Some of the most interesting recent work in philosophy of language and metaphysics is focused on questions about propositions, the abstract, truth-bearing contents of sentences and beliefs. The aim of this guide is to give instructors and students a road map for some significant work on propositions since the mid-1990s. This work falls roughly into two areas: challenges to the existence of propositions and theories about the nature and structure of propositions. The former includes both a widely discussed puzzle about (...) propositional designators as well as direct and indirect arguments against the existence of propositions. The latter is dominated by what is currently the central debate about the metaphysics of propositions, i.e. whether they are structured, composite entities or unstructured ontological simples. This issue has eclipsed older debates about whether propositions can be identified with sets of possible worlds or other kinds of sentence intensions. Author Recommends 1. Soames, Scott. 'Direct Reference, Propositional Attitudes, and Semantic Content.' Philosophical Topics 15 (1987): 47–87. Reprinted in Propositions and Attitudes . Eds. N. Salmon and S. Soames. Oxford: Oxford University Press, 1988. 197–239. Essential groundwork for more recent work on propositions. Soames gives a careful and exacting presentation of the case against identifying propositions with sets of possible worlds or other truth-supporting circumstances. Also contains a detailed statement of the Russellian conception of propositions on which propositions are ordered sets of objects, properties and relations. 2. King, Jeffrey. 'Designating Propositions.' The Philosophical Review 111 (2002): 341–71. Sometimes substituting a definite description for a corresponding 'that'-clause can lead to bizarre changes in truth-conditions: compare 'Bill fears that Hillary will be president' with 'Bill fears the proposition that Hillary will be president'. This puzzle about propositional designators threatens the relational analysis of propositional attitude reports, the view that 'believes' expresses a relation to the proposition designated by its 'that'-clause, and thereby poses an indirect threat to the existence of propositions. King's solution posits an ambiguity in verbs like 'fear' that embed both 'that'-clauses and definite descriptions. 3. Jubien, Michael. 'Propositions and the Objects of Thought.' Philosophical Studies 104 (2001): 47–62. A direct attack on the existence of propositions. Jubien deploys an analogue of the problem that Paul Benacerraf raised for set-theoretical reductions of numbers against metaphysical reductions of propositions. Just as numbers can be reduced to sets in many different ways, any reduction of propositions brings with it equally good variants, thus making any such reduction arbitrary and unmotivated. The only alternative is to treat propositions as abstract metaphysical primitives. As Jubien argues, however, abstract primitive entities are incapable of doing what propositions must do, i.e. represent objects and states of affairs on their own, without the input of thinking subjects. The upshot is the propositions cannot be reduced and they cannot be primitive, and so they must not exist. 4. Hanks, Peter. 'How Wittgenstein Defeated Russell's Multiple Relation Theory of Judgment.' Synthese 154 (2007): 121–46. Scepticism about propositions has recently led some philosophers, Jubien included, to resuscitate Russell's multiple relation theory of judgment, the idea that judgment is a many-place relation to objects, properties and relations. This paper explains why Russell himself abandoned that theory, and why the theory is still refuted by an objection due to Wittgenstein. 5. Hofweber, Thomas. 'Inexpressible Properties and Propositions.' Oxford Studies in Metaphysics . 2 vols. Ed. D. Zimmerman. Oxford: Oxford University Press, 2006. 155–206. An indirect attack on the existence of propositions. Hofweber argues that sentences like 'Bill believes something that Hillary asserted' do not commit us to the existence of propositions. His view is that propositional quantification is an instance of what he calls 'internal' or 'inferential role' quantification, a kind of quantification that carries no ontological implications. 6. Schiffer, Stephen. The Things We Mean . Oxford: Oxford University Press, 2003. esp. chs 1–2. Schiffer defends his theory of pleonastic propositions, on which propositions are unstructured, have no parts, and are very finely grained. 7. Bealer, George. 'Propositions.' Mind 107 (1998): 1–32. Bealer defends his algebraic theory of propositions, which, like Schiffer's pleonastic account, treats propositions as unstructured metaphysical simples. 8. King, Jeffrey. The Nature of and Structure of Content . Oxford: Oxford University Press, 2007. The best developed current theory of the structure in structured propositions. King identifies propositions with certain kinds of facts in which objects, properties and relations are bound together by amalgams of syntactic and semantic relations. 9. Hanks, Peter. 'Recent Work on Propositions.' Philosophy Compass 4 (2009): 1–18. A survey of work on propositions since the mid-1990s that complements this teaching and learning guide. Contains responses to Jubien's and Hofweber's arguments against propositions and critical discussions of Schiffer's pleonastic propositions and King's theory of propositional structure. Online Resources 1. http://plato.stanford.edu/entries/propositions/ Propositions (Matthew McGrath) 2. http://plato.stanford.edu/entries/propositions-structured/ Structured Propositions (Jeffrey King) 3. http://plato.stanford.edu/entries/propositions-singular/ Singular Propositions (Greg Fitch) Sample Partial Syllabus The following partial syllabus can be used as a unit on recent work on propositions in graduate level courses in philosophy of language or metaphysics. Week 1: A Substitution Puzzle About Propositional Designators King, Jeffrey. 'Designating Propositions'. Moltmann, Friederike. 'Propositional Attitudes Without Propositions.' Synthese 135 (2003): 77–118. Week 2: The Benacerraf Problem and Propositional Representation Benacerraf, Paul. 'What Numbers Could Not Be.' Philosophical Review 74 (1965): 47–73. Jubien, Michael. 'Propositions and the Objects of Thought.' Week 3: Propositional Quantification Hofweber, Thomas. 'Inexpressible Properties and Propositions'. Hofweber, Thomas. 'A Puzzle about Ontology.' Noûs 39 (2005): 256–83. Week 4: Schiffer on Pleonastic Propositions Schiffer, Stephen. 'Language-Created Language-Independent Entities.' Philosophical Topics 24 (1996): 149–67. Schiffer, Stephen. The Things We Mean , chs 1–2. Week 5: King on Structured Propositions King, Jeffrey. 'Structured Propositions and Complex Predicates.' Noûs , 29 (1995): 516–35. King, Jeffrey. The Nature and Structure of Content , chs 1–3. Focus Questions 1. Why does identifying propositions with sentence intensions, e.g. sets of possible worlds, 'require the attitudes to have a particular sort of closure under logical consequence, which they clearly don't have' (Mark Richard)? 2. How does the difference between (a) and (b) pose a threat to the existence of propositions? (a) Bill fears that Hillary will be president. (b) Bill fears the proposition that Hillary will be president. 3. What is the Benacerraf problem for metaphysical reductions of propositions? 4. Why must a proposition represent 'on its own cuff' (Michael Jubien)? Why is this a problem for the view that propositions are primitive abstract entities? 5. What does it mean to say that propositions are structured ? Give two different accounts of what propositional structure might be. (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)

We give a syntactic characterization of (finitary) theories whose categories of models are closed under the formation of connected limits (respectively the formation of pullbacks and substructures) in the category of all structures. They are also those theories whose consistent extensions by new atomic facts admit in each component an initial structure (respectively an initial term structure), and also thoseT for whichM(T) is locally finitely multi-presentable in a canonical way. We also show that these two properties of theories are (...) nonuniform. (shrink)

We give syntactic characterizations of1. the theories whose categories of models are closed under the formation of pullbacks, and of2. the locally ω-polypresentable categories.A somewhat typical example is the category of algebraically closed fields. Case is proved by classical model-theoretic methods; it solves a problem raised by H. Volger . The solution of case is in the spirit of the ones for the locally ω-presentable and ω-multipresentable cases found by M. Coste and P.T. Johnstone respectively. The problem was raised (...) in the context of Domain Theory by F. Lamarche. (shrink)

Ecological psychology (EP) and the enactive approach (EA) may benefit from a more focused view of lived temporality and the underlying temporal multiscalar nature of human living. We propose multiscalar temporality (MT) as a framework that complements EP and EA, and moves beyond their current conceptualisation of timescales and inter-scale relationships in organism-environment dynamical systems. MT brings into focus the wide ranging and meshwork-like interdependencies at play in human living and the questions concerning how agents are intimately entangled in such (...) meshworks, utilising them as resources for skilful living. We develop a conceptual toolkit that highlights temporality: Firstly, we address lived temporality. We use a case study from psychotherapy to show how a person’s skilful engagement with the world is best described as adaptive harnessing of interdependencies of constraints residing across a wide range of timescales. We call this skill time-ranging. Secondly, the case study provides a proof of concept of the integration of an idiographic approach to human conversing and a more general theory of emergent organisation rooted in theoretical biology. We introduce the existing concept of constraint closure from theoretical biology and scale it up to human interactivity. The detailed conceptualisation of constraint interdependencies constitutes the backbone of the proposal. Thirdly, we present a heuristic mapping of what we call organising frames. The mapping guides the conceptualisation of the emergence of inter-scale relationships and serves as an epistemic tool that brings together nomothetic and idiographic approaches. Finally, we combine new ideas with re-interpretations of existing EP and EA concepts and elaborate on the need of a fresh new look at the implicit and sometimes missing conceptualisations of temporality in the EP and EA literature. (shrink)

We extend classical work by Janusz Czelakowski on the closure properties of the class of matrix models of entailment relations—nowadays more commonly called multiple-conclusion logics—to the setting of non-deterministic matrices (Nmatrices), characterizing the Nmatrix models of an arbitrary logic through a generalization of the standard class operators to the non-deterministic setting. We highlight the main differences that appear in this more general setting, in particular: the possibility to obtain Nmatrix quotients using any compatible equivalence relation (not necessarily a congruence); (...) the problem of determining when strict homomorphisms preserve the logic of a given Nmatrix; the fact that the operations of taking images and preimages cannot be swapped, which determines the exact sequence of operators that generates, from any complete semantics, the class of all Nmatrix models of a logic. Many results, on the other hand, generalize smoothly to the non-deterministic setting: we show for instance that a logic is finitely based if and only if both the class of its Nmatrix models and its complement are closed under ultraproducts. We conclude by mentioning possible developments in adapting the Abstract Algebraic Logic approach to logics induced by Nmatrices and the associated equational reasoning over non-deterministic algebras. (shrink)

Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological T0-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated from the index set of Y by a recursively enumerable set, if X (...) intersects the topological closure of an effectively enumerable subset of Y. As a consequence of a more general parametric inseparability result a theorem of Rice-Shapiro type is obtained. Moreover, under some additional requirements it follows that nonopen subsets have productive index sets. This implies a generalized Rice theorem: Connected spaces have only trivial completely recursive subsets. As application some decision problems in computable analysis and domain theory are studied. It follows that the complement of the halting problem can be reduced to the problem to decide of a number whether it is a computable irrational. The same is true for the problems to decide whether two numbers are equal, whether one is not greater than the other, and whether a number is equal to a given number. In the case of an effectively given continuous complete partial order the complexity of the last problem depends on whether the given element is the smallest element, in which case the complement of the halting problem is reducible to it, whether it is a base element and maximal, then the decision problem is recursively isomorphic to the halting problem, or whether it is none of these. In this case, both the halting problem and its complement are reducible to the problem. The same is true in nontrivial cases for the problems whether an element belongs to the basis, whether two elements of the partial order are equal, or whether one approximates the other. In general, for any nonempty proper subset of the partial order either the halting problem or its complement can be reduced to the membership problem of the subset. (shrink)

A prominent class of arguments for external world skepticism rely on the plausible view that knowledge is closed under logical entailment. From the fact that one does not know that one is not a handless brain in a vat it can be inferred that one does not know that one has hands, in virtue of the fact that having hands logically entails that one is not a handless brain in a vat. The complements of knowing-how ascriptions, however, are not—obviously, (...) at least—related by logical entailment to any proposition, and therefore, they resist that skeptical argument. Even if I don’t know that I am not a brain in a vat, it does not follow that I don’t know how to, say, play a drum rudiment. Thus, knowing-how can withstand closure-based skepticism about the external world. (shrink)

Nowadays, it is frequently seen that theology education is criticized over secularism or piety concerns. In fact, it has recently been observed that those who have opposed the existence of the theology faculties within the university system for religious reasons have tried to make their voices heard on different platforms, especially on social media. The discussions conducted on different platforms mostly run without a scientific basis. The aim of this study is to determine the views of theology faculty students with (...) regard to the studying on campus and to contribute to the structure of the evaluations on higher religious education-university dilemma on a scientific basis. Metaphor technique was used for data collection. Data were collected in April 2019 using open-ended questions from 228 sophomore, junior, or senior students at Faculty of Theology in Zonguldak Bülent Ecevit University. Content analysis and chi-square technique were used in the data analysis. The research revealed that the majority of students (%73, 2) produced positive metaphors for studying theology on campus. Students mostly explain the positive experience of studying on campus through the possibility of growing up as a well-equipped theologian, recognizing real-life, and representing religion. It was also determined that the students who completed the associate degree and continued theology faculty highlighted the positive aspects of theology education on campus.Summary: While higher education throughout history has been undertaken by madrasas in the East and monastic schools in the West, it has been represented by the modern university in the last two centuries. The madrasas and monastic schools were religious institutions in terms of aims, epistemological and pedagogical understanding, institutional structures, and the lifestyle they produced. The aim of these institutions, which are subordinate to religious authority, was to educate the man on behalf of God while giving this education in accordance with the religion. The university, which replaces madrasas and monastic schools, was not different from the tradition of madrasas and monastic schools when it was first established. The first universities and colleges that were accepted as the ancestors of the well-established universities in the West were schools established for religious purposes. Indeed, many of the western universities established in the past for religious purposes continue their administrative and financial ties with the church. On the other hand, after enlightenment, education has ceased to be a business of religious institutions, and national states have established modern universities to train people suitable for their own needs. The modern university that is positivist and rationalist reveals information to educate people and to perfect society in the name of the state and the economy, not for the God. Research shows that both universities that maintain their ties with the church and state universities participate in the secularization process deeply. Nevertheless, religion continues to exist in different forms at universities, which is much more intense at universities that continue their connection with the church. In addition to the theology and religious studies programs, religion finds a place in the modern university campus through accredited student organizations, campus priests and preachers, social organizations, etc.When Darülfünun (Dār al-Fünūn) the first example of a modern university was established in Turkey in 1900, theology faculty became one of the three faculties. However, whether a modern university is a suitable place for higher religious education has been a controversial issue. In 1915, theology faculty was removed from the university system, then re-established in the university again in 1924, and in 1933, theology education was terminated due to the discussions of modernization. In 1949, the theology faculty was reintroduced at the university; and after 1959, High Islamic Institutes were established under the Ministry of National Education. The inclusion of religious education in the university has been one of the issues that frequently occupy the agenda until 1982, when all higher religious education institutions were included in the university system. In these discussions, the interesting thing is that religious people insist on being included in the university system although various groups oppose in the name of secularism principle. Even more interesting is that there are still demands for higher religious education outside the university, although the number of theology faculties has increased in recent years. In order to make the madrasas to be function as an alternative or complement to theology faculty, they claim that the theology degree completion program or open theology program must be expanded. In fact, it has recently been observed that those who have opposed the existence of the theology faculties within the university system for religious reasons have tried to make their voices heard on different platforms, especially on social media. Those who make such claims, claim that the university is not a suitable place for religious education in terms of epistemology, pedagogy, and social life.This study aims to determine the views of theology faculty students with regarding to the studying on campus and to contribute to the structure of the evaluations on higher religious education-university dilemma on a scientific basis. Within this framework, three basic questions were investigated: (i) Do students highlight positive or negative aspects of theology education on campus? (ii) What kind of experiences are reflected on the positive or negative aspects of theology education on campus from the metaphors? (iii) Is there any difference among the metaphors of the students according to the gender and enrolling types to the faculty (university entrance exam or vertical transfer exam and non-exam enrolling system)? Metaphor technique was used for data collection. Data were collected in April 2019 using open-ended questions from 228 sophomore, junior, or senior students at Faculty of Theology in Zonguldak Bülent Ecevit University. Content analysis and chi-square technique were used in the data analysis.The research revealed that the majority of students (%73, 2) produced positive metaphors for theology education on campus. Students mostly explain the positive experience depending on the possibility of growing up as a well-equipped theologian, experiencing real-life, and representing religion. Among the reasons of the negative metaphor producers, the degenerative effect of the campus environment, the exclusion, and the desire to study in a religious environment come to the fore. It was also determined that the students who completed the associate degree and continued theology faculty highlighted the positive aspects of theology education on campus. Consequently, results show strong student support for theology education at university.In our opinion, it is possible to interpret the recent debates on the inclusion of theology faculties within the university system through the general tendencies of religious people who encounter modernism. In this regard, the results provide important clues. Religious people who encounter modernism generally preferred one of the following three ways: ghetto closure, conflict with the modern, seeking a consensus-based way to continue to touch the life of modern people with the message of religion over time and space. While those who prefer ghettos and conflict reject everything that is modern, those who are accommodating seek ways to keep religion together with modern people and institutions despite some risks. Results show that most of the theology students consider the university as a place that offers opportunities for religious education despite the secular and sometimes challenging environment of the campus. This means that they have a strong self-confidence in the beauty that religion can bring to modern life and modern people. (shrink)

The scientific study of consciousness, also referred to as consciousness science, is a young scientific field devoted to understanding how conscious experiences and the brain relate. It comprises a host of theories, experiments, and analyses that aim to investigate the problem of consciousness empirically, theoretically, and conceptually. This thesis addresses some of the questions that arise in these investigations from a formal and mathematical perspective. These questions concern theories of consciousness, experimental paradigms, methodology, and artificial consciousness. -/- Regarding theories of (...) consciousness, the thesis contributes to the understanding of the mathematical structure that some of the formal theories in the field propose. The work presented here targets the theory of consciousness known as Integrated Information Theory (IIT) and the neuroscientific theory known as Predictive Processing Theory or Free Energy Principle in its Active Inference form (AI-PP). The thesis provides axiomatic definitions of the mathematical structures that constitute these theories, and uses these definitions to address some of the open questions surrounding the theories. For AI-PP, this includes a rigorous derivation of the formula for Active Inference via Free Energy minimisation and a proof of compositionality of Free Energy. For IIT, this includes resolutions of some of the criticisms of IIT's formal scope and applications, but also the identification of new issues that concern the formalism and its derivation. When possible, the definitions are provided in the mathematical framework of category theory. -/- Regarding experiments, the thesis addresses the main paradigm for testing and falsifying theories of consciousness currently applied in the field. This paradigm consists of comparing the conscious experience that a theory predicts with the conscious experience that is inferred from behavioural data or report by use of measures of consciousness. The thesis provides a formal model of this paradigm and shows that under a certain condition—if inference and prediction are independent—, any minimally informative theory of consciousness can always be falsified. This is deeply problematic since the field’s reliance on report or behaviour to infer conscious experiences, in conjunction with the general structure of most contemporary theories of consciousness, implies such independence. This observation provides the exact formal underpinning of the well-known unfolding argument. The thesis analyses the origin of the problem and identifies precisely which changes are required to avoid this problem in future research. The thesis furthermore shows that the problem of falsifying theories of consciousness, and of empirical comparisons of theories of consciousness more generally, follows from a pervasive closure paradigm in consciousness science, that consists of taking a neuroscientific account of the brain as input to a theory of consciousness, so as to explain what consciousness is, without allowing for modifications or adaptations of the neuroscientific account that would accommodate consciousness as part of the brain's functioning. As is shown in the thesis, this paradigm has implications that point to a fundamental need of revision. -/- Regarding methodological and conceptual questions, the thesis contributes to the foundations of structural research in consciousness science. Structural research aims to use mathematical structures or mathematical spaces, instead of verbal descriptions or simple categorisations, to represent conscious experiences scientifically, for example when building theories of consciousness, or when exploring new empirical avenues to measure consciousness. Despite considerable advances in this realm, there was, prior to this thesis, no explicit definition of what a mathematical structure of conscious experience should be; that is, how the attribution of mathematical structure to conscious experiences should be systematically understood. Perhaps the most important contribution of this thesis to the field is to propose such a definition. The definition, a structural concept, extends existing approaches wherever available, and provides a basis for developing a common formal language to study consciousness, bridging developments as far apart as psychophysics and phenomenology. In addition, and independently of this proposal, the thesis offers a critical analysis of which metaphysical premises need to be presumed in structural research, whether the use of particular formal tools (such as structure-preserving mappings or homomorphisms) is justified, and how structural theories of consciousness could otherwise be built in the first place. An attempt to expand the results from consciousness to more general problems in philosophy of science is made in the context of the well-known Newman problem. -/- Regarding the question of artificial consciousness—can AI feel?—, the thesis contributes two results that take the form of no-go theorems, as known from physics. The first no-go theorem shows that if consciousness is relevant for the temporal evolution of a system's states—if it is dynamically relevant—, then contemporary AI systems cannot be conscious. That is because AI systems run on CPUs, GPUs, TPUs or other processors which have been designed and verified to adhere to computational dynamics that systematically preclude or suppress deviations. The second no-go theorem is situated in the context of computational functionalism, a view which posits that consciousness is a computation. The theorem shows that if computational functionalism holds true, consciousness cannot be a Turing computation. Rather, it must be a novel type of computation that has recently been proposed by Geoffrey Hinton, called mortal computation. -/- This thesis is part of a global effort to pioneer a mathematical perspective in consciousness science, now called Mathematical Consciousness Science. The hope behind the research carried out in this PhD is to illustrate the power and usefulness of mathematical approaches in different areas of consciousness science, and in doing so, to lay the foundations for future mathematical work that complements and supports empirical and theoretical work in the further development of this exciting field. (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)

The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori knowable, then the consequent is a priori knowable as well. This principle is arguably correct under certain conditions, but there is at least one counterexample when completely unrestricted. To deal with this, Anderson proposes to restrict the closure principle to necessary truths and Horsten (...) suggests to restrict it to formulas that belong to less expressive languages. In this article it is argued that Horsten’s restriction strategy fails, because one can deduce that knowable ignorance entails necessary ignorance from the closure principle and some modest background assumptions, even if the expressive resources do not go beyond those needed to formulate the closure principle itself. It is also argued that it is hard to find a justification for Anderson’s restricted closure principle, because one cannot deduce it even if one assumes very strong modal and epistemic background principles. In addition, there is an independently plausible alternative closure principle that avoids all the problems without the need for restriction. (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)

Consciousness frameworks operate on systems already treated as bounded units of analysis. Each major framework has a formal entry point at which a candidate space — a region of physical substrate treated as supporting candidate partitions — must be specified for the framework's operations to be defined. The candidate space is not produced by the framework's apparatus; it is presupposed at the point where the apparatus becomes applicable. The paper identifies this structural feature — candidate-space dependence — in three major (...) consciousness frameworks (Integrated Information Theory, Global Workspace Theory, the Free Energy Principle) and distinguishes it from the individuation question taken up in a companion gateway. Candidate-space dependence implicates a formation question distinct from the questions consciousness frameworks have organized themselves around: under what conditions does a region of physical reality come to constitute a candidate space at all? The Identology corpus develops the formation question through a paper sequence — Constraint Topology and the Precedence of Systemhood V2, Closure Formation as Admissible Instability, Basin Genesis, Consolidation, and Closure Before Bearers — that characterizes the structural conditions for closure formation through a three-stage dependency: landscape admissibility, coupling admissibility, and closure activation. The paper does not redevelop that apparatus; it identifies the dependency structure, places the corpus's apparatus in methodological alignment with the universality-class discipline developed in critical phenomena, and clarifies the corpus's two-doorway approach to closure under maintenance: formation and individuation as complementary entry points. The contribution is positional rather than constructive: the diagnosis specifies conditions of applicability rather than critiquing framework content, and the formation question is identified as prior to the questions consciousness frameworks have asked. (shrink)

It is well known that in Bishop-style constructive mathematics, the closure of the union of two subsets of ℝ is ‘not’ the union of their closures. The dual situation, involving the complement of the closure of the union, is investigated constructively, using completeness of the ambient space in order to avoid any application of Markov's Principle.

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)

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)

Through contact algebras we study theories of mereotopology in a uniform way that clearly separates mereological from topological concepts. We identify and axiomatize an important subclass of closure mereotopologies called unique closure mereotopologies whose models always have orthocomplemented contact algebras , an algebraic counterpart. The notion of MT-representability, a weak form of spatial representability but stronger than topological representability, suffices to prove that spatially representable complete OCAs are pseudocomplemented and satisfy the Stone identity. Within the resulting class of (...) contact algebras the strength of the algebraic complementation delineates two classes of mereotopology according to the key ontological choice between mereological and topological closure operations. All closure operations are defined mereologically if and only if the corresponding contact algebras are uniquely complemented while topological closure operations highly restrict the contact relation but allow not uniquely complemented and nondistributive contact algebras. Each class contains a single ontologically coherent theory that admits discrete models. (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 paper, I address the problem wherein the same English word permits one of its complement positions to be satisfied by phrases of different categories. A well-known example of such an English word is the copula to be, whose complements include adjective phrases, noun phrases, prepositional phrases and adverbial phrases. I provide a way to treat such words, in particular verbs, as single lexical items through a conservative extension of the usual treatment of word classification as a pair comprising (...) a part of speech category and a complement list. I then show how a further conservative extension of complement lists permits a satisfactory formalization of doubly complemented English verbs which are synonymous under a permutation of their complements. These verbs include, but are not limited to, so-called double object constructions. (shrink)

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)

Identology is a formal framework addressing the structural conditions underlying identity persistence and consciousness. Its central claim is that the field of consciousness studies has presupposed a bounded, persistence-capable unit without deriving the conditions under which such a unit exists—and that closure under maintenance is the missing foundational predicate. -/- Closure is defined as boundary-precondition coupling: a binary condition in which a configuration’s internal dynamics either sustain the individuating boundary conditions or they do not. Maintenance is (...) scalar: it varies in cost, depth, and regime across systems and across time. Consciousness is the regime in which a closure-maintained system’s identity-preserving dynamics become recursively self-conditioned—not a substance added to the system, not an emergent property layered on top, but the same dynamical process described under a different aspect. -/- This status report consolidates nineteen individual papers from a corpus of approximately fifty modular papers – the collection available at ORCID - into a single citable reference. It declares the framework’s operating invariants, maps its upstream dependencies and downstream consequences for existing frameworks, specifies the open research fronts where the framework is explicitly incomplete, and provides a dependency architecture of the corpus itself. It is designed as a navigational hub: every claim points outward to the paper that establishes it. (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)

Justification logics provide frameworks for studying the fine structure of evidence and justification. Traditionally, these logics do not impose any closure requirements on justification. In this paper, we argue that for some applications they should subject justification to closure under some variety of logical consequence. Specifically, we argue, building on ideas from Beall, that the non-classical logic FDE offers a particularly attractive notion of consequence for this purpose and define a justification logic where justification is closed (...) class='Hi'>under FDE consequence. We show the resulting logic to be sound and complete. Lastly, we discuss how the closure of justification under FDE ontrasts closure under related non-classical logics and how our approach contrasts with some alternatives. (shrink)

In this paper, we prove that the lattice of all closure operators of a complete Almost Distributive Lattice L with fixed maximal element m is dual atomistic. We define the concept of a completely meet-irreducible element in a complete ADL and derive a necessary and sufficient condition for a dual atom of Φ (L) to be complemented.

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)

Philosophers have long debated ‘substrate’ and ‘bundle’ theories as to how properties hold together in objects ― but have neglected to consider that every chemical entity is defined by closure of relationships among components ― here designated ‘Closure Louis de Broglie.’ That type of closure underlies the coherence of spectroscopic and chemical properties of chemical substances, and is importantly implicated in the stability and definition of entities of many other types, including those usually involved in philosophic discourse (...) ― such as roses, statues, and tennis balls. Characteristics of composites are often presumed to ‘supervene on’ properties of components. This assumption does not apply when cooperative interactions among components are significant. Once correlations dominate, then adequate descriptions must involve different entities and relationships than those that are involved in ‘fundamental-level’ description of similar but uncorrelated systems. That is to say, descriptions must involve different semantics than would be appropriate if cooperative interactions were insignificant. This is termed ‘Closure Henri Poincaré. Networks of chemical reactions that have certain types of closure of processes display properties that make other more-complex coherences possible. This is termed ‘Closure Jacques Cauvin.’ Each of these three modes of closure provides a sufficient basis for warranted recognition of causal interaction, thus each of them has epistemological significance. Other modes of epistemologically-important closure probably exist. It is important to recognize that causal efficacy generally depends on closure of relationships of constituents. (shrink)

Single-premise epistemic closure is the principle that: if one is in an evidential position to know that P where P entails Q, then one is in an evidential position to know that Q. In this paper, I defend the viability of opposition to closure. A key task for such an opponent is to precisely formulate a restricted closure principle that remains true to the motivations for abandoning unrestricted closure but does not endorse particularly egregious instances of (...) closure violation. I focus on two brands of epistemic theory that naturally incorporate closure restrictions. The first type holds that the truth value of a knowledge ascription is relative to a relevant question. The second holds that the truth value of a knowledge ascription is relative to a relevant topic. For each approach, I offer a formalization of a leading theory from the literature and use this formalization to evaluate the theory’s adequacy in terms of a precise set of desiderata. I conclude that neither theory succeeds in meeting these desiderata, casting doubt on the viability of the underlying approaches. Finally, I offer a novel variant of the topic-sensitive approach that fares better. (shrink)

Epistemic closure under known implication is the principle that knowledge of "p" and knowledge of "p implies q", together, imply knowledge of "q". This principle is intuitive, yet several putative counterexamples have been formulated against it. This paper addresses the question, why is epistemic closure both intuitive and prone to counterexamples? In particular, the paper examines whether probability theory can offer an answer to this question based on four strategies. The first probability-based strategy rests on the accumulation (...) of risks. The problem with this strategy is that risk accumulation cannot accommodate certain counterexamples to epistemic closure. The second strategy is based on the idea of evidential support, that is, a piece of evidence supports a proposition whenever it increases the probability of the proposition. This strategy makes progress and can accommodate certain putative counterexamples to closure. However, this strategy also gives rise to a number of counterintuitive results. Finally, there are two broadly probabilistic strategies, one based on the idea of resilient probability and the other on the idea of assumptions that are taken for granted. These strategies are promising but are prone to some of the shortcomings of the second strategy. All in all, I conclude that each strategy fails. Probability theory, then, is unlikely to offer the account we need. (shrink)

Dorsal closure (DC), the closure of a hole in the dorsal epidermis of Drosophila embryos by the joining of opposing epithelial cell sheets, has been used as a model process to study the molecular and cellular mechanisms underlying epithelial spreading and wound healing. Recent studies have provided novel insights into how different tissues function cooperatively in this process. Specifically, they demonstrate a critical function of the epidermis surrounding the hole in modulating the behavior of the amnioserosa cells inside. (...) These findings shed light not only on the mechanisms by which the behavior of different tissues is coordinated during DC, but also on the general mechanisms by which tissues interact to trigger global morphogenesis, an essential but yet poorly explored aspect of embryogenesis. (shrink)

According to the principle of epistemic closure, knowledge is closed under known implication. The principle is intuitive but it is problematic in some cases. Suppose you know you have hands and you know that ‘I have hands’ implies ‘I am not a brain-in-a-vat’. Does it follow that you know you are not a brain-in-a-vat? It seems not; it should not be so easy to refute skepticism. In this and similar cases, we are confronted with a puzzle: epistemic (...) class='Hi'>closure is an intuitive principle, but at times, it does not seem that we know by implication. In response to this puzzle, the literature has been mostly polarized between those who are willing to do away with epistemic closure and those who think we cannot live without it. But there is a third way. Here I formulate a restricted version of the principle of epistemic closure. In the standard version, the principle can range over any proposition; in the restricted version, it can only range over those propositions that are within the limits of a given epistemic inquiry and that do not constitute the underlying assumptions of the inquiry. If we adopt the restricted version, I argue, we can preserve the advantages associated with closure, while at the same time avoiding the puzzle I’ve described. My discussion also yields an insight into the nature of knowledge. I argue that knowledge is best understood as a topic-restricted notion, and that such a conception is a natural one given our limited cognitive resources. (shrink)

The general principle of epistemic closure stipulates that epistemic properties are transmissible through logical means. According to this principle, an epistemic operator, say ε, should satisfy any valid scheme of inference, such as: if ε(p entails q), then ε(p) entails ε(q). The principle of epistemic closure under known entailment (ECKE), a particular instance of epistemic closure, has received a good deal of attention since the last thirty years or so. ECKE states that: if one knows that (...) p entails q, and she knows that p, then she knows that q. It is widely accepted that ECKE constitutes an important piece of the skeptical argument, but the acceptance of an unrestricted version of ECKE is still a matter of debate. On the side of the defenders of ECKE, one finds Stine (1976), Brueckner (1985), Vogel (1990), and Feldman (1995). Others proposed a refutation or a limitation of the principle, like Dretske (1970), Nozick (1981), Hales (1995), Williams (1996), and Sosa (1999). As it turns out, the relevant alternatives view (RAV) elaborated by Dretske, which restricts the scope of ECKE, has been discussed extensively and acknowledged as one of the most important contributions. There is nonetheless a major unsolved difficulty pertaining to Dretske-RAV: the notion of relevant alternatives is defined in such a way that it is bounded by counterfactual possibilities. This ontological import leaves open the door to the skeptic. Some have tried to give more precision to this notion, like Stine (1976), who appealed to a Gricean approach to define relevant alternatives in conversational contexts. My proposal is in accordance with the gist of Dretske’s strategy, i.e. to restrict the validity of ECKE, and I claim that in order to escape the difficulties inherent to RAV one has to introduce a more robust notion, the notion of epistemic context. Epistemic contexts are a subclass of propositional contexts. In that perspective, the closure property is expressed in terms of a property of a relation between epistemic contexts. ECKE holds when and only when either the epistemic context of the premisses is the same as the epistemic context of the conclusion, or the epistemic context change between the premisses and the conclusion is permissible. Permissibility of epistemic context change is a function of consistency. By means of this epistemic context approach, I will show that: (1) epistemic contexts are defined by basic propositions (unchallenged justified beliefs), (2) ECKE holds only under very specific constraints, and (3) the skeptical argument involves a non-permissible change of epistemic context and, by the same token, cannot rely upon ECKE. (shrink)

How should the contrastivist formulate closure? That is, given that knowledge is a ternary contrastive state Kspq (s knows that p rather than q), how does this state extend under entailment? In what follows, I will identify adequacy conditions for closure, criticize the extant invariantist and contextualist closure schemas, and provide a contrastive schema based on the idea of extending answers. I will conclude that only the contrastivist can adequately formulate closure.

According to Fred Dretske's externalist theory of knowledge a subject knows that p if and only if she believes that p and this belief is caused or causally sustained by the information that p. Another famous feature of Dretske's epistemology is his denial that knowledge is closed under known entailment. I argue that, given Dretske's construal of information, he is in fact committed to the view that both information and knowledge are closed under known entailment. Hence, if it (...) is true that, as Dretske also believes, accepting closure leads to skepticism, he must either embrace skepticism or abandon his information theory of knowledge. (shrink)

It is received wisdom that the skeptic has a devastating line of argument in the following. You probably think, he says, that you know that you have hands. But if you knew that you had hands, then you would also know that you were not a brain in a vat, a brain suspended in fluid with electrodes feeding you perfectly coordinated impressions that are generated by a supercomputer, of a world that looks and moves just like this one. You would (...) know you weren’t in this state if you knew you had hands, since having hands implies you are no brain in a vat. You obviously don’t know you’re not a brain in a vat, though—you have no evidence that would distinguish that state from the normal one you think you’re in. Therefore, by modus tollens, you don’t know you have hands. At least, the skeptic has a devastating argument, it is thought, if we grant him closure of knowledge under known implication, which many of us are inclined to do: roughly, if you know p, and you know that p implies q, then you know q. (shrink)

Epistemic closure refers to the assumption that humans are able to recognize what entails or contradicts what they believe and know, or more accurately, that humans’ epistemic states are closed under logical inferences. Epistemic closure is part of a larger theory of mind ability, which is arguably crucial for downstream NLU tasks, such as inference, QA and conversation. In this project, we introduce a new automatically constructed natural language inference dataset that tests inferences related to epistemic (...) class='Hi'>closure. We test and further fine tune the model RoBERTa-large-mnli on the new dataset, with limited positive results. (shrink)

Christoph Jäger has argued that Dretske’s information-based account of knowledge is committed to both knowledge and information closure under known entailment. However, in a reply to Jäger, Dretske defended his view on the basis of a discrepancy between the relation of information and the relation of logical implication. This paper shares Jäger’s criticism that Dretske’s externalist notion of information implies closure, but provides an analysis based on different grounds. By means of a distinction between two perspectives, the (...) mathematical perspective and the epistemological perspective, I present, in the former, a notion of logical implication that is compatible with the notion of information in the mathematical theory of information, and I show how, in the latter, Dretske’s logical reading of the closure principle is incompatible with his information-theoretic epistemological framework. (shrink)

Howard Robinson has criticized the contemporary revival of hylomorphism for, on the one hand, accepting the causal closure of the physical, while, on the other, ascribing a real and irreducible causal role to forms or structures. If the world is causally closed under physics, it makes no sense to postulate a structure that actively affects the distribution and motion of matter. After carefully formulating what I call Robinson’s causal closure argument against hylomorphism, I demonstrate that the argument (...) fails because it presupposes an overly strict conception of causal closure of the microphysical, according to which every physical effect is completely determined by, and has a complete explanation in terms of, bottom-level microphysical entities and their interactions governed by fundamental physical laws. Based on two case studies – one from physics (the Fractional Quantum Hall Effect), the other from microbiology (information control in microorganisms) – I argue that the argument fails, yet a more modest (and scientifically defensible) version of closure remains intact. This version of closure secures that no non-physical forces supplement the inventory of fundamental physics while allowing higher-level constraints to be causally efficacious by constraining which among multiple microphysically compatible possibilities is actualized. This means that a reformulated version of closure, capable of dealing with those cases, is also perfectly compatible with the hylomorphist (or generally anti-reductionist) claim that higher-level structures are causally efficacious and an irreducible part of physical reality. (shrink)

In his earlier writings, Fred Dretske proposed an anti-skeptical strategy that is based on a rejection of the view that knowledge is closed under known entailment. This strategy is seemingly congenial with a sensitivity condition for knowledge, which is often associated with Dretske’s epistemology. However, it is not obvious how Dretske’s early account meshes with the information-theoretic view developed in Knowledge and the Flow of Information. One aim of this paper is to elucidate the connections between these accounts. First (...) I argue that, contrary to an objection raised by Christoph Jäger, the information-theoretic account is compatible with Dretske’s anti-skeptical strategy based on the rejection of closure. This strategy invokes the notion of channel conditions, which are roughly speaking those conditions that are necessary and jointly sufficient for a signal to carry information. I propose an interpretation of the account that is based on the idea that a signal’s carrying information requires that the channel conditions are stable. It is shown that the resulting account incorporates both a sensitivity condition and a safety condition for knowledge. Finally, I demonstrate how this proposal allows for knowledge of modally robust propositions without making its acquisition too easy, as simple safety accounts do. I end with a suggestion concerning the direction that future research should take, based on the fact that in its present form the information-theoretic account does not capture inferential knowledge. (shrink)

This study examines whether Chinese complement coercion sentences with aspectual verbs will elicit processing difficulty during real-time comprehension.Complement coercionis a linguistic phenomenon in which certain verbs (e.g.,start, enjoy), requiring an event-denoting complement, are combined with an entity-denoting complement (e.g.,book), as inThe author started a book. Previous studies have reported that the entity-denoting complement elicited processing difficulty following verbs that require event argument compared with verbs that do not (e.g.,The author wrote a book). While the processing of complement coercion has been (...) extensively studied in Indo-European languages such as English and German, it is relatively under-researched in Sino-Tibetan languages such as Mandarin Chinese. Given the fact that there are many linguistic elements behaving distinctly in the different language families, for instance, verbs with respect to their semantic properties and syntactic representations of the complement, it is meaningful to investigate whether or not the existing linguistic differences have any effect on the processing of complement coercion in Mandarin. With this research goal, we recorded self-paced reading time of 61 native Mandarin speakers to investigate the processing of the entity-denoting complement in sentences with three different verb types (aspectual verbswhich require an event-denoting complement,preferred verbswhich denote a preferred interpretation of the aspectual expressions, andnon-preferred verbswhich denote a non-preferred but plausible interpretation of the aspectual expressions), as exemplified in 顾客开始/填写/查看这份问卷gù-kè kāi-shǐ/tián-xiě/chá-kàn zhè-fèn wèn-juàn“The customer started/filled in/checked the questionnaire.” It was found that the entity noun complement (e.g., 这份问卷zhè-fèn wèn-juàn“the questionnaire”) elicited significantly longer reading times in coercion sentences than non-coercion counterparts. The results are compatible with the previous findings in English that complement coercion sentences impose processing cost during real-time comprehension. The study contributes empirical evidence to coercion studies cross-linguistically. (shrink)

Graham and Maitzen think my CORNEA principle is in trouble because it entails “intolerable violations of closure under known entailment.” I argue that the trouble arises from current befuddlement about closure itself, and that a distinction drawn by Rudolph Carnap, suitably extended, shows how closure, when properly understood, works in tandem with CORNEA. CORNEA does not obey Closure because it shouldn’t: it applies to “dynamic” epistemic operators, whereas closure principles hold only for “static” ones. (...) What the authors see as an intolerable vice of CORNEA is actually a virtue, helping us see what closure principles should—and shouldn’t—themselves be about. (shrink)

Recent years saw the emergence of what some have called the hardest paradoxes for closure to date. These hybrid paradoxes combine features of the lottery and the preface paradox in a way that (i) puts pressure on the claim that justification is closed under conjunction (henceforth, simply closure) but (ii) resists familiar closure-preserving solutions previously put forward in response to the original paradoxes. This gives rise to the following question: can closure be saved from the (...) new hybrid paradoxes and, if so, how? This paper puts forward what is likely to be the most promising (general) strategy for solving the new paradoxes in a way that’s compatible with closure, considers the most prominent attempts to implement this strategy, but argues that they are ultimately unsuccessful. Hence, it’s concluded that the case against closure still stands. The paper also corrects some misconceptions about the nature of the hybrid paradoxes and weighs in on the question of what really is the hardest paradox for closure. (shrink)

It is well-known that versions of the lottery paradox and of the preface paradox show that the following three principles are jointly inconsistent: (Sufficiency) very probable propositions are justifiably believable; (Conjunction Closure) justified believability is closed under conjunction introduction; (No Contradictions) propositions known to be contradictory are not justifiably believable. This paper shows that there is a hybrid of the lottery and preface paradoxes that does not require Sufficiency to arise, but only Conjunction Closure and No Contradictions; (...) and it argues that, given any plausible solution to this paradox, if one is not ready to deny Conjunction Closure (and analogous consistency principles), then one must endorse the thesis that justified believability is factive. (shrink)

It is argued, on the basis of new counterexamples, that neither knowledge nor epistemic justification (or “epistemic rationality”) can reasonably be thought to be closed under logical implication. The argument includes an attempt to reconcile the fundamental intuitions of the opposing parties in the debate.