From: jimruttshow8596
The Incommensuration Theorem (ICT), developed by Forrest Landry, offers a profound framework for understanding the nature of knowledge and perception. A foundational concept in this framework is the precise definition and application of “domains” and their intrinsic relationship with “contexts” and “contents” within epistemic processes [01:00:17].
Defining a Domain
Forrest Landry defines a “domain” in a way that significantly differs from the common mathematical “set” [03:50:00].
Domain vs. Set
While a set can be thought of as a “bag with things in it” where elements are abstract points or numbers, a domain incorporates three core notions: content, context, and relationship [04:06:00]. Unlike a set, which focuses primarily on the collection of elements, a domain explicitly accounts for the relationships between its elements as first-class objects within the container [05:55:00].
Examples of Domains
Domains can be understood as:
- Worlds or Universes: Containing things like matter and energy [06:17:00].
- Real-world Constellations of Concepts: Such as the marketplace or the home [06:30:00], or even topics like real estate or finance, where concepts are connected to one another [06:39:00].
- Computer Languages: Like C++ or Python, which are considered domains due to their expressive power equivalence as per the Church-Turing thesis, meaning no single language is inherently more fundamental or inclusive of others as a proper subset [10:04:00].
- Baseball: As a domain, its elements are the concepts, equipment, and rules specific to the game [14:41:00].
Exclusion from Other Domains
A key distinction is that, by Landry’s definition, a domain cannot be included in other domains [07:07:07]. This means a domain extends to “the largest enclosing set that is not itself enclosed” [08:06:00]. If one domain (e.g., Baseball) is considered a member of a larger concept (e.g., Team Sports), then “Baseball” is treated as an element or an identity within the “Team Sports” domain, not as a sub-domain itself [14:38:00]. This abstraction layer prevents confusion and maintains conceptual clarity [09:56:00].
Domains and the Universe: Creation, Existence, and Interaction
When applying the concept of a domain to the “universe,” Landry identifies three necessary and sufficient concepts to understand it:
- Creation: Where matter and information originated (e.g., the Big Bang in physics) [18:58:00].
- Existence: The nature of matter and material things [18:52:00].
- Interaction: The forces and relationships between existing things [18:55:00].
Crucially, Landry distinguishes his definition of a domain by using it as a concept container for other concepts (like matter, energy, information) rather than a container of embodied things [22:57:00]. This shifts the understanding of the universe from a physical entity to an abstract concept defined by these underlying concepts [23:30:00]. This conceptual shift allows for different questions about the closure of concepts versus the closure of physical matter [24:29:00].
Context and Content as Intrinsics of Comparison
The concepts of context and content are fundamental to comparison, which is central to all epistemic processes [02:51:00].
The Museum Metaphor
To illustrate content and context, consider a painting in a museum:
- Content: The world depicted within the painting itself (the image, the paint, the man, the table) [35:25:00].
- Context: Everything surrounding the content that influences its perception, such as the frame, the wall, the museum room, and even the observer’s state of mind or free associations [36:10:00].
The “frame” acts as a periphery between the content and the context [35:55:00]. Awareness of context is essential, as ignoring it can lead to manipulation or misunderstanding [38:20:00].
Inseparable Relationship
Content and context are deemed “inseparable” [53:07:00]. Just as a painting cannot exist in an empty universe, there can be no content without context, and no context can be meaningfully asserted without distinguishable content [53:35:00]. This inherent relationship implies that each needs the other to exist [54:42:00]. This also applies to other fundamental pairs like “sameness and difference” and “subjective and objective,” which are also inseparable [54:48:00]. These six elements (sameness, difference, content, context, subjective, objective) are called the “intrinsics of comparison” [33:41:00], as they are inherent to any act of measurement, perception, or interaction [32:32:00].
Defining Symmetry and Continuity through Content and Context
The intrinsics of comparison, including content and context, are used to precisely define core concepts like symmetry and continuity:
- Symmetry: Characterized by the “sameness of content” across a “difference of context” [02:25:00]. This applies to physical laws holding true across different parts of the universe or to the act of remembering, where internal representation holds “sameness of content” to an external reality, despite being in a “different context” (the self vs. the world) [58:58:00]. Symmetry is vital for scientific knowledge and the concept of “lawfulness” [00:56:54].
- Continuity: Defined by the “sameness of content” within a “sameness of context” [02:55:00]. This applies at infinitesimal scales, similar to continuous functions in mathematics where small changes in input lead to small changes in output [01:00:46]. Continuity helps understand phenomena at microscopic scales and the “connected tissue” of ideas [01:01:13].
Implications for Epistemic Processes
The precise definition of domains and the relationship between content and context in comparison are crucial for understanding epistemic processes as a whole [01:02:02]. This framework provides a rigorous basis for analyzing the inherent limits of knowledge, as articulated in the ICT. The ICT posits that perfect symmetry and perfect continuity cannot coexist [01:12:03]. This means that:
- If we prioritize perfect symmetry (e.g., universal laws, consistent mathematical systems), we must accept perfect discontinuity (e.g., discrete particles, inherent gaps in mathematical knowledge) [01:13:11].
- If we prioritize perfect continuity (e.g., subjective experience, a causally connected universe), we must accept perfect asymmetry (e.g., the irreversible flow of time, lack of complete predictability) [01:14:50].
This implies two fundamental types of epistemic knowledge: one that emphasizes discrete, symmetrical laws (third-person perspective), and another that emphasizes continuous, asymmetrical processes (first-person perspective) [01:16:03]. This distinction provides tools to analyze longstanding problems in physics, such as quantum interpretations, by examining their underlying assumptions about how “measurement” and “knowledge” are structured by content, context, and their related intrinsics [01:30:20]. Ultimately, the framework highlights how access control limits inherent in epistemic processes restrict what can be known, revealing the fundamental relationship between the known and the unknowable [01:02:16].