Mathematics and Emotion
Whitehead’s Categories of Existence
as Tool for Interdisciplinary Studies
Whitehead's categories of existence offer a powerful framework for identifying and categorizing different aspects of reality. These categories—public matters of fact (nexus), feelings and forms of connection (prehensions), emotions (subjective forms), mathematical patterns and relations (eternal objects), individual agents with feelings and purposes of their own (actual entities), ideas about the world and lures for feeling (propositions), aesthetic relations (contrasts), and diversities (multiplicities)—provide a comprehensive set of tools for scholars across various disciplines, offering a common conceptual vocabulary.
Encouraging Interconnectedness Across Disciplines
Natural scientists might focus on public matters of fact, mathematicians on eternal objects, social scientists on individual agents, and humanists on aesthetic relations. However, Whitehead’s categories encourage each discipline to consider how their subjects interact with others. For instance, a physicist studying a nexus of particles might also explore how the same nexus relates to prehensions or subjective forms in psychology. This approach fosters a richer, more integrated understanding of complex phenomena and highlights the interconnectedness of various fields of study.
Flexibility in Applying Whitehead’s Categories
These categories are not rigid. A subject, such as a human society, encompasses not only its structural elements but also the feelings of individuals within it, their modes of enjoyment and suffering, and the decisions they make—all influenced by their interactions with others. This interconnectedness applies equally to other nexuses, such as a living cell, an ecosystem, or a solar system. Each of these entities can be understood through multiple categories, illustrating the rich complexity and interrelatedness inherent in Whitehead’s philosophy.
For Whitehead, all eight categories point to aspects of reality that are "real," even though two—actualities and eternal objects—have a certain primacy. Actual entities, as the fundamental units of reality, and eternal objects, as the pure potentials that give form to these entities, hold special significance. However, the other categories are no less real; they shape the way we perceive, interact with, and understand the world. This emphasis on the reality of all categories underscores the holistic and integrative nature of Whitehead’s thought, where every aspect of experience is interconnected and significant.
In the context of his discussion of actual entities, Whitehead's philosophy offers a nuanced understanding of causation relevant to interdisciplinary studies:
- Efficient Causation (Influence of the Past on the Present): This refers to how past events and conditions influence present occurrences, aligning with classical causation. Whitehead calls it experience in the mode of causal efficacy. In physical sciences, this might refer to how chemical reactions unfold based on established molecular properties. In a broader context, it could describe how historical events shape contemporary social realities.
- Final Causation (Pull of Possibilities Toward the Future): This highlights the influence of potentialities or possibilities on actual events. Whitehead sees this as how actual entities are drawn toward realizing certain possibilities, guided by what he calls "subjective aims." In psychology, this could relate to how individuals are motivated by future goals, guiding their behavior. It also relates to how individuals and groups feel pulled or drawn by larger ideals such as truth, goodness, and beauty.
- Self-Creativity (Decision-Making within Sentient Beings): This concerns the internal decision-making process, where an entity exercises agency in shaping its own becoming. In ethics or social sciences, this describes how individuals or groups make decisions that involve spontaneity or creativity, crucial for understanding human agency.
These types of causation—efficient, final, and self-creativity—offer a framework for understanding complex phenomena, recognizing the interplay between past influences, future possibilities, and present decisions. Any account of "why things happen as they do" need to refer to all three forms of causation.
Of course, all of this is suggestive rather than dogmatic. Scholars are encouraged to adapt and modify Whitehead's categories to suit their purposes, viewing the categories themselves as lures for feeling and reflection—essentially invitations to explore the world holistically and integratively. This flexible approach allows for creative engagement with Whitehead’s ideas, fostering new insights and perspectives across disciplines while staying true to the spirit of his philosophy.
One way that a Whiteheadian approach differs from other more mechanistic outlooks on life is that Whitehead's philosophy recognizes the importance of "purpose" in the universe. Whitehead’s categories allow for an appreciation of purposive behavior, represented by lures for feeling, within the universe, other organisms, and human life. This integrates the role of physical and chemical causation and enables a deeper understanding of the role that beauty, or contrasts, plays within organisms. This integration highlights the complex interplay between aesthetic and mechanistic aspects of reality.
Whitehead’s categories invite recognition of the intrinsic connections between objective realities, like mathematical patterns, and subjective realities, including emotions, purposes, and beauty. This synthesis allows for a more holistic view of the world, where both objective and subjective dimensions are interrelated and equally significant. This interdisciplinary approach fosters a more comprehensive understanding of complex phenomena, integrating insights from both scientific and humanistic perspectives.
By embracing these connections and the flexibility of Whitehead's categories, scholars can engage more deeply in interdisciplinary dialogue, fostering collaboration and innovation across disciplines. These categories are particularly helpful in fields such as:
- Environmental Science: Understanding ecosystem interconnectedness through nexus (public matters of fact), actual entities (individual agents), and contrasts (aesthetic relations).
- Psychology: Exploring emotions (subjective forms) and prehensions (private feelings) within social contexts (nexus).
- Artificial Intelligence: Integrating eternal objects (mathematical relations) with decisions made by actual entities (agents) and considering ethical implications (lures for feeling).
- Cultural and Social Studies: Examining cultural expressions (multiplicities), aesthetic values (contrasts), and individual experiences (prehensions) to gain deeper insights into social dynamics.
Mathematics and Emotion
One of the more intriguing applications of Whitehead’s categories is the exploration of the relationship between mathematics and emotion. At first glance, these two domains may seem unrelated—mathematics often being associated with precision, logic, and abstraction, while emotion is tied to subjective experience, feeling, and affect. However, Whitehead’s philosophy offers a framework in which these domains can be seen as interconnected and mutually informative.
Eternal Objects and Subjective Forms
In Whitehead’s system, mathematical patterns and relations fall under the category of eternal objects. These are abstract forms that can be realized in the actual world, giving shape and structure to reality. Emotions, on the other hand, are associated with subjective forms, which refer to the particular way in which an actual entity experiences and feels the world.
Whitehead distinguishes between two kinds of eternal objects: those of the objective species and those of the subjective species. Eternal objects of the objective species include mathematical entities, such as numbers, geometric forms, and other abstract patterns that can be “ingressed” (Whitehead’s term) into the physical world, forming the basis of its structure. These objective eternal objects are potentialities for the arrangement of the physical world in specific, patterned ways.
On the other hand, eternal objects of the subjective species include potentialities for feeling—ways in which experiences can be felt or interpreted. These are the potentials for emotions, such as awe, fear, curiosity, or anger. In this sense, eternal objects of the subjective species offer a framework for understanding how certain emotional responses can be consistently evoked by specific patterns or situations in the world, bridging the gap between abstract mathematical structures and the rich tapestry of human emotion.
Connecting Objective and Subjective Potentialities Across Disciplines
Certain disciplines naturally explore the connection between these two types of potentialities. For example, in theater arts, set designers create spatial arrangements—an example of objective eternal objects—that set the stage for characters whose emotions, corresponding to subjective eternal objects, are presented with the help of, not apart from, the set design. The physical environment enhances and interacts with the emotional narrative, illustrating the interplay between the objective and subjective.
In anthropology, scholars are interested in how rituals, which embody objective patterns, enable individuals and groups to experience specific emotions. Rituals provide a structured, patterned context that invites particular emotional responses, demonstrating the connection between the objective and subjective eternal objects.
Similarly, in music, the objective and mathematical aspects come together in the creation of harmonies, which are experienced emotionally. The mathematical relationships between notes create structures that evoke feelings of joy, sadness, tension, or resolution. Here, the two types of eternal objects—the mathematical (objective) and the emotional (subjective)—are intricately connected, enhancing the emotional impact of the music.
These examples illustrate how Whitehead’s categories can help us understand the deep connections between the abstract, structural aspects of reality and the rich emotional experiences they can evoke.
Mathematical Structures as Lures for Feeling
Whitehead’s concept of propositions, or lures for feeling, provides another way to understand the connection between mathematics and emotion. Mathematical structures and patterns can be seen as lures for feeling in the sense that they invite emotional responses, contemplation, and even inspiration. For instance, the discovery of a new mathematical theorem can evoke feelings of wonder, excitement, and satisfaction, reflecting the deep emotional engagement that mathematics can inspire.
In this view, mathematical structures are not just cold, detached abstractions but are infused with emotional significance. They lure us toward particular emotional states, enriching our experience and deepening our understanding of the world.
Emotional Resonance in Mathematical Patterns
Whitehead’s idea that the universe is an interconnected web of relationships suggests that mathematical patterns might resonate with emotional experiences in ways that are not always immediately obvious. For example, the Fibonacci sequence, which appears in various natural phenomena, can evoke a sense of harmony and order that resonates with our emotional experience of beauty in nature. This interplay between mathematics and emotion is a reflection of the broader interconnectedness of reality that Whitehead emphasizes.
Interdisciplinary Insights
The integration of mathematics and emotion offers rich opportunities for interdisciplinary studies. Psychologists, for example, can explore how mathematical reasoning influences emotional states, while philosophers might investigate how emotional experiences shape our understanding of mathematical concepts. Artists and musicians, who often draw on mathematical principles in their work, can offer insights into how these principles evoke emotional responses in their audiences.
By acknowledging the emotional dimension of mathematical experience, scholars can foster a more holistic understanding of mathematics, one that recognizes its power not only as a tool for understanding the world but also as a source of profound emotional and aesthetic experience.
Eternal Objects and Subjective Forms
In Whitehead’s system, mathematical patterns and relations fall under the category of eternal objects. These are abstract forms that can be realized in the actual world, giving shape and structure to reality. Emotions, on the other hand, are associated with subjective forms, which refer to the particular way in which an actual entity experiences and feels the world.
Whitehead distinguishes between two kinds of eternal objects: those of the objective species and those of the subjective species. Eternal objects of the objective species include mathematical entities, such as numbers, geometric forms, and other abstract patterns that can be “ingressed” (Whitehead’s term) into the physical world, forming the basis of its structure. These objective eternal objects are potentialities for the arrangement of the physical world in specific, patterned ways.
On the other hand, eternal objects of the subjective species include potentialities for feeling—ways in which experiences can be felt or interpreted. These are the potentials for emotions, such as awe, fear, curiosity, or anger. In this sense, eternal objects of the subjective species offer a framework for understanding how certain emotional responses can be consistently evoked by specific patterns or situations in the world, bridging the gap between abstract mathematical structures and the rich tapestry of human emotion.
Connecting Objective and Subjective Potentialities Across Disciplines
Certain disciplines naturally explore the connection between these two types of potentialities. For example, in theater arts, set designers create spatial arrangements—an example of objective eternal objects—that set the stage for characters whose emotions, corresponding to subjective eternal objects, are presented with the help of, not apart from, the set design. The physical environment enhances and interacts with the emotional narrative, illustrating the interplay between the objective and subjective.
In anthropology, scholars are interested in how rituals, which embody objective patterns, enable individuals and groups to experience specific emotions. Rituals provide a structured, patterned context that invites particular emotional responses, demonstrating the connection between the objective and subjective eternal objects.
Similarly, in music, the objective and mathematical aspects come together in the creation of harmonies, which are experienced emotionally. The mathematical relationships between notes create structures that evoke feelings of joy, sadness, tension, or resolution. Here, the two types of eternal objects—the mathematical (objective) and the emotional (subjective)—are intricately connected, enhancing the emotional impact of the music.
These examples illustrate how Whitehead’s categories can help us understand the deep connections between the abstract, structural aspects of reality and the rich emotional experiences they can evoke.
Mathematical Structures as Lures for Feeling
Whitehead’s concept of propositions, or lures for feeling, provides another way to understand the connection between mathematics and emotion. Mathematical structures and patterns can be seen as lures for feeling in the sense that they invite emotional responses, contemplation, and even inspiration. For instance, the discovery of a new mathematical theorem can evoke feelings of wonder, excitement, and satisfaction, reflecting the deep emotional engagement that mathematics can inspire.
In this view, mathematical structures are not just cold, detached abstractions but are infused with emotional significance. They lure us toward particular emotional states, enriching our experience and deepening our understanding of the world.
Emotional Resonance in Mathematical Patterns
Whitehead’s idea that the universe is an interconnected web of relationships suggests that mathematical patterns might resonate with emotional experiences in ways that are not always immediately obvious. For example, the Fibonacci sequence, which appears in various natural phenomena, can evoke a sense of harmony and order that resonates with our emotional experience of beauty in nature. This interplay between mathematics and emotion is a reflection of the broader interconnectedness of reality that Whitehead emphasizes.
Interdisciplinary Insights
The integration of mathematics and emotion offers rich opportunities for interdisciplinary studies. Psychologists, for example, can explore how mathematical reasoning influences emotional states, while philosophers might investigate how emotional experiences shape our understanding of mathematical concepts. Artists and musicians, who often draw on mathematical principles in their work, can offer insights into how these principles evoke emotional responses in their audiences.
By acknowledging the emotional dimension of mathematical experience, scholars can foster a more holistic understanding of mathematics, one that recognizes its power not only as a tool for understanding the world but also as a source of profound emotional and aesthetic experience.
Whitehead's Eight Categories of Existence
There are eight Categories of Existence:
Among these eight categories of existence, actual entities and eternal objects stand out with a certain extreme finality. The other types of existence have a certain intermediate character. The eighth category includes an indefinite progression of categories, as we proceed from ‘contrasts’ to ‘contrasts of contrasts,’ and on indefinitely to higher grades of contrasts.
Whitehead, Alfred North. Process and Reality (Gifford Lectures Delivered in the University of Edinburgh During the Session 1927-28) (p. 22). Free Press. Kindle Edition.
- Actual Entities (also termed Actual Occasions), or Final Realities, or Rēs Verae.
- Prehensions, or Concrete Facts of Relatedness.
- Nexūs (plural of Nexus), or Public Matters of Fact.
- Subjective Forms, or Private Matters of Fact.
- Eternal Objects, or Pure Potentials for the Specific Determination of Fact, or Forms of Definiteness.
- Propositions, or Matters of Fact in Potential Determination, or Impure Potentials for the Specific Determination of Matters of Fact, or Theories.
- Contrasts, or Modes of Synthesis of Entities in one Prehension, or Patterned Entities.‡
- Multiplicities, or Pure Disjunctions of Diverse Entities. Contrasts, or Modes of Synthesis of Entities in one Prehension, or Patterned Entities.
Among these eight categories of existence, actual entities and eternal objects stand out with a certain extreme finality. The other types of existence have a certain intermediate character. The eighth category includes an indefinite progression of categories, as we proceed from ‘contrasts’ to ‘contrasts of contrasts,’ and on indefinitely to higher grades of contrasts.
Whitehead, Alfred North. Process and Reality (Gifford Lectures Delivered in the University of Edinburgh During the Session 1927-28) (p. 22). Free Press. Kindle Edition.