Mathematical proof is the primary form of justification for mathematical knowledge, but in order to count as a proper justification for a piece of mathematical knowl- edge, a mathematical proof must be rigorous. What does it mean then for a mathematical proof to be rigorous? According to what I shall call the standard view, a mathematical proof is rigorous if and only if it can be routinely translated into a formal proof. The standard view is almost an orthodoxy among contemporary (...) mathematicians, and is endorsed by many logicians and philosophers, but it has also been heavily criticized in the philosophy of mathematics literature. Progress on the debate between the proponents and opponents of the standard view is, however, currently blocked by a major obstacle, namely the absence of a precise formulation of it. To remedy this deficiency, I undertake in this paper to provide a precise formulation and a thorough evaluation of the standard view of mathematical rigor. The upshot of this study is that the standard view is more robust to criticisms than it transpires from the various arguments advanced against it, but that it also requires a certain conception of how mathematical proofs are judged to be rigorous in mathematical practice, a conception that can be challenged on empirical grounds by exhibiting rigor judgments of mathematical proofs in mathematical practice conflicting with it. (shrink)

The deviation of mathematical proof—proof in mathematical practice—from the ideal of formal proof—proof in formal logic—has led many philosophers of mathematics to reconsider the commonly accepted view according to which the notion of formal proof provides an accurate descriptive account of mathematical proof. This, in turn, has motivated a search for alternative accounts of mathematical proof purporting to be more faithful to the reality of mathematical practice. Yet, in order to develop and evaluate such alternative accounts, it appears as a (...) necessary prerequisite to first possess a clear picture of what the deviation of mathematical proof from formal proof consists in. The present work aims to contribute building such a picture by investigating the relation between the elementary steps of deduction constituting the two types of proofs—mathematical inference and logical inference. Many claims have been made in the literature regarding the relation between mathematical inference and logical inference, most of them stating that the former is lacking properties that are constitutive of the latter. Such differentiating claims are, however, usually put forward without a clear conception of the properties occurring in them, and are generally considered to be immediately justified by our direct acquaintance, or phenomenological experience, with the two types of inferences. The present study purports to advance our understanding of the relation between mathematical inference and logical inference by developing a detailed philosophical analysis of the differentiating claims, that is, an analysis of the meaning of the differentiating claims—through the properties that occur in them—as well as the reasons that support them. To this end, we provide at the outset a representative list of the different properties of logical inference that have occurred in the differentiating claims, and we notice that they all boil down to the three properties of formality, generality, and mechanicality. For each one of these properties, our analysis proceeds in two steps: we first provide precise conceptual characterizations of the different ways logical inference has been said to be formal, general, and mechanical, in the philosophical and logical literature on formal proof; we then examine why mathematical inference does not appear to be formal, general, and mechanical, for the different variations of these notions identified. Our study results in a precise conceptual apparatus for expressing and discussing the properties differentiating mathematical inference from logical inference, and provides a first inventory of the various reasons supporting the observations of those differences. The differentiating claims constitute thus a set of data that any philosophical account of mathematical inference and proof purporting to be more faithful to mathematical practice ought to be able to accommodate and explain. (shrink)

The Interrogative Model of Inquiry and Dynamic Epistemic Logics are two central paradigms in formal epistemology. This paper is motivated by the observation of a significant complementarity between them: on the one hand, the IMI provides a framework for investigating inquiry represented as an idealized game between an Inquirer and Nature, along with an account of the interaction between questions and inferences in information-seeking processes, but is lacking a formulation in the multi-agent case; on the other hand, DELs model various (...) operations of information change in multi-agent systems, but the field is lacking a proper integration of question and inference dynamics, along with an application to the investigation of inquiry processes. The goal of this paper is to integrate the two paradigms in such a way as to combine their respective insights. To this end, we develop a formal system called DEL $$_\mathrm{IMI }$$ IMI which aims to represent the interaction between question and inference dynamics in inquiry—as described by the IMI—in a multi-agent setting, and this in such a way as to enable an investigation of inquiry games with multi-agent dimensions. The DEL $$_\mathrm{IMI }$$ IMI system is designed to represent the possible moves of such inquiry games through three types of epistemic actions: agents addressing questions to Nature, agents addressing questions to other agents, agents drawing logical inferences. We then show how the resulting framework can be used to formally define multi-agent inquiry games. We conclude by evaluating the interest of the DEL $$_\mathrm{IMI }$$ IMI system for the IMI and DELs paradigms. (shrink)

Although there exist today a variety of non-deductive reliable processes able to determine the truth of certain mathematical propositions, proof remains the only form of justification accepted in mathematical practice. Some philosophers and mathematicians have contested this commonly accepted epistemic superiority of proof on the ground that mathematicians are fallible: when the deductive method is carried out by a fallible agent, then it comes with its own level of reliability, and so might happen to be equally or even less reliable (...) than existing non-deductive reliable processes—I will refer to this as the reliability argument. The aim of this article is to examine whether the reliability argument forces us to reconsider the commonly accepted epistemic superiority of the deductive method over non-deductive reliable processes. I will argue that the reliability argument is fundamentally correct, but that there is another epistemic property differentiating the deductive method from non-deductive reliable processes. This property is based on the observation that although mathematicians are fallible agents, they are also self-correcting agents. This means that when a proof is produced that only contains repairable mistakes, given enough time and energy, a mathematician or a group thereof should be able to converge towards a correct proof through a finite number of verification and correction rounds, thus providing a guarantee that the considered proposition is true, something that non-deductive reliable processes will never be able to produce. From this perspective, the standard of justification adopted in mathematical practice should be read in a diachronic way: the demand is not that any proof that is ever produced be correct—which would amount to requiring that mathematicians are infallible—but rather that, over time, proofs that contain repairable mistakes be corrected, and proofs that cannot be repaired be rejected. (shrink)

1. Ḥāshīyat al-Ṣabbān ʻalá al-Sharḥ al-Ṣaghīr lil-Mullawī ʻalá al-Sullam al-murawnaq -- 2. Taqrīrāt Ḥasan ibn Riḍwān al-Ḥusaynī.

Euclidean diagrammatic reasoning refers to the diagrammatic inferential practice that originated in the geometrical proofs of Euclid’s Elements. A seminal philosophical analysis of this practice by Manders (‘The Euclidean diagram’, 2008) has revealed that a systematic method of reasoning underlies the use of diagrams in Euclid’s proofs, leading in turn to a logical analysis aiming to capture this method formally via proof systems. The central premise of this paper is that our understanding of Euclidean diagrammatic reasoning can be fruitfully advanced (...) by confronting these logical and philosophical analyses with the field of cognitive science. Surprisingly, central aspects of the philosophical and logical analyses resonate in very natural ways with research topics in mathematical cognition, spatial cognition and the psychology of reasoning. The paper develops these connections, concentrating on four issues: (1) the cognitive origins of Euclidean diagrammatic reasoning, (2) the cognitive representations of spatial relations in Euclidean diagrams, (3) the nature of the cognitive processes and cognitive representations involved in Euclidean diagrammatic reasoning seen as a form of visuospatial relational reasoning and (4) the complexity of Euclidean diagrammatic reasoning for the human cognitive system. For each of these issues, our analysis generates concrete experiment proposals, opening thereby the way for further empirical investigations. The paper is thus a prolegomenon to a research program on Euclidean diagrammatic reasoning at the crossroads of logic, philosophy and cognitive science. (shrink)

Traditional logical theories are concerned with the characterization of valid reasoning. For such logical theories, the main object of investigation is the notion of entailment, a notion that is construed as a relation between two or more declarative statements, dictating when one of them can be legitimately inferred from the others. In the course of the previous century, however, and especially since the 1970s, the scope of logical theories has become much broader. In particular, logic is no longer only concerned (...) with declarative statements, but also with questions. Accordingly, the field is no longer focusing exclusively on the entailment relation that may hold between two or more statements, but also aims to characterize fundamental relations that may hold between questions, or between questions and statements. For instance, when does a statement resolve a given question? When does a statement evoke a certain question? And when does the resolution of one question depend on the resolu .. (shrink)

Although understanding is the object of a growing literature in epistemology and the philosophy of science, only few studies have concerned understanding in mathematics. This essay offers an account of a fundamental form of mathematical understanding: proof understanding. The account builds on a simple idea, namely that understanding a proof amounts to rationally reconstructing its underlying plan. This characterization is fleshed out by specifying the relevant notion of plan and the associated process of rational reconstruction, building in part on Bratman's (...) theory of planning agency. It is argued that the proposed account can explain a significant range of distinctive phenomena commonly associated with proof understanding by mathematicians and philosophers. It is further argued, on the basis of a case study, that the account can yield precise diagnostics of understanding failures and can suggest ways to overcome them. Reflecting on the approach developed here, the essay concludes with some remarks on how to shape a general methodology common to the study of mathematical and scientific understanding and focused on human agency. (shrink)

Topological relations such as inside, outside, or intersection are ubiquitous to our spatial thinking. Here, we examined how people reason deductively with topological relations between points, lines, and circles in geometric diagrams. We hypothesized in particular that a counterexample search generally underlies this type of reasoning. We first verified that educated adults without specific math training were able to produce correct diagrammatic representations contained in the premisses of an inference. Our first experiment then revealed that subjects who correctly judged an (...) inference as invalid almost always produced a counterexample to support their answer. Noticeably, even if the counterexample always bore a certain level of similarity to the initial diagram, we observed that an object was more likely to be varied between the two drawings if it was present in the conclusion of the inference. Experiments 2 and 3 then directly probed counterexample search. While participants were asked to evaluate a conclusion on the basis of a given diagram and some premisses, we modulated the difficulty of reaching a counterexample from the diagram. Our results indicate that both decreasing the counterexample density and increasing the counterexample distance impaired reasoning performance. Taken together, our results suggest that a search procedure for counterexamples, which proceeds object‐wise, could underlie diagram‐based geometric reasoning. Transposing points, lines, and circles to our spatial environment, the present study may ultimately provide insights on how humans reason about topological relations between positions, paths, and regions. (shrink)

In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice . In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics including the (...) distinction between formal and informal proofs, visualization and artefacts, mathematical explanation and understanding, value judgments, and mathematical design. We conclude with some remarks on the potential connections between the philosophy of mathematical practice and mathematics education. (shrink)

In mathematics, any form of probabilistic proof obtained through the application of a probabilistic method is not considered as a legitimate way of gaining mathematical knowledge. In a series of papers, Don Fallis has defended the thesis that there are no epistemic reasons justifying mathematicians’ rejection of probabilistic proofs. This paper identifies such an epistemic reason. More specifically, it is argued here that if one adopts a conception of mathematical knowledge in which an epistemic subject can know a mathematical proposition (...) based solely on a probabilistic proof, one is then forced to admit that such an epistemic subject can know several lottery propositions based solely on probabilistic evidence. Insofar as knowledge of lottery propositions on the basis of probabilistic evidence alone is denied by the vast majority of epistemologists, it is concluded that this constitutes an epistemic reason for rejecting probabilistic proofs as a means of acquiring mathematical knowledge. (shrink)

In practice, mathematical proofs are most often the result of careful planning by the agents who produced them. As a consequence, each mathematical proof inherits a plan in virtue of the way it is produced, a plan which underlies its “architecture” or “unity”. This paper provides an account of plans and planning in the context of mathematical proofs. The approach adopted here consists in looking for these notions not in mathematical proofs themselves, but in the agents who produced them. The (...) starting point is to recognize that to each mathematical proof corresponds a proof activity which consists of a sequence of deductive inferences—i.e., a sequence of epistemic actions—and that any written mathematical proof is only a report of its corresponding proof activity. The main idea to be developed is that the plan of a mathematical proof is to be conceived and analyzed as the plan of the agent(s) who carried out the corresponding proof activity. The core of the paper is thus devoted to the development of an account of plans and planning in the context of proof activities. The account is based on the theory of planning agency developed by Michael Bratman in the philosophy of action. It is fleshed out by providing an analysis of the notions of intention—the elementary components of plans—and practical reasoning—the process by which plans are constructed—in the context of proof activities. These two notions are then used to offer a precise characterization of the desired notion of plan for proof activities. A fruitful connection can then be established between the resulting framework and the recent theme of modularity in mathematics introduced by Jeremy Avigad. This connection is exploited to yield the concept of modular presentations of mathematical proofs which has direct implications for how to write and present mathematical proofs so as to deliver various epistemic benefits. The account is finally compared to the technique of proof planning developed by Alan Bundy and colleagues in the field of automated theorem proving. The paper concludes with some remarks on how the framework can be used to provide an analysis of understanding and explanation in the context of mathematical proofs. (shrink)

Mathematical rigor is commonly formulated by mathematicians and philosophers using the notion of proof gap: a mathematical proof is rig­orous when there is no gaps in the mathematical reasoning of the proof. Any philosophical approach to mathematical rigor along this line requires then an account of what a proof gap is. However, the notion of proof gap makes sense only relatively to a given conception of valid mathematical reasoning, i.e., to a given conception of the validity of mathematical inference. A (...) proof gap can in particular be conceived as a failure in drawing a valid mathematical inference. The aim of this paper is to discuss two possible views of the validity of math­ematical inference with respect to their capacity to yield a plausible account of the intuitive notion(s) of proof gap present in mathematical practice. The first view is the one provided by the contemporary standards of mathematical rigor: a mathematical inference is valid if and only if its conclusion can be formally derived from its premises. We will argue that this conception does not lead to a plausible account of the intuitive notion(s) of proof gap. The second view is based on a new account of the validity of inference proposed by Prawitz: an inference is valid if and only if it consists in an operation that provides a ground for its conclusion given (previously obtained) grounds for its premises. We will first specify Prawitz's account to mathematical inference and we will then argue that the resulting ground-based account is able to capture various intuitive notions of proof gap as different types of failure in drawing valid mathematical inferences. We conclude that the ground-based account ap­pears of particular interest for the philosophy of mathematical practice, and we finally raise several challenges facing a full development of a ground-based account of the notions of mathematical rigor, proof gap and the validity of mathematical inference. (shrink)

We present a survey of the recent applications of continuous domains for providing simple computational models for classical spaces in mathematics including the real line, countably based locally compact spaces, complete separable metric spaces, separable Banach spaces and spaces of probability distributions. It is shown how these models have a logical and effective presentation and how they are used to give a computational framework in several areas in mathematics and physics. These include fractal geometry, where new results on existence and (...) uniqueness of attractors and invariant distributions have been obtained, measure and integration theory, where a generalization of the Riemann theory of integration has been developed, and real arithmetic, where a feasible setting for exact computer arithmetic has been formulated. We give a number of algorithms for computation in the theory of iterated function systems with applications in statistical physics and in period doubling route to chaos; we also show how efficient algorithms have been obtained for computing elementary functions in exact real arithmetic. (shrink)

Mathematical proofs are not sequences of arbitrary deductive steps—each deductive step is, to some extent, rational. This paper aims to identify and characterize the particular form of rationality at play in mathematical proofs. The approach adopted consists in viewing mathematical proofs as reports of proof activities—that is, sequences of deductive inferences—and in characterizing the rationality of the former in terms of that of the latter. It is argued that proof activities are governed by specific norms of rational planning agency, and (...) that a deductive step in a mathematical proof qualifies as rational whenever the corresponding deductive inference in the associated proof activity figures in a plan that has been constructed rationally. It is then shown that mathematical proofs whose associated proof activities violate these norms are likely to be judged as defective by mathematical agents, thereby providing evidence that these norms are indeed present in mathematical practice. We conclude that, if mathematical proofs are not mere sequences of deductive steps, if they possess a rational structure, it is because they are the product of rational planning agents. (shrink)

The cognitive processing of spatial relations in Euclidean diagrams is central to the diagram-based geometric practice of Euclid's Elements. In this study, we investigate this processing through two dichotomies among spatial relations—metric vs topological and exact vs co-exact—introduced by Manders in his seminal epistemological analysis of Euclid's geometric practice. To this end, we carried out a two-part experiment where participants were asked to judge spatial relations in Euclidean diagrams in a visual half field task design. In the first part, we (...) tested whether the processing of metric vs topological relations yielded the same hemispheric specialization as the processing of coordinate vs categorical relations. In the second part, we investigated the specific performance patterns for the processing of five pairs of exact/co-exact relations, where stimuli for the co-exact relations were divided into three categories depending on their distance from the exact case. Regarding the processing of metric vs topological relations, hemispheric differences were found for only a few of the stimuli used, which may indicate that other processing mechanisms might be at play. Regarding the processing of exact vs co-exact relations, results show that the level of agreement among participants in judging co-exact relations decreases with the distance from the exact case, and this for the five pairs of exact/co-exact relations tested. The philosophical implications of these empirical findings for the epistemological analysis of Euclid's diagram-based geometric practice are spelled out and discussed. (shrink)

Undoubtedly and unfortunately, COVID-19 pandemic has been politicized in media see Abbas, Rui Zhang. Although vaccines play a crucial role in eliminating the pandemic, they have been politicized by media. This article aims to show how COVID-19 vaccines are politicized in the press. The article collects some selected reports on vaccines taken from American and Chinese media. The reports are analyzed according to an analytical framework suggested by the researcher. The framework and data collection and description are clearly presented (...) in the method section. Based on data analysis, the article shows that COVID-19 vaccines have been politicized. The study recommends that diseases and vaccines should not be politicized. In other words, we should respect and trust science and our scientists for no other purpose than to reach herd immunity and overcome a dangerous pandemic that has taken and is still taking thousands of innocent lives. (shrink)

A characteristic feature of the philosophy of mathematical practice is to attend to what people do when they do mathematics. But what does it mean to do mathematics? This question raises several issues regarding the nature of action, activity, and agency in mathematical practice. The present chapter reviews contributions in the field that have attempted to theorize about these notions. It begins with some motivations for taking agents seriously in the philosophical study of mathematical practice. The core of the chapter (...) discusses, in turn, what it means to carry out mathematical activities, do things with mathematical artifacts, engage with mathematical proofs, and perform mathematical actions prescribed by mathematical texts. Taken together, the various lines of work reported here provide an initial, but already sophisticated, picture of what it means to do mathematics. The chapter ends with some suggestions for future research on agency in mathematical practice. (shrink)

Conversation is one of the main contexts in which we are conducting inquiries. Yet, little attention has been paid so far in pragmatics or epistemology to the process of inquiry in conversation. In this paper, we propose to trigger such an investigation through the development of a formal modelling based on inquisitive pragmatics—a framework offering a semantic representation of questions and answers, along with an analysis of the pragmatic principles that govern questioning and answering moves in conversations geared towards information (...) exchange. Our starting observation is that an interrogative inquiry in a conversation takes the form of a finite sequence of questioning and answering steps, and appears thereby as an inherently temporal process. The central notion of interrogative protocol introduced in this paper precisely aims to capture the temporal dimension of inquiry. Interrogative protocols are defined as branching-time tree structures encoding all the possible sequences of questioning and answering steps—i.e., all the possible inquiry paths—that can subsequently occur in a starting conversational situation in accordance with the principles of inquisitive pragmatics. They provide us with a formal environment to define and investigate the epistemological notions of interrogative inquiry and interrogative consequence in conversational contexts. One of the main interests of the resulting framework is to enable a formal investigation of central epistemological issues relative to interrogative inquiry under the form of computational problems. We frame three key inquiry problems along this line, and we then propose an algorithmic procedure for solving them in the restricted case where the inquirer has at her disposal a finite number of questions in her inquiry. We conclude by relating our approach to Wiśniewski’s Erotetic Search Scenarios and Hintikka’s Interrogative Model of Inquiry. (shrink)

This article critically studies coronavirus pandemic news in the press. The article attempts to study the way the news of COVID-19 is used for political and ideological purposes. In order to achieve the aim, two newspapers namely, The New York Times from the United States of America and Global Times from China are selected. Van Dijk’s news schemata framework is used for the analysis of the reports selected from the two newspapers. Van Dijk’s news schemata is crucial for the analysis (...) of any news story whether such a news story is taken from a news channel or a newspaper and whether broadcasted or printed. Based on data analysis, the article found out that the news of COVID-19 has been politicized and used for ideological interests. The article recommends that pandemics should not be politicized, instead we should work together to save our lives and live peacefully. (shrink)

Government is a rational necessity for mankind because a society without government leads to chaos. Government regulates the affairs of the individual and the community, implements the limits, and ensures the dignity and independence of the human society. Thinking in the main goals of the divine prophets, it is clear that achieving great goals such as liberating people from the domination and captivity of foreigners, comprehensive human education, reviving human values, establishing justice, bringing people to excellence and growth, etc., requires (...) formation. In this context, transparency is a key attribute, which can bring much power to the expected level as an effective mechanism for protecting citizens’ political, economic, social and cultural rights. This concept is thus a valuable solution in the fight against sinister phenomena, such as political and economic corruptions, which are ranked as the biggest challenges facing any society. Even though transparency is nowadays deemed an emerging concept, its roots can be traced back to Islamic teachings, mainly during the short reign of Imam Ali, (peace be upon him [PBUH]). As a central figure, Imam Ali considered transparency as essential, and shared his views on governance and practical methods with the people and all audiences based on complete honesty and openness. As per Alavi thoughts, some criteria and indicators, both structural and behavioural, are involved in order to ensure the public good and meet the interests of all by providing the prerequisites for the realisation of transparency, at odds with the predominant ideas that transparency in governance, like many concepts in the political and governance-related spheres, has a western origin. Contribution: The concept of transparency, with a proven history in global experiences, accordingly holds a special place in the literature of Islamic governments. Given the importance of this topic, the present study with an emphasis on transparency aims to examine Islamic teachings on governance in Islamic societies, and reflect on governance transparency components in such societies, relying on expert opinions. (shrink)

We propose a dynamic-epistemic analysis of the different epistemic operations constitutive of the process of interrogative inquiry, as described by Hintikka’s Interrogative Model of Inquiry (IMI). We develop a dynamic logic of questions for representing interrogative steps, based on Hintikka’s treatment of questions in the IMI, along with a dynamic logic of inferences for representing deductive steps, based on the tableau method. We then merge these two systems into a dynamic logic of interrogative inquiry which articulates a joint treatment of (...) questions and inferences, providing thereby a unified framework representing the informational dynamics of interrogative inquiry. We provide sound and complete axiomatic systems for the three dynamic logics that we introduce, we compare our framework with existing approaches, and we finally propose several directions for further work. (shrink)

Poincaré and Prawitz have both developed an account of how one can acquire knowledge through reasoning by mathematical induction. Surprisingly, their two accounts are very close to each other: both consider that what underlies reasoning by mathematical induction is a certain chain of inferences by modus ponens ‘moving along’, so to speak, the well-ordered structure of the natural numbers. Yet, Poincaré’s central point is that such a chain of inferences is not sufficient to account for the knowledge acquisition of the (...) universal propositions that constitute the conclusions of inferences by mathematical induction, as this process would require to draw an infinite number of inferences. In this paper, we propose to examine Poincaré’s point—that we will call the closure issue—in the context of Prawitz’s framework where inferences are represented as operations on grounds. We shall see that the closure issue is a challenge that also faces Prawitz’s own account of mathematical induction and which points out to an epistemic gap that the chain of modus ponens cannot bridge. One way to address the challenge is to introduce suitable additional inferential operations that would allow to fill the gap. We will end the paper by sketching such a possible solution. (shrink)

This paper deals with the comparison of students' misbehaviours in Turkish and English primary classrooms. A field study was conducted in order to discern students' misbehaviours based on students' age, gender, time of day, seating arrangement, types of learning activities and subject matter. Semi-structured in-depth interview and systematic classroom observation were used to collect data from two different cultural contexts. Participants in this study were 20 primary school teachers. The results show that there are differences and similarities between Turkish and (...) English primary classrooms in terms of the causes and types of students' misbehaviours. Certain misbehaviours that are caused by different cultural and educational contexts are frequently observed either in English or in Turkish classrooms. (shrink)

In the course of this paper, I shall argue that an absolute ineffable God of Islam is contradictory beyond the ordinary categories (substantive or insubstantive) of truth. In order to demonstrate my thesis, I shall refer to a metaphysical and epistemological inquiry. In virtue of both of these inquires, I shall establish that the contradictory assumption ‘the God of Islam is absolutely ineffable’ cannot be false in a substantive or an insubstantive sense. The metaphysical inquiry shall comprise of two related (...) phases. The first phase includes logical realism and anti-realism, while the second phase includes ontological realism and ontological deflationism. I demonstrate that the contradictory assumption ‘the God of Islam is absolutely ineffable’ cannot be considered false in virtue of these outlooks for different reasons. The epistemological inquiry refers to epistemicism. I demonstrate that although this particular view infers an indeterminate truth-value of the contradictory assumption ‘the God of Islam is absolutely ineffable’, it is incompatible with the notion of an absolute ineffable God of Islam. In light of both these inquires, it will become apparent that the contradictory assumption of an absolute ineffable God of Islam cannot be false in a substantive or insubstantive sense. This is because an absolute ineffable God of Islam transcends beyond these very categories of falsehood and truth. (shrink)

In international politics, bridging the gap between the real and knowledge poses a persistent challenge as translating the real into concepts and narratives can nurture the epistemic fallacy. Critical realism addresses this by separating ontology from epistemology at the meta-theoretical level, yet in practical research, critical realism tends to impose assumptions about the ontological complexity of the real at the transcendental level. This paper examines the practical difficulty of overcoming the epistemic fallacy in International Relations inquiries, asserting that critical realism (...) does not effectively guide practical inquiries in separating ontology from epistemology at a methodological level. Despite the meta-theoretical separation, research inquiries can remain theory-laden and epistemically dependent. The solution lies in problematizing ontological presentation, and sustaining critique at the discursive level on International Relations theories, methodologies, and implications. This approach maintains a critical focus on ontological aspects at the practical level to deal with the challenge of the epistemic fallacy. (shrink)

The application of paraconsistent logics to theological contradictions is a fascinating move. Jc Beall’s (J Anal Theol, 7(1): 400–439, 2019) paper entitled ‘Christ—A Contradiction: A Defense of ‘Contradictory Christology’ is a notable example. Beall proposes a solution to the fundamental problem of Christology. His solution aims at making the case, and defending the viability of, what he has termed, ‘Contradictory Christology’. There are at least two essential components of Beall’s ‘Contradictory Christology’. These include the dogmatic statements of Chalcedon and FDE (...) logic. The first is the theological contradiction in question. The second is the type of paraconsistent logic. Both components are integral to a contradictory theology in general. I argue that there can be no such thing as an Islamic contradictory theology. I make the case by establishing two points. These points correspond to both integral components of a contradictory theology in general. The first is that an Islamic theological contradiction does not entail an actual (logical) contradiction. The second is that FDE logic, including alternative sub-classical systems of logic, are not adequate in tolerating an Islamic theological contradiction. (shrink)

The Islamic education curriculum in Indonesia tends to be partial and dichotomous. However, Muhammadiyah has reformed the holistic–integrative curriculum as a solution for the sustainability of education. This study aims to reveal a special curriculum reform in the holistic–integrative Muhammadiyah education system to solve the dichotomous problems and the inadequacy in the Islamic education curriculum in Indonesia. Furthermore, the study describes a specific curriculum model that includes all aspects of students’ personality and integrates science and technology with Islamic values. Data (...) were collected from previous studies and special curriculum documents of Al-Islam, Kemuhammadiyahan and Arabic Language (ISMUBA). Curriculum documents were obtained from elementary, junior and Muhammadiyah senior high school, published by Primary and Secondary Education Assembly of Muhammadiyah Central Board in 2017. Data analysis used a content model with a systematic and rational framework. The results showed that the special reform curriculum based on the holistic–integrative model develops students’ potentials, including spiritual, emotional, intellectual and transcendental intelligence, in an integrated manner. Contribution: The holistic–integrative curriculum is a future Islamic education model for the sustainability of private Islamic education system in Indonesia that can form a good, faithful, pious and a noble community. (shrink)

The present study examined effects of sociodemographic, risk, and resilience factors on marital, parental, and financial stress early in the COVID-19 pandemic. A cross-sectional online survey was conducted among 480 married Palestinians living in Israel, using self-report questionnaires. Descriptive statistics and bivariate correlations were computed. Then, hierarchical multiple regression analyses were conducted to predict each of the three stress measures. Finally, dominance analyses were conducted to compare the contributions of sociodemographic, risk, and resilience factors. The results showed considerable differences between (...) predictors of marital and parental stress and predictors of financial stress. For marital and parental stress, resilience factors mainly family resilience were the strongest predictors, followed by risk factors and then sociodemographic characteristics. For financial stress, risk factors were the strongest predictors, followed by sociodemographic characteristics and resilience factors. These results suggest that family and individual resilience reduce marital and parental stress under difficult conditions, including the COVID-19 pandemic. Though resilience has been found to ameliorate financial stress to some extent, it appears that other measures are required to manage stress related to financial difficulties. (shrink)

The laws of logic and two of the broader theories of truth are fundamental components that are responsible for espousing an ontology and meaningfulness in matters of analytic philosophy. In this respect they have persisted as conventional attitudes or modes of thought which most, if not all, of analytic philosophy uses to philosophize. However, despite the conceptual productivity of these components they are unable to account for matters that are beyond them. These matters would include certain theological beliefs, for instance, (...) that transcend the purview of analytic ontology and the meaningfulness it ensues. Any attempt in making rational sense of such beliefs that are insusceptible to these methodological components would conventionally prohibit (restrict) us from rationally believing in them. This is because we would be unable to make sense of such beliefs with the aid of these methodological components. As a result of this, religious beliefs of this particular nature would be deemed irrational. I shall demonstrate this point by applying both of these components to an absolutely ineffable God of Islam. This would entail, attempting to make sense of an absolutely ineffable God of Islam in virtue of the laws of logic and two broad categories of truth theories, namely, substantive and insubstantive theories. I hope to establish that applying both of these methodological components in attempting to make sense of an absolutely ineffable God of Islam would not be conceptually viable. It would result in a contradictory notion which I shall allude to as the paradox of ineffability. (shrink)

With the advent of classical logic we are continuing to observe an adherence to the laws of logic. Moreover, the system of classical logic exhibits a prominent role within analytic philosophy. Given that the laws of logic have persistently endured in actively defining classical logic and its preceding system of logic, it begs the question as to whether it actually proves to be consistent with Islam. To consider this inquiry in a broader manner; it would be an investigation into the (...) consistency between Islam and the logic which has been the predominant driving force of analytic philosophy. Despite the well documented engagement and novel contributions made in the field of logic by Arab and Islamic theologians/logicians, I think this question deserves examination not just in terms of classical logic but also from perspectives which go beyond classical logic, namely, non-classical logic. Doing so, would I believe, retain this inquiry within the purview of analytic philosophy despite the reference to non-classical logic. To be more specific, this question would be directed toward the Islamic theologian who espouses the system of classical logic in attempting to make sense of an absolute ineffable God of Islam. The inquiry would seek to determine if classical logic is consistent (amenable) in making sense of an absolute ineffable God of Islam. This would principally involve an analysis which determines whether the metaphysical assumptions of the laws of logic (more specifically the law of non-contradiction) are consistent in making sense of an absolute ineffable God of Islam. I shall argue that it is inconsistent. I shall establish my position on this matter by demonstrating why classical logic is inconsistent (not amenable) with an absolute ineffable God of Islam. Although, I am principally concerned with classical logic, my argument is as applicable to all earlier systems of logic as much as it is to classical logic. This is on the basis that both systems of logic, namely, all preceding systems and classical logic, consider the laws of logic as defining features. (shrink)

I shall present an analysis of analytic theology as primarily characterised by Michael Rea (2011). I shall establish that if analytic theology is essentially characterised with the ambitions outlined by Rea, then it corresponds to a theological realist view. Such a theological realist view would subsequently result in an onto-theology. To demonstrate this, I shall examine how an onto-theological approach to a God of the Abrahamic Faiths (namely, a transcendent God) would prove to be (theologically) incompatible and even hostile. In (...) essence, my argument shall demonstrate that providing analytic theology is essentially characterised with the ambitions Rea alludes to, it is discordant with a transcendent God of the Abrahamic Faiths. (shrink)

Last year marked a decade since the publication of the book “Islamic Biomedical Ethics” by religious studies professor Abdulaziz Sachedina in which he called for a critical and rigorous analytical approach to the ethical inquiry of biomedical issues from an Islamic perspective. Since the publication of this landmark work, some authors have continued to call into question the ways in which Islam as a religious tradition is engaged with in the secular bioethics literature. This paper describes common argumentative issues with (...) current Islamic bioethics scholarship and offers general pearls and strategies to facilitate better engagement with religious approaches to bioethical issues. (shrink)

The declining influence of religious approaches to bioethical issues in academic medical discourse has been increasingly evident over recent decades. Most bioethical scholarship today is dominated...

Dialetheism is the view that some contradictions are true. Resorting to either metaphysical dialetheism or semantic dialetheism may seem like an appropriate resolve to certain theological contradictions. At least for those who concede to theological contradictions, and take dialetheism seriously. However, I demonstrate that neither of these types of dialetheism would serve to be amenable in resolving an Islamic theological contradiction. This is a theological contradiction that I refer to as ‘the paradox of an unknowable and ineffable God’. As a (...) result of this, I propose an alternative type of dialetheism which aims to resolve the paradox of an unknowable and ineffable God. I call this type of dialetheism, ‘mystical dialetheism’. (shrink)

There has been growing consensus to develop relevant guidance to improve the ethical review of global health policy and systems research and address the current absence of formal ethics guidance.

In May 2023, the world’s first whole-eye and partial-face transplant was performed, representing the first known whole-eye transplant in history and the “only successful combined transplant case of...

According to some commentators of the Iranian Civil Code, the definition of sale stated in Article 183 is influenced by Article 1101 of French Civil Code. They have concluded that the essence of sale is confined to mutual consent, i.e. the sale would not be valid without the consent of either party. They have taken even a step further and considered the contents of Article 338 of the civil code, which describes contract of sale, contradictory to Article 183 and argued (...) that the sale of a specified concrete object is not contained in Article 183 while the sale of unascertained goods is obliged to that article. They believe that the definition of Article 183 of civil code excludes not only all commitments, but also swap contracts because there are two mutual commitments and two agreeing legal contracts in a swap contract while there is no mentioning of them in Article 183. However, the objections are not rightfully lodged because first, the contracts and obligations are not incompatible with the definition of Article 338 as the seller and the buyer within a contract of sale are obliged to give authority to the other party over the object of sale or the price. It means that there are two commitments and the obligation of the seller to give authority over the object of sale appears in two ways: dominion over concrete object while making a transaction and dominion over non-specified object with the obligation that it does not attend to fulfil possession by the time of the sale. Secondly, Article 183 contains the phrase “their acceptance” which includes swap contract too because this phrase indicates that the acceptance is mutual. (shrink)