In modern physics, the properties like charge, spin, etc. of elementary entities like electron, proton, photon, etc. are considered to be “intrinsic properties” of the entity. Intrinsic properties are those properties that a thing possesses, irrespective of whether or not there are other contingent things. In Buddhist philosophy especially in Mādhyamik philosophy, no such concept of “intrinsic property” or svabhāva exists. The problem of origin of the universe baffled the scientists and philosophers for many centuries. Within the framework of general (...) theory of relativity as discovered by Einstein, the origin and structure of the universe were discussed in a comprehensive manner. According to the recent formulation of cosmology, the universe originates from the fluctuations of the quantum vacuum. Vacuum in modern physics is not exactly nothing but rather a “something called nothing,” meaning that it is replete with activity governed by the principle of quantum theory. From philosophical perspective, what is significant is the division of creative conceptions into those which assume that the universe arose from “nothingness” in the strong ontological meaning of the word vs. those which lead to the conclusion that it was originated from a certain “poorer” physical reality, usually called “quantum vacuum” or space-time endowed with fluctuation. This vacuum or ontologically speaking a substratum exists which is devoid of any matter but full of activities or full of potentialities. Special theory of relativity is based on two axioms, one of which is the speed of light taken as constant and maximum. (shrink)

We review and synthesize over two decades of research on ethical culture in organizations, examining eighty-nine relevant scholarly works. Our article discusses the conceptualization of ethical culture in a cross-disciplinary space and its critical role in ethical decision-making. With a view to advancing future research, we analyze the antecedents, outcomes, and mediator and moderator roles of ethical culture. To do so, we identify measures and theories used in past studies and make recommendations. We propose, inter alia, the use of validated (...) measures, application of a wider range of theories, adoption of longitudinal studies, and study of group-level data in organizations. We explore research possibilities in new and emergent forms of organizations, ways of organizing work, and technology in ethical decision-making, such as the role of artificial intelligence. We also recommend the study of a broad range of leadership styles and their influence in shaping ethical cultures in organizations. (shrink)

Notions such as śūnyatā, catuṣkoṭi, and Indra's net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nāgārjuna considered two levels of reality: one called conventional reality, and the other ultimate reality. Within this framework, śūnyatā refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuṣkoṭi refers to the claim (...) that four truth values, including contradiction, are admissible in reasoning. Indra's net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions that are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of śūnyatā. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of catuṣkoṭi. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

Our conscious experiences are qualitative and unitary. The qualitative universals given in particular experiences, i.e. qualia, combine into the seamless unity of our conscious experience. The problematics of quality and cohesion are not unique to consciousness studies. In mathematics, the study of qualities (e.g., shape) resulting from quantitative variations in cohesive spaces led to the axiomatization of cohesion and quality. Using the mathematical definition of quality, herein we model qualia space as a categorical product of qualities. Thus modeled qualia space (...) is a codomain space wherein composite qualities (e.g. shape AND color) of conscious experiences can be valued. As part of characterizing the qualia space, we provide a detailed exemplification of the mathematics of quality and cohesion in terms of the categories of idempotents and reflexive graphs. More specifically, with qualities as commutative triangles formed of cohesion-preserving functors, first we calculate the product of commutative triangles. Next, we explicitly show that the category of idempotents is a quality type. Lastly, as part of showing that the category of reflexive graphs is cohesive, we characterize the adjointness between functors relating cohesive graphs to discrete sets. In conclusion, our category theoretic construction of qualia space is a formalization of the binding of qualitative features (colors and shapes) into the cohesive objects (colored-shapes) of conscious experiences. Compared to the feature-vector accounts of conscious experiences, our product-of-qualities account of consciousness is a substantial theoretical advance. (shrink)

Notions such as Sunyata, Catuskoti, and Indra's Net, which figure prominently in Buddhist philosophy, are difficult to readily accommodate within our ordinary thinking about everyday objects. Famous Buddhist scholar Nagarjuna considered two levels of reality: one called conventional reality and the other ultimate reality. Within this framework, Sunyata refers to the claim that at the ultimate level objects are devoid of essence or "intrinsic properties", but are interdependent by virtue of their relations to other objects. Catuskoti refers to the claim (...) that four truth values, along with contradiction, are admissible in reasoning. Indra's Net refers to the claim that every part of a whole is reflective of the whole. Here we present category theoretic constructions which are reminiscent of these Buddhist concepts. The universal mapping property definition of mathematical objects, wherein objects of a universe of discourse are defined not in terms of their content, but in terms of their relations to all objects of the universe is reminiscent of Sunyata. The objective logic of perception, with perception modeled as [a category of] two sequential processes (sensation followed by interpretation), and with its truth value object of four truth values, is reminiscent of the Buddhist logic of Catuskoti. The category of categories, wherein every category has a subcategory of sets with zero structure within which every category can be modeled, is reminiscent of Indra's Net. Our thorough elaboration of the parallels between Buddhist philosophy and category theory can facilitate better understanding of Buddhist philosophy, and bring out the broader philosophical import of category theory beyond mathematics. (shrink)

Owing to its benefits on various cognitive aspects, one’s emotions and wellbeing, meditation has drawn interest from several researchers and common public alike. We have different meditation practices associated with many cultures and traditions across the globe. Current literature suggests significant changes in the neural activity among the different practices of meditation, as each of these practices contributes to distinct physiological and psychological effects. Although this is the case, we want to find out if there is an underlying commonality among (...) all these different practices. So, we ask the following questions related to different practices of meditation, the traditional goal of meditation and its significance - What is the central purpose of meditation? Do traditions define the final goal of all the practices of meditation? Are the purpose and goal of these practices different or is there a common goal to be attained through all these distinct practices? Embracing the traditional perspective, through this paper, we want to emphasize, although these techniques and practices may appear different on the periphery, eventually, they seem to subject one to the same experience at the end; a natural meditative state (discussed in various spiritual traditions as the goal of meditation). In view of future studies on different meditation practices and also those exploring this subjective state, we offer some interesting ideas based on the traditional insights on meditation. In this context, we would also like to make a few comments on the way contemporary researchers view different practices of meditation. (shrink)

We define consciousness as the category of all conscious experiences. This immediately raises the question: What is the essence in which every conscious experience in the category of conscious experiences partakes? We consider various abstract essences of conscious experiences as theories of consciousness. They are: (i) conscious experience is an action of memory on sensation, (ii) conscious experience is experiencing a particular as an exemplar of a general, (iii) conscious experience is an interpretation of sensation, (iv) conscious experience is referring (...) sensation to an object as its cause, and (v) conscious experience is a model of stimulus. Corresponding to each one of these theories we obtain a category of models of conscious experiences: (i) category of actions, (ii) category of idempotents, (iii) category of two sequential maps, (iv) category of brain-generalized figures, and (v) functor categories with intuition as base and conceptual repertoire as exponent, respectively. For each theory of consciousness we also calculate its truth value object and characterize the objective logic intrinsic to the corresponding category of models of consciousness experiences. (shrink)

In recent years, a surge of interest came up with studies in terms of the influence of different types of meditation on the brain and body. Lacking the basic understanding as to why ancient cultures conceived this practice primarily in its various facets, most of these studies mainly focus on delineating the underlying mechanisms of influence in terms of wellbeing and the cognitive enhancement. Thus, they not only involve various definitional and taxonomical issues, but also methodological issues. In this concern, (...) here, we share a new perspective and also emphasize on few issues which are fundamental to meditation research that should be addressed in future studies. (shrink)

In our recent book (Abraham and Roy 2010) we have repurposed a mathematical model for the quantum vacuum as a model of consciousness. In this model, discrete space and time are derived from a discrete cellular dynamical network. As our model is essentially atomistic, we included in our book a short support chapter on atomism. In this aticle we expand on the few pages of that chapter devoted to the history of atomism, to place the current revival of atomism in (...) a larger context. (shrink)

Bose-Einstein statistics may be characterized in terms of multinomial distribution. From this characterization, an information theoretic analysis is made for Einstein-Podolsky-Rosen like situation; using Shannon’s measure of entropy.

This book examines issues related to the concepts of space, time and causality in the context of modern physics and ancient Indian traditions. It looks at the similarity and convergence of these concepts of modern physics with those discussed in ancient Indian wisdom. The volume brings the methodologies of empiricism and introspection together to highlight the synergy between these two strands. It discusses wide-ranging themes including the quantum vacuum as ultimate reality, quantum entanglement and metaphysics of relations, identity and individuality, (...) and dark energy and anti-matter as discussed in physics and in Indian philosophical schools like Vedanta, Yoga, Buddhist, Kashmiri Shaivism and Jaina Philosophy. First of its kind, this book will be an essential read for scholars and researches of philosophy, Indian philosophy, philosophy of science, theoretical physics and social science. (shrink)

It is demonstrated that in quantized general relativity one is led to Jordan-Fock type uncertainty relations implying the occurrence of cut-off lengths. We argue that these lengths (i) represent limitations on the measurability of quantum effects of general relativity and (ii) provide a cut-off length of quantum divergences.

Cognition involves physical stimulation, neural coding, mental conception, and conscious perception. Beyond the neural coding of physical stimuli, it is not clear how exactly these component processes constitute cognition. Within mathematical sciences, category theory provides tools such as category, functor, and adjointness, which are indispensable in the explication of the mathematical calculations involved in acquiring mathematical knowledge. More speci cally, functorial semantics, in showing that theories and models can be construed as categories and functors, respectively, and in establishing the adjointness (...) between abstraction (of theories) and interpretation (to obtain models), mathematically accounts for knowing-within-mathematics. Here we show that mathematical knowing recapitulates--in an elementary form--ordinary cognition. The process of going from particulars (physical stimuli) to their concrete models (conscious percepts) via abstract theories (mental concepts) and measured properties (neural coding) is common to both mathematical knowing and ordinary cognition. Our investigation of the similarity between knowing-within-mathematics and knowing-in-general leads us to make a case for the development of the basic science of cognition in terms of the functorial semantics of mathematical knowing. (shrink)

What is cognition? Equivalently, what is cognition good for? Or, what is it that would not be but for human cognition? But for human cognition, there would not be science. Based on this kinship between individual cognition and collective science, here we put forward Isbell conjugacy---the adjointness between objective geometry and subjective algebra---as a scientific method for developing cognitive science. We begin with the correspondence between categorical perception and category theory. Next, we show how the Gestalt maxim is subsumed by (...) the mathematical construct of colimit, a generalization of summation. The universal mapping property definitions of mathematical constructs, by virtue of being the best with respect to the universe of discourse, can be learned using reinforcement learning algorithms, which raises the possibility of abstracting the architecture of mathematics by artificial intelligence. Subsequently, we present naturality (to be contrasted with miracles), understood as 'Becoming consistent with Being', which governs the transformations of both things and their theories, as the zeroth law of change. Furthermore, the contrast---physical [mechanism] vs. biological [organism]---is smoothed via natural transformation, wherein transformations are respectful of the cohesion of the objects transformed. In closing, upon recognizing the scientific value of learning difficult-to-master differential calculus by physicists, of learning a strange four-letter language by biologists, and of learning the grammar of our respective mother tongues, we make a case for learning the theory of naturality / category theory for developing cognitive science. (shrink)

The ontological model framework for an operational theory has generated much interest in recent years. The debate concerning reality of quantum states has been made more precise in this framework. With the introduction of generalized notion of contextuality in this framework, it has been shown that completely mixed state of a qubit is preparation contextual. Interestingly, this new idea of preparation contextuality has been used to demonstrate nonlocality of some $\psi$ -epistemic models without any use of Bell’s inequality. In (...) particular, nonlocality of a non maximally $\psi$ -epistemic model has been demonstrated from preparation contextuality of a maximally mixed qubit and Schrödinger’s steerability of the maximally entangled state of two qubits (Leifer and Maroney, Phys Rev Lett 110:120401, 2013). In this paper, we, show that any mixed state is preparation contextual. We, then, show that nonlocality of any bipartite pure entangled state, with Schmidt rank two, follows from preparation contextuality and steerability provided we impose certain condition on the epistemicity of the underlying ontological model. More interestingly, if the pure entangled state is of Schmidt rank greater than two, its nonlocality follows without any further condition on the epistemicity. Thus our result establishes a stronger connection between nonlocality and preparation contextuality by revealing nonlocality of any bipartite pure entangled states without any use of Bell-type inequality. (shrink)

We show that within the class of ontological models due to Harrigan and Spekkens, those satisfying preparation-measurement reciprocity must allow indeterminism comparable to that in quantum theory. Our result implies that one can design quantum random number generator, for which it is impossible, even in principle, to construct a reciprocal deterministic model.

Our manuscript addresses the foundational question of cognitive science: how do we know? Specifically, examination of the mathematics of acquiring mathematical knowledge revealed that knowing-within-mathematics is reflective of knowing-in-general. Based on the correspondence between ordinary cognition (involving physical stimuli, neural sensations, mental concepts, and conscious percepts) and mathematical knowing (involving objective particulars, measured properties, abstract theories, and concrete models), we put forward the functorial semantics of mathematical knowing as a formalization of cognition. Our investigation of the similarity between mathematics and (...) cognition led us to argue against the compartmentalization of scientific knowledge and ordinary cognition, and make a case for the understanding of the basic science of knowing in terms of functorial semantics. Recognizing functorial semantics as an elementary form of cognition can help advance cognitive science the way calculus helped in the advancement of physics. (shrink)

The authors undertake a thought experiment the purpose of which is to explore possibilities for understanding moral principles in analogy with cosmic order. The experiment is based on three proposals, which are described in detail: an ontological, a neurological, and a moral proposal. The ontological proposal accepts from the phenomena of quantum physics that there is a nonempirical domain of physical reality that consists not of material things but of what is philosophically conceptualized as a realm of nonmaterial forms. This (...) realm of forms is the realm of potentiality in physical reality that quantum physics posits as an indivisible Wholeness—the One. It is the ultimate reality because everything empirical is the actualization of its forms. The neurological proposal is the hypothesis that the brain is sensitive to the potentiality waves in the cosmic field, as ordinary measuring instruments in physics are sensitive to potentiality waves at the quantum level, so that the cosmic field can communicate with the human brain. The third proposal assumes that the communication with the cosmic field can translate into moral ideas and actions. Even though the three proposals underlying the thought experiment are highly speculative, they lead to definite implications that make sense in their own right and can be applied in a useful way. From the order of reality some simple rules of conduct follow that are identical with traditional moral rules but have the character of rules of well-ness, leading to new aspects of Aristotle's concept of eudaimonia and Kant's concept of the highest good. In analogy with the structure of physical reality, where all empirical phenomena are actualizations of nonempirical forms, it is suggested that the structure of morality, too, is that of a tacit, nonempirical form that actualizes in explicit principles and moral acts through our consciousness. The tacit form is thought to exist in the realm of cosmic potentiality, together with all the other forms that the empirical world actualizes. It can appear spontaneously in our consciousness when needed, offering its guidance to our judgment and free will. Because it does not appear in the form of commandments accompanied by threats, the actions of the tacit moral form define a higher level of morality, similar to that offered by some aspects of the Christian teaching, where one acts not out of fear but on the desire to do things right. (shrink)

This thirteenth volume of Collected Papers is an eclectic tome of 88 papers in various fields of sciences, such as astronomy, biology, calculus, economics, education and administration, game theory, geometry, graph theory, information fusion, decision making, instantaneous physics, quantum physics, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, scientific research methods, statistics, and others, structured in 17 chapters (Neutrosophic Theory and Applications; Neutrosophic Algebra; Fuzzy Soft Sets; Neutrosophic Sets; Hypersoft Sets; Neutrosophic Semigroups; Neutrosophic Graphs; Superhypergraphs; Plithogeny; (...) Information Fusion; Statistics; Decision Making; Extenics; Instantaneous Physics; Paradoxism; Mathematica; Miscellanea), comprising 965 pages, published between 2005-2022 in different scientific journals, by the author alone or in collaboration with the following 110 co-authors (alphabetically ordered) from 26 countries: Abduallah Gamal, Sania Afzal, Firoz Ahmad, Muhammad Akram, Sheriful Alam, Ali Hamza, Ali H. M. Al-Obaidi, Madeleine Al-Tahan, Assia Bakali, Atiqe Ur Rahman, Sukanto Bhattacharya, Bilal Hadjadji, Robert N. Boyd, Willem K.M. Brauers, Umit Cali, Youcef Chibani, Victor Christianto, Chunxin Bo, Shyamal Dalapati, Mario Dalcín, Arup Kumar Das, Elham Davneshvar, Bijan Davvaz, Irfan Deli, Muhammet Deveci, Mamouni Dhar, R. Dhavaseelan, Balasubramanian Elavarasan, Sara Farooq, Haipeng Wang, Ugur Halden, Le Hoang Son, Hongnian Yu, Qays Hatem Imran, Mayas Ismail, Saeid Jafari, Jun Ye, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Abdullah Kargın, Vasilios N. Katsikis, Nour Eldeen M. Khalifa, Madad Khan, M. Khoshnevisan, Tapan Kumar Roy, Pinaki Majumdar, Sreepurna Malakar, Masoud Ghods, Minghao Hu, Mingming Chen, Mohamed Abdel-Basset, Mohamed Talea, Mohammad Hamidi, Mohamed Loey, Mihnea Alexandru Moisescu, Muhammad Ihsan, Muhammad Saeed, Muhammad Shabir, Mumtaz Ali, Muzzamal Sitara, Nassim Abbas, Munazza Naz, Giorgio Nordo, Mani Parimala, Ion Pătrașcu, Gabrijela Popović, K. Porselvi, Surapati Pramanik, D. Preethi, Qiang Guo, Riad K. Al-Hamido, Zahra Rostami, Said Broumi, Saima Anis, Muzafer Saračević, Ganeshsree Selvachandran, Selvaraj Ganesan, Shammya Shananda Saha, Marayanagaraj Shanmugapriya, Songtao Shao, Sori Tjandrah Simbolon, Florentin Smarandache, Predrag S. Stanimirović, Dragiša Stanujkić, Raman Sundareswaran, Mehmet Șahin, Ovidiu-Ilie Șandru, Abdulkadir Șengür, Mohamed Talea, Ferhat Taș, Selçuk Topal, Alptekin Ulutaș, Ramalingam Udhayakumar, Yunita Umniyati, J. Vimala, Luige Vlădăreanu, Ştefan Vlăduţescu, Yaman Akbulut, Yanhui Guo, Yong Deng, You He, Young Bae Jun, Wangtao Yuan, Rong Xia, Xiaohong Zhang, Edmundas Kazimieras Zavadskas, Zayen Azzouz Omar, Xiaohong Zhang, Zhirou Ma.‬‬‬‬‬‬‬‬. (shrink)

This eleventh volume of Collected Papers includes 90 papers comprising 988 pages on Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics, written between 2001-2022 by the author alone or in collaboration with the following 84 co-authors (alphabetically ordered) from 19 countries: Abhijit Saha, Abu Sufian, Jack Allen, Shahbaz Ali, Ali Safaa Sadiq, Aliya Fahmi, Atiqa Fakhar, Atiqa Firdous, Sukanto Bhattacharya, Robert N. Boyd, Victor Chang, Victor Christianto, V. Christy, Dao The Son, Debjit Dutta, Azeddine Elhassouny, Fazal Ghani, Fazli Amin, (...) Anirudha Ghosha, Nasruddin Hassan, Hoang Viet Long, Jhulaneswar Baidya, Jin Kim, Jun Ye, Darjan Karabašević, Vasilios N. Katsikis, Ieva Meidutė-Kavaliauskienė, F. Kaymarm, Nour Eldeen M. Khalifa, Madad Khan, Qaisar Khan, M. Khoshnevisan, Kifayat Ullah,, Volodymyr Krasnoholovets, Mukesh Kumar, Le Hoang Son, Luong Thi Hong Lan, Tahir Mahmood, Mahmoud Ismail, Mohamed Abdel-Basset, Siti Nurul Fitriah Mohamad, Mohamed Loey, Mai Mohamed, K. Mohana, Kalyan Mondal, Muhammad Gulfam, Muhammad Khalid Mahmood, Muhammad Jamil, Muhammad Yaqub Khan, Muhammad Riaz, Nguyen Dinh Hoa, Cu Nguyen Giap, Nguyen Tho Thong, Peide Liu, Pham Huy Thong, Gabrijela Popović‬‬‬‬‬‬‬‬‬‬, Surapati Pramanik, Dmitri Rabounski, Roslan Hasni, Rumi Roy, Tapan Kumar Roy, Said Broumi, Saleem Abdullah, Muzafer Saračević, Ganeshsree Selvachandran, Shariful Alam, Shyamal Dalapati, Housila P. Singh, R. Singh, Rajesh Singh, Predrag S. Stanimirović, Kasan Susilo, Dragiša Stanujkić, Alexandra Şandru, Ovidiu Ilie Şandru, Zenonas Turskis, Yunita Umniyati, Alptekin Ulutaș, Maikel Yelandi Leyva Vázquez, Binyamin Yusoff, Edmundas Kazimieras Zavadskas, Zhao Loon Wang.‬‬‬‬. (shrink)

Since its original publication in 1979, The Possibility of Naturalism has been one of the most influential works in contemporary philosophy of science and social science. It is a cornerstone of the critical realist position, which is now widely seen as offering a viable alternative to move positivism and postmodernism. This revised edition includes a new foreword.

Now acknowledged as a classic in the philosophy of science, A Realist Theory of Science is one of the very few books to transform not only our understanding of science, but that of the nature of the world it studies. The book has inspired the multi-disciplinary and international movement of thought known as critical realism. Re-issued with a new introduction.

It is widely thought that the acceptability of an abstraction principle is a feature of the cardinalities at which it is satisfiable. This view is called into question by a recent observation by Richard Heck. We show that a fix proposed by Heck fails but we analyze the interesting idea on which it is based, namely that an acceptable abstraction has to “generate” the objects that it requires. We also correct and complete the classification of proposed criteria for acceptable abstraction.

Logical pluralism is the view that there is more than one formal logic that correctly (or best, or legitimately) codifies the logical consequence relation in natural language. This essay provides a taxonomy of different variations on the logical pluralist theme based on a five-part structure, and then identifies an unoccupied position in this taxonomy: perspectival logical pluralism. Perspectival pluralism provides an attractive position from which to formulate a philosophy of logic from a feminist perspective (and from other, identity-based perspectives, such (...) as critical race theory). An example of how such an account might be developed is sketched. The essay concludes by defusing an obvious objection to the perspectival approach: the claim that the correct logic (or logics), in virtue of the formal nature of logic, should be independent of considerations regarding the identity of the reasoner. (shrink)

One of the distinguishing features of mathematics is the exceptional level of consensus among mathematicians. However, an analysis of what mathematicians agree on, how they achieve this agreement, and the relevant historical conditions is lacking. This paper is a programmatic intervention providing a preliminary analysis and outlining a research program in this direction.First, I review the process of ‘negotiation’ that yields agreement about the validity of proofs. This process most often does generate consensus, however, it may give rise to another (...) kind of disagreement: whether the original and new proof are effectively the same, leading to potential disagreement about the validity of the original proof.Second, I historicize the phenomenon of consensus. I show that in earlier European mathematics and other mathematical cultures, consensus about the validity of arguments was substantially weaker or conceived differently than it is today. This means that contemporary consensus about the validity of mathematical proofs should be explained by historical changes in mathematical practice.Finally, I conjecture what brought about the contemporary form of mathematical consensus. Since a sharp rise in consensus occurs around the turn of the 20th century, it makes sense to explain this consensus by the concurrent formalization of mathematics. However, this explanation has a major flaw: it explains a really existing phenomenon (consensus) by something that hardly ever happens (writing proofs in formal languages). I will therefore explain the ways in which formalization does enter mathematical practice so as to account for contemporary forms of mathematical consensus. (shrink)

That every first-order theory has a coherent conservative extension is regarded by some as obvious, even trivial, and by others as not at all obvious, but instead remarkable and valuable; the result is in any case neither sufficiently well-known nor easily found in the literature. Various approaches to the result are presented and discussed in detail, including one inspired by a problem in the proof theory of intermediate logics that led us to the proof of the present paper. It can (...) be seen as a modification of Skolem’s argument from 1920 for his “Normal Form” theorem. “Geometric” being the infinitary version of “coherent”, it is further shown that every infinitary first-order theory, suitably restricted, has a geometric conservative extension, hence the title. The results are applied to simplify methods used in reasoning in and about modal and intermediate logics. We include also a new algorithm to generate special coherent implications from an axiom, designed to preserve the structure of formulae with relatively little use of normal forms. (shrink)

In “The Runabout Inference Ticket” AN Prior (1960) examines the idea that logical connectives can be given a meaning solely in virtue of the stipulation of a set of rules governing them, and thus that logical truth/consequence.

A neologicist set theory based on an abstraction principle (NewerV) codifying the iterative conception of set is investigated, and its strength is compared to Boolos's NewV. The new principle, unlike NewV, fails to imply the axiom of replacement, but does secure powerset. Like NewV, however, it also fails to entail the axiom of infinity. A set theory based on the conjunction of these two principles is then examined. It turns out that this set theory, supplemented by a principle stating that (...) there are infinitely many nonsets, captures all (or enough) of standard second-order ZFC. Issues pertaining to the axiom of foundation are also investigated, and I conclude by arguing that this treatment provides the neologicist with the most viable reconstruction of set theory he is likely to obtain. (shrink)

Many countries are experiencing increasing levels of demand for access to assisted reproductive technologies. Policies regarding who can access ART and with what support from a collective purse are highly contested, raising questions about what state responses are justified. Whilst much of this debate has focused on the status of infertility as a disease, we argue that this is something of a distraction, since disease framing does not provide the far-reaching, robust justification for state support that proponents of ART seem (...) to suppose. Instead, we propose that debates about appropriate state responses should consider the various implications for health and broader well-being that may be associated with difficulties starting a family. We argue that the harms and disruption to valued life projects of subfertility-related suffering may provide a stronger basis for justifying state support in this context. Further, we suggest that, whilst ART may alleviate some of the harm resulting from subfertility, population-level considerations can indicate a broader range of interventions aimed at tackling different sources of subfertility-related harm, consistent with broader public health aims. (shrink)

Harris proposes a new theory of communication, beginning with the premise that the mental life of an individual should be conceived of as a continuous attempt to integrate the present with the past and future.

Saussure as a linguist and Wittgenstein as a philosopher of language are arguably the two most important figures in the development of twentieth-century ...

Four recent turns in social thought are discussed and related to the four dimensional schema of dialectical realism the author has recently outlined. It is shown how ontology matters, and indeed is not only necessary but inevitable, The nature of the reality of ideas is demonstrated and the most prevalent mistakes in the metatheory of ideas and ideation analysed. The significance of categorical realism and the character of those specific types if ideas known as ‘ideologies’ are then discussed. Finally some (...) good and bad dialectical connections of ideas and related phenomena are sketched. (shrink)

Scientific theories of consciousness identify its contents with the spatiotemporal structure of neural population activity. We follow up on this approach by stating and motivating Dynamical Emergence Theory, which defines the amount and structure of experience in terms of the intrinsic topology and geometry of a physical system’s collective dynamics. Specifically, we posit that distinct perceptual states correspond to coarse-grained macrostates reflecting an optimal partitioning of the system’s state space—a notion that aligns with several ideas and results from computational neuroscience (...) and cognitive psychology. We relate DET to existing work, offer predictions for empirical studies, and outline future research directions. (shrink)

A difficulty for alethic pluralism has been the idea that semantic evaluation of conjunctions whose conjuncts come from discourses with distinct truth properties requires a third notion of truth which applies to both of the original discourses. But this line of reasoning does not entail that there exists a single generic truth property that applies to all statements and all discourses, unless it is supplemented with additional, controversial, premises. So the problem of mixed conjunctions, while highlighting other aspects of alethic (...) pluralism worth investigating further, does not constitute an effective objection to it. (shrink)

Offers a renovated form of Confucian liberalism that forges a reconciliation between the two extremes of anti-Confucian liberalism and anti-liberal Confucianism.

Timothy Williamson’s Modal Logic as Metaphysics is a book-length defense of necessitism about objects—roughly put, the view that, necessarily, any object that exists, exists necessarily. In more formal terms, Williamson argues for the validity of necessitism for objects (NO: ◻︎∀x◻︎∃y(x=y)). NO entails both the (first-order) Barcan formula (BF: ◇∃xΦ → ∃x◇Φ, for any formula Φ) and the (first-order) converse Barcan formula (CBF: ∃x◇Φ → ◇∃xΦ, for any formula Φ). The purpose of this essay is not to assess Williamson’s arguments either (...) for necessitism (although discussion of these arguments will play a central role in the dialectic) or for necessitism’s two famous corollaries. Instead, the focus shall be a general principle governing abstract objects—the abstract of principle (or AOP) —instances of which seems to be at work in some of Williamson’s central arguments for necessitism. The AOP can be straightforwardly formulated and applied within the neo-logicist framework—in fact, arguably the principle is most naturally formulated in neo-logicist terms. -/- After closely examining, and carefully formalizing, the AOP, the remainder of the paper focuses on arguments for necessitism-like claims (the exact meaning of “necessitism-like” will become clearer as the essay progresses) based on the AOP. In particular, we shall focus on the instance of the AOP that applies to the abstract objects governed by the most well-known and most fully studied abstraction principle: Hume’s Principle (HP). It turns out that, although we cannot reconstruct a valid argument for necessitism based on this numerical instance of the AOP, we can obtain valid arguments for weaker, but equally interesting conclusions. In particular, we shall show that, although HP combined with the AOP (and some additional, related assumptions) allows the contents of the domains of possible worlds to vary, the size of those domains must remain constant. The paper concludes by developing and critiquing some related arguments for necessitism based on applying relevant instances of the AOP to abstraction principles governing sets (or extensions), and to a simple objectual abstraction principle. (shrink)