Technical notes · Meaning (M)
M as Structured Value in Representations
This page formalizes Meaning (M) as value structured across representational states. Given Awareness (A) and Value (V), meaning arises when a system associates internal symbols or models with valued states of itself and its environment in a systematic way.
Abstract
In Informational Ontology, meaning is not a primitive, nor is it purely subjective; it is the structure of value within and across representations. We treat meaning as a mapping from representational states to value-relevant states, together with a value function over those states. This yields an IO-compatible counterpart to semantic theories that emphasize reference, use, or inferential role, integrating them into the Δ → R → I → A → V → M → P chain.
1. Representations and Targets
Let Σ be a Δ-structured set of internal representations (as in the Awareness module), and let W be a Δ-structured set of world states (including internal bodily states if relevant).
Definition 1. A semantic mapping is a partial function:
σ: Σ ⇀ W
assigning to some representational states σ a corresponding target state in W. For σ(σ) = w, we say that "σ represents w".
2. Meaning as Value-Informed Representation
Suppose we also have a value function V: W → ℝ as before. We can then define:
M(σ) = V(σ(σ))
for all σ in the domain of the semantic mapping. Here M(σ) is the meaning-strength or value-content of the representational state σ: how much it matters to the system, given what it stands for.
Definition 2. Meaning (in IO's technical sense) is the function M: Σ ⇀ ℝ defined by composition of semantic mapping σ with value function V.
In this sense, meaning is literally "structured value" over representational space.
3. Inferential Role and Networks of Meaning
Representations in Σ are typically related to each other by inferential or associative links (e.g. one concept leading to another). Let RΣ ⊆ Σ × Σ be such a relation.
A representation's meaning then depends not only on the value of what it directly stands for, but on the network of consequences it participates in. We can formalize a simple version:
M*(σ) = M(σ) + ∑σ': RΣ(σ, σ') w(σ, σ') · M(σ')
where w(σ, σ') are weights reflecting the strength of inferential or associative links. M* is a network-augmented measure of meaning: a representation signifies more insofar as it opens pathways toward other valued representations.
4. Misrepresentation and Error
Misrepresentation in IO occurs when σ(σ) ≠ w, i.e. when the system's mapping from representation to world state is incorrect, yet the value structure still treats σ as if σ(σ) were correct.
This is crucial for understanding meaning dynamically: M is not a static assignment but can be revised when the system detects that its representational mappings fail to support valued outcomes.
5. From Meaning to Purpose
Purpose (P) in IO is defined as meaning extended through time: the organization of meaningful representations into trajectories of action. Once a system:
- represents the world (Σ, σ),
- values outcomes (V), and
- connects representations in ways that shape action (RΣ),
we can speak of its "purposes": stable patterns of behavior oriented toward configurations of high M*.
The next technical module makes this explicit in terms of policies, trajectories, and teleodynamic structure.