A Defence of Information Closure (6 of 9)

Podcast

This episode is part of a series — click "See More" for all the episodes.

---

Central Problem

Can the principle of information closure (PIC) withstand the sceptical objection that has been deployed against it? The principle states that if an agent S holds the information that p, and S holds the information that p entails q, then S holds the information that q. Critics like Dretske and Nozick argue that PIC is “too good to be true”: if accepted, it would provide an easy refutation of radical scepticism, which contradicts the widely accepted thesis that factual information alone cannot answer sceptical doubts.

The problem has broader implications beyond epistemology. PIC is logically equivalent to the axiom of distribution in modal logic — one of the defining conditions that discriminates between normal and non-normal modal logics. If the sceptical objection against PIC succeeds, this would force the adoption of non-normal modal logics for formalizing “S is informed that p.” Conversely, if PIC can be defended, the normal modal logic B (KTB) remains a plausible formalization.

The challenge is to determine whether PIC genuinely falls to the sceptical objection, or whether the objection misallocates blame to the wrong component of the argument.

Main Thesis

Floridi defends the principle of information closure against the sceptical objection by showing that the objection “mis-allocates the blame.” The real troublemaker is not PIC itself, but the initial assumption that one can start with an uncontroversial piece of factual information (p) held by S.

The Canonical Formulation of PIC:

PIC: (Ip ∧ I(p → q)) → Iq

Where I is the modal operator “is informed (holds the information) that.”

The Sceptical Objection Reconstructed:

The objection uses a modus tollens:

1. If PIC holds, S holds p (“S is in Edinburgh”), and S holds e (“if in Edinburgh, then not a brain in a vat on Alpha Centauri”)
2. Then S can generate q (“not a BiVoAC”) a priori
3. But q answers the sceptical doubt
4. This contradicts the thesis that information alone cannot answer sceptical doubts
5. Therefore, PIC must be rejected

The Defence:

The entailment e (if p then q) is analytically true — it does not extend knowledge beyond p. Valid deductions do not generate new information (the “scandal of deduction”). The anti-sceptical force comes entirely from assuming p is true and that S holds it. No shrewd sceptic will concede p in the first place, because conceding any genuine information opens the floodgates: “informationally, it never rains, it pours.”

PIC merely “exchanges” the higher informativeness of p (where S is) into the lower informativeness of q (where S is not). The principle is “only following orders” — it is the initial input p that does the anti-sceptical work, not PIC.

Historical Context

The chapter engages with a debate in epistemology and philosophy of information that intensified in the late twentieth century. Dretske’s work on information and knowledge (1981, 1999, 2006) and Nozick‘s tracking theory of knowledge (1981) both rejected closure principles, finding the sceptical objection convincing.

The formalization of epistemic and information logics has roots in Hintikka‘s pioneering work (1962) on epistemic logic, which first systematically applied modal logic to knowledge and belief. The distinction between normal and non-normal modal logics became crucial: normal logics include the axiom of distribution, strong necessitation, and uniform substitution; dropping any of these yields non-normal alternatives.

The “statal” versus “actional” distinction in being informed — whether S holds information versus becomes informed — derives from grammatical analysis of passive verbal forms. This distinction structures contemporary debates about information logic, with Primiero (2009) developing the actional dimension and Allo (2011) exploring non-normal alternatives.

The broader context involves the “scandal of deduction” (Hintikka 1973) — the puzzle that valid deductions seem not to generate new information — and concerns about logical omniscience in epistemic logic, which D’Agostino and Floridi (2009) address through feasibility considerations.

Philosophical Lineage

flowchart TD
    Hintikka --> Dretske
    Hintikka --> Floridi
    Dretske --> Nozick
    Dretske --> Kerr
    Moore --> Floridi
    Descartes --> Dretske
    Wittgenstein --> Floridi
    Quine --> Floridi
    Carnap --> Hintikka

    class Hintikka,Dretske,Nozick,Floridi,Moore,Descartes,Wittgenstein,Quine,Carnap,Kerr internal-link;

Key Thinkers

Thinker	Dates	Movement	Main Work	Core Concept
Dretske	1932-2013	Epistemology	Knowledge and the Flow of Information	Rejection of epistemic closure
Nozick	1938-2002	Epistemology	Philosophical Explanations	Tracking theory, closure denial
Hintikka	1929-2015	Logic	Knowledge and Belief	Epistemic logic, possible worlds
Moore	1873-1958	Analytic Philosophy	A Defence of Common Sense	Common sense anti-scepticism
Descartes	1596-1650	Rationalism	Meditations	Radical scepticism, methodological doubt

Key Concepts

Concept	Definition	Related to
Principle of Information Closure (PIC)	(Ip ∧ I(p → q)) → Iq — if S holds p and holds that p entails q, then S holds q	Floridi, Modal Logic
Axiom of Distribution	□(φ → ψ) → (□φ → □ψ) — logically equivalent to PIC; distinguishes normal from non-normal modal logics	Modal Logic, Hintikka
Statal vs Actional Information	Statal: S holds information; Actional: S becomes informed — grammatical distinction applied to information states	Floridi, Epistemology
Known Entailment	Requiring that S holds not just p but also the information that p entails q	Epistemology, Dretske
Scandal of Deduction	Valid deductions do not generate new information; analytically true implications do not extend knowledge	Hintikka, Logic
Normal Modal Logic	Logic satisfying axiom of distribution, strong necessitation, and uniform substitution	Modal Logic
Logical Omniscience	Problem that closure principles seem to attribute unlimited inferential capacity to agents	Hintikka, Epistemology
Sufficient Procedure	Handling implication as showing q is obtainable a priori from the available information base	Floridi, Epistemology
Informational Co-variance	F(a) carries information that G(b) when systems a and b are coupled such that a’s being F correlates to b’s being G	Dretske, Information Theory
Veridicality Thesis	p qualifies as semantic information only if p is true	Floridi, Epistemology

Authors Comparison

Theme	Floridi	Dretske	Nozick
Information closure	Defends PIC; sceptical objection misallocates blame	Rejects closure; no informational basis for anti-sceptical claims	Rejects closure; tracking theory
Sceptical scenarios	Cannot be answered by factual info, but this doesn’t undermine PIC	Used to show closure fails	Used to motivate tracking conditions
Modal logic	Normal logic B (KTB) remains plausible	Would require non-normal logic	Neighbourhood semantics
Role of entailment	Must be held as information by S (known entailment)	Informational basis cannot extend to heavyweight implications	Tracking conditions not closed under entailment
Logic vs empirical	PIC is logical/prescriptive, not empirical description	Conflates logical and empirical processing	Focus on counterfactual conditions

Influences & Connections

• Predecessors: Floridi ← influenced by ← Hintikka, Moore, Quine, Wittgenstein
• Contemporaries: Floridi ↔ debates with ↔ Dretske, Kerr, Pritchard
• Technical development: Allo → develops → non-normal modal alternative to PIC
• Opposing views: Dretske ← rejects PIC ← Nozick
• Parallel debates: D'Agostino ↔ addresses ↔ logical omniscience and feasibility

Summary Formulas

• Floridi: The principle of information closure is defensible; the sceptical objection mis-allocates blame to PIC when the real troublemaker is the assumption that S holds genuine factual information p. Conceding p already defeats scepticism; PIC merely extracts what is already implicit.

• Dretske: Information closure fails because one can have an informational basis for ordinary beliefs (being in Edinburgh) without having an informational basis for anti-sceptical beliefs (not being a brain in a vat), even while knowing the relevant entailment.

• Hintikka: Epistemic logic can be formalized using normal modal logic with the axiom of distribution, though this generates the scandal of deduction and logical omniscience problems.

• Moore: If you know something, you know a lot more than just that something — knowledge of one’s hands provides leverage against scepticism.

Timeline

Year	Event
1962	Hintikka publishes Knowledge and Belief, founding epistemic logic
1973	Hintikka identifies the “scandal of deduction”
1981	Dretske publishes Knowledge and the Flow of Information
1981	Nozick publishes Philosophical Explanations with tracking theory
2004	Greco and Floridi begin work on logic of being informed
2006	Floridi publishes initial formulation of PIC
2009	D'Agostino and Floridi address feasibility in epistemic logic
2011	Allo develops non-normal modal logic alternative
2012	Kerr and Pritchard formulate sceptical objection against PIC

Notable Quotes

“Informationally (but also epistemically), it never rains, it pours: you never have just a bit of information; if you have some, you ipso facto have a lot more.” — Floridi

“PIC is only following orders, as it were. For PIC only exchanges the higher informativeness of a true p into the lower informativeness of a true q.” — Floridi

“I take logic to be a prescriptive not a descriptive discipline. From this perspective, PIC seems to be perfectly fine.” — Floridi

---

Warning

This annotation was normalised using a large language model and may contain inaccuracies. These texts serve as preliminary study resources rather than exhaustive references.