Steve Watson

Information

February 13, 2026 – 4:13 pm

An important aspect of communication relates to the transfer of information, but the treatment of information as a sociological phenomenon cannot be limited to its associations with communication alone: of equal importance are questions of creation, access, accumulation, transformation, function, social effect, etc. To address such issues, we will need to begin with an appropriate understanding of what ‘information’ means in the sociological context. Unfortunately, ‘information’ in that context (or in most others for that matter) is a term that is more widely used than analysed; and we do not get much relevant enlightenment from the few fields of study where it has been treated rigorously such as Computer Science and Communication Studies. The definitions and investigations of information and its characteristics appropriate to those fields are those inspired by the work of Shannon and Weaver ((1949) The Mathematical Theory of Communication, Urbana, IL: University of Illinois Press) and are concerned with quantitative aspects of ‘information’ such as the amount of uncertainty in a variable or the ability to reconstruct messages sent over noisy channels rather than anything relevant to the questions mentioned above.

The (non-quantitative) understanding of information that is intuitively appealed to in most other fields is rather that identified by Dretske (1981/1999, Knowledge and the Flow of Information, CSLI:LSJU) as the nuclear sense of the term. There (p 44) he argues that “Roughly speaking, information is that commodity capable of yielding knowledge, and what information a signal carries is what we can learn from it” and (p. 45) “A state of affairs contains information about X to just that extent to which a suitably placed observer could learn something about X by consulting it.” As Dretske acknowledges, information is supposed to yield true beliefs, and so we can loosely say that information has to be true: although we may speak colloquially of ‘false’ information or of ‘misinformation,’ the nuclear sense rejects that possibility. On this view then, a state of affairs could be said to contain information when a true proposition which is apt for belief could be derived from that state of affairs.

This, though better, is still not an appropriate approach to information as a sociological phenomenon. The truth of a claim that is current in society is of no particular interest to the sociologist, and the effect that that claim has on society is only indirectly (and often very weakly) related to its truth or falsity. The sociologically important characteristic of such a claim – which is apt for belief on the part of some agent(s) – is the degree to which and the manner in which it affects the actions of those in the society associated with that claim in the relevant way. The relationship between this and the nuclear view of information is that the effect of the claim can be related to the belief on the part of the relevant agents that the claim is a true (or false) one and therefore a good (or bad) guide to actions, where good and bad can be understood as meaning likely to lead to good or bad results for the relevant agents. That something like this is involved in the non-specialist use of the term ‘information’ is suggested by, for example, the use of the term ‘information society’ when the subject of discussion ranges over all forms of production, consumption, and exchange of claims regardless of their relationship to truth. (Further considerations on the characteristics that should be considered in the formulation of a definition of ‘information’ for sociological purposes may be found in H. Garfinkel (ed. A. Rawls) (2008) Toward a Sociological Theory of Information, Boulder CO: Paradigm, pp.110 ff.)

Adduction and Information

The nature of the processes by which information in this relevant general sense is derived from a state of affairs is both uncertain and to a certain degree beyond the scope of our interest. The discussion will therefore be conducted at a level of abstraction that does not prejudge that nature. It will be assumed that the only relevant criteria here are that the processes are systematic and that they are dependent upon the contents of the state of affairs in question

1. Propositional Function: Adduction

A possible way that the world is may be represented as a set of propositions describing the world,

Define σ, a State of Affairs, as:

σ = {σ_i: i ∈ ℕ, s_i ∈ ℙ, σ_i is a partial description of the way the world is} where

1. σ is a consistent set

• A state of affairs is a subset of a complete description of the world.
• Σ = ∪{σ: σ is a state of affairs} is the Possible States of Affairs

Let h be a function such that

h:Σ → ℙ

h is an Adduction from a state of affairs σ iff

(∀p ∈ ℙ) [h(σ) = p ⇒ (∃S⊂σ) [h(σ\S) ≠ p]]

» An adduction is the production of a proposition apt for belief from a description of a state of affairs s. It is sensitive to the contents of s. This is a non-triviality condition.

• Write H(h, σ)
• In this case p is an Adduct of σ by h, and we say p is Adduced from σ by h.
• Not every adduction will be well-defined for every state of affairs.
• An adduction is not guaranteed to yield a true proposition, nor is it even guaranteed to yield a result that is consistent with σ.
• The set of possible adductions is barely constrained by the condition given, and we can be sure that the set of adductions that the agents of a population are actually capable of performing is a much more limited set. The discovery of which possible adductions are actually applied by agents is a matter for empirical (psychological) enquiry and will form part of the agent theory.
• The work of Sperber and Wilson (e.g. (1986) Relevance) would suggest that the actually applied adductions will turn out to be more context sensitive or otherwise complex than a mere propositional function. Nevertheless, for the simplicity of this initial development we shall maintain that assumption.

Above, h is defined as a function on the propositions of σ. However, it need not be supposed implausibly that only the complete set of propositions in σ should be necessary and sufficient for any particular h. We suppose instead that there will be a subset σ_h (proper or otherwise) for which:

1. h(σ_h) = h(σ)

» The propositions of σ_h are collectively sufficient for the adduction to yield the same result.

1. (∀s∈σ_h) [h(σ_h\s) ≠ h(σ)], or

» The propositions of σ_h are collectively necessary for the adduction to yield the same result.

• Call σ_h so characterized, the Adduction-Relevant State of Affairs for h on σ.
• We need not assume that σ_h is a unique such subset of σ
• Write ARSA(σ_h, σ, h)
• We will assume in what follows that where appropriate the state of affairs in question is an adduction-relevant one. Including the restriction in each definition, though strictly required, would add clutter to definitions which are already cluttered enough.

2. Action: Adducement

An agent is able to access the results of an adduction on a state of affairs, σ, when it is able to perform an action by which it applies some adduction h to that state of affairs and the result of that adduction is added to B_x. Such an action we shall call an Adducement for h from σ. Thus, when an agent x performs the adducement, η_x∈α_x, for the adduction h from σ:

Q(η_x,i, q_x,i) ⊃ B_x,i+1[ h(σ) ]

• All the normal indices are applicable in the obvious way.
• Write Add(η, h, σ) – though it may not be necessary to include s in the arguments.
• We may write η_h to acknowledge that the adducement applies the adduction h

3. Motivation: Interrogation

Agent x performs an adducement (quâ adducement) when he has a question that he needs answered (or is in a situation that is effectively identical to this) and which he knows or suspects can be answered by an application of an adduction on the facts presented in the current state of affairs.

We will adapt an approach to the semantics of questions by Groenendijk & Stokhof (1984, Studies in the Semantics of Questions and the Pragmatics of Answers, PhD Thesis, U. Amsterdam,) by which a question may be treated as a partition of the set of all propositions (van Rooy, R. (2003) ‘Quality and Quantity of Information Exchange’ in Journal of Logic, Language, and Information, 12.4 pp. 423-451) where the members of that partition are the correct answers to that question in declarative form.

Let ω = { ω_i } ∈ 2^ℙ be a question,

((∀p)[~B_x[ p∈ω ]] &
B_x[ (∀p∈ω)[ q_x’ = q_x ∪ B_x[ p∈ω ] ⇒ ( T(C(A_x(q_x’, c_x), c_x), I_x) > T(C(A_x(q_x, c_x), c_x), I_x)))
⇒ D_x[ (∃p∈ω)B_x[ p∈ω ] ]

» If x believes that knowing an answer to the question ω will enable an improvement in that agent’s total satisfaction then x will desire to know that answer

• Under some fairly plausible assumptions for the logic of the B_x operator

B_x[ p∈ω ] ⇒ B_x[ p ]

But, given opacity in the D_x operator, it does not necessarily follow that

D_x[ (∃p∈ω)B_x[ p∈ω ] ⇒ D_x[ (∃p∈ω)B_x[ p ] ]

Let ω = { ω_i } ∈ 2^ℙ be a question, σ a state of affairs, h an adduction on σ; η∈α_x then

( D_x[ (∃p∈ω)B_x[ p∈ω ] ] ∈ q_x,i

» If x wants to know an answer to the question ω

& B_x[ (∃p)[p∈ω] ⇒ (∀p)[h(σ)=p ⇒ p∈ω] ] ∈ q_x,i

» and believes that if there is an answer to ω that it would be found by the adduction h on σ

& B_x[ Add(η, h, σ) ] ∈ q_x,I )

» and believes that the action η which x can perform is an adducement for h from σ

⇒ A_x(q_x,i, c_x,i) = η

» then x does η

• A more complete description of this condition would include reference to expected outcomes, weighted interests, alternative actions, and so on, but they can be ignored here for the sake of simplicity.
• Let the antecedent of that conditional be abbreviated as Mot(ω, x, h, σ, η) and read it as ω motivates x to apply h on σ using η.

Mot(ω, x, h, σ, η) ⇒ A_x(q_x,i, c_x,i) = η

• Again, note that this assumes success in adductions

4. Information

Define the (Total) Information contained in σ, as

It_σ = {p ∈ ℙ: (∃x)(∃ω)(∃h)[H(h,σ) &h(σ)=p & B_x [(∀p)[h(σ)=p ⇒ p∈ω]]]}

» The (total) information in a state of affairs is all the statements that are adducible from it by some adduction which some agent believes would thereby answer some question.

• Note that if no agent believes the adduced statement answers a relevant question, then that statement will not thereby count as information (even if it does answer the question.)
• We also say of any p ∈It_σ that it is information in σ.

Define the Information Relative to x contained in σ, as

Ir_x,σ = {p ∈ ℙ: (∃ω)(∃h)(∃η∈α_x) [H(h,σ) &h(σ)=p & Add(η, h, σ) &
                             B_x[(∀p)[h(σ)=p ⇒ p∈ω]]]}

» The information relative to an agent in a state of affairs is all the statements that may be adduced from it by the agent which he believes may answer some question.

• Ir_x,σ may be an inconsistent set
• The information relative to a population X in σ is given in the obvious way

Ir_X,σ = ∪_x∈XIr_x,σ

• Define the Population Informationally Related to i ⊂ It_σ as

Xr_i,σ = {x ∈ X:i ⊂ Ir_x,σ }

Define the Information Available to x contained in σ, as

Iv_x,σ = {p ∈ ℙ: (∃ω)(∃h)(∃η∈α_x) [H(h,σ) &h(σ) = p & Add(η, h, σ) &
                             B_x [(∀p)[h(σ)=p ⇒ p∈ω] & Add(η, h, σ) & η∈α_x]]}

» The information available to an agent in a state of affairs is all the statements that may be adduced from it by the agent which he believes may answer some question using adductions that he can perform.

• Iv_x,σ may be an inconsistent set
• The information available to a population X in σ is given in the obvious way

Iv_X,σ = ∪_x∈XIv_x,σ

• Define the Population Informationally Availed of i ⊂ It_σ as

Xv_i,σ = {x ∈ X:i ⊂ Iv_x,σ }

 

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