We show that (i) it is consistent with that there are infinite sets X on which every metric is discrete; (ii) the notion of real infinite is strictly stronger than that of metrically infinite; (iii) a set X is metrically infinite if and only if it is weakly Dedekind‐infinite if and only if the cardinality of the set of all metrically finite subsets of X is strictly less than the size of ; and (iv) an infinite set X is weakly (...) Dedekind‐infinite if and only if has infinite towers if and only if X has countable partitions. (shrink)

The notion of an ‘ideal language’ or ‘concept-script’ is explicated and defended, and constraints upon formal systems imposed by the ideal of transparency are explored. It is argued that non-singular symbolisms, including non-singular variables, largely fail to satisfy such constraints. In general, the semantics of non-singular expressions do not transparently reflect the corresponding ontic categories. The conditions for the possibility of transparent non-singular assertions, freed from the concept of identity, are briefly explored. The questionable influence within philosophy of the ‘Classical’ (...) Weltanschaung is highlighted. (shrink)

Journal of Mathematical Logic, Ahead of Print. In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an ‘essential’ way. A common feature of such theories is that they do not interpret any infinite discrete structures. We investigate a stronger condition that is easier to establish and use it to give an example of a strictly simple continuous theory that does not interpret any infinite discrete structures: the theory of richly branching (...) [math]-forests with generic binary predicates. We also give an example of a superstable theory that fails to satisfy this stronger condition but nevertheless does not interpret any infinite discrete structures. (shrink)

The blackbody radiation field is studied from different points of view. The existence of zero-point fluctuations is shown to be crucial in determining the form of the thermal part of the spectrum. The notion of a continuous field is seen to be compatible with a discrete structure for its interaction: The description normally used in the quantum context does not refer to the field but to its interaction with atomic systems, which involves statistically independent elementary acts of absorption and emission. (...) The same classical field has different effects on absorption and on emission, and these are conveniently, but not necessarily, described in terms of non-commuting operators. (shrink)

In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an ‘essential’ way. A common feature of such theories is that they do not interpret any infinite discrete structures. We investigate a stronger condition that is easier to establish and use it to give an example of a strictly simple continuous theory that does not interpret any infinite discrete structures: the theory of richly branching [Formula: see text]-forests with generic binary predicates. (...) We also give an example of a superstable theory that fails to satisfy this stronger condition but nevertheless does not interpret any infinite discrete structures. (shrink)

The theory of beauty has always rested on the representation of the infinite, understood in its finite expression and perceptible through the senses. The relationship of beauty to truth, of art to science, is inevitably modified with the new way of treating the infinite in the modern conception of the world. Non-classical science works with the notions of “infinitely large” and “infinitely small,” modifying their meanings in terms of experimental observations. We put these words in quotation marks because the (...) Whole may be considered as finite or infinite according to the angle from which it is viewed: the “infinitely small” only becomes so in determined circumstances, for example, when we consider the extended and discrete elements of space and time in a macroscopic approximation, as infinitely small elements of perpetual motion. Modern science studies these two poles of being—the Whole and its parts—in their interaction, admitting the dependence of macroscopic and even cosmic processes with regard to the processes being created in infinitely small spheres (or, according to another interpretation, finite but extremely small). However, as characteristic of our time as these concepts are—most often hypothetical—they nonetheless express a very old historical tradition that contemporary retrospection, turned toward classical science and the past of science in general, allows us to discern very clearly. All the culture of the past was dominated by the principle of the authority of the Whole over its parts. In peripatetic cosmology and physics, individual processes depended on the cosmic harmony of the center and frontiers of the universe, on the spheres and places toward which bodies tend. This authority of the general law, of universal harmony, of the system hinging on individual processes, is confirmed in Aristotle's Physics, but not only there: we find it in almost all the thinkers of antiquity. On the plane of general logic, it received expression in the Hegelian concept of the true infinite, a concept constituting to a high degree the philosophical equivalent of classical science. In Hegel's time, this last was already drawing away somewhat from the idea of an absolute and strict subordination of elementary processes to integrating systems and general laws, laws being realized through the probability of microprocesses, thus statistical laws, and whose exact application ignored individual acts, for example, the mechanism of molecules in thermodynamics. The statistical theory of heat has rendered continual a discrete microcosm—for the movement of individual molecules it substituted the average speed of the molecules—and continual laws became supreme points determining macroscopic processes. These laws had a differential nature. In other words, they prescribed the defined relationships between the infinitely small increases in size. Also, the schema of the classic law consisted in defining infinitely small processes by an infinitely large integral legality because of the number of processes. The infinitely true of Hegel is the actual infinite being realized in each of its finite elements; it is the subjection of the finite element to the infinite. (shrink)

We examine a case in which non-computable behavior in a model is revealed by computer simulation. This is possible due to differing notions of computability for sets in a continuous space. The argument originally given for the validity of the simulation involves a simpler simulation of the simulation, still further simulations thereof, and a universality conjecture. There are difficulties with that argument, but there are other, heuristic arguments supporting the qualitative results. It is urged, using this example, that absolute (...) validation, while highly desirable, is overvalued. Simulations also provide valuable insights that we cannot yet (if ever) prove. (shrink)

We begin by distinguishing computationalism from a number of other theses that are sometimes conflated with it. We also distinguish between several important kinds of computation: computation in a generic sense, digital computation, and analog computation. Then, we defend a weak version of computationalism—neural processes are computations in the generic sense. After that, we reject on empirical grounds the common assimilation of neural computation to either analog or digital computation, concluding that neural computation is sui generis. Analog computation requires continuous (...) signals; digital computation requires strings of digits. But current neuroscientific evidence indicates that typical neural signals, such as spike trains, are graded like continuous signals but are constituted by discrete functional elements (spikes); thus, typical neural signals are neither continuous signals nor strings of digits. It follows that neural computation is sui generis. Finally, we highlight three important consequences of a proper understanding of neural computation for the theory of cognition. First, understanding neural computation requires a specially designed mathematical theory (or theories) rather than the mathematical theories of analog or digital computation. Second, several popular views about neural computation turn out to be incorrect. Third, computational theories of cognition that rely on non-neural notions of computation ought to be replaced or reinterpreted in terms of neural computation. (shrink)

Enaction, as put forward by Varela and defended by other thinkers (notably Alva Noë, 2004; Susan Hurley, 2006; and Kevin O’Regan, 1992), departs from traditional accounts that treat mental processes (like perception, reasoning, and action) as discrete, independent processes that are causally related in a sequen- tial fashion. According to the main claim of the enactive approach, which Thompson seems to fully endorse, perceptual awareness is taken to be a skill-based activity. Our perceptual contact with the world, according to the (...) enactionists, is not mediated by representations but is enacted, and the notion of representation, belonging to the classic computational paradigm, has no place in this alternative approach. Though Thompson does not pronounce directly on the issue of representationalism, he is most definitely keeping the company of anti-representationalists, and in that context it is not unreasonable to take his silence for consent. In this paper, we will argue that the enactive approach to imagery is unworkable unless it makes appeal to representations, understood in a particular way. Not understood as pictures, to be sure. Or sentences for that matter. But those aren’t the only options. (shrink)

In constructive mathematics it is of interest to consider a more general, but classically equivalent, notion of linear order, a so-called pseudo-order. The prime example is the order of the constructive real numbers. We examine two kinds of constructive completions of pseudo-orders: order completions of pseudo-orders and Cauchy completions of ordered groups and fields. It is shown how these can be predicatively defined in type theory, also when the underlying set is non-discrete. Provable choice principles, in particular a generalisation of (...) dependent choice, are used for showing set-representability of cuts. (shrink)

We introduce a natural two-cardinal version of Bagaria’s sequence of derived topologies on ordinals. We prove that for our sequence of two-cardinal derived topologies, limit points of sets can be characterized in terms of a new iterated form of pairwise simultaneous reflection of certain kinds of stationary sets, the first few instances of which are often equivalent to notions related to strong stationarity, which has been studied previously in the context of strongly normal ideals. The non-discreteness of these (...) two-cardinal derived topologies can be obtained from certain two-cardinal indescribability hypotheses, which follow from local instances of supercompactness. Additionally, we answer several questions posed by the first author, Holy and White on the relationship between Ramseyness and indescribability in both the cardinal context and in the two-cardinal context. (shrink)

_In this symposium, Roberto A. Carleo III, Gregory Doukas and Imogen M. Sullivan think alongside Carlos Alberto Sánchez about the contingency of human existence as it is understood in Mexican existentialism. They ask: Should the notion of a metaphysical substance be discarded altogether due to its misuse in the history of European philosophy? Or are there philosophical reasons to avoid ontological uncertainty by, for example, postulating the notion of a non-discrete substance? And if attempts to define human substantiality merely seek (...) to defy this accidentality, should scholars with deviant identities deliberately engage in a wandering beyond dominant frameworks to evade the material and hermeneutical hostility of these frameworks? How should they work alongside others to best take up their responsibility? In his reply, Sánchez considers what the project of accidentalization would imply for each of these carefully-crafted interventions._. (shrink)

The notion of an object file figures prominently in recent work in philosophy and cognitive science. Object files play a role in theories of singular reference, object individuation, perceptual memory, and the development of cognitive capacities. However, the philosophical literature lacks a detailed, empirically informed theory of object files. In this paper, we articulate and defend the multiple-slots view, which specifies both the format and architecture of object files. We argue that object files represent in a non-iconic, propositional format that (...) incorporates discrete symbols for separate features. Moreover, we argue that features of separate categories are stored in separate memory slots within an object file. We supplement this view with a computational framework that characterizes how information about objects is stored and retrieved. (shrink)

As central as the notion of mind is for Berkeley, it is not surprising that what he means by mind stirs debate. At issue are questions about not only what kind of thing a mind is but also how we can know it. This convergence of ontological and epistemological interests in discussing mind has led some commentators to argue that Berkeley's appeal to the Cartesian vocabulary of 'spiritual substance' signals his appropriation of elements of Descartes's theory of mind. But in (...) his account of spiritual substance, Berkeley focuses much more than Descartes on the intrinsic relation between mind and its ideas and less on the nature of mind as such. This makes it difficult to justify the claim that mind is... (shrink)

Traditional notions of crime control often position the police against an individual, known or not yet known, who is responsible for the commission of a crime. However, with increasingly sophisticated technology, policing increasingly prioritizes the prevention of crime, making it necessary to ascertain who, or what class of persons, may be the next likely criminal before a crime can be committed, termed predictive policing. This causes a shift from individualized suspicion toward predictive profiling that may sway the expectations of (...) a police patrol. Classically, where a patrol officer forms reasonable suspicion prior to a stop, it is based upon his/her analysis of the situation taken as a whole in context. However, where a predictive profile is employed, information available to the officer accordingly adjusts his/her perception of context and affects the application of the reasonable suspicion standard. This article addresses the way in which new approaches to forming reasonable suspicion affect the due process protection of individuals’ fundamental rights. It argues that while an officer still operates with good faith discretion, using predictive profiling causes reasonable suspicion to be based on an augmented understanding of reality and as a result, due process guarantees are weakened. The rights to non-discrimination and the presumption of innocence are assessed and argued as illustrative of this weakening and shift in policing standards. The article ultimately argues that while predictive policing cannot be categorically labeled as inconsistent with criminal justice, changes as seemingly moderate as the manner in which discretion operates have larger effects on individuals’ rights. (shrink)

This article addresses nominal quantification in English in relation to discrete and continuous quantity, the two semantic categories of discrete and continuous / mass being analysed as interpretations of syntax. It re-examines the hypothesis of non-quantifiable continuous nouns as well as some theoretical questions such as overloaded definitions, unexploited oppositions or notions found without an explicit definition, as is sometimes the case with the concept of collective. The study then proceeds to examine semantic multiplicity in connection with grammatical number. (...) Plural is examined in association with numerals and fuzzy quantifiers. The singular category also also yields interpretations of multiplicity, whether with mass-nouns or with discrete collective nouns. This, together with the possible conversion of the latter into mass-nouns, draws one’s attention to a mode of reference shared by mass nouns and collective discrete nouns. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine – (...) Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

Since the discovery of incommensurability in ancient Greece, arithmeticism and geometricism constantly switched roles. After ninetieth century arithmeticism Frege eventually returned to the view that mathematics is really entirely geometry. Yet Poincaré, Brouwer, Weyl and Bernays are mathematicians opposed to the explication of the continuum purely in terms of the discrete. At the beginning of the twenty-first century ‘continuum theorists’ in France (Longo, Thom and others) believe that the continuum precedes the discrete. In addition the last 50 years witnessed the (...) revival of infinitesimals (Laugwitz and Robinson—non-standard analysis) and—based upon category theory—the rise of smooth infinitesimal analysis and differential geometry. The spatial whole-parts relation is irreducible (Russell) and correlated with the spatial order of simultaneity. The human imaginative capacities are connected to the characterization of points and lines (Euclid) and to the views of Aristotle (the irreducibility of the continuity of a line to its points), which remained in force until the ninetieth century. Although Bolzano once more launched an attempt to arithmetize continuity, it appears as if Weierstrass, Cantor and Dedekind finally succeeded in bringing this ideal to its completion. Their views are assessed by analyzing the contradiction present in Grünbaum’s attempt to explain the continuum as an aggregate of unextended elements (degenerate intervals). Alternatively a line-stretch is characterized as a one-dimensional spatial subject, given at once in its totality (as a whole) and delimited by two points—but it is neither a breadthless length nor the (shortest) distance between two points. The overall aim of this analysis is to account for the uniqueness of discreteness and continuity by highlighting their mutual interconnections exemplified in the nature of a line as a one-dimensional spatial subject, while acknowledging that points are merely spatial objects which are always dependent upon an extended spatial subject. Instead of attempting to reduce continuity to discreteness or discreteness to continuity, a third alternative is explored: accept the irreducibility of number and space and then proceed by analyzing their unbreakable coherence. The argument may be seen as exploring some implications of the view of John Bell, namely that the “continuous is an autonomous notion, not explicable in terms of the discrete.” Bell points out that initially Brouwer, in his dissertation of 1907, “regards continuity and discreteness as complementary notions, neither of which is reducible to each other.”. (shrink)

The empty set of course contains no computable point. On the other hand, surprising results due to Zaslavskiĭ, Tseĭtin, Kreisel, and Lacombe have asserted the existence of non-empty co-r. e. closed sets devoid of computable points: sets which are even “large” in the sense of positive Lebesgue measure.This leads us to investigate for various classes of computable real subsets whether they always contain a computable point.

To clarify the notion of computation and its role in cognitive science, we need an account of implementation, the nexus between abstract computations and physical systems. I provide such an account, based on the idea that a physical system implements a computation if the causal structure of the system mirrors the formal structure of the computation. The account is developed for the class of combinatorial-state automata, but is sufficiently general to cover all other discrete computational formalisms. The implementation relation is (...) non-vacuous, so that criticisms by Searle and others fail. This account of computation can be extended to justify the foundational role of computation in artificial intelligence and cognitive science. (shrink)

We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief (...) over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing probabilistic “action models” and proposing a notion of probabilistic update product, that comes together with appropriate reduction laws. (shrink)

L’article se propose, à partir de l’expérience de la construction et de l’exploitation des bases de données dialectales de la BDLC (corse) et du THESOC (occitan), de cerner ce qu’un grand corpus est susceptible d’apporter à la phonologie. La réponse, appuyée sur quelques cas d’espèces, fait intervenir trois niveaux : celui de l’établissement des faits à soumettre à l’analyse, celui de la validation des hypothèses émises, celui de la valeur heuristique des données prises en compte. Les faits aléatoirement rassemblés dans (...) un grand corpus et donc non nécessairement pris en compte dans l’analyse initiale sont en effet de nature à transformer la vision de la clôture du corpus, à confirmer (ou infirmer ce qui, in fine, est aussi important) les hypothèses avancées, à suggérer d’autres solutions aux problèmes rencontrés que celles initialement envisagées. Un des points saillants, en outre, est, au plan théorique, la mise en discussion de la notion d’entité discrète, tant en matière d’unités phonologiques (de type phonème) que d’unités systémiques (de type idiome localisé) tant il est vrai qu’en matière de langue il n’existe qu’un continuum. L’idiolecte est déjà composite, l’idiome local n’est qu’un chaînon dans le continuum aréal. Les unités discrètes constituent donc l’instrument d’analyse incontournable du fait linguistique, une réalité dans la représentation qu’un locuteur a de son système ; mais l’observable est un continuum, un ensemble de cellules perméables les unes aux autres, si c’est bien dans la conscience collective que se trouve (déposée) la langue, conformément au dire saussurien. (shrink)

The theorem to the effect that the languageL introduced in [2] is mutually interpretable with the first order language is proved. This yields several model-theoretical results concerningL.

The Tree of Nature represents an IT-based approach to understanding Nature in the light of present-day scientific knowledge. The universe, in this view, consists of discrete entities; these are not material particles, however, but information processing events that produce observable changes in the world. The surprising result of this analysis is that the workings of Nature are based on a decision tree consisting of two dozen parameters. The tree is similar to the evolutionary phylogenetic system of the various forms of (...) life, but it is far more fundamental; constituting, as it does, the very base of everything that exists. The overall conclusion is that the universe is steadily producing new information. Metaphorically speaking, it constitutes a self-unfolding story in which events do not pass away into non-existence but instead remain forever as an indelible part of the whole. This also holds true for integrated sets of events, such as the lifetime experiences of an individual. The Tree of Nature leads to the following testable prediction: A successful quantum-gravity theory will involve the notion of a strong complementarity between gravity and the strong nuclear force. (shrink)

The conceptualization of the notion of subjectivity within the Anthropocene finds in Rosi Braidotti’s posthumanism one of its most explicit and profuse modulations. This essay argues that Braidotti’s model powerfully accounts for the Anthropocene’s subjectivity by conceiving the “self” as a transversal multiplicity and its relationality to the “others” and the “world” as non-hierarchized by nature–culture distinctions; however, by being ontologically grounded on a neo-Spinozistic monism, Braidotti’s model blurs the notions of finitude, agency, and change, obscuring the possibility of (...) critical dissent while decreasing the overall theory’s consistency. An alternative ontological model capitalizing on these elements can be found in Object-Oriented Ontology and its notion of withdrawal. By associating OOO’s non-onto-taxonomical pluralism with Braidotti’s posthuman subjectivity, this essay aims at ontologically discretizing the latter in order to overcome these limitations. Grounded on this association and invoking a narrative imaginary propelled by the Greek terms xenos and xenia, the article paves the way for a form of subjectivity deviating from Braidotti’s ecological model and defined as xenological, arguing that, within the context of the Anthropocene, it constitutes an adequate alternative to Braidotti’s subjectivity. (shrink)

: The founder of Wahhabism, Muḥammad ibn ‘Abd al-Wahhāb, is on the side of those who advocate that ijtihād’s gate is open. In his thought, the continuity of knowledge about the truth is based on the sustainability of ijtihād, and in every period, there have been mujtahids to interpret the nass in consistent with the issues. The later scholars have developed the thoughts related to ijtihād on this platform. Wahhābī thought does not describe madhhab as a systematic integrated approach. According (...) to them, the madhhab is the ḥukm that were made within the discretion of mujtahids on the basis of nass on the issues open and free to ijtihād. With this approach, they have tried to explain what refers to the word of “Our madhhab is the one of Ahmad ibn Hanbal ”. It has been suggested that this acknowledgment does not mean taqlīd that the words of madhhab imāms are replaced with the Qur’ān and Sunna just as some other members of madhhab do so. Either Muḥammad ibn ‘Abd al-Wahhāb or his disciples have based their own opinions of such as ijtihād, madhhab, taqlīd, ittibā and ikhtilāf upon the proofs that Ḥanbalī Madhhab, Ibn Taymiyya and Ibn Qayyim used. Our aim in this study is to determine how the issues regarding such as ijtihād,taqlīd, madhhab, ikhtilāf, etc. were examined in the primary sources that formed Wahhābī thought. In the early period Wahhābī sources, it is not possible to find definitions of Islamic law in technical terms. Topics have been dealt with within the framework of the answer to a problem/fatwā or a criticism. For this reason, our method will be based on reaching a conclusion about "The Status of Ijtihād in the Early Period of Wahhābī Thought and The Meaning of Commitment to a Madhhab on Fiqh." in the light of the opinions of the first period thinkers. Summary: The connection and similarity of the Wahhābī movement, which started in the Islamic world at a time close to the time when the reform ideas appeared, have been hesitantly welcomed for a few reasons. The fact that members of the Wahhābī movement are intolerant in terms of reform in people’s beliefs, and they use the concept of takfīr, are chief among these reasons. Another reason is that Muḥammad ibn ‘Abd al-Wahhāb does not accept any religious discipline and individual as an authority. The reactions and discourses developed by Wahhābī thinkers against the established practices of faith, ijtihād, taqlīd and denominationalism has brought many objections and criticism. The founder of Wahhabism, Muḥammad ibn ‘Abd al-Wahhāb, is on the side of those who advocate that ijtihād’s gate is open. In his thought, the continuity of knowledge about the truth is based on the sustainability of ijtihād, and in every period, there have been mujtahids to interpret the nass in consistent with the issues. According to him, in a number of controversial cases where no right path has been declared in the naṣṣ, all the efforts of a believer should be focused on understanding the command of God and his messenger and act accordingly. Muḥammad ibn ‘Abd al-Wahhāb does not seek the condition of being a mujtahid to understand the Qur’ān and the sunna. He therefore opposed those who claimed that it is imperative for non-mujtahids to taqlīd a madhhab to understand the provisions of religion. According to him, everybody who has the ability to understand the Qur’ān and the sunna must make ijtihād. Blind allegiance to man-made law against the teachings of God and the Qur’ān is a type of shirk. Fuqahā’ are human and not infallible. The ‘ulamā’ that followed also developed their thoughts about ijtihād and taqlīd on this ground. The Wahhābīs say that they do not completely reject the taqlīd of the ‘ulamā’, but what they do not accept is no one, except the absolute mujtahid, can perform ijtihād. Differentiating ittibā‘, which means accepting an opinion based on evidence, from taqlīd despite the evidence, the Wahhābī ‘ulamā’ have defined the criteria of issuing or accepting a fatwā as performing ijtihād and ittibā‘ to those who have evidence of the Qur’ān and the sunna, or to the remarks of the scholars who are eligible for the Qur’ān and the sunna. According to the Wahhābīs, neither ijtihād nor taqlīd on the issues of ‘aqā’id is permissible in religion. The individual must learn what God and His messenger commands and forbids in terms of ‘aqā’id and worshipping. Ibn ‘Abd al-Wahhāb accepts that taqlīd in furū‘ al-fiqh is permissible in absolutely necessary situations such as not being able to reach sources from various views, and not having the time to evaluate these sources. According to Muḥammad ibn ‘Abd al-Wahhāb, the notion that the dispute of ‘ulamā’ is a blessing is superstitious. According to him, the alliance and agreement of ‘ulamā’ is a deed, and their unity is a blessing. Despite this, the way to be followed in a matter of dispute is not in the madhhab views but the presentation of the matter in the Qur’ān and the sunna. Defining the field of dispute, Muḥammad ibn ‘Abd al-Wahhāb said that the predecessor and the successor disagreed in the matters of furū‘ al-fiqh that were not declared in the naṣṣ; and in such affairs, the duty of the believer is to investigate what is the covenant of God and His messenger, and to show respect for the ‘ulamā’ even if it is mistaken. However, according to him, showing respect to the ‘ulamā’ is not saying ‘’they know better than us’’ despite the presence of evidence in matters of dispute. Wahhābī thought does not describe madhhab as a systematic integrated approach. According to them, the madhhab is the ḥukm that were made within the discretion of mujtahids on the basis of naṣṣ on the issues open and free to ijtihād. With this approach, they have tried to explain what refers to the word of “Our madhhab is the one of Aḥmad ibn Ḥanbal ” It has been suggested that this acknowledgment does not mean taqlīd that the words of madhhab imāms are replaced with the Qur’ān and the sunna just as some other members of madhhab do so. Muḥammad ibn ‘Abd al-Wahhāb and his followers emphasize in many places the movement is not a fifth and a new madhhab, they are members of the Ḥanbalī madhhab and they do not direct anyone to any organization in the form of fiqh, kalām, or ṣūfī. However, they say that madhhabs are not religion, and even if a new madhhab is aimed, this is not a problem. Although an emphasis of being part of the Ḥanbalī madhhab is made without sectarian fanaticism, it is stated that it is imperative to take the views of other madhhabs where the evidence is strong. With the emphasis of being part of the Ḥanbalī madhhab, they support their discourse of not being a new madhhab. However, the general description of the Ḥanbalī madhhab has a stricter approach regarding the way of accepting and using mental and transitional evidence than the other madhhabs. Accordingly, the Wahhābīs are described by a stricter version of the description. Muḥammad ibn ‘Abd al-Wahhāb used their methodology to arrive at judgments instead of taking the specific provisions of the madhhabs, and accepted the adoption of provisions and refused bigotry and the madhhabs are authorities almost equal to God. The Qur’ān, the sunna and ijmā‘ were accepted as the primary authorities and the four madhhabs were not denied as long as they were not contrary to majority of Muslim community. The Wahhābīs, who follow Ibn Taymiyya on the matter of practicing according to a judgment of another madhhab in the presence of evidence, believe that changing a madhhab without any reason or for worldly reasons is not permissible in religion. Although the Wahhābīs do not display a clear attitude on denying madhhabs, they have developed a supra-madhhabs approach with the thoughts of direct access to the ḥukms and accepting the ḥukm of any madhhab as long as the ḥukm is in accordance with the evidence. As a matter of fact, one of the criticisms made in this respect is that they take the views from other madhhabs that suit them, and reject the others. The Wahhābī ‘ulamā’ of the first periods shaped their opinions on issues such as ijtihād, taqlīd, madhhab, ittibā‘, and ikhtilāf, based on the evidences used by the Ḥanbalī madhhab, Ibn Qayyim and especially Ibn Taymiyya. For this reason, it is not possible to say that they have a thought system of their own. Taking this fact into consideration, it seems possible to collect the approach of the method of almost all Wahhābī thinkers in issues that are the subject of this article under three items. First, the necessity of those with strength and ability to perform ijtihād to understand religious provisions; second, solving issues of dispute based on the Qur’ān and the sunna; and third, the presence of evidence overruling any kind of madhhab view. (shrink)

The global public health threat posed by infectious disease is well recognised. The obligation to treat whilst exposed to risk, and its limits, is debated with each novel serious and communicable pathogen. Within national jurisdictions, different responses are forthcoming. Some, like France in 2009, give government the power to require healthcare staff to work, and even to requisition staff, including retired professionals. Others rely on notions of solidarity and professional duty, with scope for individual discretion. Our research with staff (...) in the West Midlands in 2008/2009– including non-professionals – suggested a strong correlation between feeling a duty to work and willingness to work during a pandemic. This was more influential than removing other barriers to working. Medical military personnel can already be ordered into risky situations. Our research in 2015/16 with those who worked in the Ebola treatment unit in Sierra Leone suggested that their concerns about risk were complex: the perceived magnitude of the risk was only one factor, even though tolerance was high. The type of risk and circumstances requiring that risk to be taken were also influential.Against this background, it will be argued, with caveats, that:military medical personnel should be willing to accept greater risk than civilian medical staff;and that to maintain national health services during a communicable disease emergency:civilian medical staff ought to accept greater risks than they currently appear willing to tolerate;conscription – from civilian or military populations – is permissible, even though it may elevate personal risk. (shrink)

This chapter considers several dimensions of humanity’s “in-betweenness,” starting from the historical roots of the idea in Western theology, philosophy, and science. A fundamental distinction is highlighted between “human” as a continuous property and as a discrete entity. The former focuses on the human as a state of being into and out of which something might pass, whereas the latter focuses on being human as a state that something is or is not at a given moment. Both conceptualizations of the (...) human bear on the construction and significance of the Turing Test, which aims to distinguish a human from a computer simply based on responses to questions posed by a human. Usually, the Turing Test is seen as selecting the computer as non-human, but it may be redeployed to select the computer as human. This latter prospect is dubbed “Turing Test 2.0” and explored in the rest of the chapter, especially in terms of the figure of the cyborg, which has passed from cybernetics through science fiction to the lived experience of an increasing number of beings. Implied in Turing Test 2.0 is “judgement” on how a candidate might count as human. Here, foundational questions about the ontology of art are applied to understand the requisite sense of judgement involved. In the modern period, these have tended to undermine any strong connection between a work’s origin and its value. In the spirit of Turing Test 2.0, they oppose “cishumanity,” namely, the notion that one must be born human to be human. (shrink)

Since summer 2019 there is a new document that defines what in science should be regarded as being one second, one meter, and one kilogram, respectively. It is the ninth edition of the SI Brochure. Compared with older editions, a new definitional approach has been used. The seven base units are now defined by being directly related to a so-called defining constant. The paper discusses the second, the meter, and the kilogram. One odd salient, but nonetheless not discussed, feature of (...) the formulations of the definitions is that, from a purely linguistic point of view, they are circular. That is, symbols for what is to be defined appear also in the defining expressions. However, underneath the circularities there are, appearances notwithstanding, substantially non-circular definitions. The aim of the paper is to uncover these never before presented definitional structures. It is made by means of the two notions absolutely discrete quantities and metrical coordinative definitions. When the true definitional structures become visible, two important substantial metrological facts can be seen. First, the new definition of the kilogram is very much in need of further discussion. Second, contrary to what the Brochure hints at, there is no need to try to exchange the atomic parameter used in the definition of the second. (shrink)

The idea that the world is made of particles — little discrete, interacting objects that compose the material bodies of everyday experience — is a durable one. Following the advent of quantum theory, the idea was revised but not abandoned. It remains manifest in the explanatory language of physics, chemistry, and molecular biology. Aside from its durability, there is good reason for the scientific realist to embrace the particle interpretation: such a view can account for the prominent epistemic fact that (...) only limited knowledge of a portion of the material universe is needed in order to make reliable predictions about that portion. Thus, particle interpretations can support an abductive argument from the epistemic facts in favor of a realist reading of physical theory. However, any particle interpretation with this property is untenable. The empirical adequacy of modern particle theories requires adoption of a postulate known as permutation invariance — the claim that interchanging the role of two particles of the same kind in a dynamical state description results in a description of the identical state. It is the central claim of this essay that PI is incompatible with any particle interpretation strong enough to account for the epistemic facts. This incompatibility extends across all physical theories. To frame and motivate the inconsistency argument, I begin by fixing the relevant notion of particle. To single out those accounts of greatest appeal to the realist, I develop the logically weakest particle ontology that entails the epistemic fact that the world is piecewise predictable, an ontology I call ‘minimal atomism’. The entire series of scientific conceptions of the particle, from Newton’s mechanically interacting corpuscles to the ‘centers of force’ in classical field theories, all comport with MA. As long as PI is left out, even quantum mechanics can be viewed this way. To assess the impact of PI on this picture, I present a framework for rigorously connecting interpretations to physical theories. In particular, I represent MA as a set of formal conditions on the models of physical theories, the mathematical structures taken to represent states of the world. I also formulate PI — originally introduced as a postulate of non-relativistic quantum mechanics — in theory independent terms. With all of these pieces in hand, I am then able to present a proof of the inconsistency of PI and MA. In the second part of the essay, I survey responses to the inconsistency result open to the scientific realist. The two most plausible approaches involve abandoning particles in one way or another. The first alternative interpretation considered takes the property bearing objects of the world to be regions of space rather than particles. In this view, the properties once attributed to particles in quantum states are attributed instead to one or more regions of space. PI no longer obtains in this case, at least not as a statement about the permutation symmetry of property bearers. Rather, the new interpretation naturally imposes an analogous constraint on quantum states. The second major approach to evading the inconsistency result is to dispense with objects altogether. This is the recommendation of so-called ‘Ontic Structural Realism’. The central OSR thesis is that structure rather than entities are the basic ontological components of the world. OSR is intended to embrace the ‘miracle’ argument in favor of scientific realism while avoiding the pessimistic meta-induction. I demonstrate that one principal motivation for OSR based on the under-determination of interpretations in QM is actually dissolved by the incompatibility result. At the same time, I suggest reasons to think that OSR fares no better with respect to the pessimistic meta-induction than traditional realism does. Thus, while PI and MA may be incompatible, object ontologies remain the best option for the realist. (shrink)

In this article I deal with time as a notion of epistemological content associated though with the notion of a subjective consciousness co-constitutive of physical reality. In this phenomenologically grounded approach I attempt to establish a ‘metaphysical’ aspect of time, within a strictly pistemological context, in the sense of an underlying absolute subjectivity which is non-objectifiable within objective temporality and thus non-susceptible of any ontological designation. My arguments stem, on the one hand, from a version of quantum-mechanical theory in view (...) of its formal treatment of two different aspects of time within a quantum context. The discrete, partial-ordering properties and the dynamical-parameter properties reflected in the wave equations of motion. On the other hand, to strengthen my arguments for a transcendental factor of temporality, I attempt an interpretation of some relevant conclusions in the work of J. Eccles and of certain results of experimental research of S. Deahaene et al. and others. (shrink)

Within the context of an involutive monoidal category the notion of a comparison relation ${\mathsf{cp} : \overline{X} \otimes X \rightarrow \Omega}$ is identified. Instances are equality = on sets, inequality ${\leq}$ on posets, orthogonality ${\perp}$ on orthomodular lattices, non-empty intersection on powersets, and inner product ${\langle {-}|{-} \rangle}$ on vector or Hilbert spaces. Associated with a collection of such (symmetric) comparison relations a dagger category is defined with “tame” relations as morphisms. Examples include familiar categories in the foundations of quantum (...) mechanics, such as sets with partial injections, or with locally bifinite relations, or with formal distributions between them, or Hilbert spaces with bounded (continuous) linear maps. Of one particular example of such a dagger category of tame relations, involving sets and bifinite multirelations between them, the categorical structure is investigated in some detail. It turns out to involve symmetric monoidal dagger structure, with biproducts, and dagger kernels. This category may form an appropriate universe for discrete quantum computations, just like Hilbert spaces form a universe for continuous computation. (shrink)

The physical, mathematical, and philosophical foundations of the quantum theory of free Bose fields in fixed general relativistic spacetimes are examined. It is argued that the theory is logically and mathematically consistent whereas semiclassical prescriptions for incorporating the back-reaction of the quantum field on the geometry lead to inconsistencies. Still, the relations and heuristic value of the semiclassical approach to canonical and covariant schemes of quantum gravity-plus-matter are assessed. Both conventional and rigorous formulations of the theory and of its principal (...) predictions, cosmological particle creation and horizon radiation, are expounded and compared. Special attention is devoted to spacetime properties needed for the existence or uniqueness of the relevant theoretical elements , renormalization of the stress tensor). The emergence of unitarily inequivalent representations in a single dynamical context is used as motivation for the introduction of the abstract $\rm C\sp{\*}$-algebraic axiomatic formalism. The operationalist and conventionalist claims of the original abstract algebraic program are criticized in favor of its tempered outgrowth, local quantum physics. The interpretation of the theory as a wave mechanics of classical field configurations, deriving from the Schrodinger representations of the abstract algebra, is discussed and is found superior, at least on the level of analogy, to particle or harmonic oscillator interpretations. Further, it is argued that the various detector results and the Fulling nonuniqueness problem do not undermine the particle concept in the ways commonly claimed. In particular, arguments are offered against the attribution of particle status to the Rindler quanta, against the physical realizability of the Rindler vacuum, and against the more general notion of observer-dependence as to the definition of 'particle' or 'vacuum'. However, the question of the ontological status of particles is raised in terms of the consistency of quantum field theory with non-reductive realism about particles, the latter being conceived as entities exhibiting attributes of discreteness and localizability. Two arguments against non-reductive realism about particles, one from axiomatic algebraic local quantum theory in Minkowski spacetime and one from quantum field theory in curved spacetime, are developed. (shrink)

So-called identity theories that postulate the identity of mental phenomena with brain states are usually associated with materialistic ontology. However, the historical picture of the actual attempts at spelling out the mind–brain identities is more complex. In the eighteenth century such identities were most enthusiastically proposed by dualists, whereas non-reductionistic materialists such as Diderot tried to get along without them. In the nineteenth century physiologists such as Broca, Charcot and Wernicke, who postulated discrete and localizable neural correlates for ideas and (...) mental images, ended up, despite their professed materialism, defending theories that resembled Cartesian schemes and the theories of their eighteenth-century dualistic predecessors. Some problems resulting from the use of these theoretical models postulating local and discrete traces, images or representations in the brain in the context of materialist ontology are obviously related to their dualistic origins and to the fact that they are necessarily bound up with dualistic presuppositions. In the context of the criticism of the nineteenth-century memory trace paradigm it is, however, important to bear in mind that functional localization as such is not dependent on the notion of localizable representations. Nor are materialist theories of the mind necessarily dependent on postulating specific type–type identities between the mental and the physiological. (shrink)

Intelligent systems are faced with the problem of securing a principled (ideally, veridical) relationship between the world and its internal representation. I propose a unified approach to visual representation, addressing both the needs of superordinate and basic-level categorization and of identification of specific instances of familiar categories. According to the proposed theory, a shape is represented by its similarity to a number of reference shapes, measured in a high-dimensional space of elementary features. This amounts to embedding the stimulus in a (...) low-dimensional proximal shape space. That space turns out to support representation of distal shape similarities which is veridical in the sense of Shepard's (1968) notion of second-order isomorphism (i.e., correspondence between distal and proximal similarities among shapes, rather than between distal shapes and their proximal representations). Furthermore, a general expression for similarity between two stimuli, based on comparisons to reference shapes, can be used to derive models of perceived similarity ranging from continuous, symmetric, and hierarchical, as in the multidimensional scaling models (Shepard, 1980), to discrete and non-hierarchical, as in the general contrast models (Tversky, 1977; Shepard and Arabie, 1979). (shrink)

Abstract: The article aims to sharpen the neo-republican contribution to international political thought by challenging Pettit’s view that only representative states may raise a valid claim to non-domination in their external relations. The argument proceeds in two steps: First I show that, conceptually speaking, the domination of states, whether representative or not, implies dominating the collective people at least in its fundamental, constitutive power. Secondly, the domination of states – and thus of their peoples – cannot be justified normatively in (...) the name of promoting individual non-domination because such a compensatory rationale misconceives the notion of domination in terms of a discrete exercise of power instead of as an ongoing power relation. This speaks in favour of a more inclusive law of peoples than Pettit (just as his liberal counterpart Rawls) envisages: In order to accommodate the claim of collective peoples to non-domination it has to recognize every state as a member of the international order. (shrink)

Nonprofit organizations play a crucial role in society. Unfortunately, many such organizations are chronically underfunded and struggle to meet their objectives. These facts have significant implications for corporate philanthropy and Kant’s notion of imperfect duties. Under the concept of imperfect duties, businesses would have wide discretion regarding which charities receive donations, how much money to give, and when such donations take place. A perceived problem with imperfect duties is that they can lead to moral laxity; that is, a failure on (...) the part of businesses to fulfill their financial obligations to nonprofit organizations. This article argues the problem of moral laxity rests on a misinterpretation of Kantian ethics and, therefore, is really not a problem at all. As such, we argue corporate philanthropy while an imperfect duty should be interpreted more akin to perfect duties and, as a consequence, moral laxity does not arise for those corporations committed to acting on the basis of the moral law. More specifically, firms have duty-based obligations on the basis of benevolence, and as good corporate citizens, to help fund non-profit organizations. (shrink)

We introduce and discuss a concept of approximation of a topological algebraic system A by finite algebraic systems from a given class K. If A is discrete, this concept agrees with the familiar notion of a local embedding of A in a class K of algebraic systems. One characterization of this concept states that A is locally embedded in K iff it is a subsystem of an ultraproduct of systems from K. In this paper we obtain a similar characterization of (...) approximability of a locally compact system A by systems from K using the language of nonstandard analysis. In the signature of A we introduce positive bounded formulas and their approximations; these are similar to those introduced by Henson [14] for Banach space structures (see also [15, 16]). We prove that a positive bounded formula φ holds in A if and only if all precise enough approximations of φ hold in all precise enough approximations of A. We also prove that a locally compact field cannot be approximated arbitrarily closely by finite (associative) rings (even if the rings are allowed to be non-commutative). Finite approximations of the field R can be considered as possible computer systems for real arithmetic. Thus, our results show that there do not exist arbitrarily accurate computer arithmetics for the reals that are associative rings. (shrink)

After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles, the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being (...) discrete it can describe localized states and measurements, solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (shrink)

Medieval interpretations of hylomorphism, in which substances are conceived as metaphysical composites of prime matter and substantial form, are receiving attention in contemporary philosophy. It has even been suggested that a recovery of Aquinas's conception of prime matter as a ‘pure potentiality’, lacking any actuality apart from substantial form, may be expedient in hylomorphic interpretations of quantum mechanics. In this paper, we consider a recent hylomorphic interpretation of non-relativistic quantum mechanics, the theory of Cosmic Hylomorphism, which does not explicitly invoke (...) any notion of prime matter in its original formulation. We argue that prime matter does in fact play a role in constituting and individuating particles in this theory. However, we demonstrate that the notion of prime matter which features in the extended version of Cosmic Hylomorphism that we propose here is distinct from Aquinas's conception of prime matter, inasmuch as it has discrete metaphysical parts. (shrink)

Quantum Theory, similar to Relativity Theory, requires a new concept of space-time, imposed by a universal constant. While velocity of lightcnot being infinite calls for a redefinition of space-time on large and cosmological scales, quantization of action in terms of a finite, i.e. non vanishing, universal constanthrequires a redefinition of space-time on very small scales. Most importantly, the classical notion of “time”, as one common continuous time variable and nature evolving continuously “in time”, has to be replaced by an infinite (...) manifold of transition rates for discontinuous quantum transitions. The fundamental laws of quantum physics, commutation relations and quantum equations of motion, resulted from Max Born’s recognition of the basic principle of quantum physics:To each change in nature corresponds an integer number of quanta of action. Action variables may only change by integer values ofh, requiring all other physical quantities to change by discrete steps, “quantum jumps”. The mathematical implementation of this principle led to commutation relations and quantum equations of motion. The notion of “point” in space-time looses its physical significance; quantum uncertainties of time, position, just as any other physical quantity, are necessary consequences of quantization of action. (shrink)

The cultural consumption research landscape of the 21st century is marked by an increasing cross-disciplinary fermentation. At the same time, cultural theory and analysis have been marked by successive ‘inter-’ turns, most notably with regard to the Big Four: multimodality (or intermodality), interdiscursivity, transmediality (or intermediality), and intertextuality. This book offers an outline of interdiscursivity as an integrative platform for accommodating these notions. To this end, a call for a return to Foucault is issued via a critical engagement with (...) the so-called practice-turn. This re-turn does not seek to reconstitute venerably Foucauldianism, but to theorize ‘inters-’ as vanishing points that challenge the integrity of discrete cultural orders in non-convergent manners. The propounded interdiscursivity approach is offered as a reading strategy that permeates the contemporary cultural consumption phenomena that are scrutinized in this book, against a pan-consumptivist framework. By drawing on qualitative and mixed methods research designs, facilitated by CAQDAS software, the empirical studies that are hosted here span a vivid array of topics that are directly relevant to both traditional and new media researchers, such as the consumption of ideologies in Web 2.0 social movements, the ability of micro-celebrities to act as cultural game-changers, the post-loyalty abjective consumption ethos. The theoretically novel approaches on offer are coupled with methodological innovations in areas such as user-generated content, artists’ branding, and experiential consumption. (shrink)

Focused on city-scale automation, and using self-driving cars (SDCs) as a case study, this article reflects on the role of AI—and in particular, computer vision systems used for mapping and navigation—as a catalyst for urban transformation. Urban research commonly presents AI and cities as having a one-way cause-and-effect relationship, giving undue weight to AI’s impact on cities and overlooking the role of cities in shaping AI. Working at the intersection of data science and social research, this paper aims to counter (...) this trend by exploring the reverse perspective: how do cities affect the development, and expose the present limits, of SDCs? The contribution of this paper is threefold. First, by comparing urban and nonurban environments and thoroughly examining the relationship between computer vision and city-specific sociality and form, it defines machine autonomy/automation as a function of the sociotechnical milieu in which an AI system operates. Second, and related, the paper problematizes the notion of SDCs as autonomous technologies and the role it plays in envisioning contending policy arrangements and technical solutions for achieving full driving automation. Finally, the article offers insight into a materialist and spatialized understanding of AI—namely, not as an abstract quality susceptible to replication within discrete machines, but rather as a distributed property emerging through embodied interactions among a multiplicity of agents (human, non-human, and technological) within/with their environments. (shrink)