In this article it is argued that the relation between the socalled Gutenberg galaxis of print culture and the Turing galaxis of digital media is not one of opposition and substitution, but rather one of co-evolution and integration. Or more precisely: that the Gutenberg galaxis on the one hand can be inscribed into the Turing galaxis, which on the other hand is textual in character since it is based on linear and serially processed representations manifested in a binary (...) class='Hi'>alphabet. In continuation of this text and hypertext is described as notions of related but different sorts of complex systems and it is argued that both texts and hypertexts are best thought of as sequentially organised. The first part of the paper contains a description of the basic properties of computers and digital representation answering the question: what are the properties common to all kinds of use of computers – whether used for one purpose or another? The second part is concerned with the relationship between printed and electronic text. The third part addresses the idea of hypertext as systems which exploits modal shifts between node-mode and link-mode as a significant part of the semantics of the system. (shrink)

Until the late 19th century scientists almost always assumed that the world could be described as a rule-based and hence deterministic system or as a set of such systems. The assumption is maintained in many 20th century theories although it has also been doubted because of the breakthrough of statistical theories in thermodynamics (Boltzmann and Gibbs) and other fields, unsolved questions in quantum mechanics as well as several theories forwarded within the social sciences. Until recently it has furthermore been assumed (...) that a rule-based and deterministic system was also predictable if only the rules were known, but this assumption has now been undermined by modern chaos-theory describing rule-based and deterministic, but unpredictable systems, while catastrophe-theory delivers a set of types describing various kinds of instability and conditions for the stability of a given system. Hence the main trait in the theoretical development in the 20th-century science can be described as a basic modification and limitation of some of the fundamental and strong assumptions forwarded in the previous epochs of modern science. Ironically, the very same process has been a process in which the human capacity to intervene in nature has expanded dramatically and mainly with the help of the very same theories, and not least because they allow nature to be described and made manipulable on a lower level and a more fine-grained scale. While the overall theoretical consistency between the various theories has gone, the reach of human intervention in nature has increased based on quite new dimensions whether in the area of physics (e.g.: energy technologies, chemical technologies, nanotechnologies etc.) or biology (ge¬netic manipulation) or in the area of psychology, sociology and culture (artificial simulations of mental processes, new means of communication, implying changes in the social infrastructure and cultural behaviour etc.). While some of these changes and new conditions can be reflected from within the conceptual framework of rule-based systems, albeit more complex than formerly recognized, others seem to give rise to the question of whether there are »systems« and relations between different systems in the world which are not rule-based? For instance, it seems to be obvious that the notion of instability represents a major conceptual break with former theories of rule-based systems, as the stability of the latter is an axiomatically given property implied in the very notion of rule-based systems, while instability can only be the result of external influence which should be explained as the result of another rule-based sy¬stem. While there are no difficulties implied concerning the stability of rule-based systems, the notion of unstable states of a system raises the question of how there can be a system at all if there are no invariant stabilising principles? This is the first question which I will address. And I shall do so by taking two examples of such systems as my point of departure. The first example will be the computer and the second will be ordinary language. In both cases I will argue that the stability of these systems (which are both defined by the existence/presence of human intentions) are provided by the help of - differently organised - redundancy functions which both allow the maintenance of systems in unstable macro-states, suspension of previous rules, underdetermination and overdetermination and generation/emergence/creation of new rules more or less independent of previous rules by the help of optional recursions to the permanently accessible underlying levels as for instance the level of binary representation in computers. Since the notion of redundancy is both controversial as such and often avoided, the concept is discussed (as defined in Claude Shannon's mathematical theory of information and in the semiotic framework of J. J. Greimas) and leading to a more general definition in which the redundancy functions serve to overcome noisy conditions, but at the cost of rule-based stability, determination, and predictability. A second question will be how the notion of rule-generating systems relates to the notion of anticipatory systems and it will be argued that rule-generating systems share some features with an¬ticipatory systems and that the former from a certain viewpoint can be seen as a subclass of the latter, although anticipative features are not necessarily a part of the definition of rule-generating systems. On the other hand, it will be discussed whether anticipatory systems which are not rule-generating systems can exist and it will be argued that the capacity to anticipate is strongly limited if it is not part of a rule-generating system. Therefore, it is concluded that the most powerful anticipatory systems need to be rule-generating systems. (shrink)

Electronic text can be defined on two different, though interconnected, levels. On the one hand, electronic text can be defined by taking the notion of “text” or “printed text” as the point of departure. On the other hand, electronic text can be defined by taking the digital format as the point of departure, where everything is represented in the binary alphabet. While the notion of text in most cases lends itself to being independent of medium and embodiment, it (...) is also often tacitly assumed that it is in fact modeled on the print medium, instead of, for instance, on hand-written text or speech. In late 20th century, the notion of “text” was subjected to increasing criticism, as can be seen in the question that has been raised in literary text theory about whether “there is a text in this class.” At the same time, the notion was expanded by including extralinguistic sign modalities (images, videos). A basic question, therefore, is whether electronic text should be included in the enlarged notion that text is a new digital sign modality added to the repertoire of modalities or whether it should be included as a sign modality that is both an independent modality and a container that can hold other modalities. In the first case, the notion of electronic text would be paradigmatically formed around the e-book, which was conceived as a digital copy of a printed book but is now a deliberately closed work. Even closed works in digital form will need some sort of interface and hypertextual navigation that together constitute a particular kind of paratext needed for accessing any sort of digital material. In the second case, the electronic text is defined by the representation of content and (some parts of the) processing rules as binary sequences manifested in the binary alphabet. This wider notion would include, for instance, all sorts of scanning results, whether of the outer cosmos or the interior of our bodies and of digital traces of other processes in-between (machine readings included). Since other alphabets, such as the genetic alphabet and all sorts of images may also be represented in the binary alphabet, such materials will also belong to the textual universe within this definition. A more intriguing implication is that born-digital materials may also include scripts and interactive features as intrinsic parts of the text. The two notions define the text on different levels: one is centered on the Latin, the other on the binary alphabet, and both definitions include hypertext, interactivity, and multimodality as constituent parameters. In the first case, hypertext is included as a navigational, paratextual device; whereas in the second case, hypertext is also incorporated in the narrative within an otherwise closed work or as a constituent element on the textual universe of the web, where it serves the ongoing production of (possibly scripted) connections and disconnections between blocks of textual content. Since the early decades of early 21st century still represent only the very early stages of the globally distributed universe of web texts, this is also a history of the gradual unfolding of the dimensions of these three constituencies—hypertext, interactivity, and multimodality. The result is a still-expanding repertoire of genres, including some that are emerging via path dependency; some via remediation; and some as new genres that are unique for networked digital media, including “social media texts” and a growing variety of narrative and discursive multiple-source systems. (shrink)

Throughout what is now the more than 50-year history of the computer many theories have been advanced regarding the contribution this machine would make to changes both in the structure of society and in ways of thinking. Like other theories regarding the future, these should also be taken with a pinch of salt. The history of the development of computer technology contains many predictions which have failed to come true and many applications that have not been foreseen. While we must (...) reserve judgment as to the question of the impact on the structure of society and human thought, there is no reason to wait for history when it comes to the question: what are the properties that could give the computer such far-reaching importance? The present book is intended as an answer to this question. The fact that this is a theoretical analysis is due to the nature of the subject. No other possibilities are available because such a description of the properties of the computer must be valid for any kind of application. An additional demand is that the description should be capable of providing an account of the properties which permit and limit these possible applications, just as it must make it possible to characterize a computer as distinct from a) other machines whether clocks, steam engines, thermostats, or mechanical and automatic calculating machines, b) other symbolic media whether printed, mechanical, or electronic and c) other symbolic languages whether ordinary languages, spoken or written or formal languages. This triple limitation, however, (with regard to other machines, symbolic media and symbolic languages) raises a theoretical question as it implies a meeting between concepts of mechanical-deterministic systems, which stem from mathematical physics, and concepts of symbolic systems which stem from the description of symbolic activities common to the humanities. The relationship between science and the humanities has traditionally been seen from a dualistic perspective, as a relationship between two clearly separate subject areas, each studied on its own set of premises and using its own methods. In the present case, however, this perspective cannot be maintained since there is both a common subject area and a new - and specific - kind of interaction between physical and symbolic processes. (shrink)

This paper explores the possibility of a standard legal language (e.g. English) for a principled evolution of law in line with technological development. In doing so, reference is made to blockchain networks and smart contracts to emphasise the discontinuity with the liberal legal tradition when it comes to decentralisation and binary code language. Methodologically, the argument is built on the underlying relation between law, semiotics and new forms of media adding to natural language; namely: code and symbols. In what (...) follows, I will concentrate on the study of factors that explain why such approach can be fruitful for the future of law and innovation. I have three reasons for selecting this topic. The first is a more pragmatic reason, based on my current research of law as a linguistic phenomenon. Secondly, the topic does also touch the matter on binary code language, rivalrous to legal alphabetic language. Lastly, the study aims at emphasizing the pivotal role of the jurist as an interpreter in a changing society accommodating diverging realms of reality. The study is structured as follows. Firstly, a quick exam of the traits of blockchain networks would provide the contextual link to establish the arguments in support of the need of a standard legal language. Secondly, a comparison between liberal legal institutions and theory of semiotics is set to perceive their functioning and ascertain their limits in the light of todays unprecedented changes. Thirdly, a summary on blockchain networks’ legal features would constitute the thrust behind the idea of a uniform legal language. Methodologically, the argument does also establish some relations with classical laws of physics and philosophy of media. Its aim is to demonstrate how the suggested legal interpretation and semiotic-based approach can contribute to overcome existing stumbling blocks including, but not limited to, the lack of cooperation at the international level as well as the gap in State norms when it comes to innovation. In this sense, the proposed strategies do not intend to replace current advances in the legal thought. In contrast, it seeks to harmonise their results providing a methodical approach that can concur to inform a new technique to address new controversial issues. In practice, the proposed method regarding the adoption of a uniform legal language would lower transactive costs in terms of normative coordination in the matter of international cooperation and in the definition of applicable law among different legal systems. Alternatively, it might contribute to the convergence of legal systems and/or their underlying concepts. Differently put, article’s contribution can be envisaged in fostering juridical consistency with regards to different forms of languages’ coexistence. (shrink)

The set of all words in the alphabet {l, r} forms the full binary tree T. If x ∈ T then xl and xr are the left and the right successors of x respectively. We consider the monadic second-order language of the full binary tree with the two successor relations. This language allows quantification over elements of T and over arbitrary subsets of T. We prove that there is no monadic second-order formula φ * (X, y) such (...) that for every nonempty subset X of T there is a unique y ∈ X that satisfies φ * (X, y) in T. (shrink)

The case of ungapped alignment of two literal sequences under constrains is considered. The analysis lead to general formulas for probability mass function and cumulative distribution function for the general case of using an alphabet with a chosen number of letters in the expression of the literal sequences. Formulas for three statistics including mean, mode, and standard deviation were obtained. Distributions are depicted for three important particular cases: alignment on binary sequences, alignment of trinomial series, and alignment of (...) genetic sequences. A particular case when sequences contain each letter of the alphabet at least once in both sequences has also been analyzed and some statistics for this restricted case are given. (shrink)

C. Karp has shown that if α is an ordinal with ω α = α and A is a linear ordering with a smallest element, then α and $\alpha \bigotimes A$ are equivalent in L ∞ω up to quantifer rank α. This result can be expressed in terms of Ehrenfeucht-Fraïssé games where player ∀ has to make additional moves by choosing elements of a descending sequence in α. Our aim in this paper is to prove a similar result for Ehrenfeucht-Fraïssé (...) games of length ω 1 . One implication of such a result will be that a certain infinite quantifier language cannot say that a linear ordering has no descending ω 1 -sequences (when the alphabet contains only one binary relation symbol). Connected work is done by Hyttinen and Oikkonen in [H] and [O]. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:American Journal of Philology 122.2 (2001) 270-274 [Access article in PDF] Elizabeth S. Belfiore. Murder among Friends: Violation of "Philia" in Greek Tragedy. New York: Oxford University Press, 2000. xix + 282 pp. Cloth, $55. In explaining the kinds of situations that are dreadful or pitiable, Aristotle tells us in the Poetics (1453b14-23) that all actions occur between friends (philoi), enemies, or neither: the classification is evidently meant to (...) be exhaustive, and the third term, is added to the usual binary, friend or foe, for the sake of greater precision. Acts between enemies or neutral parties do not arouse pity, apart from the nature of the event itself (pathos). What one wants, then, is situations in which they occur en tais philiais, such as brother killing brother, son father, mother son, son mother, and the like--in other words, to judge from the instances Aristotle offers, when violence takes place within the family. The somewhat odd phrase, "within affective relationships"--embraces familial bonds, whereas en tois philois would, I believe, have suggested rather friends who are unrelated by blood.Such, at least, is my interpretation of the passage. Elizabeth Belfiore disagrees: in an appendix to the first chapter of her book, in which she discusses my published views on the question, she maintains that here "the noun philos surely has the same range as philia, and both refer primarily, if not exclusively, to relationships among close blood kin" (20). Whatever the sense of philos, however, Aristotle clearly means that tragedy is best at eliciting pity when it deals with tensions within the family, and, as Belfiore notes, such bonds are "central to more than half" the extant tragedies (xv)--and relations by marriage are not included in this figure. Of those fragmentary plays whose plots can be reconstructed with some confidence (Belfiore analyzes 141), 69 involve harm or the threat of harm to blood relatives, according to Belfiore. A dozen more focus on spouses, again classified separately under the heading "reciprocal relationships," which covers also xenia and suppliancy (202-3), although Belfiore (6) notes that Aristotle lists marriage under philia sungenikê (NE 9.4; EE 7.6-7), while guest-friendship belongs rather to koinônikê (supplication is not discussed in NE 8-9). "Reciprocal relationships" is thus a problematic class, since it includes bonds that the Greeks would, I think, have seen as quite distinct. Be that as it may, "Murder among Kin" might have been a more suitable title for this volume, especially [End Page 270] given that violence between friends in the narrow or modern sense is virtually nonexistent in Greek tragedy. It is an unfortunate consequence of broadening the meaning of philos that this circumstance goes unexplained in Belfiore's discussion.Before examining Belfiore's argument in more detail, let me first give an overview of the structure of the book. It falls into two halves of about equal length. The first part consists of a general overview of philia relations in Greek literature, followed by close readings of five tragedies. These include Euripides' Iphigenia in Tauris, where the danger is fratricide; Aeschylus' Suppliant Women, the theme of which is defined as "the suppliant bride"; Sophocles' Philoctetes, which is treated as a play about xenia; Euripides' Andromache; and Sophocles' Ajax, in which suicide is taken to be a violation of the most intimate kind of philia, that which obtains with oneself (the chapter title is "Killing One's Closest Philos").The second part consists of three appendices, the first of which summarizes the plots of the surviving tragedies other than the five singled out for treatment in the body of the text. These are arranged by category: blood kinship, subdivided in turn into "parent harms child," "child harms parent," "sibling harms sibling," and "harm to other blood kin" (17 plays in all); reciprocal relationships, covering marriage, xenia, and "suppliancy"; and exceptional plays, including Sophocles' Ajax and Euripides' Andromache. Within each subcategory, plays are treated by author, with individual works arranged in alphabetical order of the English titles. Thus, "parent harms child" begins with Aeschylus' Eumenides, followed... (shrink)

This commentary responds to Moti Gorin's article “What Is the Aim of Pediatric ‘Gender‐Affirming’ Care?” We argue that Gorin's case against pediatric gender‐affirming care rests upon numerous false conceptual binaries: female/male, public/private, objective/subjective, and medically necessary/elective. Drawing on feminist bioethics, we show how such dichotomous thinking is both inaccurate and marginalizing of gender minorities.

Despite a recent wave in global recognition of the rights of transgender and gender-diverse populations, referred to in this text by the umbrella label of trans*, international law continues to presume a cisgender binary definition of gender — dismissing the lived realities of trans* individuals throughout the world. This gap in international legal recognition and protection has fundamental implications for health, where trans* persons have been and continue to be subjected to widespread discrimination in health care, longstanding neglect of (...) health needs, and significant violations of bodily autonomy. (shrink)

This article exploits the “binary license” offered by the title of the symposium in which it appears (“Comparative Relativism”) as a kind of promise of connection. The author suggests, however tentatively, that in the challenge of heterogeneity, fractality, perspective/-alism, and multiplicities lies the power of the forking pathway: the moment a relation is created through divergence. If we are invited—in the same breath—to consider forms of comparison and forms of relativism (dropping difference and similarity), we are also offered two (...) paths, one based on a world of singularities and multiplicities, and the other on a world of not-quite repetitions. The article asks if the binary is not essential to the epistemic work that Western (Euro-American) scholars might want to do, since we forever reinvent the divide between the modern and the post-/pre-modern. Strathern assumes the anthropologist's license to talk about concepts through persons, and begins by asking how Papua New Guineans who come together in a city compare themselves, and in contrast to ethnic comparisons elsewhere (e.g., contra Sarah Green's Balkan interactions). In talking about persons through concepts, it is worth asking what is entailed in relativizing one scholar's work through that of another. The author says that her “hunch” is that in both cases the analyst might wish to have the liberty of discerning—in the same breath—the multiplicities of what John Law and Annemarie Mol call perspectivalism (their very general alternative to comparison) and Eduardo Viveiros de Castro's radically divergent perspectivism (a self-contained, recursive and above all socially specific relativism). (shrink)

Chinese translation courtesy of Zhuanxu Xu. We want to know what gender is. But metaphysical approaches to this question solely have focused on the binary gender kinds men and women. By overlooking those who identify outside of the binary–the group I call ‘genderqueer’–we are left without tools for understanding these new and quickly growing gender identifications. This metaphysical gap in turn creates a conceptual lacuna that contributes to systematic misunderstanding of genderqueer persons. In this paper, I argue that (...) to better understand genderqueer identities, we must recognize a new type of gender kind: critical gender kinds, or kinds whose members collectively resist dominant gender ideology. After developing a model of critical gender kinds, I suggest that genderqueer is best modeled as a critical gender kind that stands in opposition to `the binary assumption', or the prevalent assumption that the only possible genders are the binary, discrete, exclusive, and exhaustive kinds men and women. (shrink)

Hypatia and Synesius lived in a highly divisive time with religious extremism on the rise and the meaning and role of Classical cultural fixtures like paideia, philosophia and manteia being questioned and redefined. I examine Synesius’ Letters, Dion, and De Insomniis to tease out the universalizing and harmonizing tendencies between pagan and Christian, theoria and paideia, philosophia and manteia that Synesius’ writings, life and career embody. I look at Synesius’ synthesis of Iamblichean and Plotinian tendencies, a binary found in (...) modern scholarship, to show that theurgy was likely part of Hypatia’s teaching within a well-rounded curriculum that included classical paideia and philosophical theoria. Synesius advocates for the importance of paideia, including rhetoric and philosophia as aids in the step-by-step approach to the spiritual ascent, while also acknowledging the value and universal accessibility of theoria reached by desert monks and the dream-divination (oneiromanteia) that everyone can experience in sleep. Paideia makes the fall from the heights of theoria more pleasant, while philosophia (which in Synesius’ mind included theurgy) is essential for purifying the pneuma and making it receptive to divinely inspired dreams. I propose that it was in Hypatia’s school that Synesius internalized a quote (from a lost work of Aristotle) that reconciles the two approaches (curated and amateur) to the ascent. While society at large was obsessed with ever widening opposites and binaries, Hypatia’s Synesius both overtly and covertly emphasized harmonization and unity that are at the heart of philosophia. (shrink)

Orthogonality of all families of pairwise weakly orthogonal 1-types for ℵ0-categorical weakly o-minimal theories of finite convexity rank has been proved in 6. Here we prove orthogonality of all such families for binary 1-types in an arbitrary ℵ0-categorical weakly o-minimal theory and give an extended criterion for binarity of ℵ0-categorical weakly o-minimal theories . © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.

A type quantifier F is symmetric iff F ( X, X )( Y ) = F ( Y, Y )( X ). It is shown that quantifiers denoted by irreducible binary determiners in natural languages are both conservative and symmetric and not only conservative.

We shall prove here that any binary relation on a base E with cardinality n > 6 is reconstructible from its restrictions of cardinality 2, 3, 4 and . This proof needs results of part I of this paper where we characterize any pair of relations R, R' which are 2-, 3- and 4-hypomorphic. As a corollary we obtain that any binary relation is -reconstructible.

We describe a deep generative model in which the lowest layer represents the word-count vector of a document and the top layer represents a learned binary code for that document. The top two layers of the generative model form an undirected associative memory and the remaining layers form a belief net with directed, top-down connections. We present efficient learning and inference procedures for this type of generative model and show that it allows more accurate and much faster retrieval than (...) latent semantic analysis. By using our method as a filter for a much slower method called TF-IDF we achieve higher accuracy than TF-IDF alone and save several orders of magnitude in retrieval time. By using short binary codes as addresses, we can perform retrieval on very large document sets in a time that is independent of the size of the document set using only one word of memory to describe each document. (shrink)

The Yijing/Binary System Episode involved Leibniz' discovery of a de facto representation of the binary number system in the sixty-four-hexagram Fu Xi "Yijing." Scholars have left the match unexplained, since they have found no evidence of a forgotten binary number system in ancient China. The interesting similarities and differences are discussed between the thought of Leibniz and that of Shao Yong, both of whom, it is argued, understood and recognized the importance of the double geometric progression in (...) the diagram. (shrink)

Black-white, male-female — these and other markers, applied maliciously or not, enable the social dominance of one group.

Recently, a concern has been raised about a particular kind of behaviour that is adversely affecting the quality of nursing theoretical discourse. With the behaviour being attributed to nurses’ tendency to think in binary terms, it has been proposed that nurses replace their binary way of thinking with thinking that is inclusive and expansive and is based on an epistemology of contradiction. While agreeing that the behaviour of concern is indeed unscholarly, I disagree that the culprit is the (...) binary. In this commentary, I argue that the culprit is sophistical argumentation involving a binary (real or not) and that, by not making room for legitimate binaries, we run the danger of ‘throwing out the baby with the bathwater’. Further, I argue that the proffered solution is illusory. Its epistemological basis prohibits the deliverance of that which is promised. (shrink)

Everyday thinking and scientific theorizing about human action control are equally driven by the apparently obvious contrast between will and habit or, in their more modern disguise: intentional and automatic processes, and model-based and model-free action planning. And yet, no comprehensive category system to systematically tell truly willed from merely habitual actions is available. As I argue, this is because the contrast is ill-conceived, because almost every single action is both willed and habitual, intentional and automatic, and model-based and model-free, (...) simply because will and habit (and their successors) do not refer to alternative modes or pathways of action control but rather to different phases of action planning. I further discuss three basic misconceptions about action control that binary theorizing relies on: the assumption that intentional processes compete with automatic processes (rather than the former setting the stage for the latter), the assumption that action control is targeting processes (rather than representations of action outcomes), and the assumption that people follow only one goal at a time (rather than multiple goals). I conclude that (at least the present style of) binary theorizing fails to account for action control and should thus be replaced by a more integrative view. (shrink)

We introduce the notion of a convex tree. We show that the binary expansion for real numbers in the unit interval ) is equivalent to weak König lemma ) for trees having at most two nodes at each level, and we prove that the intermediate value theorem is equivalent to \ for convex trees, in the framework of constructive reverse mathematics.

A case has been made by various authors that the normative and processual notion of personhood found in African philosophy is discriminatory: it has been labelled as sexist, ableist and anti-queer. Within the anti-queer critique, one area that has not been specifically addressed in the literature is whether this notion of personhood is biased against people who identify as non-binary with respect to gender. This includes people who are gender fluid and gender neutral, among others. In this article, we (...) argue that the binary conception of gender is deeply connected to a colonial agenda, and does not accurately fit extra-colonial gender conceptions. Through an analysis of extra-colonial language and logic, read together with the flexibility inherent in the processual notion of personhood (on our reading), we argue that binaries do not sit comfortably with extra-colonial African thinking, and as such, processual and normative personhood can be understood in a way that embraces non-binary individuals. Further, the standards for achieving personhood are set by and achieved within the community, so a community which recognises and celebrates non-binary individuals can set up a framework for them to achieve personhood. Accordingly, normative personhood in African thought is found not to exclude those of non-binary gender. This reading saves the normative approach from some of the critiques levelled against it, as well as: i) enhancing consistency in an African world view; ii) strengthening the decolonial agenda; and iii) showing normative personhood to be fairer and more inclusive. (shrink)

The first collection of Leibniz's key writings on the binary system, newly translated, with many previously unpublished in any language. -/- The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today's digital computing. This book offers the first collection of Leibniz's most important writings on the binary system, all newly translated by the (...) authors with many previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system. -/- As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz's original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory “headnote” that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz's mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz's development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age. (shrink)

According to Act Consequentialism, an act is right if and only if its outcome is not worse than the outcome of any alternative to that act. This view, however, leads to deontic paradoxes if the alternatives to an act are all other acts that can be done in the situation. A typical response is to only apply this rightness criterion to maximally specific acts and to take the alternatives to a maximally specific act to be the other maximally specific acts (...) that can be done in the situation. (This view can then be supplanted by a separate account for the rightness of acts that are not maximally specific.) This paper defends a rival view, Binary Act Consequentialism, where, for any voluntary act, that act is right if and only if its outcome is not worse than the outcome of not doing that act. Binary Act Consequentialism, which dates back to Jeremy Bentham, has few supporters. A number of seemingly powerful objections have been considered fatal. In this paper, I rebut these objections and put forward a positive argument for the view. (shrink)

The transitive closure of a binary relation R can be thought of as the best possible approximation of R "from above" by a transitive relation. We consider the question of approximating a relation from below by transitive relations. Our main result is that every thick relation (a relation whose complement contains no infinite chain) on a countable set has a transitive thick subrelation. This allows for a solution to a problem arising from previous work by the author and Alan (...) Taylor. We also exhibit a thick relation on an uncountable set with no transitive thick subrelation. (shrink)

Working in the weakening of constructive Zermelo-Fraenkel set theory in which the subset collection scheme is omitted, we show that the binary refinement principle implies all the instances of the exponentiation axiom in which the basis is a discrete set. In particular binary refinement implies that the class of detachable subsets of a set form a set. Binary refinement was originally extracted from the fullness axiom, an equivalent of subset collection, as a principle that was sufficient to (...) prove that the Dedekind reals form a set. Here we show that the Cauchy reals also form a set. More generally, binary refinement ensures that one remains in the realm of sets when one starts from discrete sets and one applies the operations of exponentiation and binary product a finite number of times. (shrink)

We compute the domination monoid in the theory of dense meet‐trees. In order to show that this monoid is well‐defined, we prove weak binarity of and, more generally, of certain expansions of it by binary relations on sets of open cones, a special case being the theory from [7]. We then describe the domination monoids of such expansions in terms of those of the expanding relations.

In their interesting and informative paper ‘From Szasz to Foucault: On the Role of Critical Psychiatry,’ Pat Bracken and Phil Thomas contrast, in a clear and helpful way, some central themes in the works of Thomas Szasz and Michel Foucault. They go on to endorse a form of critical psychiatry inspired by the latter. Szasz’s critique of psychiatry, they explain, is premised on binary oppositions, principally that between ‘mental’ and ‘bodily.’ Szasz begins by assuming the legitimacy of the distinction (...) and proceeds to argue that the term ‘illness’ can only be legitimately applied to what is ‘bodily.’ According to Szasz, there are medical pathologies, which are to be understood in naturalistic, biological terms, and .. (shrink)

“Basic equality” is the thesis that all (or nearly all) human beings are equal in moral status. Widespread interpersonal differences among humans make the task of justifying basic equality notoriously difficult. One strategy for circumventing this difficulty is to identify some morally significant binary (“all-or-nothing”) property that all humans have. This strategy seems promising: if the basis of equality is binary, then those who have it have it equally. However, skeptics have argued against this strategy on the grounds (...) that a proper defense of basic equality requires that we identify a morally significant property that can vary among humans but does not in fact vary. This paper examines various ways in which this skeptical argument can be motivated and concludes that they all fail. (shrink)

Pylyshyn makes a convincing case that early visual processing is cognitively impenetrable, and although I question the utility of binary oppositions such as penetrable/impenetrable, for the most part I am in agreement. The author does not provide explicit designations or denotations for the terms penetrable and impenetrable, which appear quite arbitrary. Furthermore, the use of focal attention smacks of an homunculus, and the account appears to slip too easily between the perceptual, the cognitive, and the neurophysiological.

We investigate the formal theory of binary quantifiers, that is, quantifiers that take seriously the surface structure of natural language quantifier phrases. We show how to develop a natural deduction system for logics of this sort and demonstrate soundness and completeness results.

Social care responses to extra-familial harm require social workers to work across the binaries of welfare and justice, victim and perpetrator, parent and professional, risk and protection. This paper examines the ethical consequences of working in this manner, through qualitative data (focus groups, interviews, observations, case file analysis and documentary review) from three children's social care organisations in England who trialled new child protection pathways for significant harm outside of family homes/relationships. The extent to which these pathways created five conditions (...) for a welfare response to extra-familial harm are considered, before these results are brought into conversation with Bourdieu’s meta theory of capital, habitus and doxa, and Fenton's practice theory of ethical stress. The challenges identified evidence of the importance foregrounding social work values in the pursuit of welfare-based response to extra-familial harm. They also offer a rationale for studying theories of care ethics in social work in the context of interagency practice. (shrink)

The article explores the landscape in higher education in which old binary divisions are officially denied yet have been reinvigorated through a mix of conservative and neo-liberal policies. Efforts to resist such pressures can happen at different levels, including, in this case, module design and classroom practice. The rationale for such resistance is considered in relationship to the authors’ political and moral standpoints. Debates within higher education policy circles are invariably reduced to a series of oppositions: theory and practice; (...) training and education; research and teaching. The article seeks to break down such polarities through an exploration of classroom practice. In fact, we argue that such distinctions help to legitimize the existing inequalities in higher education and group-based harms, which characterize the sector. Instead, a case is made for a pedagogy that enables students, particularly those from diverse and disadvantaged backgrounds, to use their experiences, values, etc. to exchange and develop ideas in a group context, thereby providing an important means of collective empowerment (intellectual and practical, both at work and in their private lives). In this process students are encouraged to use ethical theories as tools to explain and underpin their understanding of work-based scenarios. The role of the academic is to facilitate such exchanges and foster new ethical approaches and a public awareness and engagement that goes beyond the classroom. The pedagogic approach, drawing on notions of relational autonomy and narrative methods as well as providing spaces for the co-production of new knowledge, confirms the indivisibility of research and teaching. (shrink)

We welcome Stibbard-Hawkes's empirical contributions and discussion of interpretive challenges for archaeology, but question some of his characterizations and conclusions. Moving beyond critique, it is time to develop new research methods that eschew simplistic modern/premodern binaries. We advocate an inductive, probabilistic approach using multiple lines of evidence to infer the causes and consequences of behavioral variability across time and space.