Closure Principle Research Articles

Freedom, Omniscience and the Contingent A Priori

Abstract One of the major challenges in the philosophy of religion is theological fatalism — roughly, the claim that divine omniscience is incompatible with free will. In this article, I present new reasons to be sceptical of what I consider to be the strongest argument for theological fatalism. First, I argue that divine foreknowledge is not necessary for an argument against free will if we take into account divine knowledge of contingent a priori truths. Second, I show that this argument can be generalized so that ordinary human knowledge of contingent a priori truths also leads to an argument against free will. This, I believe, results in an absurd conclusion that is unacceptable to both theists and non-theists. But if there is something wrong with this argument, there is something wrong, too, with the argument for theological fatalism. Although there is a range of possible responses, I suggest that the core issue in all cases is a closure principle — specifically, the principle that ‘no choice about’ is closed under entailment (or strict implication).

An eye-tracking-based investigation on the principle of closure in logo design

An eye-tracking-based investigation on the principle of closure in logo design

Using Eye Movement to Determine Whether Closed-Frame Shots Attract Viewers’ Attention

There is a large variety of photographic composition, and these compositions can illicit different visual and psychological responses in the audience. However, there is limited knowledge of the key factors in these compositions in photography that actually affect the viewing process, and also no empirical support for the relationship between emotional responses and visual cognition. This research applied eye-tracking to calculate the degree of fixation distribution in the process of viewing photographic works through the quantitative characteristics of fixation trajectory in the investigation of the influence of eye-movement information on closed and open image compositions. This research attempts to understand the psychological differences in viewing framed and unframed images and identify the crucial factors that affect the composition of photographic images. Results from the eye movement data found that closed text and photos displayed traits of the principle of closure, and that different compositions can significantly affect the fixation point and sightline distribution. Image compositions with property of closure tend to be more attractive, generating higher number of fixation and longer fixation duration, indicative of easier focus on the primary object in the picture frame and regulating the viewer’s field of view. Photographers try to make good use of frame composition to herd viewer focus as well as increase their interest, making their image composition as complete, concise, pleasant, and pleasurable to the eye, typically applied to landscape, still life or portrait photography. This study has the potential to become a reference that contributes to photography educational and visual communication.

A general consonance principle for closure tests based on -values.

The closure principle is a powerful approach to constructing efficient testing procedures controlling the familywise error rate in the strong sense. For small numbers of hypotheses and the setting of independent elementary -values we consider closed tests where each intersection hypothesis is tested with a -value combination test. Examples of such combination tests are the Fisher combination test, the Stouffer test, the Omnibus test, the truncated test, or the Wilson test. Some of these tests, such as the Fisher combination, the Stouffer, or the Omnibus test, are not consonant and rejection of the global null hypothesis does not always lead to rejection of at least one elementary null hypothesis. We develop a general principle to uniformly improve closed tests based on -value combination tests by modifying the rejection regions such that the new procedure becomes consonant. For the Fisher combination test and the Stouffer test, we show by simulations that this improvement can lead to a substantial increase in power.

Self-Calibration Method for Circular Encoders Based on Inertia and a Single Read-Head.

This article proposes a new self-calibration method for circular encoders based on inertia and a single read-head. The velocity curves of the circular encoder are fitted with polynomials and, based on the principle of circle closure and the periodicity of the distribution for angle intervals, the proportionality between the theoretical value and the actual value of each angle interval is obtained. In the experimental system constructed, the feasibility of the proposed method was verified through self-calibration experiments, repeatability experiments, and comparative experiments with the time-measurement dynamic reversal (TDR) method. In addition, this article also proposes an iterative method to improve the self-calibration accuracy. Experimental verification was carried out, and the results show that the new method can effectively compensate for the error of angle measurement in the circular encoder. The peak-to-peak value of the error of angle measurement was reduced from 239.343" to 11.867", and the repeatability of the calibration results of the new method was less than 2.77".

Safety’s coordination problems

The safety conception of knowledge holds that a belief constitutes knowledge iff relevantly similar beliefs—its epistemic counterparts—are true. It promises an instructive account of why certain general principles of knowledge hold. We focus on two such principles that anyone should endorse: the closure principle that knowledge is downward closed under competent conjunction elimination, and the counter-closure principle that knowledge is upward closed under competent conjunction introduction. We argue that anyone endorsing the former must also endorse the latter on pains of an unacceptable form of bootstrapping. We devise new formal models to identify necessary and sufficient conditions for these principles to hold on conceptions that construe knowledge in terms of true counterparts. These conditions state that counterparts of premise and conclusion beliefs are coordinated in certain ways whenever these beliefs stand in the relevant inferential relations. We show that the safety conception faces insuperable problems vindicating these coordination principles, because its epistemic counterpart relation is symmetric. We conclude that it thus proves unable to account for minimal closure properties of knowledge. More generally, our formal results establish parameters within which any conception must operate that construes knowledge in terms of true counterparts.

The online closure principle

The online closure principle

Human Face Reconstruction using Divine Proportions and Gestalt for Occluded Video Face Recovery in Forensic Analysis using Deep Learning

Forensic video analysis has been used in diverse kind of high-profile cases, global discrepancies, and conflict zones. It is a three-phase process of scientific examination, comparison, and evaluation of video in legal matters. Human face reconstruction using deep learning for occluded video face recovery to aid in forensic analysis is the main objective of this paper. Forensic facial reconstruction is a combination of both scientific methods and artistic skill. In this paper, we introduce a method to reconstruct human faces occluded due to short noise innight-time video clips. A skull database is created with unique skull models with varying shapes, forms and proportions. Human body mathematical model biometric using golden ratio algorithm is proposed and used to find the occluded face proportions. Closure principle of gestalt theory of visual perception is used to fill in the missing parts of a face design and to create a whole face image using gan. The proposed model is found to have 50% lesser reduced Median error rate and 20% reduced Stdev than PrNet and 10% lower Mean error rate than 3Dddfav2.

An Eye-Tracking Study on Viewer Compliance with the Gestalt Closure Principle: Analyzing the Impact of Gap Size and the Golden Ratio

Abstract The Gestalt principle of closure refers to brain activity filling in missing information to perceive objects as complete, even when partially hidden. Designers leverage this principle to imply shapes without explicitly showing them. However, evaluating viewer responses poses challenges. The author conducted a comprehensive eye-tracking experiment to determine when viewers mentally completed a gap in a circle and explored the potential influence of the golden ratio on the closure principle. The golden ratio, approximately 1.618, is associated with visual harmony and is used in art and design to create pleasing proportions. Findings showed that viewers tend to mentally close gaps up to 135° but avoid closure beyond 150°. This suggests the golden ratio’s relevance in applying the closure principle to design.

Safety, Closure, and Extended Methods

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.

For a Postmedial Image: The Challenge of Enunciation for the Digital Practices of the Contemporary Image

This paper aims to propose some suggestions on what role semiotic analysis of the visual can take in the postmediality environment. Taking a case study from the field of scientific research on biodiversity, that is, the INaturalist platform, what we wish to highlight is how, with the development of digital technologies and the proliferation of new practices of use related to visuality, the landscape of media has changed to such an extent that the need to revise certain semiotic categories developed from the principle of textual closure has become evident. Algorithms, datasets and computer vision technologies include images within complex and heterogeneous configurations in the realm of enunciation, which call for different planes of immanence beyond textuality that become particularly clear from the perspective of a material turn. Considered within the materiality of its substrate, a text becomes an object, and as an object it is included in a network of possible practices of use: scientific research represents in this sense a very accurate context for observing how digital visual texts, even in their apparent immateriality, display the process through which we do things with images.

The Fluid Margin between Physical Causal Closure and Non-Physical Causal Closure, extended to The Neutrosophic Causal Closure Principle

We plead for a fluid margin, or mixed/indeterminate buffer zone, between Physical and Non-Physical Causal Closures, and for a Neutrosophic Causal Closure Principle claiming that the chances of all physical effects are determined by their prior partially physical and partially non-physical causes.

Vibration mitigation using finite graded metamaterials: a rod with attached local resonators

The paper concerns the analysis of vibration transmission and mitigation in a finite rod performing axial vibrations with attached multiple damped resonators. The resonators are not assumed to be periodically spaced or to have similar dynamic properties. The behaviour is analysed in terms of waves travelling between the discontinuities. Reflection and transmission coefficients of the rod with one local resonator attached are utilised in the analysis. Values of these coefficients for each of the attached resonators, along with the boundary conditions and field transfer function, are used to derive analytical expressions for the displacement of the finite rod at any point. Once the displacement is determined, the transmission loss is calculated. Moreover, the eigenfrequencies of the graded metamaterial finite rod are identified using the phase closure principle. The influence of the mass, the damping and the location of the resonators on the vibration attenuation are investigated. Numerical examples are presented. Good agreement is noted between the results of the analytical studies and finite element simulations in COMSOL. It is shown that the graded metamaterial rod can provide better vibration attenuation as compared to the conventional periodic metamaterial.

Non-Factualist Interpretation of the Skeptical Solution and the Self-Refutation Argument

The skeptical solution is based on two assumptions — the rejection of semantic facts and the denial of semantic nihilism. On the basis of the non-factualist interpretation of this solution, these two assumptions are reconciled by stating that meaning ascriptions possess non-descriptive function. Nonetheless, Alexander Miller argues that this position is self-refuting since, as despite its non-descriptivism, by rejecting any kind of semantic facts, it inevitably leads to semantic nihilism. In this text, I demonstrate that Miller’s argument is not sound. I argue that a coherent non-factualist way of formulating the conditions of correct use of meaning ascriptions may be performed by rejecting the closure principle of assertibility of meaning ascriptions. On this basis, I demonstrate that argument formulated against non-factualist interpretation by Miller may be refuted. What is more, I argue that rejection of the closure principle should be regarded as the central aspect of Kripke’s skeptical solution.

Against the anti-closure response to the factivity problem for epistemic contextualism

It appears that there is an inconsistency in combining epistemic contextualism with a plausible closure principle for knowledge and the view that knowledge is factive. I discuss the proposal that in order to avoid inconsistency the contextualist should reject closure and retain factivity. The proposal offers an alternative to closure and an argument that warrant fails to transmit through inference in the relevant cases. I criticize both accounts. The proposed alternative to closure is not well motivated and leaves unresolved the question of why standard closure should not hold. The argument that warrant does not transmit is based on an inaccurate model of warrant transmission. An important lesson that emerges is that known propositions themselves can serve as warrant for further propositions, which may be known provided they are competently deduced from the former. Indeed it is arguably the factivity of knowledge that accounts for the fact that known propositions themselves serve as warrant. Thus, the strategy of rejecting closure while retaining factivity is a bad one not merely because the proposed alternatives to standard closure are inadequate and transmission failure in relevant cases would not imply closure failure, but because factivity ensures that warrant transmission worries in the relevant cases are unfounded.

The Mental Causality Exclusion Argument and the Levels of Organization of Living Objects

The paper aims to demonstrate the possibility of consistently accepting the existence of effective mental causality in the fundamentally physical world. We suppose that the concept of causality in J. Kim’s exclusion argument against mental causation, which implies а generative conception of causal relations, can be revised taking into account the specificity of the multilevel organization of living objects. Rejection of the mechanistic model of causality as a linear process, allows you to maintain commitment to the principle of causal closure of the physical world and at the same time explain how top-down causality at the macro level is possible. For this, we use the model of a fractal tree of causal chains by J. Lowe, in which mental causality plays the role of an indirect cause of a fact. We carry out a meaningful distinction between the causality of facts and events by resorting to the multilevel model of J. Ellis, in which mental causality can be considered as a macro-level fact that has a selective effect on physical events of lower levels, taking into account a wide environmental context.

A Defense of Explanationism against Recent Objections

Abstract In the recent literature on the nature of knowledge, a rivalry has emerged between modalism and explanationism. According to modalism, knowledge requires that our beliefs track the truth across some appropriate set of possible worlds. Modalists tend to focus on two modal conditions: sensitivity and safety. According to explanationism, knowledge requires only that beliefs bear the right sort of explanatory relation to the truth. In slogan form: knowledge is believing something because it's true. In this paper, we aim to vindicate explanationism from some recent objections offered by Gualtiero Piccinini, Dario Mortini, and Kenneth Boyce and Andrew Moon. Together, these authors present five purported counterexamples to the sufficiency of the explanationist analysis for knowledge. In addition, Mortini devises a clever argument that explanationism entails the violation of a plausible closure principle on knowledge. We will argue that explanationism is innocent of all these charges against it, and we hope that the strength of the defense we offer of explanationism is evidence in its favor, and a reason to investigate explanationism further as the long-elusive truth about the nature of knowledge.

Characterizing growth in decentralized socio-economic networks through triadic closure-related network motifs

The emergence of the Web3 paradigm has led to more and more systems built on blockchain technology and relying on cryptocurrency tokens – both fungible and non-fungible – to sustain themselves and generate profit. The growth and success of these platforms are strongly dependent on the growth and evolution of the trade relationships among users. In this context, it is of paramount importance to understand the mechanism behind the evolution and growth dynamics of these economic ties: however, in these systems the trade relationships are strictly intertwined with social dynamics, posing significant challenges in the analysis. One of the most important mechanisms behind the evolution of social networks is the triadic closure principle: given the strict link between social and economic spheres, the mechanism emerges as a potential candidate among mechanisms in literature. Therefore in this work, we extend the existing methodology for triadic closure studies and adapt it to directed networks. We performed an analysis centered around 3-node subgraphs known as “triads” and statistically significant triads referred to as “triadic motifs”, both from a static and temporal perspective. The methodology was applied to various decentralized socio-economic networks with distinct levels of social components. These networks include currency transfers from the blockchain-based online social media platform Steemit, trade relationships among NFT sellers and buyers on the Ethereum blockchain, and a blockchain-based currency designed for humanitarian aid called Sarafu. Our measurements show how triadic closure is relevant during the evolution of these platforms and, for a few aspects, more impactful than centralized online social networks, where triadic closure is also incentivized by recommendation systems. Moreover, we are able to highlight both similarities and differences across networks with different levels of social components, both from a static and temporal standpoint. Overall our work presents strong evidence that triadic closure is an important evolutionary mechanism in decentralized socio-economic networks. Our findings provide a stepping stone in the study of decentralized socio-economic networks. Understanding the evolution of other decentralized networks, not following the same Web3 paradigm or with different social components will provide valuable insight into the understanding of dynamics in decentralized systems and potentially improve their design process.

Transcendental Knowability, Closure, Luminosity and Factivity: Reply to Stephenson

Abstract Stephenson (2022) has argued that Kant’s thesis that all transcendental truths are transcendentally a priori knowable leads to omniscience of all transcendental truths. His arguments depend on luminosity principles and closure principles for transcendental knowability. We will argue that one pair of a luminosity and a closure principle should not be used, because the closure principle is too strong, while the other pair of a luminosity and a closure principle should not be used, because the luminosity principle is too strong. Stephenson’s argument also depends on a factivity principle for transcendental knowability, which we will argue to be false.

Naturalized metaphysics or displacing metaphysicians to save metaphysics

Naturalized metaphysics aims to establish justified metaphysical claims, where metaphysics is meant to carry its usual significance, while avoiding the traditional methods of metaphysics—a priori reasoning, conceptual analysis, intuitions, and common sense—which naturalized metaphysics argues are not epistemically probative. After offering an explication of what it means to do metaphysics, this paper argues that naturalized metaphysics, at the outset, is hospitable to doing metaphysics. The underdetermination of metaphysics by science, however, changes the picture. Naturalized metaphysics has to break this underdetermination, but the criticism of the traditional methods of metaphysics leaves no resources with which to do so. Naturalized metaphysics must therefore be more restrictive than originally intended to ensure that some metaphysical features avoid underdetermination. In this restrictive naturalized metaphysics, however, metaphysicians are only left the task of surveying the opinions of scientists which, it is argued, does not qualify as doing metaphysics. Thus, to fulfill its promise to save metaphysics, naturalized metaphysics displaces the metaphysician. Furthermore, the attempt to re-employ them via the principle of naturalistic closure is argued to fail. Metaphysicians should therefore not be happier with naturalized metaphysics than they are with the more explicitly eliminative trends in contemporary metametaphysics, such as neo-Carnapian deflationism, despite the promise of naturalized metaphysics, likely to Carnap’s dismay, to deliver justified claims about ultimate reality.