The five classical elements of creation are also known as Panch Tattva or the basic elements of life. Within these, and through these, life has prevailed and evolved. Although various religious philosophies differ in many details, they emphasize the fundamental unity of the universe through recognizing these elements as the basis of creation. Thus, Panch Tattva's knowledge helps us transcend the notion of an isolated individual self and identify ourselves with the ultimate reality.

The five classical elements of creation are also known as Panch Tattva or the basic elements of life. Within these, and through these, life has prevailed and evolved. Although various religious philosophies differ in many details, they emphasize the fundamental unity of the universe through recognizing these elements as the basis of creation. Thus, Panch Tattva's knowledge helps us transcend the notion of an isolated individual self and identify ourselves with the ultimate reality.

Various religious philosophies the world over, although differ in many details, yet they all emphasize the basic unity of the universe, through the recognition of panch tattva as the basis of creation. Most of these philosophies agree that a continuous exchange between these basic elements life and the creation, helps to balance the ever ongoing cycles of creation and destruction. The existence of panch tattva, with their extraordinary qualities, makes us aware of the unity and mutual interrelation of all things. (...) They help us to transcend the notion of an isolated individual self and to identify ourselves with the ultimate reality. In this article on panch tattva, a perspective from Sri Guru Granth Sahib is outlined. (shrink)

Air is one of the five classical elements, which make all the creation. We can perceive air in the things it moves, be it leaves or hair. It is an invisible mixture of nitrogen, oxygen, and minute amounts of other gases surrounding the Earth. It is all around us. Yet, we cannot see it. Pure air has no odour. It has many uses. It provides a breath of life to all living beings. As, atmosphere, it prevents the excessive heat (...) of the Sun from reaching us. Oxygen, one of its constituents, supports combustion. Thereby it helps us to cook food, generate heat and electricity, run industries and drive vehicles. Its other two components, nitrogen and carbon dioxide, are essential for the growth of plants. Another beneficial constituent of air is Ozone, which in the form of the Ozone layer around our planet protects us from the adverse effects of the Sun's UV rays. Compressed air is used to fill tyres. Many machines and drills work on compressed air. Wind enables the movement of sailboats and gliders. It runs windmills to generate electricity and helps in the dispersal of seeds. Guru Arjan appreciating the priceless importance of air to all of us articulates [1-2]; He (Creator) gave you the invaluable air. (Mehl 5, SGGS, p 913). (shrink)

Air is one of the five classical elements, which make all the creation. We can perceive air in the things it moves, be it leaves or hair. It is an invisible mixture of nitrogen, oxygen, and minute amounts of other gases surrounding the Earth. It is all around us. Yet, we cannot see it. Pure air has no odour. It has many uses. It provides a breath of life to all living beings. As, atmosphere, it prevents the excessive heat (...) of the Sun from reaching us. Oxygen, one of its constituents, supports combustion. Thereby it helps us to cook food, generate heat and electricity, run industries and drive vehicles. Its other two components, nitrogen and carbon dioxide, are essential for the growth of plants. Another beneficial constituent of air is Ozone, which in the form of the Ozone layer around our planet protects us from the adverse effects of the Sun's UV rays. Compressed air is used to fill tyres. Many machines and drills work on compressed air. Wind enables the movement of sailboats and gliders. It runs windmills to generate electricity and helps in the dispersal of seeds. Guru Arjan appreciating the priceless importance of air to all of us articulates [1-2]; He (Creator) gave you the invaluable air. (Mehl 5, SGGS, p 913). (shrink)

In this paper, I present a new framework supporting the claim that some elements in science play a constitutive function, with the aim of overcoming some limitations of Friedman's (2001) account. More precisely, I focus on what I consider to be the gradualism implicit in Friedman's interpretation of the constitutive a priori, that is, the fact that it seems to allow for degrees of 'constitutivity'. I tease out such gradualism by showing that the constitutive character Friedman aims to track can (...) be captured by three features - namely, quasi-axiomaticity (QA), generative potential (GP), and empirical shielding (ES) - which are exhibited to a maximal degree by the examples Friedman deploys, particularly in his analysis of Newtonian mechanics. I argue that not all varieties of 'constitutivity' can be captured by the kind of gradualism implicit in Friedman's view, although developing the gradualism itself might provide useful insights. To show this, I analyse the function of the Hardy-Weinberg principle (HWP) in population genetics in terms of its QA, GP, and ES. Whereas the HWP does not count as constitutive in classical philosophical interpretations (Sober 1984), nor does it within Friedman's framework, it does nonetheless perform a minimally constitutive function. By means of historical details and considerations on the prospects of replacing the HWP, I show that the HWP is minimally constitutive by being a counterfactual instantiation of a paradigmatically constitutive stability principle, where the latter might itself be regarded as an enabling condition for a variety of modelling practices across the sciences. (shrink)

Arthur Pap worked in analytic philosophy while maintaining a strong Kantian or neo-Kantian element throughout his career, stemming from his studying with Ernst Cassirer. I present these elements in the different periods of Pap’s works, showing him to be a consistent critic of logical empiricism, which Pap shows to be incapable of superseding the Kantian framework. Nevertheless, Pap’s work is definitely analytic philosophy, both in terms of the content and the style. According to Pap, the central topics of analytic (...) philosophy concern meaning, modality, and analysis. Pap was also influenced by pragmatism, especially in his dissertation, although he does not fully embrace it in either its classical or its Quinean form. (shrink)

I identify two mutually exclusive notions of formalism in Kant’s Critique of Aesthetic Judgement: a thin concept of aesthetic formalism and a thick concept of aesthetic formalism. Arguably there is textual support for both concepts in Kant’s third critique. I offer interpretations of three key elements in the Critique of Aesthetic Judgement which support a thick formalism. The three key elements are: Harmony of the Faculties, Aesthetic Ideas and Sensus Communis. I interpret these concepts in relation to the conditions for (...) theoretical Reason, the conditions for moral motivation and the conditions for intersubjectivity, respectively. I conclude that there is no support for a thin concept of aesthetic formalism when the key elements of Kant’s Critique of Aesthetic Judgement are understood in the context of his broader critical aims. (shrink)

The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements (...) of subsets so there is a dual concept of logical entropy which is the normalized counting measure on distinctions of partitions. Thus the logical notion of information is a measure of distinctions. Classical logical entropy naturally extends to the notion of quantum logical entropy which provides a more natural and informative alternative to the usual Von Neumann entropy in quantum information theory. The quantum logical entropy of a post-measurement density matrix has the simple interpretation as the probability that two independent measurements of the same state using the same observable will have different results. The main result of the paper is that the increase in quantum logical entropy due to a projective measurement of a pure state is the sum of the absolute squares of the off-diagonal entries ("coherences") of the pure state density matrix that are zeroed ("decohered") by the measurement, i.e., the measure of the distinctions ("decoherences") created by the measurement. (shrink)

We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is (...) defined in terms of a \-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints. (shrink)

In this paper, I generalise the logical concept of compatibility into a broader set-theoretical one. The basic idea is that two sets are incompatible if they produce at least one pair of opposite objects under some operation. I formalise opposition as an operation ′ ∶ E → E, where E is the set of opposable elements of our universe U, and I propose some models. From this, I define a relation ℘U × ℘U × ℘U^℘U, which has (mutual) logical compatibility (...) as its more natural interpretation. (shrink)

This paper deals with Austinian ifs of every stripe within classical logic. It is argued that they are truth-functional and the theory of conditional elements is used. Ellipsis is key. Corrects an error in Fulda (2010) in translation and therefore scope. -/- The PDF is made available gratis by the Publisher.

In this paper I contend that the 'superfluity' of triangles is only apparent; all those specified are indeed required for the smallest sub-units, so long as the symmetry of the final body to be constructed is taken into account at earlier stages.

As the word demos denotes, the democracy is generally considered as the rule or governance based on the general base of people in which monarchy or oligarchy form is excluded. We have a classical view about the four forms of government, which was proposed by Platonic concepts. Most idealistic form of government, in his prongs, could be found in Crete and Sparta, which was nevertheless not a democratic form. His accolade of these two nations, which, of course, would be (...) a kind of God’s product so to be most benevolent, humanly appealing, efficient and philanthropic. This means the democratic form of government is not best, but most favored alternative to police the society. The political terms, henceforth, would supervene the concept of democracy, and, for many reasons and on historical wake, democracy is generally accepted as practically most desired form of rule or governance. While some modern scholar revealed, a mini-republic can be a niche to contest the merits of various forms of governance. We can gauge a scope of elements we value through the governance process, human intrinsic, efficiency, equality, welfare and even individual happiness. As the time is a small city community, called a polis, in Plato and Socrates, a mini republic can be well envisaged in understanding the Platonic Republic. In that case, most benevolent ruler may be superior to any other form of governance, which can be a philosopher’s Republic. The ideal ruler would behave and govern with mighty intelligence and concomitant power to rule. It is idealistic to produce maximum happiness of polis constituents. The worst contras, however, a tyranny, comes that the constituents legitimately expel their ruler by a collective vote. This extreme contrast and the way of process also could be ascertained in the ancient form of oriental monarchy. The dynasty could be legitimately revoked to restore new heritage of emperor or Kings where a kind of rebellion, as elucidated by Locke, is well justified in the name of heaven’s command. Given the size of polis or governed territory, there are separate ways to redress the evils of tyranny while the Oriental culture has not recognized the kind of formal vote methods. Any means to expel the tyranny could be embraced to rebel. For our purpose of grasp through this working paper, I would theorize on the traditional elements of public policy and democratic form of government. (shrink)

In this dissertation, I present a novel account of the components that have a peculiar epistemic role in our scientific inquiries, since they contribute to establishing a form of coordination. The issue of coordination is a classic epistemic problem concerning how we justify our use of abstract conceptual tools to represent concrete phenomena. For instance, how could we get to represent universal gravitation as a mathematical formula or temperature by means of a numerical scale? This problem is particularly pressing when (...) justification for using these abstract tools comes, in part or entirely, from knowledge which is not independent from them, thus leading to threats of circularity. Achieving coordination between some abstract conceptual tools and the concrete phenomena that they are supposed to represent is usually a complex process, which involves several epistemic components. Some of these components eventually provide stable conditions for applying those abstract representations to concrete phenomena. It is in this sense of providing certain conditions of applicability that different philosophical traditions, as well as some contemporary reappraisals, view these components as constitutive or a priori. In this work, I present a new gradualist, contextualist, and relational approach to understand these constitutive components of scientific inquiry. It is gradualist inasmuch as the degree to which some component is constitutive depends on three quantifiable features: quasi-axiomaticity, generative potential, and empirical shielding. Since the quantification of these three features impinges on the history and practice of using these components in a scientific context, my approach is a contextualist one. Finally, my approach is relational in a double sense: first, it identifies ordinal relationships among epistemic components with respect to their constitutive character; second, these relationships are relative to a scientific framework of inquiry. After introducing my account and a classic example of constitutively a priori principles, i.e., Friedman’s (2001) analysis of Newtonian mechanics, I turn to my own case studies to demonstrate the advantages of my approach. Firstly, I discuss Okasha’s (2018) view of endogenization as a pervasive theoretical strategy in evolutionary biology and suggest that the constitutive character of the core Darwinian principles progressively increases with endogenization. Secondly, I apply a conceptual distinction between two varieties or scopes of coordination – general coordination and coordination in measurement – to Ohm’s work on electrical conductivity. This distinction allows me to pinpoint to what extent components along different dimensions (e.g., instrumentation, measurement, theorising, etc.) were constitutive of the forms of coordination which Ohm relied on. Thirdly, I discuss the epistemic function of the Hardy-Weinberg principle in the history and practice of population genetics. I assess this principle in terms of my account and identify approximation and stability as two components that are highly constitutive, in that they contribute to justifying its use in population genetics. Finally, applying my account to these case studies enables me to identify at least three qualitatively different types of constitutive components: domain-specific theoretical principles, material components, and domain-independent assumptions underlying reasoning abilities. In the light of my results, I draw some general conclusions on epistemic justification and scientific knowledge. (shrink)

We present a new metaphysical framework for physics that is conceptually clear, ontologically parsimonious, and empirically adequate. This framework relies on the notion of self-subsisting structure, that is, a set of fundamental physical elements whose individuation and behavior are described in purely relational terms, without any need for a background spacetime. Although the specification of the fundamental elements of the ontology depends on the particular physical domain considered---and is thus susceptible to scientific progress---, the empirically successful structural features of the (...) framework are preserved through theory change. The kinematics and dynamics of these self-subsisting structures are technically implemented using the theoretical framework of Pure Shape Dynamics, which provides a completely relational physical description of a system in terms of the intrinsic geometry of a suitably defined space called shape space. (shrink)

This article aims to provide a metaphysical elucidation of the notion of Theism and a coherent theological synthesis of two extensions of this notion: Classical Theism and Neo-Classical Theism. A model of this notion and its extensions is formulated within the ontological pluralism framework of Kris McDaniel and Jason Turner, and the (modified) modal realism framework of David Lewis, which enables it to be explicated clearly and consistently, and two often raised objections against the elements of this notion (...) can be successfully answered. (shrink)

This essay aims to provide an account of the differences between what I call the “Classical Marxist” conception of science which was adhered to by Marx and Engels and further developed by Boris Hessen and others on the one hand, and the conception of science which characterizes “Western Marxism” as it developed through the work of the theorists of the Frankfurt School on the other hand. I argue that Western Marxists such as Herbert Marcuse and Max Horkheimer did not (...) in fact successfully criticize the logical positivist account of the modern natural sciences. Instead I argue that they implicitly accepted the positivists’ characterization of the modern natural sciences (as they interpreted it) and then proceeded to devalue the modern natural sciences on this basis. I also show that Marcuse and Horkheimer, even though they presented themselves as revolting against the alleged “economism” of Classical Marxism, ended up endorsing a view of science which is functionally equivalent to a reductive economistic conception of science. I argue that the Classical Marxists’ conception of science is far richer and far more interesting than either a stereotyped “economistic” conception of science or the Western Marxist conception of modern science as merely an element in a historical process centered on the oppressive universalization of instrumental reasoning. (shrink)

The classical Confucian philosopher Xunzi proposed a naturalistic virtue ethics account of ritual: rituals are practices that channel human emotion and desire so that one develops virtues. In this paper I show that William of Auxerre’s Summa de Officiis Ecclesiasticis can be understood as presenting a similar account of ritual. William places great emphasis on the emotional power of the liturgy, which makes participants like the blessed in heaven by developing virtue. In other words, he has a virtue ethics (...) of ritual closely aligned with that of Xunzi. Xunzi’s writings on ritual illuminate and enrich one’s reading of the Summa de Officiis. But unlike Xunzi, William is not a naturalist with regard to ritual: although much of William’s language about the causal power of liturgy can be explained in Xunzian terms, Christian liturgy has an irreducible supernatural element. (shrink)

This paper presents Duns Scotus’s theory of mixture in the context of medieval discussions over Aristotle’s theory of mixed bodies. It revisits the accounts of mixture given by Avicenna, Averroes, and Thomas Aquinas, before presenting Scotus’s account as a reaction to Averroes. It argues that Duns Scotus rejected the Aristotelian theory of mixture altogether and that his account went contrary to the entire Latin tradition. Scotus denies that mixts arise out of the four classical elements and he maintains that (...) both the elemental forms and the elemental qualities are lost in the mixture. Consequently, he denies the distinction between the process of mixture and that of substantial change through generation and corruption. The reassessment of Scotus’s account modifies the current historical representation of this discussion, inherited from Anneliese Maier. (shrink)

In the world of Avatar: The Last Airbender (ATLA) and The Legend of Korra (LOK) —let’s call it the Bending World—some people (“benders”) are endowed with telekinetic superpowers to maneuver surrounding objects without physical interaction, by mentally steering (“bending”) one of the four classical “elements of nature” composing the objects: air, fire, water, and earth. Perhaps, in a world where the fundamental laws of nature are radically different from those of our world, the fundamental conditions and manifestations of politics (...) should be radically different too. That, of course, is not to deny that political bodies familiar to us are depicted in ATLA and LOK: tribes, monarchies, autonomous townships, city-states, loose federations, colonial empires, and democracies. Despite those familiar depictions, however, it’s worth contemplating how the existence of supernatural power might fundamentally alter the norms and rationales of politics—and how it might in turn help us better understand our own political reality. (shrink)

Nature, a treasure trove of wisdom, is a great teacher of amazingly priceless life lessons to live a happy and worthwhile life. It speaks to us through its various phenomena. Gurbani helps up to decode Nature's invaluable lessons. Gurbani enunciates that Nature helps us to develop compassion and inner balance. It also guides us to help others to lead better lives. The interplay of five classical elements-air, water, fire, earth and akasha is the fundamental cause of all-natural phenomena. Let (...) us reflect on some of the social, ethical and spiritual lessons being provided by these. (shrink)

Nature, a treasure trove of wisdom, is a great teacher of amazingly priceless life lessons to live a happy and worthwhile life. It speaks to us through its various phenomena. Gurbani helps us to decode Nature's invaluable lessons. Gurbani enunciates that Nature helps us to develop compassion and inner balance. It also guides us to help others to lead better lives. The interplay of five classical elements - air, water, fire, earth, and akasha is the fundamental cause of all-natural (...) phenomena. Let us reflect on some of the social, ethical and spiritual lessons being provided by these. Nature comprises the totality of material reality that does not result from human will. It is also defined as the whole universe as a place, source, and result of material phenomena, including humans. Sikhs commonly use the term Gurbani to refer to the hymns in the holy Sikh scripture, Sri Guru Granth Sahib. Nature and Gurbani both provide very crucial lessons in the social, ethical, and spiritual spheres. Some of these lessons are outlined hereafter. (shrink)

In recent decades, plural logic has established itself as a well-respected member of the extensions of first-order classical logic. In the present paper, I draw attention to the fact that among the examples that are commonly given in order to motivate the need for this new logical system, there are some in which the elements of the plurality in question are internally singularized (e.g. ‘Whitehead and Russell wrote Principia Mathematica’), while in others they are not (e.g. ‘Some philosophers wrote (...) Principia Mathematica’). Then, building on previous work, I point to a subsystem of plural logic in which inferences concerning examples of the first type can be adequately dealt with. I notice that such a subsystem (here called ‘discrete plural logic’) is in reality a mere variant of first-order logic as standardly formulated, and highlight the fact that it is axiomatizable while full plural logic is not. Finally, I urge that greater attention be paid to discrete plural logic and that discrete plurals are not used in order to motivate the introduction of full-fledged plural logic—or, at least, not without remarking that they can also be adequately dealt with in a considerably simpler system. (shrink)

This paper elaborates on relationalism about space and time as motivated by a minimalist ontology of the physical world: there are only matter points that are individuated by the distance relations among them, with these relations changing. We assess two strategies to combine this ontology with physics, using classical mechanics as example: the Humean strategy adopts the standard, non-relationalist physical theories as they stand and interprets their formal apparatus as the means of bookkeeping of the change of the distance (...) relations instead of committing us to additional elements of the ontology. The alternative theory strategy seeks to combine the relationalist ontology with a relationalist physical theory that reproduces the predictions of the standard theory in the domain where these are empirically tested. We show that, as things stand, this strategy cannot be accomplished without compromising a minimalist relationalist ontology. (shrink)

Toleration classically denotes a relation between two agents that is characterised by three components: objection, power, and acceptance overriding the objection. Against recent claims that classical toleration is not applicable in liberal democracies and that toleration must therefore either be understood purely attitudinally or purely politically, we argue that the components of classical toleration are crucial elements of contemporary cases of minority accommodation. The concept of toleration is applicable to, and is an important element of descriptions of (...) such cases, provided that one views them as wholes, rather than as sets of isolated relations. We explain this by showing how certain cases of toleration are multi-dimensional and how the descriptive concept of toleration might be understood intersectionally. We exemplify this by drawing on case studies of mosque controversies in Germany and Denmark. Finally, we propose that intersectionality is not only relevant to the descriptive concept of toleration but also captures an important aspect of normative theories of toleration. We illustrate this by discussing ideals of respect-based toleration, which we also apply to the case studies. (shrink)

ABSTRACT The philosophical tradition approaches to morals have their grounds predominantly on metaphysical and theological concepts and theories. Among the traditional ethics concepts, the most prominent is the Divine Command Theory (DCT). As per the DCT, God gives moral foundations to the humankind by its creation and through Revelation. Morality and Divinity are inseparable since the most remote civilization. These concepts submerge in a theological framework and are largely accepted by most followers of the three Abrahamic traditions: Judaism, Christianity, and (...) Islam: the greatest part of the human population. Holding faith and Revelation for its grounds, the Divine Command Theories are not strictly subject to the demonstration. The opponents to the Divine Command conception of morals, grounded in the impossibility of demonstration of its metaphysical and religious assumptions, have tried for many centuries (albeit unsuccessfully) to devalue its importance. They held the argument that it does not show material evidence and logical coherence and, for this reason, cannot be taken into account for scientific nor philosophical purposes. It is just a belief and, as so, should be understood. Besides these extreme oppositions, many other concepts contravene the Divine Command theories, in one or another way, in part or in full. Many philosophers and social scientists, from the classic Greek philosophy up to the present date, for instance, sustain that morality is only a construct, and thus culturally relative and culturally determined. However, this brings many other discussions and imposes the challenge to determine what is the meaning of culture, which elements of culture are morally determinant, and finally, what are the boundaries of such relativity. Moral determinists claim that everything related to human behavior, including morality, is determined, once free will does not exist. More recently, modern thinkers argued that there is a strict science of morality. However, the scientific method alone, despite explaining several facts and evidence, cannot enlighten the entire content and full meaning of ethics. Morals’ understanding requires a broader perception, and an agreement among philosophers, which they have never achieved. All of these questions have many different configurations depending on each philosophical strand, and start complex analysis and endless debates, as long as many of them are reciprocally conflictive. The universe and the atmosphere involving this thesis are the dominions of all these conceptual conflicts, observed from an objective and evolutionary standpoint. Irrespective of this circumstance and its intrinsic importance, however, these questions are far distant from the methodological approach of an analytical discussion on objective morals, what is, indeed, the aim and scope of this work. We should briefly revisit these prominent traditional theories because this thesis shelters a comparative study, and its assumptions at least differ profoundly from all traditional theories. Therefore, it becomes necessary offering direct and specific elements of comparison to the reader, for the right criticism, dispensing interruptive researches. However, even revisiting the traditional theories, for this comparative and critical exposure purpose, they will be kept by the side of our main concerns, as “aliena materia.” Irrespective of the validity of any or all of the elements of this discussion, and their meaning as the philosophical universe of this thesis, the purpose of this work is demonstrating and justifying the existence and meaning of prehistoric moral archetypes arisen directly from the very first social needs and efforts for survival. These archetypes are the definition of the essential foundation of ethics, its aggregation to the collective unconscious and corresponding logic organization and transmission to evolutionary stages of the human genome and different relations space-time, irrespective of any contemporary experience of the individuals. The system defined by these archetypes composes an evolutionary human social model. Is this a metaethical position? Yes, it is. Moreover, as in any metaethical reasoning, we should look carefully for the best and coherent routes, as the Analytical Philosophy offers them. Thus, this work should reasonably demonstrate that morals are not a cultural product of the civilized men or modern societies and that despite being subject to several cultural relative aggregations and subtractions, its essential foundations are archetypal and have never structurally changed. This reasoning induces that morality is an original attribute of the “homo sapiens”; it is not a property and nor an accident: it integrates the human essence and belongs to the realm of the ontological human identity. The human phenomena is a continuing process, playing its role between random determination and free will, and we need to question how morality began and how did it come to us in the present. (shrink)

Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences (...) of a flaw. However, since different programs and machines can interact with (or be nested into) one another, we need to account for different kind of errors, and this calls for an evaluation of systems with multiple contaminating values. In this paper, we make steps toward these evaluation systems by considering two logics, HYB1 and HYB2, whose semantic interpretations account for two contaminating values beside classical values 0 and 1. In particular, we provide two main formal contributions. First, we give a characterization of their relations of (multiple-conclusion) logical consequence—that is, necessary and sufficient conditions for a set Δ of formulas to logically follow from a set Γ of formulas in HYB1 or HYB2 . Second, we provide sound and complete sequent calculi for the two logics. (shrink)

The epistemic status of Natural Selection has intrigued to biologists and philosophers since the very beginning of the theory to our present times. One prominent contemporary example is Elliott Sober, who claims that Natural Selection, and some other theories in biology, and maybe in economics, are peculiar in including explanatory models/conditionals that are a priori in a sense in which explanatory models/conditionals in Classical Mechanics and most other standard theories are not. In this paper, by analyzing what we take (...) to be the four possible interpretations of Sober’s claim, we argue that, terminological preferences aside, the possible senses in which explanatory models in Natural Selection can qualify, or include elements that can qualify, as a priori, also apply to Classical Mechanics and other standard, highly unified theories. (shrink)

Many approaches to quantum gravity -the theory that should account for quantum and gravitational phenomena under the same theoretical umbrella- seem to point at some form of spacetime emergence, i.e., the fact that spacetime is not a fundamental entity of our physical world. This tenet has sparked many philosophical discussions: from the so-called empirical incoherence problem to different accounts of emergence and mechanisms thereof. In this contribution, I focus on the partial order relation of causal set theory and argue that (...) causation can be characterized as an a-temporal constraint over the kinematic space defined by the theory. The relation constrains the growth of a new element/event with respect to the other elements/events of a given set. Therefrom, the flow of time emerges from the collection of the possible growths of the given set, where each possibility is characterized by a classical probability assigned by the dynamics of the theory. (shrink)

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, (...) the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets and their applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Neutrosophic triplet was first defined in 2016 by Florentin Smarandache and Mumtaz Ali and they also introduced the neutrosophic triplet groups in the same year. For every element “x” in a neutrosophic triplet set A, there exist a neutral of “x” and an opposite of “x”. Also, neutral of “x” must be different from the classical neutral element. Therefore, the NT set is different from the classical set. Furthermore, a NT of “x” is showed by . This first volume collects original research and applications from different perspectives covering different areas of neutrosophic studies, such as decision making, Triplet, topology, and some theoretical papers. This volume contains three sections: NEUTROSOPHIC TRIPLET, DECISION MAKING, AND OTHER PAPERS. (shrink)

K denotes both the knowledge predicate satisfied by every currently known theorem and the finite set of all currently known theorems. The set K is time-dependent, publicly available, and contains theorems both from formal and constructive mathematics. Any theorem of any mathematician from past or present forever belongs to K. Mathematical statements with known constructive proofs exist in K separately and form the set K_c⊆K. We assume that mathematical sets are atemporal entities. They exist formally in ZFC theory although their (...) properties can be time-dependent (when they depend on K) or informal. The true statement "K is non-empty" is outside K forever because K is not a formal set. Paul Cohen proved in 1963 that the equality 2^{\aleph_0}=\aleph_1 is independent of ZFC. Before 1963, the statement "There is a known constructively defined integer n⩾1 such that 2^{\aleph_0}=\aleph_n" was outside K. Since 1963, this statement is outside K forever. The true statement "There exists a set X⊆{1,...,49} such that card(X)=6 and X never occurred as the winning six numbers in the Polish Lotto lottery" refers to the current non-mathematical knowledge and is outside K forever. In Martin-Löf's terminology, every currently known theorem is actually true whereas every theorem (known or unknown) is potentially true. Actual truth is knowledge dependent and tensed. Potential truth is knowledge independent and tenseless. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivially true statements on decidable sets X⊆N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X. For every such statement, its truth concerning the current mathematical knowledge is implied by a true statement of the form: (the conjunction of i conditions of the form α∈K)∧(the conjunction of j conditions of the form β∉K)∧(the conjunction of k conditions of the form γ∈K_c)∧(the conjunction of l conditions of the form δ∉K_c), where i,j,k,l∈N and α,β,γ,δ are mathematical statements. In constructive mathematics and the traditional Brouwerian intuitionism, the truth of a mathematical statement means that we know a constructive proof. Therefore, the truth of a mathematical statement depends on time, where the statement is formally stated in the classical mathematics without the predicate K. In this article, mathematical statements on decidable sets X⊆N refer to time because they refer to the current mathematical knowledge on X. They cannot be formally stated in the classical mathematics without the predicate K and their logical values may change in time. For a set X⊆N whose infiniteness is false or unproven, we define which elements of X are classified as known. No known set X⊆N satisfies Conditions (1)-(4) and is widely known in number theory or naturally defined, where this term has only informal meaning. (1) A known algorithm with no input returns an integer n satisfying card(X)<ω ⇒ X⊆(-∞,n]. (2) A known algorithm for every k∈N decides whether or not k∈X. (3) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(X)=ω" is outside K. (4) There are many elements of X and it is conjectured, though so far unproven, that X is infinite. (5) X is naturally defined. The infiniteness of X is false or unproven. X has the simplest definition among known sets Y⊆N with the same set of known elements. No set X⊆N will satisfy Conditions (1)-(4) forever, if for every algorithm with no input, at some future day, a computer will be able to execute this algorithm in 1 second or less. The physical limits of computation disprove the assumption of the above statement. We prove that the set X={n∈N: the interval [-1,n] contains more than 29.5+(11!/(3n+1))∙sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. We present a table that shows satisfiable conjunctions of the form #(Condition1)∧(Condition 2)∧#(Condition 3)∧(Condition 4)∧#(Condition 5), where # denotes the negation ¬ or the absence of any symbol. We prove that there exists a naturally defined set C⊆N which satisfies the following conditions (6)-(11). (6) A known and simple algorithm for every k∈N decides whether or not k∈C. (7) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(C)=ω" is outside K. (8) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(N\C)=ω" is outside K. (9) It is conjectured, though so far unproven, that C is infinite. (10) For every known algorithm A with no input, the statement "A returns an integer n satisfying card(C)<ω ⇒ C⊆(-∞,n]" is outside K. (11) For every known algorithm A with no input, the statement "A returns an integer m satisfying card(N\C)<ω ⇒ N\C⊆(-∞,m]" is outside K. The set C={k∈N: 2^{2^k}+1 is composite} is naturally defined and satisfies conditions (6)-(11). (shrink)

It is proposed a critique of existing interpretations of quantum mechanics, both anti-realistic and realistic, and, in particular, the Copenhagen interpretation, the interpretations with hidden variables, the metaphysical interpretation of H. Everett’s interpretation, the many-worlds interpretation by D. Wallace, QBism by C. Fuchs, D. Mermin and R. Schack, the relational interpretation by C. Rovelli, neo-Kantian and phenomenological interpretations by M. Bitbol, the informational interpretation by A. Zeilinger, the Nobel Prize Winner in Physics 2022, and others. As is known compared to (...) classical physics, quantum mechanics is a new physical paradigm. The author argues that from a philosophical point of view quantum mechanics is an anomaly within the paradigm of (post)modern philosophy. A new approach to understanding quantum mechanics and resolving its paradoxes, rejecting the assumptions and prejudices of (post)modern philosophy, is proposed – contextual quantum realism (CQR). It is a moderately deflationary approach that combines elements of (neo-)Copenhagen, informational and realist interpretations and recognizes the possibility of knowing the things themselves. From the point of view of CQR, the measurement problem – the basic problem of philosophy of quantum mechanics – is a pseudo-problem . (shrink)

In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false.

Although being widely considered as only a Western tradition, individualism is not absent in traditional Chinese philosophy and culture. In some of the classic Chinese philosophic works such as Zhuangzi, we can clearly identify some elements which can be appropriately attributed to “individualism”, such as the awareness of individual “self” as an independent and unique existence, advocating individual freedom and liberty, emphasizing on the value and dignity of individual life, favoring individuals’ autonomy and privacy, pursuing unconstrained development in personality and (...) spirituality. However, due to its particular pre-Qin social cultural background and its unique Daoist philosophic origin, this kind of individualism in Zhuangzi has its own unique characteristics, which has made it distinguishable from the variety of other individualist thoughts emerged in different times and places in the West. Zhuangzi has a dynamic and open view on individual or “self”, he does not consider individuals as fixed and interchangeable “atoms” but as dynamic, changing and unique beings, he set the unlimited and indefinable Dao as the only and ultimate source for individuals to conform to, thus to release individual mind into an realm of infinite openness and freedom. Zhuangzian individualism is “inward” rather than “outward”, which means while concentrating on individuals’ freedom of spirit and innate nature, it cares less about individuals’ outside material interests and rights in social reality, and does not encourage competition and rivalry among individuals. The special type of individualism in Zhuangzi has a profound influence on Chinese culture, providing a spiritual space for the development of individuality and personality in ancient China. It also provides an alternative understanding of individual as an existence. (shrink)

Coherence and correspondence are classical contenders as theories of truth. In this paper we examine them instead as interacting factors in the dynamics of belief across epistemic networks. We construct an agent-based model of network contact in which agents are characterized not in terms of single beliefs but in terms of internal belief suites. Individuals update elements of their belief suites on input from other agents in order both to maximize internal belief coherence and to incorporate ‘trickled in’ elements (...) of truth as correspondence. Results, though often intuitive, prove more complex than in simpler models (Hegselmann & Krause 2002, 2006; Grim, Singer, Reade & Fisher 2015). The optimistic finding is that pressures toward internal coherence can exploit and expand on small elements of truth as correspondence is introduced into epistemic networks. Less optimistic results show that pressures for coherence can also work directly against the incorporation of truth, particularly when coherence is established first and new data is introduced later. (shrink)

The COVID-19 pandemic has been overwhelming public health-care systems around the world. With demand exceeding the availability of medical resources in several regions, hospitals have been forced to invoke triage. To ensure that this difficult task proceeds in a fair and organised manner, governments scrambled experts to draft triage guidelines under enormous time pressure. Although there are similarities between the documents, they vary considerably in how much weight their respective authors place on the different criteria that they propose. Since most (...) of the recommendations do not come with ethical justifications, analysing them requires that one traces back these criteria to their underlying theories of distributive justice. In the literature, COVID-19 triage has been portrayed as a value conflict solely between utilitarian and egalitarian elements. While these two accounts are indeed the main antipodes, I shall show that in fact all four classic theories of distributive justice are involved: utilitarianism, egalitarianism, libertarianism, and communitarianism. Detecting these in the documents and classifying the suggested criteria accordingly enables one to understand the balancing between the different approaches to distributive justice—which is crucial for both managing the current pandemic and in preparation for the next global health crisis. (shrink)

In this article, some classical paradoxes of infinity such as Galileo’s paradox, Hilbert’s paradox of the Grand Hotel, Thomson’s lamp paradox, and the rectangle paradox of Torricelli are considered. In addition, three paradoxes regarding divergent series and a new paradox dealing with multiplication of elements of an infinite set are also described. It is shown that the surprising counting system of an Amazonian tribe, Pirah ̃a, working with only three numerals (one, two, many) can help us to change our (...) perception of these paradoxes. A recently introduced methodology allowing one to work with finite, infinite, and infinitesimal numbers in a unique computational framework not only theoretically but also numerically is briefly described. This methodology is actively used nowadays in numerous applications in pure and applied mathematics and computer science as well as in teaching. It is shown in the article that this methodology also allows one to consider the paradoxes listed above in a new constructive light. (shrink)

In his classic Film as Art, Rudolf Arnheim sets out to refute the claim that “Film cannot be art, for it does nothing but reproduce reality mechanically”.1 The usual argument in favor of that claim, he explains, contrasts film with realist painting, and goes something like this: There’s no doubt that what appears on the canvas depends on the way the painter sees the world, on her particular technique, on the colors she’s using, and so on. It is elements like (...) these that justify aesthetic appreciation. What appears on celluloid, on the other hand, is the result of a purely mechanical process of light rays collecting and transforming into an image. In other words, a camera is merely a mechanical recording device, and for this very reason film cannot be art. (shrink)

This essay critically examines some classic philosophical and legal theories of privacy, organized into four categories: the nonintrusion, seclusion, limitation, and control theories of privacy. Although each theory includes one or more important insights regarding the concept of privacy, I argue that each falls short of providing an adequate account of privacy. I then examine and defend a theory of privacy that incorporates elements of the classic theories into one unified theory: the Restricted Access/Limited Control (RALC) theory of privacy. Using (...) an example involving data-mining technology on the Internet, I show how RALC can help us to frame an online privacy policy that is sufficiently comprehensive in scope to address a wide range of privacy concerns that arise in connection with computers and information technology. (shrink)

Abstract. The aim of this paper is to present a topological method for constructing discretizations (tessellations) of conceptual spaces. The method works for a class of topological spaces that the Russian mathematician Pavel Alexandroff defined more than 80 years ago. Alexandroff spaces, as they are called today, have many interesting properties that distinguish them from other topological spaces. In particular, they exhibit a 1-1 correspondence between their specialization orders and their topological structures. Recently, a special type of Alexandroff spaces was (...) used by Ian Rumfitt to elucidate the logic of vague concepts in a new way. According to his approach, conceptual spaces such as the color spectrum give rise to classical systems of concepts that have the structure of atomic Boolean algebras. More precisely, concepts are represented as regular open regions of an underlying conceptual space endowed with a topological structure. Something is subsumed under a concept iff it is represented by an element of the conceptual space that is maximally close to the prototypical element p that defines that concept. This topological representation of concepts comes along with a representation of the familiar logical connectives of Aristotelian syllogistics in terms of natural settheoretical operations that characterize regular open interpretations of classical Boolean propositional logic. In the last 20 years, conceptual spaces have become a popular tool of dealing with a variety of problems in the fields of cognitive psychology, artificial intelligence, linguistics and philosophy, mainly due to the work of Peter Gärdenfors and his collaborators. By using prototypes and metrics of similarity spaces, one obtains geometrical discretizations of conceptual spaces by so-called Voronoi tessellations. These tessellations are extensionally equivalent to topological tessellations that can be constructed for Alexandroff spaces. Thereby, Rumfitt’s and Gärdenfors’s constructions turn out to be special cases of an approach that works for a more general class of spaces, namely, for weakly scattered Alexandroff spaces. This class of spaces provides a convenient framework for conceptual spaces as used in epistemology and related disciplines in general. Alexandroff spaces are useful for elucidating problems related to the logic of vague concepts, in particular they offer a solution of the Sorites paradox (Rumfitt). Further, they provide a semantics for the logic of clearness (Bobzien) that overcomes certain problems of the concept of higher2 order vagueness. Moreover, these spaces help find a natural place for classical syllogistics in the framework of conceptual spaces. The crucial role of order theory for Alexandroff spaces can be used to refine the all-or-nothing distinction between prototypical and nonprototypical stimuli in favor of a more fine-grained gradual distinction between more-orless prototypical elements of conceptual spaces. The greater conceptual flexibility of the topological approach helps avoid some inherent inadequacies of the geometrical approach, for instance, the so-called “thickness problem” (Douven et al.) and problems of selecting a unique metric for similarity spaces. Finally, it is shown that only the Alexandroff account can deal with an issue that is gaining more and more importance for the theory of conceptual spaces, namely, the role that digital conceptual spaces play in the area of artificial intelligence, computer science and related disciplines. Keywords: Conceptual Spaces, Polar Spaces, Alexandroff Spaces, Prototypes, Topological Tessellations, Voronoi Tessellations, Digital Topology. (shrink)

Neutral monism is a position in metaphysics defended by Mach, James, and Russell in the early twentieth century. It holds that minds and physical objects are essentially two different orderings of the same underlying neutral elements of nature. This paper sets out some of the central concepts, theses and the historical background of ideas that inform this doctrine of elements. The discussion begins with the classic neutral monism of Mach, James, and Russell in the first part of the paper, then (...) considers recent neo-Russellian versions in the second half. The chances for a revival of neutral monism are probably slight; its key ideas and starting points lie far from those in contemporary philosophy of mind. A better route might be through the philosophy of science and a deeper understanding of causation. (shrink)

This is a brief review of the Rasa theory of Indian aesthetics and the works I have done on the same. A major source of the Indian system of classification of emotional states comes from the ‘Natyasastra’, the ancient Indian treatise on the performing arts, which dates back to the 2nd Century AD (or much earlier, pg. LXXXVI: Natyasastra, Ghosh, 1951). The ‘Natyasastra’ speaks about ‘sentiments’ or ‘Rasas’ (pg.102: Natyasastra, Ghosh, 1951) which are produced when certain ‘dominant states’ (sthayi Bhava), (...) ‘transitory states’ (vyabhicari Bhava) and ‘temperamental states’ (sattvika Bhava) of emotions come together (pgs.102, 105: Natyasastra, Ghosh, 1951). This Rasa theory, which is still widely followed in classical Indian performing arts, classifies eight Rasas or sentiments which are: Sringara (erotic), Hasya (comic), Karuna (pathetic), Raudra (furious), Vira (heroic), Bhayanaka (terrible), Bibhatsa (odious) and Adbhuta (marvellous). There was a later addition of the ninth sentiment or Rasa called Santa (peace) in later Sanskrit poetics (pg.102: Natyasastra, Ghosh, 1951). According to ancient Indian aesthetics (especially in the context of Bharatas’ ‘Natyasastra’, Anandavardhana’s ‘Dhvanyaloka’ and Abhinavagupta’s ‘Abhinavabharati’), ‘Rasa’ is the relishable state of elemental human emotions called ‘Bhavas’. Bharata’s ‘Natyasastra’ originally spoke of eight Rasas. The concept of the 9th Rasa was a later interpolation by the Kashmiri Shaivist Abhinavagupta (10th Century AD) and also his predecessor Anandavardhana (9th Century AD). Abhinavagupta extends the eight Rasas by adding the concept of the Santa Rasa which he regards as the essence of all Rasas. It is this 9th Rasa which according to Abhinavagupta lets the Rasika attain the aesthetic detachment and savour the essences of all other Rasas and therefore the true aesthetic delight. The introduction of 9th Rasa integrates the concepts of Bharata’s Rasasutra and Patanjali’s Yoga theory – the detachment necessary to introspect inwards into the inherent state of freedom and bliss (aesthetic consciousness). (shrink)

ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment). ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any (...) arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)

Recent work in contemporary compatibilist theory displays considerable sophistication and subtlety when compared with the earlier theories of classical compatibilism. Two distinct lines of thought have proved especially influential and illuminating. The first developed around the general hypothesis that moral sentiments or reactive attitudes are fundamental for understanding the nature and conditions of moral responsibility. The other important development is found in recent compatibilist accounts of rational self-control or reason responsiveness. Strictly speaking, these two lines of thought have developed (...) independent of each other. However, in the past decade or so they have been fused together in several prominent statements of compatibilist theory. I will refer to theories that combine these two elements in this way as RS theories. RS theories face a number of familiar difficulties that relate to each of their two components. Beyond this, they also face a distinct set of problems concerning how these two main components relate or should be integrated. My concerns in this paper focus primarily on this set of problems. According to one version of RS compatibilism, the role of moral sentiments is limited to explaining what is required for holding an agent responsible. In contrast with this, the role of reason responsiveness is to explain what moral capacities are required for an agent to be responsible, one who is a legitimate or fair target of our moral sentiments. More specifically, according to this view, moral sense is not required for rational selfcontrol or reason responsiveness. There is, therefore, no requirement that the responsible agent has some capacity to feel moral sentiment. Contrary to this view, I argue that a responsible agent must be capable of holding herself and others responsible. Failing this, an agent’s powers of rational self-control will be both limited and impaired. In so far as holding responsible requires moral sense, it follows that being responsible also requires moral sense. (shrink)

When game theory was introduced to biology, the components of classic game theory models were replaced with elements more befitting evolutionary phenomena. The actions of intelligent agents are replaced by phenotypic traits; utility is replaced by fitness; rational deliberation is replaced by natural selection. In this paper, I argue that this classic conception of comprehensive reapplication is misleading, for it overemphasizes the discontinuity between human behavior and evolved traits. Explicitly considering the representational roles of evolutionary game theory brings to attention (...) neglected areas of overlap, as well as a range of evolutionary possibilities that are often overlooked. The clarifications this analysis provides are well-illustrated by—and particularly valuable for—game theoretic treatments of the evolution of social behavior. (shrink)

Healthcare systems across the globe are struggling with increasing costs and worsening outcomes. This presents those responsible for overseeing healthcare with a challenge. Increasingly, policymakers, politicians, clinical entrepreneurs and computer and data scientists argue that a key part of the solution will be ‘Artificial Intelligence’ (AI) – particularly Machine Learning (ML). This argument stems not from the belief that all healthcare needs will soon be taken care of by “robot doctors.” Instead, it is an argument that rests on the classic (...) counterfactual definition of AI as an umbrella term for a range of techniques that can be used to make machines complete tasks in a way that would be considered intelligent were they to be completed by a human. Automation of this nature could offer great opportunities for the improvement of healthcare services and ultimately patients’ health by significantly improving human clinical capabilities in diagnosis, drug discovery, epidemiology, personalised medicine, and operational efficiency. However, if these AI solutions are to be embedded in clinical practice, then at least three issues need to be considered: the technical possibilities and limitations; the ethical, regulatory and legal framework; and the governance framework. In this article, we report on the results of a systematic analysis designed to provide a clear overview of the second of these elements: the ethical, regulatory and legal framework. We find that ethical issues arise at six levels of abstraction (individual, interpersonal, group, institutional, sectoral, and societal) and can be categorised as epistemic, normative, or overarching. We conclude by stressing how important it is that the ethical challenges raised by implementing AI in healthcare settings are tackled proactively rather than reactively and map the key considerations for policymakers to each of the ethical concerns highlighted. (shrink)

Using Bernard Suits’s brilliant analysis (contra Wittgenstein) of playing a game, this paper examines the intrinsic value of game-playing. It argues that two elements in Suits’s analysis make success in games difficult, which is one ground of value, while a third involves choosing a good activity for the property that makes it good, which is a further ground. The paper concludes by arguing that game-playing is the paradigm modern (Marx, Nietzsche) as against classical (Aristotle) value: since its goal is (...) intrinsically trivial, its value is entirely one of process rather than product, journey rather than destination. (shrink)

The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in (...) Posterior analytics is used to distinguish between conceptions that share the same name but are substantively different: for example the search for a broader genus including all mathematical objects; the search for a common character of different species of mathematical objects; and the effort to treat magnitudes as numbers. (shrink)