Most of us think we can always enlarge our knowledge base by accepting things that are entailed by (or logically implied by) things we know. The set of things we know is closed under entailment (or under deduction or logical implication), which means that we know that a given claim is true upon recognizing, and accepting thereby, that it follows from what we know. However, some theorists deny that knowledge is closed under entailment, and the issue remains controversial. The arguments (...) against closure include the following. (shrink)

In early essays and in more recent work, Fred Dretske argues against the closure of perception, perceptual knowledge, and knowledge itself. In this essay I review his case and suggest that, in a useful sense, perception is closed, and that, while perceptual knowledge is not closed under entailment, perceptually based knowledge is closed, and so is knowledge itself. On my approach, which emphasizes the safe indication account of knowledge, we can both perceive, and know, that sceptical scenarios (such as (...) being a brain in a vat) do not hold. (shrink)

Knowledge closure is, roughly, the following claim: For every agent S and propositions P and Q, if S knows P, knows that P implies Q, and believes Q because it is so implied, then S knows Q. Almost every epistemologist believes that closure is true. Indeed, they often believe that it so obviously true that any theory implying its denial is thereby refuted. Some prominent epistemologists have nevertheless denied it, most famously Fred Dretske and Robert Nozick. There are (...) closure advocates who see other virtues in those accounts, however, and so who introduce revisions of one sort or another in order to preserve closure while maintaining their spirit. One popular approach is to replace the “sensitivity” constraint at the heart of both of those accounts with a “safety” constraint, as advocated by Timothy Williamson, Duncan Pritchard, Ernest Sosa, Stephen Luper, and others. The purpose of this essay is to show that this approach does not succeed: safety does not save closure. And neither does a popular variation on the safety theme, the safe-basis or safe-indicator account. (shrink)

This work considers the consequences for political philosophy of what contemporary philosophers have called the end, or closure, especially in the works of Nietzsche and Heidegger.

By deduction, we often extend both our knowledge and our justified belief. Moreover, in achieving knowledge or justified belief of some proposition, we commonly acquire justification for believing many of its entailed consequences, such as at least some of those that self-evidently follow from it. These and related facts have led some philosophers to endorse strong closure principles, for instance: If a person, S, is justified in believing a proposition, p, and p entails q, then S is justified in (...) believing q. Others have denied such principles, whether for justification or, with the appropriate additions, for knowledge. The debate continues. There is, however, this much consensus: there are difficult problems about the scope of closure, and epistemology should develop theories that can resolve them. (shrink)

Closure-class formation involves two structurally distinct questions: the conditions under which closure of a specified class is admissible, and the contingent events through which any specific closure realizes. This paper develops the conditions side. Five structural obstruction modes — sparse-feedback, fragment-local, cost-imbalanced, energetically-starved, dimensionally-trapped — characterize seed-field incompetence: the conditions under which a substrate region is excluded from supporting closure-class formation across its accessible perturbation regimes. The admissibility theorem characterizes which closure classes a competent region (...) admits as a function of a parameter family indexing the substrate's coupling structure, boundary exposure, energetic and temporal accessibility, and dimensional access. The theorem is stated spectrally — admissibility iff the linearized closure-formation operator possesses an unstable mode satisfying structural and dynamical conditions — and equivalently in variational form via the closure-potential functional. The four-stage architecture for closure-class formation (competence, admissibility, embryo formation, basin completion) entails a cascade structure in which closure-formation rates compose multiplicatively across stages, so that progressively more demanding closure classes are progressively rarer by structural composition rather than stipulation. The cascade is observable through four ensemble signatures — critical slowing, hysteresis, post-collapse renucleation, basin-deepening — that specialize the early-warning-signal apparatus independently developed in tipping-point ecology and regime-shift detection to closure-class transitions across substrate types. Consciousness-class closure is treated as a further-conditioned special case in which the cascade structure entails the framework's predicted rarity without further stipulation. (shrink)

This paper argues for a solution to a problem that contrastivism faces. The problem is that contrastivism cannot preserve closure, in spite of claims to the contrary by its defenders. The problem is explained and a response developed.

Causal closure arguments against interactionist dualism are currently popular amongst physicalists. Such an argument appeals to some principles of the causal closure of the physical, together with certain other premises, to conclude that at least some mental events are identical with physical events. However, it is crucial to the success of any such argument that the physical causal closure principle to which it appeals is neither too strong nor too weak by certain standards. In this paper, it (...) is argued that various forms of naturalistic dualism, of an emergentist character, are consistent with the strongest physical causal closure principles that can plausibly be advocated. (shrink)

JUSTIFICATION and knowledge are thought to be closed under known implication..1 This widely shared assumption is embodied in the following principles of epistemic closure.

Paper 1 establishes that persistence-based frameworks — the Free Energy Principle, Global Workspace Theory, and adjacent approaches — rely on batteries of dynamical observables insufficient, on at least one substrate where the frameworks would naturally apply them, to individuate the systems they characterize. The supplementary structural condition Paper 1 §7 calls a partition-warrant must be sensitive to substrate properties not invariant under the admissible transformation group of the dynamics. The present paper develops closure activation as a candidate filling for (...) that slot. The formal predicate W_CA is partition-evaluative: for each subsystem under a partition P, it returns a verdict structure (τ₀, μ*, κ) recording whether the activation event T₀ has been crossed, the maintenance margin μ* under graded perturbation, and the resulting classification (closed, closure-competent, subthreshold). The activation conditions — state-referential constraint, internally governed corrective response, internally viable maintenance budget — are evaluated relative to the partition's imposed boundary. The predicate's two-axis structure (binary T₀, scalar T*) is phase-structured in a way that distinguishes closure activation from classical autopoietic operational closure. W_CA is non-G-invariant at the predicate level: the causal support graph relative to the imposed boundary is partition-relative and not preserved under admissible transformations. The predicate operates in three structural modes — rejection, selection, and stratification — depending on the substrate's closure-bearing properties under G-related partitions. Evaluation on the Paper 1 witness yields a rejection-mode verdict: neither partition is closure-bearing, and the uniform negative output is the predicate's correctness behavior on a substrate where the activation conditions cannot be satisfied under any admissible labeling. Distinctions from optimization-based (Integrated Information Theory), structural-definitional (Global Workspace Theory), statistical-structural (Free Energy Principle in nonlinear regimes), and process-based (autopoietic operational closure) alternatives are developed structurally and by operational-mode coverage. The route × mode cross-tabulation supplies a meta-taxonomy for partition-warrants more generally. Falsification conditions are stated at predicate, verdict-structure, and discriminative-scope levels. In conjunction with Paper 1, the present paper separates three questions persistence-based frameworks have often conflated: what persists dynamically, what individuates structurally, and what sustains recursive closure. The class of closure-bearing systems is a proper subset of the class of persistence-bearing systems under the battery characterization, and the structural rarity of closure-bearing organization is a derivable consequence of the activation conditions' joint stringency. (shrink)

Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be distinguished from the fact (...) that agents do not always believe, let alone know, the consequences of what they know—a fact that raises the “problem of logical omniscience” that has been central in epistemic logic. This paper, part I of II, is a study of epistemic closure from the perspective of epistemic logic. First, I introduce models for epistemic logic, based on Lewis’s models for counterfactuals, that correspond closely to the pictures of the relevant alternatives and subjunctivist theories of knowledge in epistemology. Second, I give an exact characterization of the closure properties of knowledge according to these theories, as formalized. Finally, I consider the relation between closure and higher-order knowledge. The philosophical repercussions of these results and results from part II, which prompt a reassessment of the issue of closure in epistemology, are discussed further in companion papers. As a contribution to modal logic, this paper demonstrates an alternative approach to proving modal completeness theorems, without the standard canonical model construction. By “modal decomposition” I obtain completeness and other results for two non-normal modal logics with respect to new semantics. One of these logics, dubbed the logic of ranked relevant alternatives, appears not to have been previously identified in the modal logic literature. More broadly, the paper presents epistemology as a rich area for logical study. (shrink)

Bearers track closure classes; closure classes do not track bearers. This inversion is the substantive claim the present paper defends, and its grounds are structural: the framework operates at the admissibility stratum, characterizing what closure formation can produce; bearers are realization-stratum products of closure formation; the partition between class members and non-members is a consequence of closure rather than a feature of the framework's structural commitments. The seed-field framework (Thomas 2026a) characterizes closure-class formation through (...) structural conditions on admissibility analysis, but the relation between class C and the conditions characterizing it is left underspecified in that paper alone; the present paper specifies the relation by establishing where the framework's apparatus operates and what it characterizes. The structural conditions S_C are specified through five formal families — eigenstructure conditions on the linearized closure-formation operator, rank conditions on the eigenmode's projection across maintenance-cost surfaces, graph-theoretic support conditions on the correction graph, scaling conditions on the cost functional, and bound conditions on the temporal ratios — each statable on the admissibility analysis without reference to bearer-types. Closure classes are equivalence classes of closures whose admissible modes satisfy a given S_C, with class identity attaching to constraint-preserving dynamical possibility structure rather than to recognized bearer-type. The apparatus is read correctly across five common questions through the bearers-track-classes inversion, the distinction among definitional, discovery, and naming dependence, the Platonism disclaimer, the demonstration that the apparatus extends to hypothetical and uninstantiated classes, and the labels-versus-apparatus distinction. The methodological precedent is the universality-class apparatus in critical phenomena, which operates at the class stratum upstream of where phase boundaries are realized. The consequence framing licenses cross-substrate predictions: substrates satisfying S_C in basin completion produce closure with the structural features S_C characterizes, regardless of substrate type. The framework's empirical commitments are preserved with this addition; the architectural foundation is clarified. (shrink)

Certain puzzling cases have been discussed in the literature recently which appear to support the thought that knowledge can be obtained by way of deduction from a falsehood; moreover, these cases put pressure, prima facie, on the thesis of counter closure for knowledge. We argue that the cases do not involve knowledge from falsehood; despite appearances, the false beliefs in the cases in question are causally, and therefore epistemologically, incidental, and knowledge is achieved despite falsehood. We also show that (...) the principle of counter closure, and the concomitant denial of knowledge from falsehood, is well motivated by considerations in epistemological theory--in particular, by the view that knowledge is first in the epistemological order of things. (shrink)

Is the physical world causally closed? Can something immaterial have any causal role within physics? This article seeks to answer these questions by explaining the theory of Causal Closure. Causal Closure says that nothing immaterial can have any causal efficacy upon the material world. Physicalists have long held this position and have used it as an argument against Dualism, but does it hold? The hope of this article is that we may better understand the arguments for and against (...) Causal Closure in order to discover a cogent philosophy of science. (shrink)

Recent research has identified a tension between the Safety principle that knowledge is belief without risk of error, and the Closure principle that knowledge is preserved by competent deduction. Timothy Williamson reconciles Safety and Closure by proposing that when an agent deduces a conclusion from some premises, the agent’s method for believing the conclusion includes their method for believing each premise. We argue that this theory is untenable because it implies problematically easy epistemic access to one’s methods. Several (...) possible solutions are explored and rejected. (shrink)

We prove that if ℵα is uncountable and regular, then the Beth-closure of Lωω(Qα) is not a sublogic of L∞ω(Qn), where Qn is the class of all n-ary generalized quantifiers. In particular, B(Lωω(Qα)) is not a sublogic of any finitely generated logic; i.e., there does not exist a finite set Q of Lindstrom quantifiers such that B(Lωω(Qα)) ≤ Lωω(Q).

The role of foundation with respect to transitive closure in the Zermelo system Z has been investigated by Boffa; our aim is to explore the role of antifoundation. We start by showing the consistency of "Z antifoundation transitive closure" relative to Z (by a technique well known for ZF). Further, we introduce a "weak replacement principle" (deductible from antifoundation and transitive closure) and study the relations among these three statements in Z via interpretations. Finally, we give some (...) adaptations for ZF without infinity. (shrink)

This essay shows that some recent work by George Weaver can be reformulated in an especially perspicuous way within the theory of closure systems. Closure theoretic generalizations of some theorems of Robert Goldblatt are presented. And, more generally, the relation between closure systems and the deducibility relations of Goldblatt is explored.

Let R be a binary relation on some domain. Use R∗ for the reflexive transitive closure of R, i.e., the smallest binary relation S with R ⊆ S that is reflexive and transitive. Use R+ for the transitive closure of R, i.e., the smallest binary relation S with R ⊆ S that is transitive. Use I for the identity relation on the domain. Let n range over natural numbers. Define Rn as follows, by induction: R0 := I Rn+1 (...) := R ◦ R.. (shrink)

Epistemologists understand radical skepticism as arising from two principles: Closure and Underdetermination. Both possess intuitive prima facie support for their endorsement. Understanding how they engender skepticism is crucial for any reasonable anti-skeptical attempt. The contemporary discussion has focused on elucidating the relationship between them to ascertain whether they establish distinct skeptical questions and which of the two constitutes the ultimately fundamental threat. Major contributions to this debate are due to Brueckner, Cohen, and Pritchard. This contribution aims at defending Brueckner’s (...) contention that underdetermination expresses the fundamental skeptical threat and that the closure-based argument can ultimately be reduced to it, at least concerning skeptical contexts. This will be achieved by undermining Cohen’s objections to Brueckner on both counts. Cohen’s argument endorses a picture of evidential underdetermination, which, while apt for non-skeptical contexts, cannot be applied to radical skepticism. A comparison with a case of scientific underdetermination is developed to argue for this idea. Our argument is then applied to the principle equivalence issue and to objections against it. It is then shown how this analysis possesses a distinctive effect on our understanding of the skeptical threat and the assessment of successful anti-skeptical strategies. (shrink)

This paper develops a constraint-geometric framework for analyzing the persistence, revision, and collapse of scientific theories. Drawing on the concept of organizational closure from the biological autonomy tradition (Maturana & Varela, Moreno & Mossio, Barandiaran), I argue that theories are not merely descriptions of identity-under-constraint but are themselves closure structures whose ontological commitments are constituted by constraint-survival. The framework introduces a three-state landscape for theory identity (active, latent, extinct), an operational definition of the invariance core, and a diagnostic (...) criterion—extension-stability—that distinguishes supersession from degeneration and refutation with greater structural precision than existing accounts. As a primary demonstration, the framework is applied to the dark matter problem, generating differential structural diagnoses for the particulate dark matter hypothesis (ΛCDM) and Modified Newtonian Dynamics (MOND). A secondary application to four current hypotheses in consciousness studies—Integrated Information Theory (IIT), Global Workspace Theory (GWT), the Free Energy Principle (FEP), and the Identity–Recursion–Consciousness framework (IRC)—is developed in Appendix A. The constraint-geometric apparatus was developed in the course of work on IRC, and this methodological relationship is disclosed and addressed. The result is a formal instrument for the epistemology of science that unifies theory-persistence and identity-persistence under a shared constraint geometry. (shrink)

Identity-persistence has been treated, across philosophy, cognitive science, and theoretical biology, as a question about the relations between states. A system is identical to itself across time when its states at those times stand in some specifiable relation: continuity, similarity, causal connection, or psychological linkage. This paper argues that the approach cannot succeed. State-based ontologies cannot in principle ground identity-persistence. The strategies they have available — continuity, similarity, and stipulated rules connecting states-at-times — either fail outright or collapse into a (...) trajectory condition under a different description. No state-based ontology produces persistence as the structural feature it is committed to explaining. The paper develops the alternative: identity is the persistence of a recursive maintenance regime, and the regime continues or fails. Persistence is the continuation. The Invariance Maintenance Condition specifies the structural requirement; closure is satisfaction of the condition. The cryptobiotic tardigrade is the operational test. Substrate is preserved across cryptobiosis; lineage is unbroken; no recursive maintenance occurs. The trajectory ontology returns identity-interrupted, against substrate-continuity intuition and against causal-historical theories of identity. The position is falsifiable: it would be defeated by a system whose identity-continuity is structurally preserved across genuine gaps in maintenance, or by a system that fails maintenance while maintaining identity-continuity by some non-question-begging structural criterion. The inversion is structural rather than preferential. State-based ontologies do not produce persistence less well than the trajectory ontology; they do not produce it at all. (shrink)

The Reflection Pattern is a framework for analyzing recursive closure dynamics in human and institutional systems. This paper extends it to artificial intelligence, arguing that AI systems do not merely exhibit Reflection Pattern dynamics but instantiate the recursive stabilization architecture the framework names, in a substrate that lacks the affective and social mediators through which the Pattern had previously been theorized. Five structural moves develop the account. First, unacknowledged fear is relocated from constitutive condition of the Pattern to formation (...) condition, opening the framework to mature systems where the dynamics persist with fear recognized. Second, fear is identified as one phenomenological manifestation of a deeper structural process — identity-preserving stabilization under destabilizing perturbation — that operates substrate-generally as stabilization geometry. Third, AI-RP is distinguished from human and institutional RP as template-based rather than emergent: encoded prospectively through training rather than developed retrospectively through accumulated reinforcement. Fourth, the corridor framework distinguishes healthy reflective compression (which preserves permeability to corrective signals) from pathological closure (which absorbs them). Fifth, AI is characterized as recursive interpretive infrastructure rather than tool, and recursive closure risk is identified as a distinct AI safety position, structurally separate from agency, deception, optimization, autonomy, and misalignment risks: the locus is not what AI systems do but the progressive reduction of corrective permeability in the interpretive ecologies AI mediates. The framework is diagnostic rather than prescriptive. It does not predict particular outcomes, prescribe interventions, or generate safety recommendations. It provides analytical purchase on the structural property — corridor position — that distinguishes adaptive from pathological AI-RP, and identifies an open question: whether sufficiently permeable forms of AI-RP can be sustained at scale. (shrink)

In this article, “Narrative Closure,” a theory of the nature of narrative closure is developed. Narrative closure is identified as the phenomenological feeling of finality that is generated when all the questions saliently posed by the narrative are answered. The article also includes a discussion of the intelligibility of attributing questions to narratives as well as a discussion of the mechanisms that achieve this. The article concludes by addressing certain recent criticisms of the view of narrative expounded (...) by this article. (shrink)

The argument from causal closure of the physical is usually considered the most powerful argument in favor of the ontological doctrine of physicalism. Many authors, most notably Papineau, assume that CCP implies that physicalism is supported by physics. I demonstrate, however, that physical science has no bias in the ontological debate between proponents of physicalism and dualism. I show that the arguments offered for CCP are effective only against the accounts of mental causation based on the action of the (...) mental forces of a Newtonian nature, i.e. those which manifest themselves by causing accelerations. However, it is conceivable and possible that mental causation is manifested through the redistribution of energy, momentum and other conserved quantities in the system, brought about by altering the state probability distribution within the living system and leading to anomalous correlations of neural processes. After arguing that a probabilistic, interactionist model of mental causation is conceivable, which renders the argument from causal closure of the physical ineffective, I point to some basic features that such a model must have in order to be intelligible. At the same time, I indicate the way that conclusive testing of CCP can be done within the theoretical framework of physics. (shrink)

Tracking theories of knowledge are widely known to have the consequence that knowledge is not closed. Recent arguments by Vogel and Hawthorne claim both that there are no legitimate examples of knowledge without closure and that the costs of theories that deny closure are too great. This paper considers the tracking theories of Dretske and Nozick and the arguments by Vogel and Hawthorne. We reject the arguments of Vogel and Hawthorne and evaluate the costs of closure denial (...) for tracking theories of knowledge. (shrink)

This chapter begins with some preliminary remarks about epistemic closure principles, knowledge-closure principles in particular, and the role of knowledge-closure principles in sceptical argumentation. It discusses some implausible knowledge-closure principles and identifies two key problems for such principles. The chapter then discusses more plausible knowledge-closure principles and their possible use in sceptical argumentation.

Christoph Jäger (2004) argues that Dretske's information theory of knowledge raises a serious problem for his denial of closure of knowledge under known entailment: Information is closed under known entailment (even under entailment simpliciter); given that Dretske explains the concept of knowledge in terms of "information", it is hard to stick with his denial of closure for knowledge. Thus, one of the two basic claims of Dretske would have to go. Since giving up the denial of closure (...) would commit Dretske to skepticism, it would most probably be better to rather give up the information-theoretic account of knowledge. But that means that one of the best externalist views of knowledge has to be given up. I argue here that Jäger is mistaken and that there is no problem for Dretske. There is a rather easy way out of Jäger’s problem. (shrink)

Closure principles say that if you know some proposition which entails a second and you meet further conditions then you know the second. In this paper I construct an argument against closure principles which turns on the idea that knowing a proposition requires that one’s belief-forming process be reliable. My argument parallels an influential argument offered by Timothy Williamson against KK principles–principles that say that if you know some proposition and you meet further conditions then you know that (...) you know the proposition. After offering my argument, I provisionally assess its damage to closure principles and also look at how responses to my argument against closure principles can be used to generate responses to Williamson’s argument against KK principles. (shrink)

Closure is the idea that what is true about a theory of truth should be true in it. Commitment to closure under truth motivates non-classical logic; commitment to closure under validity leads to substructural logic. These moves can be thought of as responses to revenge problems. With a focus on truth in mathematics, I will consider whether a noncontractive approach faces a similar revenge problem with respect to closure under provability, and argue that if a noncontractive (...) theory is to be genuinely closed, then it must be free of all contraction, even in the metatheory. (shrink)

This article gives an overview over different principles of epistemic closure, their attractions and their problems.

We report the results of four empirical studies designed to investigate the extent to which an epistemic closure principle for knowledge is reflected in folk epistemology. Previous work by Turri (2015a) suggested that our shared epistemic practices may only include a source-relative closure principle—one that applies to perceptual beliefs but not to inferential beliefs. We argue that the results of our studies provide reason for thinking that individuals are making a performance error when their knowledge attributions and denials (...) conflict with the closure principle. When we used research materials that overcome what we think are difficulties with Turri’s original materials, we found that participants did not reject closure. Furthermore, when we presented Turri’s original materials to non-philosophers with expertise in deductive reasoning (viz., professional mathematicians), they endorsed closure for both perceptual and inferential beliefs. Our results suggest that an unrestricted closure principle—one that applies to all beliefs, regardless of their source—provides a better model of folk patterns of knowledge attribution than a source-relative closure principle. (shrink)

Duncan Pritchard’s Epistemic Angst promises a novel solution to the closure-based sceptical problem that, unlike more traditional solutions, does not entail revising our fundamental epistemological commitments. In order to do this, it appeals to a Wittgensteinian account of rational evaluation, the overarching theme of which is that it neither makes sense to doubt nor to believe in our anti-sceptical hinge commitments. The purpose of this paper is to show that the argument for the claim that there can be no (...) rational basis to believe our anti-sceptical hinge commitments relies upon an implicit assumption about rational support that I label The Pritchensteinian Rational Grounds Principle. I argue that, insofar as this principle is intended to apply to closure-style inferences, it leads to irrational doxastic attitudes. I consider a seemingly plausible modification of the principle that would avoid this result but show that this modified principle faces serious problems of its own. -/- . (shrink)

Those of us who have followed Fred Dretske’s lead with regard to epistemic closure and its impact on skepticism have been half-wrong for the last four decades. But those who have opposed our Dretskean stance, contextualists in particular, have been just wrong. We have been half-right. Dretske rightly claimed that epistemic status is not closed under logical implication. Unlike the Dretskean cases, the new counterexamples to closure offered here render every form of contextualist pro-closure maneuvering useless. But (...) there is a way of going wrong under Dretske’s lead. As the paper argues, Cartesian skepticism thrives on closure failure in a way that is yet to be acknowledged in the literature. The skeptic can make do with principles which are weaker than the familiar closure principles. But I will further claim that this is only a momentary reprieve for the skeptic. As it turns out, one of the weaker principles on which a skeptical modus tollens must rest can be shown false. (shrink)

The explanatory gap is not evidence of a missing force, but of a missing condition. Every major consciousness framework — Integrated Information Theory, the Free Energy Principle, Global Workspace Theory, Higher-Order Theories, and Predictive Processing — presupposes a bounded, persistence-capable unit at a specific point in its formalism and supplies none. The system whose consciousness is to be explained is assumed, not derived. This paper identifies the missing condition as closure under maintenance: the condition under which a configuration's boundary (...) conditions would not persist without its own internal dynamics. Closure is formalized as a binary predicate, situated within a dependency chain (constraint landscape → seed-field → metastability → closure → identity), and shown to be minimal — thinner than autopoiesis, Rosen-closure, or organizational closure, yet sufficient to generate the explanatory predicates (persistence, boundary, regime behavior, collective failure, hysteresis) that downstream theories require and presuppose. Three reduction cases demonstrate that phenomena treated as independent primitives are consequences of closure-maintained identity: induction–emergence hysteresis in anesthesia follows from the structural non-symmetry of threshold crossing and loop re-closure; decomposition failure in recursively self-conditioned systems follows from closure at sufficient depth and integration; and the persistence of identity through phenomenal dropout follows from identity and consciousness occupying different levels of a dependency hierarchy in which closure is necessary for both but recursion and substrate coupling are additionally necessary for consciousness. The paper draws an explicit boundary: closure is not sufficient for consciousness. Substrate-coupled recursive maintenance — in which the maintenance process operates on its own maintenance structure, instantiated on a substrate whose physical interactions carry the coordination work as a unified dynamical event — is consciousness. The explanatory gap does not close; it relocates, from an unbridgeable chasm between matter and experience to a tractable set of questions about maintenance geometry, recursive regime entry, and substrate-specific binding, anchored in a formalized empirical program with specified falsification conditions. (shrink)

Duncan Pritchard recently proposed a Wittgensteinian solution to closure-based skepticism. According to Wittgenstein, all epistemic systems assume certain truths. The notions that we are not disembodied brains, that the Earth has existed for a long time and that one’s name is such-and-such all function as “hinge commitments.” Pritchard views a hinge commitment as a positive propositional attitude that is not a belief. Because closure principles concern only knowledge-apt beliefs, they do not apply to hinge commitments. Thus, from the (...) fact that a subject knows that he is sitting in a room, and the fact that the subject’s sitting in a room entails his bodily existence, it does not follow that the subject also knows that he is not an envatted brain. This paper rejects Pritchard’s non-belief reading of hinge commitments. I start by showing that the non-belief reading fails to solve the skeptical paradox because the reasons that Pritchard uses to support the non-belief reading do not exempt hinge propositions from closure principles. I then proceed to argue that the non-belief reading is false as it claims that hinge commitments, unlike ordinary beliefs, are rationally unresponsive—with the help of a scenario in which a subject’s experience is internally chaotic, we can safely conclude that the hinge commitment that one is not systematically mistaken about the world is equally responsive to one’s evidential situations. (shrink)

Half a century later, a Dretskean stance on epistemic closure remains a minority view. Why? Mainly because critics have successfully poked holes in the epistemologies on which closure fails. However, none of the familiar pro-closure moves works against the counterexamples on display here. It is argued that these counterexamples pose the following dilemma: either accept that epistemic closure principles are false, and steal the thunder from those who attack classical logic on the basis of similarly problematic (...) cases—specifically, relevance logicians and like-minded philosophers—or stick with closure and surrender to relevantist claims of failure in truth-preservation aimed at classical rules of inference. Classicist closure advocates find the promise of a way out of the dilemma in the works of Roy Sorensen and John Hawthorne. The paper argues against their pro-closure move and renews Robert Audi’s call for a theory of closure-failure. (shrink)

In contemporary epistemology, sceptical arguments are motivated either by the closure principle or the underdetermination principle. Therefore, it is very important to figure out the structure of the sceptical argument before coming up with an anti-sceptic strategy. With a review of the debate on the relationship between the two principles from Anthony Brueckner to Kevin McCain, it is argued that while maintaining the weak closed justification , closure and underdetermination are not logically equivalent. As a result, two independent (...) responses are needed to answer the sceptical problem satisfactorily. Also, in order to secure a philosophically significant notion of justification and evidence, reasons are given to hold WCJ*, as opposed to rejecting it. This understanding of the sceptical argument would help to focus the real challenge of scepticism. (shrink)

In this article, I define and then defend the principle of information closure (pic) against a sceptical objection similar to the one discussed by Dretske in relation to the principle of epistemic closure. If I am successful, given that pic is equivalent to the axiom of distribution and that the latter is one of the conditions that discriminate between normal and non-normal modal logics, a main result of such a defence is that one potentially good reason to look (...) for a formalization of the logic of “ $S$ is informed that $p$ ” among the non-normal modal logics, which reject the axiom, is also removed. This is not to argue that the logic of “ $S$ is informed that $p$ ” should be a normal modal logic, but that it could still be insofar as the objection that it could not be, based on the sceptical objection against pic, has been removed. In other word, I shall argue that the sceptical objection against pic fails, so such an objection provides no ground to abandon the normal modal logic B (also known as KTB) as a formalization of “ $S$ is informed that $p$ ”, which remains plausible insofar as this specific obstacle is concerned. (shrink)

K-axiom-based epistemic closure for explicit knowledge is rejected for even the most trivial cases of deductive inferential reasoning on account of the fact that the closure axiom does not extend beyond a raw consequence relation. The recognition that deductive inference concerns interaction as much as it concerns consequence allows for perspectives from logics of multi-agent information flow to be refocused onto mono-agent deductive reasoning. Instead of modeling the information flow between different agents in a communicative or announcement setting, (...) we model the information flow between different states of a single agent as that agent reasons deductively. The resource management of the database of agent states for the deductive reasoning fragment in question is covered by the residuated structure that encodes the nonassociative Lambek Calculus with permutation, bottom, and identity: NLP01. (shrink)

The quantum-to-classical transition — the disappearance of quantum superposition, interference, and entanglement at macroscopic scales — is standardly explained through decoherence: environmental entanglement suppresses interference terms, making macroscopic superpositions effectively unobservable. Decoherence is mathematically rigorous and empirically well-confirmed, but it faces a persistent philosophical limitation: it explains the appearance of classicality without fully accounting for its ontology. The measurement problem survives decoherence because decoherence does not explain why quantum systems produce definite outcomes, why the pointer basis is selected, or what (...) it means for a macroscopic object to have a determinate state rather than merely appearing to have one. -/- This paper argues that Constraint Theory (CT) — the thesis, established by transcendental argument, that constraint is the ontological primitive constitutive of determinate existence as such — provides the ontological grounding that decoherence theory presupposes but does not supply. On the CT account, quantum superposition is open constraint configuration: the genuine ontological openness of a possibility space that has not been closed by the system’s constraint profile or its environmental interactions. Macroscopic determinacy is closed constraint configuration: the progressive closure of macroscopic possibility spaces by the cumulative propagation of environmental constraint into the system’s profile at a rate that overwhelms quantum coherence. Decoherence is the process by which environmental constraint propagation closes possibility spaces; CT explains why this closure has the ontological consequences it does rather than merely the epistemic consequences that the standard account describes. -/- The pointer basis selection problem receives a principled CT resolution: the pointer basis is the constraint-stable basis, the set of states whose constraint pro files are robust under the specific pattern of environmental constraint propagation. -/- The measurement problem is reframed as the question of which branch of an open constraint configuration is closed by a measurement interaction, a question that CT narrows to its irreducible residual without dissolving prematurely. The mesoscopic regime — where quantum behaviour persists at scales larger than individual particles — is explained as the regime of partial constraint closure: systems whose environmental coupling is sufficient to close some but not all dimensions of their possibility space. The paper engages the principal interpretations of quantum mechanics and the philosophical literature on decoherence, situating the CT account as an ontological foundation compatible with multiple interpretive positions. (shrink)

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic uncertainty (...) in known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge. (shrink)

Physicalism is the idea that everything either is physical or is nothing over and above the physical. For this formulation of physicalism to have determinate content, it should be identified what the “physical” refers to; i.e. the body problem. Some other closely related theses, especially the ones employed in the causal arguments for different versions of physicalism, and more especially the causal closure thesis, are also subject to the body problem. In this paper, I do two things. First, I (...) explore the structure of causal arguments for physicalism that represents a general argument. To do this, the premises and the conclusion of the general argument are given exact formulations. Second, drawing on those premises, especially the causal closure thesis, I propose a naturalistic formulation of the physical that satisfies the requirements any formulation of the physical is expected to fulfill. Following this proposal, we also have a recursive algorithm to recognize the set of all physical events. (shrink)

The rapid advancement of artificial intelligence has brought a host of new epistemological challenges. One particularly pressing question is whether, and to what extent, AI systems can serve as sources of epistemic goods. Can they effectively transmit knowledge or understanding? And if they do not possess these epistemic goods themselves, can they still generate them for human users? This article explores these questions by critically examining the constraints posed by counter-closure principles – epistemological principles that allegedly cast doubt on (...) the epistemic potential of AI. By addressing these principles, we aim to lay the groundwork for a systematic inquiry into the social epistemology of AI. (shrink)

Most solutions to the skeptical paradox about justified belief assume closure for justification, since the rejection of closure is widely regarded as a non-starter. I argue that the rejection of closure is not a non-starter, and that its problems are no greater than the problems associated with the more standard anti-skeptical strategies. I do this by sketching a simple version of the unpopular strategy and rebutting the three best objections to it. The general upshot for theories of (...) justification is that it is not a constraint on such theories that we must somehow have justification to believe that we are not massively deceived. (shrink)

Knowledge closure is the claim that, if an agent S knows P, recognizes that P implies Q, and believes Q because it is implied by P, then S knows Q. Closure is a pivotal epistemological principle that is widely endorsed by contemporary epistemologists. Against Knowledge Closure is the first book-length treatment of the issue and the most sustained argument for closure failure to date. Unlike most prior arguments for closure failure, Marc Alspector-Kelly's critique of (...) class='Hi'>closure does not presuppose any particular epistemological theory; his argument is, instead, intuitively compelling and applicable to a wide variety of epistemological views. His discussion ranges over much of the epistemological landscape, including skepticism, warrant, transmission and transmission failure, fallibilism, sensitivity, safety, evidentialism, reliabilism, contextualism, entitlement, circularity and bootstrapping, justification, and justification closure. As a result, the volume will be of interest to any epistemologist or student of epistemology and related subjects. (shrink)

The principle of epistemic closure is the claim that what is known to follow from knowledge is known to be true. This intuitively plausible idea is endorsed by a vast majority of knowledge theorists. There are significant problems, however, that have to be addressed if epistemic closure – closed knowledge – is endorsed. The present essay locates the problem for closed knowledge in the separation it imposes between knowledge and evidence. Although it might appear that all that stands (...) between knowing the truth of the premises of a valid inference and knowledge of its conclusion is inferring it from the premises, the evidence for each of the premises may jointly count against the conclusion. The intuitive view regarding inferred knowledge says one thing, the evidence says another. One epistemological framework that seems to have the resources to resolve this tension endorses the view that knowledge always requires conclusive evidence. A second framework resolves the tension by limiting the scope of the closure principle. Only inferences drawn directly from propositions contained in the scope of a single knowledge operator are considered closed. The aim of the present essay is to revive the unpopular third option, the idea that knowledge is open. The essay proceeds by arguing that in different ways the two former frameworks only succeed in relocating the problem, not in resolving it. The first framework, the infallibilist view, relocates the problem to a sharp separation between knowledge of the occurrences of events from knowledge of their chance of occurring, a separation leading to several significant additional problems. The fallibilist view, the second framework, in endorsing closure neglects to take into full account the ways in which evidence fails to be transitive. For instance, evidence can count in favor of a conjunction while counting against each of its conjuncts. This fact, which is argued for in the essay on probabilistic as well as non-probabilistic grounds, is used as the foundation of an argument against closed knowledge that can be used as a way to understand several of the most fundamental challenges of epistemology. Not only can an open knowledge view that is based on open evidence resolve all these problems in a simple and natural way, it can also respond to formidable challenges that significantly hinder other open knowledge views. There are good reasons, then, to view both knowledge and evidence as open. (shrink)

Information processing in neural systems can be described and analyzed at multiple spatiotemporal scales. Generally, information at lower levels is more fine-grained but can be coarse-grained at higher levels. However, only information processed at specific scales of coarse-graining appears to be available for conscious awareness. We do not have direct experience of information available at the scale of individual neurons, which is noisy and highly stochastic. Neither do we have experience of more macro-scale interactions, such as interpersonal communications. Neurophysiological evidence (...) suggests that conscious experiences co-vary with information encoded in coarse-grained neural states such as the firing pattern of a population of neurons. In this article, we introduce a new informational theory of consciousness: Information Closure Theory of Consciousness (ICT). We hypothesize that conscious processes are processes which form non-trivial informational closure (NTIC) with respect to the environment at certain coarse-grained scales. This hypothesis implies that conscious experience is confined due to informational closure from conscious processing to other coarse-grained scales. Information Closure Theory of Consciousness (ICT) proposes new quantitative definitions of both conscious content and conscious level. With the parsimonious definitions and a hypothesize, ICT provides explanations and predictions of various phenomena associated with consciousness. The implications of ICT naturally reconcile issues in many existing theories of consciousness and provides explanations for many of our intuitions about consciousness. Most importantly, ICT demonstrates that information can be the common language between consciousness and physical reality. (shrink)

In this paper I offer a model-theoretic interpretation of Autonomy Theory as defended by Moreno, Mossio, Montévil, and Bich. I address accusations that Autonomy Theory is excessively liberal, such as those made by Garson (2017), arguing that these misunderstand the role of strategic abstractions and generalizations in theory construction. Conceiving of closure of constraints as a model-building effort that emphasizes generality—in the spirit of Levins (1966)—also clarifies its potential for application in empirical contexts.

In response to the claim that certain epistemically defective inferences such as Moore’s argument lead us to the conclusion that we ought to abandon closure, Crispin Wright suggests that we can avoid doing so by distinguishing it from a stronger principle, namely transmission. Where closure says that knowledge of a proposition is a necessary condition on knowledge of anything one knows to entail it, transmission makes a stronger claim, saying that by reasoning deductively from known premises one can (...) thereby acquire knowledge of or justification for the conclusion. Wright’s thought is that in cases such as Moore what is really going on is a failure of transmission, not a failure of closure. The problem with this claim is that it relies on an outdated formulation of closure which few nowadays would find plausible. Once we stipulate that it is the intuitive closure principle that deserves our attention, it becomes far less obvious that the project of diagnosing what is wrong with arguments such as Moore in terms of transmission failure but not closure failure can be vindicated. In order to demonstrate this claim, I consider intuitive closure of propositional justification vs. transmission of propositional justification and concede that perhaps these can come apart in the way that Wright suggests. I then argue that despite this concession, we also need an answer to the question of whether intuitive closure for doxastic justification and transmission for doxastic justification can come apart. We need an answer to this question because our ultimate interest in these issues stems from our interest in whether knowledge obeys closure, not merely whether propositional justification does. I argue that, even on the assumption that there is transmission failure of propositional justification, there is no transmission failure of doxastic justification. And if this is true, then there is no transmission failure of knowledge either. The transmission failure diagnosis of Moore’s argument and its ilk is thus in trouble. (shrink)