “dust” alight in the first place? In other words, since there is no mind, there can be no defilement.

Instead of using the metaphor of mirror and dust, Huineng claims that the state of mind of an unenlightened individual is “the same way as the sun may be thickly veiled by cloud and unable to show his light.” (Mou-Lam and Price, p.85) This contrasts with Shenxiu’s metaphor as even if one cannot see the sun, it is still bright and clear. The clouds do not affect the brilliant nature of the sun, in the same way as erroneous views and false conceptions do not change the pure nature of our mind. Based on this metaphor, I present what I take to be the strongest argument put forward by Huineng simply as follows: instead of “beholding the mind”, one should employ inborn wisdom to realize his/her essential nature. The most crucial distinction between “mind” and “nature” is that we can never lose our nature, but we might lose our mind. “Nature” is essential, meaning that without which no existence can be possible. One should take note that although Huineng still uses the term “mind” on many occasions, he often interprets “mind” in the way that “nature” is normally understood. For example, Huineng says in the platform sutra, “our essence of mind is intrinsically pure” (Mou-Lam and Price, p.86). In other words, our mind (nature) is originally pure and clean and it remains pure and clean at all times. Huineng further associates the intrinsic mind with Buddha-nature by saying “Clear, free, empty, and silent, perception and action equally enlightened, mirrorlike awareness unobstructed – this is truly the inherent Buddha-nature” (Cleary, p.108). Therefore, our intrinsic mind is also our Buddha nature, which implies that all of us can become Buddhas. If one can see this point, one immediately gains enlightenment. Since all we have to do is to see our own mind, be our own teacher, and realize our own Buddhahood, the enlightenment process is innate, sudden, and spontaneous, as stated in the Platform Sutra, “A foolish passing thought makes one an ordinary man, while an enlightened second thought makes one a Buddha” (Mou-Lam and Price, p.83). As a result, one may say that the Southern School teaches sudden enlightenment.

All in all, it could be seen that the Northern School of Chan emphasizes self-purification, which is an accumulated effort. Hence, enlightenment has to be a gradual process. While for the Southern School of Chan, one has to employ inborn wisdom to realize his/her essential nature.

Despite finding arguments from both the Northern and Southern Schools compelling and sound, I am personally more inclined to the teachings of the Southern School for their close connections with my favorite branch of Chinese Philosophy – Daoism. For example, Zhuangzi takes Dao to be universal and permanent and claims that our ability to perceive Dao is innate, which is similar to Southern School’s idea of realizing the intrinsic mind and buddha-nature. In practice, Daoism also emphasizes the importance of following our intuitions instead of obeying a particular sutra or authority. I believe the similarities and differences between Daoism and Chan would be an interesting topic for future explorations.

Works Cited

Shenxiu. Guan Xin Lun.

Wong Mou-Lam, A. F. (2005). The Diamond Sutra and the Sutra of Hui-nen. N/A: Shambhala Publication.

Cleary, T. (1998). The Sutra of Hui-neng, Grand Master of Zen: With Hui-neng’s Commentary on the Diamond Sutra. N/A: Shambhala.

Exegetical Writing 2: The Analects – 4:10, 4:11, 14:22

September 28, 2021January 22, 2022Michael LiuLeave a comment

Translated Text

[4:10] The Master said: “When the noble man deals with the world he is not prejudiced for or against anything. He does what is Right.

[4:11] The Master said: “The superior man thinks of virtue; the inferior man thinks of possessions. The superior man seeks discipline; the inferior man seeks favors.”

[14:22] Zi Lu asked how to deal with a ruler. Confucius said, “Do not impose on him, and, moreover, withstand him to his face.”

Analysis

In passage 4:11, Confucius draws a clear distinction between a superior man and an inferior man. Confucius says, “The superior man thinks of virtue; the inferior man thinks of possessions. The superior man seeks discipline; the inferior man seeks favors.” From a general reading of the passage, it can be seen that a superior man is a morally exemplary person who possesses virtue and acts in accordance with moral principles, whereas an inferior man disregards virtues and focuses on petty affairs such as benefits and reputations. However, at a deeper level, it is crucial to understand how such a distinction is established.

A close reading of the passage 4:11 would require an examination of the verbs’ think’ and ‘seek.’ Both verbs, though appear to mean differently, are translated from the same Chinese character ‘Huai 怀.’ In common usage, ‘Huai’ means having an attitude or an emotion toward something or someone. For example, one may possess (Huai) a sense of respect toward her teacher. ‘Huai’ also implies that attitude can influence action, just as a person who is respectful to his teacher would go to class on time, participate in class, etc. In the context of Passage 4:11, what Confucius implies by ‘Huai’ is that a person habituates moral concerns with which she would carry out her moral judgments and act accordingly. In Great Learning, this idea is described as “What truly is within will be manifested without.” While the common conception of ‘think’ may allow assorted considerations, ‘Huai’ demands one’s devotion to a particular moral position. Perhaps, it would be better to say, “The superior man [cherishes] virtue.”

Passage 14:22 could serve as a further illustration of the idea of ‘Huai’ or ‘cherish.’ When Confucius’ student Zi Lu asks how a ruler should be served, Confucius replies, “Do not impose on him, and, moreover, withstand him to his face.” An explanation of this passage would be that an inferior man would avoid criticizing and upsetting the ruler. Instead, he flatters the ruler to gain favors and rewards for himself. On the other hand, a superior man who cherishes virtue would restrain himself from personal desires and preferences when dealing with public affairs as he is solely devoted to Confucius’s moral principles. He will be honest with the ruler and will stand up against the ruler’s wrong deeds.

Moreover, in passage 4:10, Confucius says, “A superior man in dealing with the world is not for anything or against anything. He follows righteousness as the standard.” One could treat this passage as a restatement of the arguments outlined in passage 4:11. The interpretation goes: a superior man in dealing with the (public) world is not for or against anyone’s personal benefits and preferences. He only makes moral judgments against the principle of righteousness (or virtue). In the context of this passage, righteousness carries a very similar meaning as ‘virtue’. This could be shown by passage 4:16, which is almost identical to passage 4:11, where Confucius says, “The superior man is versed in what is righteous. The inferior man is versed in what is profitable.”

To sum up, an inferior man would take personal benefits and preferences as his priority. His judgments are not morally guided, and his actions do not incorporate virtue. Conversely, a superior man would take virtues as his standard. He bases his moral judgments solely on moral principles and restrains himself from personal desires. Therefore, his actions are always appropriate to the Way.

Original Text

[4:10] 子曰：「君子之於天下也，無適也，無莫也，義之與比。」

[4:11] 子曰：「君子懷德，小人懷土；君子懷刑，小人懷惠。」

[14:22] 子路問事君。子曰：「勿欺也，而犯之。」