This paper presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → (B → C)⊩B → (A → C) trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ((A → B)∧ (B → C)) → (A → C) and (A → ¬A) → ¬A, the fusion connective and the Ackermann constant. An (...) overview over various ways to formulate Leibniz’s law in non-classical logics and two new triviality proofs for naïve set theory are also provided. (shrink)

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is (...) translatable to a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics. (shrink)

We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to (...) embeddings, semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as a means by which labelled sequent systems can be transformed into nested sequent systems through the introduction of propagation rules and the elimination of structural rules, followed by a notational translation. The nested systems we obtain incorporate propagation rules that are parameterized with formal grammars, (...) and which encode certain frame conditions expressible as first-order Horn formulae that correspond to a subclass of the Scott-Lemmon axioms. We show that our nested systems are sound, cut-free complete, and admit hp-admissibility of typical structural rules. (shrink)

This paper proposes a metaphysical solution to the hard problem of consciousness by presenting a formal theorem that uses set theory and modal logic to demonstrate the equivalence of Being, Self, and the Absolute. Through a series of self-evident axioms and logical propositions it establishes that Being is necessary for all possible entities, Self is necessary for all possible phenomena, and entities imply phenomena while Being implies Self. Furthermore, it posits that there can only be one Absolute, since multiple non-contingent (...) entities lead to a paradox of interdependence; resulting in reductio ad absurdum. Hence, Being, which is Absolute in the objective sense, and Self, which is Absolute in the subjective, are in fact a single Absolute Conscious Being (God). The final postulate takes the form of an imperative which elucidates the Self’s inherent potential for knowledge of itself – commonly mistaken for the individual (body with a mind in a world) – and reveals the path for direct realization of this Absolute Identity. Personal application, cultural integration, and ethical implications are discussed. (shrink)

This article proposes a way of doing type theory informally, assuming a cubical style of reasoning. It can thus be viewed as a first step toward a cubical alternative to the program of informalization of type theory carried out in the homotopy type theory book for dependent type theory augmented with axioms for univalence and higher inductive types. We adopt a cartesian cubical type theory proposed by Angiuli, Brunerie, Coquand, Favonia, Harper, and Licata as the implicit foundation, confining our presentation (...) to elementary results such as function extensionality, the derivation of weak connections and path induction, the groupoid structure of types, and the Eckmman–Hilton duality. (shrink)

Universe silence … Why? TechnoSfera … Where does it move? BioSfera … Where is the ―non-return point? NooSfera … What to do? The deep mind looks for primordial senses of the ―LifeWorld(LebensWelt). Сonsciousness, matter, memory … Self-Consciousness… Сonsciousness is attracting senses vector magnitude, intentional effect of absolute complexity. The Vector of Сonsciousness - the Triune Vector of absolute forms of existence of matter (limit states), the Vector of the Absolute Existential Field of the Universe, a polyvalent sense phenomenon of Ontological (...) (structural, cosmic) Memory. Open Сonsciousness Vs. Closed Сonsciousness. Сonceptual and mathematical proto-Eidoses Absolute forms of existence of matter. On the basis of ontological and existential constracting method – method of a discretion and a reflection of existential repère-point, the Vector of Сonsciousness places milestones on ProtoGeometre's long way – the way of ―knowledge of good and evil, of rises and fallings, of births of ―absolutely another, from the point ―Alpha to the modern ―point of ultimate tension of the Absolute Existential Field of the Universe. Big waves of Consciousness. Existential risks of Humanity and Open Science. New Open Generation realizing all existential risks of Humanity passable way and risks of coming Information era creates the Self-Aware Universe, filling it with the most deep meanings of the ―LifeWorld, at the heart of which Axiom of an absolute freedom of choice is laid. The minimum Program to overcome existential risks. Great Integrative Paradigm. Creation of a common sense picture of the World for physicists and lyricist. The United Humanity raises up five Great Philosophers' Stones in memory of Protogeometre's rises and fallings on a long way of becoming of Humanity and frees the Horse. Humanity is on a threshold of an Era of Eonic thinking... Far from Perfect … I start the path... (shrink)

When a technology is seen as the right solution to a recognized problem, the development of alternative technologies comes under threat. To secure much-needed resources, proponents of alternative technologies must, in these conditions, restart societal discussion on the status quo, a process at once technological and discursive known as ‘path creation’. In this article, we investigate discussion-restarting strategies employed by supporters of emerging technologies in the field of solar fuels, particularly the advocates of a technology referred to as ‘artificial (...) photosynthesis’. For illustrative purposes we explore four such strategies: revisiting weak spots, resizing the problem, redefining the game, and renegotiating labels. We conclude with a methodological reflection on the empirical study of discursive strategies in a socio-technical system. We further suggest a more systematic application of discourse-analytical and argumentation-theoretical insights that can complement current scholarship on path dependence and path creation. (shrink)

Peirce and Dewey were generally more concerned with the process of scientific activity than purely mathematical work. However, their accounts of knowledge production afford some insights into the epistemology of mathematical postulates, especially definition and axioms. Their rejection of rationalist metaphysics and their emphasis on continuity in inquiry provides the pretext for the pragmatic a priori – hypothetical and operational assumptions whose justification relies on their fruitfulness in the long run. This paper focuses on the application of this idea to (...) the epistemology of definitions and an account of progress in mathematics, although it has broader implications for the study of conceptual change and the function and basis of presuppositions in the sciences. (shrink)

This study used a path analytic approach to examine the composite interaction of supervisory and records management with secondary school system effectiveness in terms of students' academic performance, teachers' job effectiveness and principals' administrative effectiveness. Two research questions were answered while one null hypothesis was tested. The study adopted a factorial research design. Convenience sampling technique was adopted by the researchers in selecting a sample of 1,200 respondents which comprised 271 principals and 929 teachers from a population of 271 (...) principals, and 4,878 teachers. Principal Innovative Management Practices and Administrative Effectiveness Questionnaire (PIMPAEQ), Teachers work effectiveness questionnaire (TWEQ), and Students Mathematics Achievement Test (SMAT) were all used as instruments for data collection. Collected data were analyzed using descriptive statistics, the research questions and null hypothesis were answered and tested (at .05 level of significance) respectively using multiple regression and path analyses with the aid of SPSS v25 and Amos v22. Findings from the study established amongst others that; supervisory management and records management practices have a significant joint contribution to students’ academic performance by 66.4%, teachers’ job effectiveness by 71%, and principals’ administrative effectiveness by 86.8%. Supervisory management and records management practices had a significant influence on students’ academic performance (F= 1183.641, p<.05), teachers’ job effectiveness (F= 1465.615, p<.05), and principals’ administrative effectiveness (F=3924.763, p<.05). It was recommended amongst others that; secondary school principals should jointly use supervisory and records management practices as innovative techniques for improving students’ academic performance, teachers’ job effectiveness and their own administrative effectiveness. KEYWORDS:. (shrink)

The current “exemplarist turn” within virtue ethics is increasingly shedding light on the importance of exemplars both as enabling one to identify the virtues and for the importance they bear for orienting one’s conduct, as well as for educating the novice. However, even if categorizations of exemplars have already been proposed, there seems to be a lack of discussion on the kind of imitation different exemplars are supposed to elicit. In order to offer a preliminary answer to this question, in (...) this paper I present three paths to flourishing via imitation of exemplary individuals: The Platonic, the Stoic, and the Aristotelian. Then, I sketch an attempt to reconcile these models. In conclusion, I suggest that, when it comes to education, this reconciliation becomes necessary. Along these lines, I recommend that a multi-step educational program is elaborated. (shrink)

This paper focuses on the path of appearance and awareness.

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in Maudlin and Malament. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of Tarski : a predicate of betwenness and a four place (...) predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane—which obeys the Euclidean axioms in Tarski and Givant, 175–214 1999)—and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagoras’ theorem. We conclude with a Representation Theorem relating models \ of our system \ that satisfy second order continuity to the mathematical structure \, called ‘Minkowski spacetime’ in physics textbooks. (shrink)

A cause may influence its effect via multiple paths. Paradigmatically (Hesslow [1974]), taking birth control pills both decreases one’s risk of thrombosis by preventing pregnancy and increases it by producing a blood chemical. Building on Pearl ([2001]), I explicate the notion of a path-specific effect. Roughly, a path-specific effect of C on E via path P is the degree to which a change in C would change E were they to be transmitted only via P. Facts about (...) such effects may be gleaned from the structural equations commonly used to represent the causal relationships among variables. I contrast my analysis of the Hesslow case with those given by theorists of probabilistic causality, who mistakenly link it to issues of causal heterogeneity, token-causation and indeterminism. The reason probabilistic theories misdiagnose this case is that they pay inadequate attention to the structural relationships among variables. (shrink)

Spinoza's causal axiom is at the foundation of the Ethics. I motivate, develop and defend a new interpretation that I call the ‘causally restricted interpretation’. This interpretation solves several longstanding puzzles and helps us better understand Spinoza's arguments for some of his most famous doctrines, including his parallelism doctrine and his theory of sense perception. It also undermines a widespread view about the relationship between the three fundamental, undefined notions in Spinoza's metaphysics: causation, conception and inherence.

Although the concept of uncertainty is as old as Epicurus’s writings, and an excellent quantitative theory, with entropy as the measure of uncertainty having been developed in recent times, there has been little exploration of the qualitative theory. The purpose of the present paper is to give a qualitative axiomatization of uncertainty, in the spirit of the many studies of qualitative comparative probability. The qualitative axioms are fundamentally about the uncertainty of a partition of the probability space of events. Of (...) course, it is common to speak of the uncertainty, or randomness, of a random variable, but only the partition defined by the values of the random variable enter into the definition of uncertainty, not the actual values. It is straightforward to add axioms for decision making following the general line of Savage from the 1950s. Indeed, in the spirit of Epicurus, it is really our intuitive feeling about the uncertainty of the future that motivates much of our thinking about decisions. Here, the distinction between the concepts of probability and uncertainty can be made by citing many familiar examples. Without spelling out the technical details, the axiomatization of qualitative probability with uncertainty as the most important primitive concept, it is possible to raise a different kind of question about bounded rationality. This new question is whether or not one should bound the uncertainty in thinking and investigating any detailed framework of decision making. Discussion of this point is certainly different from the question of bounding rationality by not maximizing expected utility. In practice, we naturally bound uncertainty in our analysis of decision-making problems. As in the case of formulating an alternative for maximizing expected utility, so is the case of rational alternatives to maximizing uncertainty. There are several issues to consider. In the spirit of my other work in qualitative probability, I explore alternatives rather than attempt to give a definitive argument for one single solution. (shrink)

Axiom weakening is a technique that allows for a fine-grained repair of inconsistent ontologies. Its main advantage is that it repairs on- tologies by making axioms less restrictive rather than by deleting them, employing the use of refinement operators. In this paper, we build on pre- viously introduced axiom weakening for ALC, and make it much more irresistible by extending its definitions to deal with SROIQ, the expressive and decidable description logic underlying OWL 2 DL. We extend the (...) definitions of refinement operator to deal with SROIQ constructs, in particular with role hierarchies, cardinality constraints and nominals, and illustrate its application. Finally, we discuss the problem of termi- nation of an iterated weakening procedure. (shrink)

In this article I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us, all directions are the same to us and all units of length we use to create geometric figures are the same to us. On the other hand, through the process of algebraic simplification, this system of axioms directly provides the Weyl’s (...) system of axioms for Euclidean geometry. The system of axioms, together with its a priori interpretation, offers new views to philosophy and pedagogy of mathematics: it supports the thesis that Euclidean geometry is a priori, it supports the thesis that in modern mathematics the Weyl’s system of axioms is dominant to the Euclid’s system because it reflects the a priori underlying symmetries, it gives a new and promising approach to learn geometry which, through the Weyl’s system of axioms, leads from the essential geometric symmetry principles of the mathematical nature directly to modern mathematics. (shrink)

Ontology engineering is a hard and error-prone task, in which small changes may lead to errors, or even produce an inconsistent ontology. As ontologies grow in size, the need for automated methods for repairing inconsistencies while preserving as much of the original knowledge as possible increases. Most previous approaches to this task are based on removing a few axioms from the ontology to regain consistency. We propose a new method based on weakening these axioms to make them less restrictive, employing (...) the use of refinement operators. We introduce the theoretical framework for weakening DL ontologies, propose algorithms to repair ontologies based on the framework, and provide an analysis of the computational complexity. Through an empirical analysis made over real-life ontologies, we show that our approach preserves significantly more of the original knowledge of the ontology than removing axioms. (shrink)

Formalizing Euclid’s first axiom. Bulletin of Symbolic Logic. 20 (2014) 404–5. (Coauthor: Daniel Novotný) -/- Euclid [fl. 300 BCE] divides his basic principles into what came to be called ‘postulates’ and ‘axioms’—two words that are synonyms today but which are commonly used to translate Greek words meant by Euclid as contrasting terms. -/- Euclid’s postulates are specifically geometric: they concern geometric magnitudes, shapes, figures, etc.—nothing else. The first: “to draw a line from any point to any point”; the last: (...) the parallel postulate. -/- Euclid’s axioms are general principles of magnitude: they concern geometric magnitudes and magnitudes of other kinds as well even numbers. The first is often translated “Things that equal the same thing equal one another”. -/- There are other differences that are or might become important. -/- Aristotle [fl. 350 BCE] meticulously separated his basic principles [archai, singular archê] according to subject matter: geometrical, arithmetic, astronomical, etc. However, he made no distinction that can be assimilated to Euclid’s postulate/axiom distinction. -/- Today we divide basic principles into non-logical [topic-specific] and logical [topic-neutral] but this too is not the same as Euclid’s. In this regard it is important to be cognizant of the difference between equality and identity—a distinction often crudely ignored by modern logicians. Tarski is a rare exception. The four angles of a rectangle are equal to—not identical to—one another; the size of one angle of a rectangle is identical to the size of any other of its angles. No two angles are identical to each other. -/- The sentence ‘Things that equal the same thing equal one another’ contains no occurrence of the word ‘magnitude’. This paper considers the problem of formalizing the proposition Euclid intended as a principle of magnitudes while being faithful to the logical form and to its information content. (shrink)

Despite being a milestone in the history of statistical causal inference, Sewall Wright’s 1918 invention of path analysis did not receive much immediate attention from the statistical and scientific community. Through a careful historical analysis, this paper reveals some previously overlooked philosophical issues concerning the history of causal inference. Placing the invention of path analysis in a broader historical and intellectual context, I portray the scientific community’s initial lack of interest in the method as a natural consequence of (...) relevant scientific and philosophical conditions. In addition to Karl Pearson’s positivist refutation of causation, I contend that the acceptance of path analysis faced several other challenges, including the introduction of a new formalism, conceptual barriers to causal inference, and the lack of model-based statistical thinking. The presence of these challenges shows that the delayed progress in causal inference in the early twentieth century was inevitable. (shrink)

The literature on indicative conditionals contains two appealing views. The first is the selectional view: on this view, conditionals operate by selecting a single possibility, which is used to evaluate the consequent. The second is the informational view: on this view, conditionals don’t express propositions, but rather impose constraints on information states of speakers. Both views are supported by strong arguments, but they are incompatible on their standard formulations. Hence it appears that we have to choose between mutually exclusive options. (...) But the options are not exclusive. This paper develops a theory of the semantics and assertability of conditionals that is both selectional and informational. The theory vindicates the signature inferences of both selectional and informational theories, including so-called Conditionals Excluded Middle and principles about the interplay between conditionals and ‘might’. It also predicts some interesting and puzzling facts about the assertion of conditionals. (shrink)

This book examines the philosophy of the nineteenth-century Indian mystic Sri Ramakrishna and brings him into dialogue with Western philosophers of religion, primarily in the recent analytic tradition. Sri Ramakrishna’s expansive conception of God as the impersonal-personal Infinite Reality, Maharaj argues, opens up an entirely new paradigm for addressing central topics in the philosophy of religion, including divine infinitude, religious diversity, the nature and epistemology of mystical experience, and the problem of evil.

The Hyperuniverse Programme, introduced in Arrigoni and Friedman (2013), fosters the search for new set-theoretic axioms. In this paper, we present the procedure envisaged by the programme to find new axioms and the conceptual framework behind it. The procedure comes in several steps. Intrinsically motivated axioms are those statements which are suggested by the standard concept of set, i.e. the `maximal iterative concept', and the programme identi fies higher-order statements motivated by the maximal iterative concept. The satisfaction of these statements (...) (H-axioms) in countable transitive models, the collection of which constitutes the `hyperuniverse' (H), has remarkable 1st-order consequences, some of which we review in section 5. (shrink)

A framing effect occurs when an agent's choices are not invariant under changes in the way a decision problem is presented, e.g. changes in the way options are described (violation of description invariance) or preferences are elicited (violation of procedure invariance). Here we identify those rationality violations that underlie framing effects. We attribute to the agent a sequential decision process in which a “target” proposition and several “background” propositions are considered. We suggest that the agent exhibits a framing effect if (...) and only if two conditions are met. First, different presentations of the decision problem lead the agent to consider the propositions in a different order (the empirical condition). Second, different such “decision paths” lead to different decisions on the target proposition (the logical condition). The second condition holds when the agent's initial dispositions on the propositions are “implicitly inconsistent,” which may be caused by violations of “deductive closure.” Our account is consistent with some observations made by psychologists and provides a unified framework for explaining violations of description and procedure invariance. (shrink)

Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face (...) complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence of extensions violating maximality axioms. An analysis of two kinds of multiversism, a Zermelian form and Skolemite form, leads to the conclusion that the kind of maximality captured by an axiom differs substantially according to background ontology. (shrink)

During the past few decades, everyday aesthetics has established itself as a new branch of philosophical aesthetics alongside the more traditional philosophy of art. The Paths from Philosophy of Art to Everyday Aesthetics explores the intimate relations between these two branches of contemporary aesthetics. The essays collected in this volume discuss a wide range of topics from aesthetic intimacy to the nature of modernity and the essence of everydayness, which play important roles both in the philosophy of art and everyday (...) aesthetics. With these essays, the writers and editors of this volume wish to commemorate professor Arto Haapala on his 60th birthday. -/- This collection of articles is intended for scholars and students working in the fields of aesthetics, philosophy, and art studies. (shrink)

In the face of an impossibility result, some assumption must be relaxed. The Mere Addition Paradox is an impossibility result in population ethics. Here, I explore substantially weakening the decision-theoretic assumptions involved. The central finding is that the Mere Addition Paradox persists even in the general framework of choice functions when we assume Path Independence as a minimal decision-theoretic constraint. Choice functions can be thought of either as generalizing the standard axiological assumption of a binary “betterness” relation, or as (...) providing a general framework for a normative (rather than axiological) theory of population ethics. Path Independence, a weaker assumption than typically (implicitly) made in population ethics, expresses the idea that, in making a choice from a set of alternatives, the order in which options are assessed or considered is ethically arbitrary and should not affect the final choice. Since the result establishes a conflict between the relevant ethical principles and even very weak decision-theoretic principles, we have more reason to doubt the ethical principles. (shrink)

This article studies the political dimension of friendship in Robert Guédiguian’s cinema, delving into the crucial role that conversation plays in this relationship, and taking Stanley Cavell’s thought as a main reference. Aristotle’s concept of civic friendship, along with its contemporary readings, and Cavell’s notion of conversation provide a theoretical frame for the analysis of three recent feature films directed by Guédiguian that present a strong thematic and narrative unity (and have barely received attention in previous scholarship): Les Neiges du (...) Kilimandjaro/The Snows of Kilimanjaro (2011), La Villa/The House by the Sea (2017) and Gloria Mundi (2019). Based on, but going beyond, Cavell’s moral theorisation of the filmic portrayal of human relationships, the analysis of these films has identified four milestones in the transformative process—both personal and political—that stems from conversation with friends: conformity, confrontation, acknowledgement and renewed community. In all three films, this process of change is not only presented as a progressive discovery of one’s own voice, but also as a progressive unmasking: both are necessary prerequisites for welcoming foreigners in need of acknowledgement and, consequently, for the renewal of community. (shrink)

In quantum theory every state can be diagonalized, i.e. decomposed as a convex combination of perfectly distinguishable pure states. This elementary structure plays an ubiquitous role in quantum mechanics, quantum information theory, and quantum statistical mechanics, where it provides the foundation for the notions of majorization and entropy. A natural question then arises: can we reconstruct these notions from purely operational axioms? We address this question in the framework of general probabilistic theories, presenting a set of axioms that guarantee that (...) every state can be diagonalized. The first axiom is Causality, which ensures that the marginal of a bipartite state is well defined. Then, Purity Preservation states that the set of pure transformations is closed under composition. The third axiom is Purification, which allows to assign a pure state to the composition of a system with its environment. Finally, we introduce the axiom of Pure Sharpness, stating that for every system there exists at least one pure effect occurring with unit probability on some state. For theories satisfying our four axioms, we show a constructive algorithm for diagonalizing every given state. The diagonalization result allows us to formulate a majorization criterion that captures the convertibility of states in the operational resource theory of purity, where random reversible transformations are regarded as free operations. (shrink)

The present article is a sympathetic critique of the most prominent contemporary articulations of family abolitionism. It examines whether queer communist family abolitionism is successful in linking an account of reasons for abolition, with an account of the means of abolition, and finally with an account of the ends of abolition in the form of speculation on a possible world without families. Recent work by M.E. O’Brien has developed these connections in ways that have never been done so thoroughly before; (...) but the rejection of states as an institutional form of political power leaves it unclear what forms of equality we could expect in such a world, and why coercive power would be unnecessary there. Family abolition is a utopian political agenda; but that utopianism needs to be constrained by a realist concern with issues of power, resources, and human capacities. This will require confronting trade-offs and imperfections within possible worlds without families. The recognition that there are many paths to a world without families, and many possible such worlds, is the first step towards aligning reasons, means, and ends and confronting the social and political trade-offs that this entails. (shrink)

A structural equation modelling approach was used to analyse 32 factors affecting students’ attitudes towards test-taking in secondary schools. Data for the study were obtained from a sample of 1,276 students using the proportionate stratified random sampling technique. The instrument used for data collection was a Rating Scale on Factors Affecting Students’ Attitudes Towards Test-Taking (RSFASATTT). Findings of the study revealed a total of 21 factors that significantly affect students’ attitudes towards test-taking in secondary schools. Out of these significant factors, (...) 14 had a positive effect while 7 factors negatively affected students’ attitudes towards test-taking. However, 11 factors were not significant predictors of students’ attitudes towards test-taking. Based on these findings, it was concluded that students’ attitudes towards test-taking are affected by several factors. These factors are either traceable to the students’ emotions, their family background, or the school environment. Based on this conclusion, recommendations and policy implications were made. (shrink)

This paper analyses the hidden use of new axioms in set-theoretic practice with a focus on large cardinal axioms and presents a general overview of set-theoretic practices using large cardinal axioms. The hidden use of a new axiom provides extrinsic reasons in support of this axiom via the idea of verifiable consequences, which is especially relevant for set-theoretic practitioners with an absolutist view. Besides that, the hidden use has pragmatic significance for further important sub-groups of the set-theoretic community---set-theoretic (...) practitioners with a pluralist view and set-theoretic practitioners who aim for ZFC-proofs. By describing this, the paper gives a more complete picture of new axioms in set-theoretic practice. These observations, for instance, show that set-theoretic practitioners interested in ZFC-proofs use tools that go beyond ZFC. The analysis is based on empirical data that was collected in an extensive interview study with set-theoretic practitioners. (shrink)

Chains of causes appear when the existence of God is discussed. It is claimed by some that these chains must be finite and terminated by God. But these chains seem endless through our knowledge search. This endlessness for the physical reasons for any world event expresses the greatness and complexity of God’s creation and so the transcendence of God. So, only we can put our hands on physical reasons in an endless forage for knowledge. Yet, the endlessness of the physical (...) causes chains confirms the existence of God, and this is what our paper tries using Zorn’s lemma, an equivalent for one of the most celebrated axioms of mathematics, the Axiom of Choice. (shrink)

Under the assumption that anticipatory models are required for anticipatory behavior, an important question arises about the different manners in which organisms acquire anticipatory models. This article aims to articulate four different non-exhaustive ways that anticipatory models might possibly be acquired over both phylogenetic and ontogenetic timescales and explore the relationships among them. To articulate these different model-acquisition mechanisms, four schematics will be introduced, each of which represents a particular acquisition structure that can be used for the purposes of comparison, (...) analysis, and hypothesis formulation. By bringing to the fore the differences and similarities between each of the four ways that anticipatory models are acquired, a more complete picture of both anticipatory behavior and its pervasive role in biological self-maintenance can be offered. In doing so, this article helps not only to shed light on how anticipatory behavior might arise in the wide range of organisms that it has been observed in but also to throw into relief the subtle and often still overlooked causal interplay between ontogenetic and phylogenetic plasticity. (shrink)

Path-dependence offers a promising way of understanding the role historicity plays in explanation, namely, how the past states of a process can matter in the explanation of a given outcome. The two main existing accounts of path-dependence have sought to present it either in terms of dynamic landscapes or branching trees. However, the notions of landscape and tree both have serious limitations and have been criticized. The framework of causal networks is both more fundamental and more general that (...) that of landscapes and trees. Within this framework, I propose that historicity in networks should be understood as symmetry breaking. History matters when an asymmetric bias towards an outcome emerges in a causal network. This permits a quantitative measure for how path-dependence can occur in degrees, and offers suggestive insights into how historicity is intertwined both with causal structure and complexity. (shrink)

I propose a framework for comparative Islamic—Western ethics in which the Islamic categories "Islam, Iman," and "Ihsan" are juxtaposed with the concepts of obligation, value, and virtue, respectively. I argue that "shari'a" refers to both the obligation component and the entire structure of the Islamic ethic; suggesting a suspension of the understanding of "shari'a" as simply Islamic "law," and an alternative understanding of "usul al-fiqh" as a moral epistemology of obligation. I will test this approach by addressing the question of (...) reason in Islamic moral epistemology via an examination of an argument advanced by a founding usul scholar Muhammad bin Idrīs al-Shāfi'ī. (shrink)

I highlight three features of P.F. Strawson’s later, neglected work on freedom and responsibility. First, in response to a criticism by Rajendra Prasad, Strawson explicitly rejects an argument put forward in ‘Freedom and Resentment’ against the relevance of determinism to moral responsibility. Second, his remarkable acceptance of Prasad’s criticism motivates him to take the ‘straight path’, that is, to be straightforward about the relation between determinism, freedom, the ability to do otherwise and the conditions of responsibility. He claims that (...) the ability to do otherwise is a necessary condition of responsibility and provides a list of additional conditions, including a knowledge condition. Third, he clarifies the relation between responsibility, quality of will and the reactive attitudes. The latter do not figure essentially in his answer to the question, ‘What are the conditions of responsibility?’, but they do play an essential role in his answer to the question, ‘Why do we have the concept of responsibility?’ We have it, Strawson suggests, because of our natural concern about the quality of will with which people act, a concern expressed in our reactive attitudes. I argue that, although Strawson’s later work definitely involves a shift of emphasis when compared to ‘Freedom and Resentment’, his overall account of freedom and responsibility is coherent. The later work helps to better understand the nature and significance of Strawson’s contribution, and to identify problems with common interpretations of and objections to ‘Freedom and Resentment’. (shrink)

In this paper, I explore the feasibility of a realistic interpretation of the quantum mechanical path integral - that is, an interpretation according to which the particle actually follows the paths that contribute to the integral. I argue that an interpretation of this sort requires spacetime to have a branching structure similar to the structures of the branching spacetimes proposed by previous authors. I point out one possible way to construct branching spacetimes of the required sort, and I ask (...) whether the resulting interpretation of quantum mechanics is empirically testable. (shrink)

In the early 1900s, Russell began to recognize that he, and many other mathematicians, had been using assertions like the Axiom of Choice implicitly, and without explicitly proving them. In working with the Axioms of Choice, Infinity, and Reducibility, and his and Whitehead’s Multiplicative Axiom, Russell came to take the position that some axioms are necessary to recovering certain results of mathematics, but may not be proven to be true absolutely. The essay traces historical roots of, and motivations (...) for, Russell’s method of analysis, which are intended to shed light on his view about the status of mathematical axioms. I describe the position Russell develops in consequence as “immanent logicism,” in contrast to what Irving (1989) describes as “epistemic logicism.” Immanent logicism allows Russell to avoid the logocentric predicament, and to propose a method for discovering structural relationships of dependence within mathematical theories. (shrink)

I've previously suggested that the historical evidence used to challenge scientific realism should lead us to embrace what I call Uniformitarianism, but many recently influential forms of scientific realism seem happy to share this commitment. I trace a number of further points of common ground that collectively constitute an appealing Middle Path between classical forms of realism and instrumentalism, and I suggest that many contemporary realists and instrumentalists have already become fellow travelers on this Middle Path without recognizing (...) how far they have thereby diverged from those who share their labels and slogans. I conclude by describing their central remaining disagreement and the sorts of evidence needed to resolve it. (shrink)

This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent conceptions of harmony through category (...) theory. This categorical harmony is stated in terms of adjoints and says that any concept definable by iterated adjoints from general categorical operations is harmonious. Moreover, it has been shown that identity in a categorical setting is determined by an adjoint in the relevant way. Furthermore, path induction as a rule comes from this definition. Thus we arrive at an account of how path induction, as a rule of inference governing identity, can be justified on mathematically motivated grounds. (shrink)

We show in this paper that the answer to the question in the title is in the negative. In modern optics, Snell’s law of reflection is derived using Leibniz’s calculus method that identifies the least time path, chosen by rays of light in going from a given point A, to another given point B, undergoing reflection at a point P on their way. We demonstrate, taking two examples of reflection: (1) at a plane reflector and (2) at elliptical reflector, (...) that Snell’s law of reflection is not a consequence of least time path principle and, that Leibniz’s method of derivation of Snell’s law of reflection is invalid. In (1), we prove that, if a light ray is reflected at point P on a line, along the least time path APB, then at every point Pi on that line, rays from A are reflected to point B, satisfying Snell’s law. However, paths, APB and APiB do not have equal travel times. In (2), we prove that, if a light ray is reflected along the least time path APB, from focus A to focus B incident at point P on an ellipse, satisfies Snell’s law, then points Pi, not lying on the ellipse, also reflect light rays from A to B, satisfying Snell’s law. However, the paths APB and APiB do not have equal travel times. Thus, both examples prove that least time path is not a criterion for reflection and, that Snell’s law of reflection is not a consequence of least time path principle. (shrink)

Guru Nanak reports that there are three cardinal principles for walking upon the path of truthful living. These are Kirat Karna, Vand Chakna and Nam Japna. Kirat Karna means to earn righteously through one's own efforts. Vand Chakna is to share one's abundance and talents with others. Nam Japna means the contemplation of Truth. In his hymns, Guru Nanak exhorts Sikhs to imbibe love of God and his creation in their life, earn their living by honest labour, and share (...) it with others as; “Sing, and listen, and let your mind be filled with love (for God and His Creation).”[SGGS, 2] “One who earns by honest labour, and shares some of what he has with others, - O Nanak, he knows the true way of life.” [SGGS: 1245] In this second part of the article further elaboration on the path of truthful living is described. (shrink)

Truth is the foundation for a fair and just society. Most modern religions place a high value on the principle of Truthfulness. Truth is a hallmark virtue for anyone walking the path of righteousness because it keeps us genuine and dispels the veils of illusion that would otherwise bind us in temporal life. In his Jap composition, Guru Nanak delineates how to live a truthful life. In this article, the path suggested by Guru Nanak, for a truthful living (...) is described. (shrink)