From: jimruttshow8596
The Incommensuration Theorem (ICT), derived from Forres Landry’s imminent metaphysics, describes the fundamental nature of the relationship between what he calls symmetry and continuity [00:01:56]. This theorem provides a framework for understanding the profound distinction between first-person and third-person perspectives of knowledge [01:17:20].
Foundations of Epistemic Process
All epistemic process, which is the study of how we come to know something, is based upon perception [00:55:23]. Every perception, measurement, or interaction is fundamentally a kind of comparison [00:31:34].
Intrinsics of Comparison
Comparison itself is subsumed by six fundamental concepts, referred to as “intrinsics,” because they are intrinsic to its nature [00:33:41]. These intrinsics are:
- Subjective (the perceiver) [00:29:27]
- Objective (the perceived) [00:29:31]
- Sameness (constancy, non-changingness) [00:32:11]
- Difference (change of state, new knowledge) [00:32:19]
- Content (the thing being perceived or described) [00:35:25]
- Context (the environment or situation in which perception occurs, including the observer’s state of mind) [00:35:46]
These intrinsics are “distinct inseparable and non-interchangeable” [00:30:24]. For example, there cannot be content without context, nor sameness without difference [00:54:42].
Defining Domains
A “domain” differs from a set by including the relationships among its elements as “first-class objects” [00:05:55]. Domains are defined such that they cannot be included in other domains; they extend to the “largest enclosing set that is not itself enclosed” [00:08:06]. This means a domain is treated as a concept container for other concepts [00:23:01]. For instance, the “universe” as a domain is defined by the concepts of creation, existence, and interaction [00:19:52].
This definition of domain as abstract entities, rather than concrete ones (like matter and energy), is a fundamental distinction [00:24:11].
Characterizing Perspectives
The intrinsics of comparison can be used to define four higher-order concepts, each representing a way of experiencing or encoding knowledge:
- Symmetry: A sameness of content across a difference of context [00:58:00]. It represents lawfulness or consistency (e.g., physical laws applying everywhere) [00:56:54].
- Continuity: A sameness of content within a sameness of context [01:00:36]. This relates to connectedness and smooth transitions.
- Asymmetry: A difference of content in a sameness of context. For example, the irreversibility of perception, where “not knowing” changes to “knowing” [01:02:14].
- Discontinuity: A difference of content across a difference of context. This shows up at boundaries, like the division between the knowable and unknowable [01:02:22].
The Incommensuration Theorem (ICT)
The ICT asserts that two modes of knowing are fundamentally incommensurate:
- First-Person Perspective: Characterized by continuity and asymmetry [01:16:54].
- This is the felt immediacy of experience, the sense of self persisting through time (continuity) [01:19:24].
- It includes the inherent asymmetry of time (we cannot access the future or predict everything with certainty) [01:19:05].
- It implies subjectivity and hard randomness [01:34:04].
- Third-Person Perspective: Characterized by symmetry and discontinuity [01:17:06].
- This represents objective knowledge, like scientific laws or mathematical patterns [01:20:24].
- Laws often assume symmetry and apply across different contexts [01:24:51].
- It often deals with discrete concepts and boundaries (discontinuity) [01:21:13].
- This perspective “factors out” the subjective [01:20:26].
The theorem posits that it is “conceptually impossible” [01:12:19] to have “perfected symmetry and perfected continuity at the same time” [01:11:54]. If we prioritize symmetry, we must accept discontinuity; if we prioritize continuity, we must accept asymmetry [01:25:02].
Implications and Examples
In Physics and Knowledge
The ICT helps clarify the distinction between how we experience the world (first-person) and how we describe it scientifically (third-person).
- Access Control Limits: Physics theories vary in their “access control limits” on what is knowable [00:46:12].
- Newtonian mechanics has no inherent access control limits, implying that in principle, all information could be accessed if computational support were sufficient [00:47:57]. It’s a deterministic, clockwork universe [00:47:26].
- General relativity describes limits, such as the event horizon of a black hole, where information flow is one-way, creating hard boundaries [00:48:31].
- Quantum mechanics introduces inherent access limits, like the Heisenberg Uncertainty Principle, where simultaneously knowing position and momentum is impossible [00:46:41].
The arrow of time in the first-person perspective, preventing causal flow backward, can be seen as an access control limit due to the “broken symmetry” of continuity [01:22:37].
Quantum Interpretations and Bell’s Theorem
The ICT offers a lens through which to examine quantum interpretations [01:33:00]:
- Copenhagen Interpretation: Asserts hard randomness, subjectivity, and an arrow of time [01:35:12], aligning with the first-person perspective (continuity and asymmetry).
- Many Worlds Interpretation: Denies hard randomness, subjectivity, and an arrow of time [01:34:55], representing a “perfected third-person point of view” [01:35:04] (symmetry and discontinuity).
The ICT implies that these two types of interpretations are fundamentally distinct: those that assume the elements of subjectivity, hard randomness, and temporality, and those that assume none of them [01:35:31]. This partitions the total field of quantum interpretations [01:35:45].
The ICT supports a stronger version of Bell’s Theorem [01:27:10] by showing that a choice must be made: emphasize symmetry (lawfulness) and live with discontinuity, or emphasize continuity (connectedness) and accept asymmetry [01:25:02]. Bell’s theorem is seen as a special case of the ICT, consistent with its general notion that perfected symmetry and continuity cannot coexist [01:25:20].
Gödel’s Incompleteness Theorem in Mathematics
The ICT also projects into mathematics, clarifying Gödel’s Incompleteness Theorem [01:38:09].
- Consistency: Isomorphic to symmetry (no contradictory statements) [01:38:31].
- Completeness: Isomorphic to continuity (all true knowledge is connected within one domain) [01:40:07].
Gödel’s theorem asserts that a formal system cannot be both complete and consistent [01:42:00]. This reflects the ICT: if mathematics prioritizes consistency (symmetry), it must accept incompleteness (discontinuity) [01:42:09]. This means a purely mathematical (third-person) view of the universe, like the Many Worlds interpretation, is inherently incomplete because it cannot account for its own grounding in the first-person epistemic process [01:44:00].
The ICT offers a simpler proof for Gödel’s theorem, by looking at the reflexivity of conceptualizing about perception, connecting the embodied (first-person) and abstract (third-person) domains [01:41:29].
The recurring pattern of the ICT at the “deep foundations of what it means to know anything at all” [01:41:50] highlights its profound importance in understanding the very nature of knowledge and reality.