Steve Watson

Information Flow

February 18, 2026 – 9:18 pm

There is a fundamental sociological interest in the infrastructure or social conditions that facilitate the distribution of information in a society. Unfortunately, treatments of the ‘Flow of Information’ in the context of sociological or organizational theory typically refer to the ‘information channels’ that play that role with minimal if any definition or consideration of the criteria that need to be met in order for anything to play that role, while treatments in the context of Network Theory or in the domain of Logic, Language, and Computation offer only definitions that are irrelevant to the sociological context.

Begin with the necessary relevant agent interactions with information.

1. Insertion

For some proposition p, agent x∈X, a_x ∈ α_x considered as a state transformation such that a_x(σ₁) = σ₂ is an Insertion of p into σ₁ iff

1. (∃y∈X)[ (∃{x_i:i = 0, …, n}⊂ X) (∃<a_xi ∈α_xi: i = 0, …, n>) [ a_xi(σ_1+i) = σ_2+i & a_x0 = a_x ] &
   p ∈ Iv_y,σ(2+n) \Iv_y,σ1 ]
2. B_x [ ‘i.’ ] ∈ q_x
3. D_x [ ‘i.’ ] ∈ q_x

» An insertion is the deliberate addition to a state of affairs of an item of information that can be made available to some agent by some sequence of state-transforming actions by other agents.

• Write Ins(a_x, p, σ₁).
• We can also say that x Inserts p into σ₁ by a_x and write In(x, p, σ₁, a_x)
• The restriction to available information is justified by the fact that information that is not available to any agent is sociologically inert.
• The agent making the insertion must be supposed to be intending (desiring and believing) that the information will be sociologically active or else there is no sociological import to the insertion.
• Note that in the case that n = 0, condition (i) is equivalent to
  • (∃y∈X) GenIv(a_x, σ₁, p, y) or
  • (∃y∈X)[ p ∈ genIv(a_x, σ₁, y) ]
• Refinements to this definition are possible to account for situations in which condition (i) fails, or in which conditions (ii) and (iii) are not required to hold at the time of the action. For example, to take an extreme case, the Voyager spacecraft plaques would not qualify under this definition. Whether these possibilities should be considered need not delay us here.

Define an Information Insertion Point as a state of affairs, σ₁ such that

1. (∃p∈ℙ) (∃x∈X) (∃a_x∈α_x) [ a_x(σ₁) = σ₂ &
2. (∃y∈X)[ (∃{x_i:i = 0, …, n} ⊂ X) (∃<a_xi ∈a_xi: i = 0, …, n>) [ a_xi(σ_1+i) = σ_2+i & a_x0 = a_x ] &
   p ∈ Iv_y,σ(2+n) \Iv_y,σ1 ] &
3. B_x [ ‘ii.’ ] ∈ q_x ]

» An information insertion point is a state of affairs to which some agent correctly believes he may add an item of information that can be made available to some agent by some sequence of state-transforming actions by other agents.

• Write IIP(s₁)

We shall also define the Information Insertion Point for p or P as an insertion point defined for a particular proposition p or class of propositions P as a state of affairs, σ₁ such that

1. (∀p∈ℙ) (∃x∈X) (∃a_x∈α_x) [ a_x(σ₁) = σ₂ &
2. (∃y∈X)[ (∃{x_i:i = 0, …, n} ⊂ X) (∃<a_xi ∈a_xi: i = 0, …, n>) [ a_xi(σ_1+i) = σ_2+i & a_x0 = a_x ] &
   p ∈ Iv_y,σ(2+n) \Iv_y,σ1 ] &
3. B_x [ ‘ii.’ ] ∈ q_x ]

» An information insertion point for p/P is a state of affairs such that for every proposition of a certain kind some agent correctly believes he may insert that proposition as an item of information that can be made available to some agent by some sequence of state-transforming actions by other agents.

• Without danger of ambiguity, we may write IIP(σ₁, p) when referring to the case for single propositions or IIP(σ₁, P) for the case of classes of propositions, and say that σ₁ is an information insertion point for p or P.

2. Extraction

For some proposition p, agent x∈X, state of affairs σ, a_x ∈ α_x is an Extraction of p from σ iff

(∃ω)(∃h)[ Mot(ω, x, h, σ, a_x) &

» Some question ω motivates x to apply some supposed adduction h on σ using a_x

Add(a_x, h, σ) & h(σ) = p) ]

» which actually is an adducement applying the adduction h to σ, yielding p.

• Write Ext(a_x, p, σ) and say that a_x is an extraction of p from σ.
• We can also say that x Extracts p from σ by a_x and write Ex(x, p, σ, a_x)
• The agent making the extraction must be supposed to be intending (desiring and believing) the action to adduce information, otherwise the retrieval of information is merely an accidental effect of the action and cannot be part of a sociologically significant process.

Define an Information Extraction Point as a state of affairs, σ such that

(∃p∈ℙ) (∃x∈X) (∃a_x∈a_x) [ (∃ω)(∃h)[ Mot(ω, x, h, σ, a_x) & Add(a_x, h, σ)
⇒ h(σ) = p]

» An information extraction point is a state of affairs from which some agent correctly believes he may extract an item of information that he is motivated to discover that is available to some agent.

• Write IEP(σ)

We shall also define the Information Extraction Point for p or P as an insertion point defined for a particular proposition p or class of propositions P as a state of affairs, σ such that

(∀p∈ℙ) (∃x∈X) (∃a_x∈a_x) [ (∃ω)(∃h)[ Mot(ω, x, h, σ, a_x) & Add(a_x, h, σ)
⇒ h(σ) = p]

» An information extraction point for p/P is a state of affairs such that for every proposition of a certain kind some agent correctly believes he may extract that proposition as an item of information that he is motivated to discover that is available to some agent.

• Without danger of ambiguity, we may write IEP(σ, p) when referring to the case for single propositions or IEP(σ, P) for the case of classes of propositions, and say that σ is an information extraction point for p or P.

3. Transmission

Let p be a proposition, σ₁ a state of affairs, such that IIP(σ₁, p)

σ = (σ₁, …, σ_n+2) is an Information Arc for p if

(∃<τ_i: i = 0, …, n >)[ τ_i(σ_1+i) = σ_2+i &
(∃x∈X) (∃a_x∈α_x)[ In(x, p, σ₁, a_x) & τ₀ = a_x &
~IEP(σ₁, p) &
IEP(σ_2+n, p) &
(~Ins(a_x, p, σ₁) ⇒ ~IEP(σ_2+n, p)) ]]

» An information arc for a proposition is a sequence of states of affairs produced by state transformations of an information insertion point at which that proposition has been inserted that ends in an information extraction point for it.

• Write IA(σ, p)
• Note that n = 0 is possible, in which case we can talk of a Null Information Arc for p.

Define an Information Channel as a state of affairs χ, such that

(∃P⊂ℙ) (∀p∈P) (∃σ) [ IA(σ, p) &
(∀σ_i∈σ) [χ ⊂ σ_i & (~(χ ⊂ σ_i) ⇒ ~IIP(σ_i, p) & ~IEP(σ_i, p)) ]]

» An information channel is a stable state of affairs that facilitates information arcs for a class of propositions as items of information.

• Write IC(χ)
• We can call P⊂ℙ that appears in the definition above the Matter of χ, and write that M(χ)=P

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