While collaboration has always played an important role in many cases of discovery and creation, recent developments such as the web facilitate and encourage collaboration at scales never seen before, even in areas such as mathematics, where contributions by single individuals have historically been the norm. This new scenario poses a challenge at the theoretical level, as it brings out the importance of various issues which, as of yet, have not been sufficiently central to the study of problem-solving, discovery, and (...) creativity. We analyze the case of collective and web-based proof events in mathematics, which share their temporal and social nature with every case of collective problem-solving. We propose that some ideas from cognitive architectures, in particular, the notion of codelet—understood as an agent engaged in one of a multitude of available tasks—can illuminate our understanding of collective problem-solving and act as a natural bridge from some of the theoretical aspects of collective, web-based discovery to the practical concern of designing cognitively inspired systems to support collective problem-solving. We use the Pythagorean Theorem and its many proofs as a case study to illustrate our approach. (shrink)

The Web may critically transform the way we understand the activity of proving. The Web as a collaborative medium allows the active participation of people with different backgrounds, interests, viewpoints, and styles. Mathematical formal proofs are inadequate for capturing Web-based proofs. This article claims that Web provings can be studied as a particular type of Goguen's proof-events. Web-based proof-events have a social component, communication medium, prover-interpreter interaction, interpretation process, understanding and validation, historical component, and styles. To (...) demonstrate its claim, the article discusses the Kumo and Polymath projects, both of which employ Web-based communication as part of proving. Web proving is a novel type of proving activity that may have a serious impact on the change in mathematical practices, despite the fact that it is not currently a universally acceptable methodology. (shrink)

Proof requires a dialogue between agents to clarify obscure inference steps, fill gaps, or reveal implicit assumptions in a purported proof. Hence, argumentation is an integral component of the discovery process for mathematical proofs. This work presents how argumentation theories can be applied to describe specific informal features in the development of proof-events. The concept of proof-event was coined by Goguen who described mathematical proof as a public social event that takes place in space (...) and time. This new meta-methodological concept is designed to cover not only “traditional” formal proofs but all kinds of proofs and inference steps, including incomplete or purported proofs. Our approach attempts to make proof-events more comprehensive to express the complete trajectory of a mathematical proof-event until the ultimate validation of the proving outcome. Thus, we advance an extended version of proof-event calculus which is built on argumentation theories designed to capture the internal and external structure of collaborative mathematical practice and highlight the relationship between proof, human reasoning, and cognitive processes. In addition, another area in which argumentation can make a significant contribution is dealing with the defeasible knowledge of the Web which is a product of its open and ubiquitous nature. This approach seems to be sufficient for the presentation of Web-based proving processes as manifested in the case of the Mini-Polymath 4 project. (shrink)

This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence (...) in such contexts in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centred spatio-temporal processes by means of the language of the calculus of events, which adequately captures certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a “loose” semantics for the proof events by means of Kolmogorov’s calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving. (shrink)

In this paper, we suggest the broader concept of proof-event, introduced by Joseph Goguen, as a fundamental methodological tool for studying proofs in history of mathematics. In this framework, proof is understood not as a purely syntactic object, but as a social process that involves at least two agents; this highlights the communicational aspect of proving. We claim that historians of mathematics essentially study proof-events in their research, since the mathematical proofs they face in the extant (...) sources involve many informal components, often not completely formalizable, and convey some kind of semantic content calling for understanding and verification. We illustrate the application of this methodological approach in some outstanding historical cases, paying particular attention to the process of proof interpretation that makes a proof-event alive. Finally, we suggest a classification of proof-events, according to the conditions imposed upon problem-solving. This enables us to speak about broad classes of proof-events in history of mathematics that share a common characteristic. (shrink)

In this paper, we explore certain exemplifications of transgression in the history and philosophy of mathematics. We recognize transgressive acts in the transition from a “real” to an “imaginary” world. Further, we suggest the concept of proof-events that transgress traditional concepts of mathematical proof. The theory of proof-events provides us with means to identify transgressive acts in the development of a discovery proof-event. These concern the creative understanding of a purported mathematical proof by (...) reconstructing the meaning conveyed by it, eventually supplementing it, surpassing stylistic hindrances in the narrative formulated by a prover, exceeding the boundaries of the (local) logic of a prover, etc. Finally, we identify transgressive acts with discontinuous points of change in the development of proof-events and suggest formal measures for their recognition. (shrink)

In this paper, we study the parameters that come into play when assessing the truth conditions of say reports and contrast them with belief attributions. We argue that these conditions are sensitive in intricate ways to the connection between the interpretation of the complement of say and the properties of the reported speech act. There are three general areas this exercise is relevant to, besides the immediate issue of understanding the meaning of say: (i) the discussion shows the need to (...) go beyond the simplest view of propositional attitudes, which treats them as restricted quantifiers over worlds; (ii) the complex connections that must exist between the say report and its source speech act show that one has to be able to differentiate between various layers of meaning for the antecedent sentences; (iii) finally, this paper is a small step towards a typology of propositional attitudes that allows us to uncover the complex web of relationships that grammatical mood is sensitive to. (shrink)

To appear in the Proceedings of Logic Colloquium 2006. (28 pages).

This paper explores the relationship between informal reasoning, creativity in mathematics, and problem solving. It underscores the importance of environments that promote interaction, hypothesis generation, examination, refutation, derivation of new solutions, drawing conclusions, and reasoning with others, as key factors in enhancing mathematical creativity. Drawing on argumentation logic, the paper proposes a novel approach to uncover specific characteristics in the development of formalized proving using “proof-events.” Argumentation logic can offer reasoning mechanisms that facilitate these environments. This paper proposes (...) how argumentation can be implemented to discover certain characteristics in the development of formalized proving with “proof-events”. The concept of a proof-event was introduced by Goguen who described mathematical proof as a multi-agent social event involving not only “classical” formal proofs, but also other informal proving actions such as deficient or alleged proofs. Argumentation is an integral component of the discovery process for a mathematical proof since a proof necessitates a dialogue between provers and interpreters to clarify and resolve gaps or assumptions. By formalizing proof-events through argumentation, this paper demonstrates how informal reasoning and conflicts arising during the proving process can be effectively simulated. The paper presents an extended version of the proof-events calculus, rooted in argumentation theories, and highlights the intricate relationships among proof, human reasoning, cognitive processes, creativity, and mathematical arguments. (shrink)

In [HKL00] (henceforth HKL), Hamm, Kamp and van Lambalgen declare ‘‘there is no opposition between formal and cognitive semantics,’’ notwithstanding the realist/mentalist divide. That divide separates two sides Jackendo¤ has (in [Jac96], following Chomsky) labeled E(xternalized)-semantics, relating language to a reality independent of speakers, and I(nternalized)-semantics, revolving around mental representations and thought. Although formal semanticists have (following David Lewis) traditionally leaned towards E-semantics, it is reasonable to apply formal methods also to I-semantics. This point is made clear in HKL via (...) two computational approaches to natural language semantics, Discourse Representation Theory (DRT, [KR93]) and the Event Calculus (EC) presented in [LH05]. In this short note, I wish to raise certain questions about EC that can be traced to the applicability of formal methods to E-semantics and I-semantics alike. These opposing orientations suggest di¤erent notions of time, event and representation. (shrink)

Journal of Experimental Social Psychology, 44, 2-9.

of (from British Columbia Philosophy Graduate Conference) Despite the apparent polarity between the philosophies of Wittgenstein and G�del, I here seek to demonstrate and consider important similarities in these two allegedly disparate interpretations of mathematical proposition. Wittgenstein asserts that the meaning is comprised by proof, while G�del relegates provability to an intrinsically imperfect status. Each represents metamathematical statements as severely limited, and analysis emphasizing the complementary here yields a rich interpretation of mathematical proposition: invention, but not without a basis (...) for describing these inventions as incomplete. As contrivances that exhibit a necessarily imperfect correlation to hypothetical completeness, the extent to which any one system is comparatively useful is thus a reflection of the degree of imperfection with which it correlates to the otherwise inarticulable qualities that dictate usefulness. Inconsistency produced by our necessarily incomplete systems should therefore be viewed as a natural consequence of the inherent imperfect correlation, and so admits of meaningful interpretation. (shrink)

I develop a critique of Hume’s infamous problem of induction based upon the idea that the principle of induction (PI) is a normative rather than descriptive claim. I argue that Hume’s problem is a false dilemma, since the PI might be neither a “relation of ideas” nor a “matter of fact” but rather what I call a contingent normative statement. In this case, the PI could be justified by a means-ends argument in which the link between means and end is (...) established solely by deductive reasoning. The means-ends argument is an elementary result from formal learning theory that you must be willing to make inductive generalizations if you want to be logically reliable in the types of examples Hume described. This justification of the PI avoids both horns of Hume’s dilemma. Since no contradiction ensues from rejecting logical reliability as an aim, the PI is contingent. Yet since the proof concerning the PI and logical reliability is not based on inductive reasoning, there is no threat of circularity. (shrink)

We present some new data about binding and a theory that explains the phenomena by appeal to event quantification.

Preface/Introduction: The question under discussion is metaphysical and truly elemental. It emerges in two aspects — how did we come to be conscious of our own existence, and, as a deeper corollary, do existence and awareness necessitate each other? I am bold enough to explore these questions and I invite you to come along; I make no claim to have discovered absolute answers. However, I do believe I have created here a compelling interpretation. You’ll have to judge for yourself. -/- (...) What follows is the presentation of three essays I have worked on over the past several years seeing publication for the first time. “Hollows of Experience” was written first as an invited chapter for a collection on the ontology of consciousness. However, when cuts became necessary, my chapter got the knife. Its length has prohibited it from publication in any print journal. “Myth and Mind” was written next as a journal article, but as my involvement with it grew so did its length, so it has also idled on my websty awaiting its call. “From Panexperientialism to Conscious Experience” was written most recently, but it is the only one to have been available to the public elsewhere than my own website. Under the name, “The Continuum of Experience”, it was Target Article #95 on the recently closed Karl Jaspers Forum (for discussion purposes only). -/- I have put them in a different sequence here, for reasons of logical sense. Up first, “Panexperientialism” deals with an idea difficult for many to accept, namely that conscious experience is a particular mode of symbolically reflected experience that is largely unique to our species. However, I aver that experienced sensation in itself (as found, for example, in autonomic sensory response systems) goes “all the way down” into nature, and thus the title, panexperientialism. -/- Understanding this idea is helpful to dealing with the focus on language in Part I of “Hollows”, next, since here speech and general symbolic interaction in general are found to be the catalysts for the creation of our consciously experienced world (our “lived reality”). In Part II, however, I explore how experienced sensations must be coeval with existence, and, with even greater temerity, how all this sensational existence might have arisen within some literally inconceivable background of awareness-in-itself that yet has a dynamism that occasionally breaks into existence as experiential events and entities. (The latter may sound wacky, but physicists and cosmologists are themselves attempting to come to terms with that which seethes with vast potential energy in what they refer to as the quantum vacuum.) -/- “Myth and Mind” was put third since it deals with a major lacuna in “Hollows” — that presumed prehistoric period when members of our species made the painful crossing of the symbolic threshold into the beginnings of cultural consciousness. Speech plays a central role here, too, but I look more at narrative structures from the dawn of self-awareness when ritual and myth became vital to human survival. Why would fantastic stories and bizarre rituals be necessary? I speculate that growing foresight led to the unavoidable realization of certain mortality, from which, in turn, emerged the secondary realization that we were now alive. In contrast to our yet-to-come death, we have life here and now, and by ritually identifying with a symbolically expanded mythic, i.e., sacred, reality, we may continue to live on after bodily death, just as our ancestors and loved ones must also do. Language and mythmaking are necessary to avoid mortal despair and they remain at the core of human consciousness. -/- As Ernst Cassirer (1944) has noted, language and myth are “twin creatures”, both metaphoric webs over a reality we can never wholly comprehend. We live in the symbolic and construct our works of imagination and wars of conquest to make life meaningful, to feel immortal, and to sense that we ourselves participate in a reality greater than ourselves. No doubt we do, but this does not mean our culturally constructed self-identities survive the death of our bodies, and it does not imply that our symbolic concepts can ever indicate the ultimate truth. We simply must symbolize an extended reality that was sacred to our ancestors: “Is it not our way, as illusory as it may be, to force continuance on our world and our life in the face of their inevitable ending? Are we not compelled to extend those imaginary horizons as far as we can despite the terror and the sometime joy their extension incites? Is their closure not a form of death?” (Crapanzano, p. 210) -/- Of course, this leaves me in the uncomfortable position of being forced to admit that this venture of mine must inevitably be another attempt at meaningful mythmaking. But what else could it be? This is certainly not a scientific proof though it is indeed an academically rigorous exploration. (Just try to count the citations!) I hope the reader will judge my thesis on the basis of its coherence, the sense of meaning it evokes, my intellectual responsibility, and, finally, the engagement it inspires. If you have read my expositions and found yourself immersed in the timeless questions I here call forth, I would call these writings successful (even if you violently disagree with my answers). -/- I am very grateful to Huping Hu for granting me this special issue of JCER in which to present my ideas in some detail. He has patiently dealt with my exuberant approach and allowed the many changes I kept coming up with right until the final publication date. I also wish to thank the many potential commentators who politely replied to my invitation, and, even more, I thank those who made time to write actual commentaries. -/- References -/- Cassirer, E. (1944). An Essay on Man: An Introduction to a Philosophy of Human Culture. New Haven/London: Yale UP. -/- Crapanzano, V. (2004). Imaginative Horizons: An Essay in Literary-Philosophical Anthropology. Chicago: U of Chicago Press. -/- Gregory M. Nixon University of Northern British Columbia Prince George, British Columbia, Canada Email: doknyx@shaw.ca Websty: http://members.shaw.ca/doknyx. (shrink)

The goal of this inquiry is to discover whether a plausible naturalistic case can be made for personal survival after death. Personal survival is defined, and a plausibility scale developed as a tool. ;Various analytical objections to survival are considered and rejected as faulty. A key empirical objection is then examined: namely, that personal identity depends on memories, memories are stored in the brain, and personal identity thus cannot survive the brain's death. First, we distinguish habit memories from "pure" memories (...) of individual events and insights; the latter alone are crucial to personal identity. We then review memory findings and cases in neurology, neurophysiology, psychology, psychiatry and phenomenology, concluding that brain storage of "pure" memories is highly implausible. This being so, the memory argument against personal survival fails. ;A plausible self-structure is proposed, with pure memories lodged in the inmost self, fed by the experiencing self. Further evidence and argument indicate, with moderate plausibility, that the inmost/experiencing self is not reducible to, or identical with, or intextricably dependent on, the brain; nor is it merely a cell in the social web or the natural environment. ;Further inquiry suggests that survival of the inmost/experiencing self, after death of the organic self, coheres with a defensible ontology. Building on insights of recent philosophers of becoming, this ontology grounds human existence in temporality or real duration, stretching from birth to death. In this system our mental life, largely in the inmost self, greatly overflows our cerebral life, so that, as Bergson wrote, "survival becomes so probable that the onus of proof falls on him who denies it rather than on him who affirms it." ;The inquiry then widens and deepens this ontological discussion, without entering into theology, and also offers some speculation on what a naturalistic personal survival might be like. The inquiry concludes that such survival is plausible, that is, its reality is supported by substantial evidence outweighing the opposing evidence. (shrink)

This is the diary of an observant mathematician who documented the drama of the resolution of Fermat's Last Theorem as it unfolded around him from 1993 to 1995. Pierre Fermat claimed around 1637, in the most famous marginalia in the history of mathematics, to have a proof of the theorem that xn + yn = zn has no whole number solutions for n greater than 2. The other principal figure is the British mathematician Andrew Wiles, who emigrated to Princeton (...) University in the 1980s and who in 1993, at what for mathematicians is the relatively advanced age of forty, announced a proof of FLT. In the course of Wiles's initial exposition to mathematicians, before a full‐fledged proof could be published, a gap was discovered. This was too late to forestall announcements in the world press of an imminent proof. What had been an almost secretive devotion to the task by Wiles now became a rather more public and pressurized effort over the course of nearly a year. Wiles wondered at times if success could be achieved, but with the help of other mathematicians the gap was filled in and the full formal proof published in 1995.The statement of the theorem is likely to be the only part of the 1990s story that a nonspecialist can immediately appreciate, and the author has not especially addressed his book to the nonspecialist. Rather, this account is analogous to a well‐illustrated exhibition guidebook that serves as a memento and record to those who visited in person but that is not intended fully to inform those who did not experience it. For a broader account of the historical and mathematical background a reader can consult the three principal books published previously on the same topic by Amir Aczel, Simon Singh, and Alfred J. van der Poorten. The author knew many of the main players, attended most of the key talks, took notes, made recordings, and photographed. A major part of the book is a selection of sixty‐two photographs from the total of three thousand made by the author. He asked questions of Wiles and others and recorded both formal and informal reactions that he observed around him during the many public and nonpublic presentations that were made. Also, in keeping with the journal nature of his work, he has recorded his own reactions. Appendixes include an excerpt from Wiles's 1995 Annals of Mathematics publication and a synopsis by Ram Murty of the key results by Gerhard Frey, Jean‐Pierre Serre, and Kenneth Ribet that formed a basis for Wiles's work.It may interest historians and archivists to learn of the extent to which the primary sources for this story include e‐mail, web pages, photographs, and newspaper and television interviews. Though we recognize this reality of contemporary science, a diary account probably brings the issue home more directly than would studies by professional historians, who might feel obligated to do more of their own interviews, for example, rather than rely on the media. Mathematics has rarely had such a public spotlight turned on it—the proof of the four‐color theorem in 1976 is the only comparable event that comes to mind. Consequently, it has opened an unusual window into how mathematicians do mathematics. (shrink)

In 2004 Orlando Florida was hit with an almost unprecedented series of storms and hurricanes. Within two months, Hurricanes Charley, Frances, and Jeanne hit, and Hurricane Ivan made a near miss. Billions of dollars of damage resulted from these disasters, and several dozen lives were lost. It is tempting, in the case of extreme events, to either regard them as having no need of interpretation (that is, as simply given, material events shared by everyone), or as a kind (...) of rare window on the workings of a community.1 In this paper I want to examine the public construction of the meaning of the hurricane in Orlando, particularly as represented in reports at the time in the major newspaper, the Orlando Sentinel. I am especially interested in placemaking, that is, the ways in which places gain or fail to gain meaning in times of stress. I will suggest that opportunities for place-making were lost in Orlando because of the frame the events around Hurricane Charley were given. Hurricane Frances, though, was treated differently in the Orlando press, and the discourse around the hurricanes of 2004 provides a contrast to the kind of rhetorical response that circulated during the disastrous hurricane season of 2005. In the case of some disasters, community is reinforced, and the skills of place-making are exercised. The reaction to Hurricane Charley in Orlando, on the other hand, tended not to reinforce community, and tended not to contribute to place-making. While it is extremely difficult to measure sense of place or sense of community quantitatively, it is possible to make sense out of the interpretive tools people have at their disposal in a disaster. What comes out of all this, I think, is something I want to call “place-making imagination”. This is analogous to the 1 concept of “moral imagination” in ethics (Johnson). Our moral options extend as far as our imagination will allow. A person might boil the moral universe down to polarized options – fight or flight, kill or be killed, choose A or B – when in fact a more cultivated and aware imagination may have afforded other options, perhaps better ones than either polarized one.. (shrink)

While the story of Stanislav Petrov – the Soviet Lieutenant Colonel who likely saved the world from nuclear holocaust in 1983 – is often trotted out to advocate for the view that human beings ought to be kept “in the loop” of automated weapons’ responses, I argue that the episode in fact belies this reading. By attending more closely to the features of this event – to Petrov’s professional background, to his familiarity with the warning system, and to his decisions (...) to defy his protocol – it becomes clear that Petrov was not seamlessly working “in his loop,” but reassessing it entirely. I claim that this exhibits a paradox intrinsic to all automated loops: namely, that their optimum function in fact rests on unforeseen human interventions that cannot be reliably codified ex ante, that is, that good judgment cannot simply be “programmed into” their protocols. This dependence, moreover, reveals automation’s ineluctable need for virtue ethics – not in the usual sense (whereby ethics deliberates about, say, possible damages and loss of life), but in the sense that ethical judgment, rightly understood, entails the reassessment of all of the conditions surrounding a decision, including whether a protocol should be followed at all. (shrink)

The concept of proof can be studied from many different perspectives. Many types of proofs have been developed throughout history such as apodictic, dialectical, formal, constructive and non-constructive proofs, proofs by visualisation, assumption-based proofs, computer-generated proofs, etc. In this paper, we develop Goguen’s general concept of proof-events and the methodology of algebraic semiotics, in order to define the concept of mathematical style, which characterizes the proofs produced by different cultures, schools or scholars. In our view, style can (...) be defined as a semiotic meta-code that depends on the underlying mode of signification (semiosis), the selected code and the underlying semiotic space and determines the individual mode of integration (selection, combination, blending) into a narrative structure (proof). Finally, we examine certain historical types of styles of mathematical proofs, to elucidate our viewpoint. (shrink)

Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such (...) systems from logic to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated. (shrink)

String representations of events are applied to Robin Cooper’s proposal that propositions in natural language semantics are types of situations. Links with the higher types of prooftheoretic semantics are forged, deepening type-theoretic interpretations of Discourse Representation Structures to encompass event structures.

Proof and Disproof in Formal Logic is a lively and entertaining introduction to formal logic providing an excellent insight into how a simple logic works. Formal logic allows you to check a logical claim without considering what the claim means. This highly abstracted idea is an essential and practical part of computer science. The idea of a formal system-a collection of rules and axioms, which define a universe of logical proofs-is what gives us programming languages and modern-day programming. This (...) book concentrates on using logic as a tool: making and using formal proofs and disproofs of particular logical claims. The logic it uses-natural deduction-is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations. The book is divided into four parts: Part I "Basics" gives an introduction to formal logic with a short history of logic and explanations of some technical words. Part II "Formal Syntactic Proof" show you how to do calculations in a formal system where you are guided by shapes and never need to think about meaning. Your experiments are aided by Jape, which can operate as both inquisitor and oracle. Part III "Formal Semantic Disproof" shows you how to construct mathematical counterexamples to shoe that proof is impossible. Jape can check the counterexamples you build. Part IV " Program Specification and Proof" describes how to apply your logical understanding to a real computer science problem, the accurate description and verification of programs. Jape helps, as far as arithmetic allows. Aimed at undergraduates and graduates in computer science, logic, mathematics and philosophy, the text includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web. (shrink)

We construct an event-based computer simulation model of the Einstein-Podolsky-Rosen-Bohm experiments with photons. The algorithm is a one-to-one copy of the data gathering and analysis procedures used in real laboratory experiments. We consider two types of experiments, those with a source emitting photons with opposite but otherwise unpredictable polarization and those with a source emitting photons with fixed polarization. In the simulation, the choice of the direction of polarization measurement for each detection event is arbitrary. We use three different procedures (...) to identify pairs of photons and compute the frequency of coincidences by analyzing experimental data and simulation data. The model strictly satisfies Einstein’s criteria of local causality, does not rely on any concept of quantum theory and reproduces the results of quantum theory for both types of experiments. We give a rigorous proof that the probabilistic description of the simulation model yields the quantum theoretical expressions for the single- and two-particle expectation values. (shrink)

Under the standard modal explication of consequence, a conclusion is a consequence of some premises just in case necessarily, if the latter are true, so is the former. Notoriously, this explication yields some results that at first glance are counter-intuitive. In particular, a necessary truth is a consequence of arbitrary premises, and premises that cannot all be true together entail arbitrary conclusions. In his paper ‘On Ground and Consequence’ (Synthese, 2021), Benjamin Schnieder introduces a novel notion of web consequence, defined (...) on the basis of the concept of ground, which, he argues, fits our intuitive conception better. Building on his idea, the present paper examines the concept of web consequence in more detail. In particular, I provide three alternative, and simpler semantic characterizations of Schnieder’s propositional logic of web consequence, two within a form of truthmaker semantics, one within a many-valued setting. I then consider some natural variations on that logic and establish their connections to well-known subclassical logics such as FDE, $$\hbox {K}_3$$ K 3, and LP. Finally, I provide sound and complete tableaux-based proof systems for each of the logics of web consequence so obtained. (shrink)

I EXISTENTIAL PROOFS INTRODUCTION Metaphysical problems, like all philosophical problems, arise from a sense of puzzlement. What is puzzling is that the ...

Writing strategic documents is a major practice of many actors striving to see their educational ideas realised in the curriculum. In these documents, arguments are systematically developed to create the legitimacy of a new educational goal and competence to make claims about it. Through a qualitative analysis of the writing strategies used in these texts, I show how two of the main actors in the Czech educational discourse have developed a proof that a new educational goal is needed. I (...) draw on the connection of the relational approach in the sociology of education with Lyotard’s analytical semantics of instances in the event. The comparison of the writing strategies in the two documents reveals differences in the formation of a particular pattern of justification. In one case the texts function as a herald of pure reality, and in the other case as a messenger of other witnesses. This reveals different regimens of proof, although both of them were written as prescriptive directives – normative models of the educational world. (shrink)

God Exists! 50 Profound Proofs By: Matthew Armstrong Some of the most important questions in one’s life are: Where will I live for all eternity? Is God real? Will I live in His kingdom? Is it possible to prove the existence of God? God Exists! explores fifty proofs that God absolutely exists. Prophecy demonstrates the existence of God. Events taking place in the world today reveal that God exists and knows what will happen well in advance. The universe displays (...) the handiwork of God. (shrink)

A proof is given that there does not exist an event, that is not already in the past for some possible distant observer at the (our) moment that the latter is "now" for us. Such event is as "legally" past for that distant observer as is the moment five minutes ago on the sun for us (irrespective of the circumstance that the light of the sun cannot reach us in a period of five minutes). Only an extreme positivism: "that (...) which cannot yet be observed does not yet exist", can possibly withstand the conclusion concerned. Therefore, there is determinism, also in micro-physics. (shrink)

One of the major events that has caused a resurgence in the use of formal ontologies is the advent of the Semantic Web, which seeks to do for knowledge representation what the Web did for hypertext...

On the standard reading of Hume, the belief that the necessity associated with the causal relation is “an entirely mind-independent phenomenon” in the world isunjustified. For example, Jonathan Bennett writes that necessary connections of the sort that Hume allows are not “relations which hold objectively between the ‘objects’ or events which we take to be causally related.” Similarly, Barry Stroud writes that, according to Hume, we believe falsely “that necessity is something that ‘resides’ in the relation between objects or (...) events in the objective world.” In this paper I argue that this reading of Hume is mistaken and that there is a sense of justification (viz., justification qua “proof”) according to which human beings are justified in holding the belief that the necessity associated with the causal relation is “an entirely mind-independent phenomenon” in the world. (shrink)

The aim of this essay is to develop a coherence theory for the justification of evidentiary judgments in law. The main claim of the coherence theory proposed in this article is that a belief about the events being litigated is justified if and only if it is a belief that an epistemically responsible fact finder might hold by virtue of its coherence in like circumstances. The article argues that this coherentist approach to evidence and legal proof has the (...) resources to meet some of the main objections that may be addressed against attempts to analyze the justification of evidentiary judgments in law in coherentist terms. It concludes by exploring some implications of the proposed version of legal coherentism for a jurisprudence of evidence. (shrink)

The semantics of progressive sentences presents a challenge to linguists and philosophers alike. According to a widely accepted view, the truth-conditions of progressive sentences rely essentially on a notion of inertia. Dowty suggested inertia worlds to implement this “inertia idea” in a formal semantic theory of the progressive. The main thesis of the paper is that the notion of inertia went through a subtle, but crucial change when worlds were replaced by events in Landman and Portner :760–787, 1998), and (...) that this new, event-related concept of inertia results in a possibility-based theory of the progressive. An important case in point in the paper is a proof that, despite its surface structure, the theory presented in Portner does not implement the notion of inertia in Dowty ; rather, it belongs together with Dowty’s earlier, 1977 theory according to which the progressive is a possibility operator. (shrink)

Purpose The purpose of this study is to examine the primary sources and methods of Web-based messaging during the early stages of the coronavirus pandemic. The authors use ethical lens to develop a conceptual framework to inform and reduce conflicts of Web-based messaging associated with COVID-19. Design/methodology/approach This paper provides a comprehensive review of three different ethical schools and identifies the cohesive theme of common good across them. Common good leading to a greater good serves as the overarching ethical construct (...) for Web-based messages that focus on society and not the singular individual, business or political ideology. Findings The findings suggest that the ethical construct of common good focuses on prioritizing the society over the individual and draws upon utilitarian principles focused on consequences, Kantian principles focused on intentions and Aristotelian principles focused on the definition of good. Web-based messaging on COVID-19 originates from diverse public and private sources and ethically can be governed by adherence to achieving the greatest good for society. Pervasive conflicts with COVID-19 messaging can be mitigated by pursuing a more ethical agenda with messages. Originality/value This manuscript provides a conceptual framework, based on ethical principles, to serve as a blueprint for Web-based messaging during a pandemic. This work offers an ethical perspective for communication during a pandemic and it is original in conceptualizing the components of Web-based messaging and decomposing them into the different levels where conflicts can occur. This article can serve as a template for Web-based communication pertaining to future pandemics and other events that benefit from prioritizing the impact on society over the impact on the individual. (shrink)

Event integration – the conflation of multiple events into a unitary event – plays a vital role in language and cognition. However, the conditions under which event integration occurs in linguistic representation and the differences in how linguistic forms encode complex events remain unclear. This corpus study examines two types of Japanese complex predicates – compound verbs [V1-V2]V and complex predicates consisting of a deverbal compound noun and the light verb suru ‘do’ [[V1-V2]N suru]V – using an original (...) “related-event approach”. Findings indicate that [[V1-V2]N suru]V can be established based on coextensiveness alone, whereas [V1-V2]V typically requires direct or shared causality (“the inevitable co-occurrence constraint”). The related-event approach examines related events of linguistic concepts, such as causes and purposes of an event, identified through “complex sentences” from ultra-large-scale web corpora. This study demonstrates that such an approach is effective in clarifying causal relationships between verbs. Furthermore, this paper contributes to the “iconicity versus frequency” debate by showing that conceptually more accessible events (causality plus coextensiveness) tend to be represented in a simpler form than less accessible events (coextensiveness only), due to “efficiency”. The frequency of usage is a result of the nature of concepts rather than the driving force of coding asymmetries. (shrink)

The advent of the Web is one of the defining technological events of the twentieth century, yet its impact on the fundamental questions of philosophy has not yet been explored, much less systematized. The Web, as today implemented on the foundations of the Internet, is broadly construed as the space of all items of interest identified by URIs. Originally a space of linked hypertext documents, today the Web is rapidly evolving as a universal platform for data and computation. Even (...) swifter is the Web-driven transformation of many previously unquestioned philosophical concepts of privacy, belief, intelligence, cognition, and even embodiment in surprising ways. The ensuing essays in this collection hope to explore the philosophical foundation of the World Wide Web and open the debate on whether or not the changes caused by the Web to technology and society warrant the creation of a philosophy of the Web. (shrink)

In this contribution, we will discuss the opportunities and challenges arising from memory institutions' need to redefine their archival strategies for contemporary collecting in a world of big data. We will reflect on this topic by critically examining the case study of the UK Web Archive, which is made up of the six UK Legal Deposit Libraries: the British Library, National Library of Scotland, National Library of Wales, Bodleian Libraries Oxford, Cambridge University Library and Trinity College Dublin. The UK Web (...) Archive aims to archive, preserve and give access to the UK web space. This is achieved through an annual domain crawl, first undertaken in 2013, in addition to more frequent crawls of key websites and specially curated collections which date back as far as 2005. These collections reflect important aspects of British culture and events that shape society. This commentary will explore a number of questions including: what heritage is captured and what heritage is instead neglected by the UK Web archive? What heritage is created in the form of new data and what are its properties? What are the ethical issues that memory institutions face when developing these web archiving practices? What transformations are required to overcome such challenges and what institutional futures can we envisage? (shrink)

We show how Peirce's architectonics folds on itself and finds local consequences that correspond to the major global hypotheses of the system. In particular, we study how the pragmaticist maxim can be technically represented in Peirce's existential graphs, well-suited to reveal an underlying continuity in logical operations, and can provide suggestive philosophical analogies. Further, using the existential graphs, we formalize — and prove one direction of — a “local proof of pragmaticism,” trying thus to explain the prominent place that (...) existential graphs can play in the architectonics of pragmaticism, as Peirce persistently advocated. Finally, we present a web of “continuous iterations” of some key Peircean concepts that supports a “lattice of partial proofs” of pragmaticism. (shrink)

The advent of the Web is one of the defining technological events of the twentieth century, yet its impact on the fundamental questions of philosophy has not yet been explored, much less systematized. The Web, as today implemented on the foundations of the Internet, is broadly construed as the space of all items of interest identified by URIs. Originally a space of linked hypertext documents, today the Web is rapidly evolving as a universal platform for data and computation. Even (...) swifter is the Web‐driven transformation of many previously unquestioned philosophical concepts of privacy, belief, intelligence, cognition, and even embodiment in surprising ways. The ensuing essays in this collection hope to explore the philosophical foundation of the World Wide Web and open the debate on whether or not the changes caused by the Web to technology and society warrant the creation of a philosophy of the Web. (shrink)

In an attempt to improve upon Alexander Pruss’s work (The principle of sufficient reason: A reassessment, pp. 240–248, 2006), I (Weaver, Synthese 184(3):299–317, 2012) have argued that if all purely contingent events could be caused and something like a Lewisian analysis of causation is true (per, Lewis’s, Causation as influence, reprinted in: Collins, Hall and paul. Causation and counterfactuals, 2004), then all purely contingent events have causes. I dubbed the derivation of the universality of causation the “Lewisian argument”. (...) The Lewisian argument assumed not a few controversial metaphysical theses, particularly essentialism, an incommunicable-property view of essences (per Plantinga’s, Actualism and possible worlds, reprinted in: Davidson (ed.) Essays in the metaphysics of modality, 2003), and the idea that counterfactual dependence is necessary for causation. There are, of course, substantial objections to such theses. While I think a fight against objections to the Lewisian argument can be won, I develop, in what follows, a much more intuitive argument for the universality of causation which takes as its inspiration a result from Frederic B. Fitch’s work (J Symb Logic 28(2):135–142, 1963) [with credit to who we now know was Alonzo church’s, Referee Reports on Fitch’s Definition of value, in: (Salerno (ed.), New essays on the knowability paradox, 2009)] that if all truths are such that they are knowable, then (counter-intuitively) all truths are known. The resulting Church–Fitch proof for the universality of causation is preferable to the Lewisian argument since it rests upon far weaker formal and metaphysical assumptions than those of the Lewisian argument. (shrink)

In cybersecurity, there is a call for adaptive, accurate and efficient procedures to identifying performance shortcomings and security breaches. The increasing complexity of both Internet services and traffic determines a scenario that in many cases impedes the proper deployment of intrusion detection and prevention systems. Although it is a common practice to monitor network and applications activity, there is not a general methodology to codify and interpret the recorded events. Moreover, this lack of methodology somehow erodes the possibility of (...) diagnosing whether event detection and recording is adequately performed. As a result, there is an urge to construct general codification and classification procedures to be applied on any type of security event in any activity log. This work is focused on defining such a method using the so-called normalized compression distance (NCD). NCD is parameter-free and can be applied to determine the distance between events expressed using strings. As a first step in the concretion of a methodology for the integral interpretation of security events, this work is devoted to the characterization of web logs. On the grounds of the NCD, we propose an anomaly-based procedure for identifying web attacks from web logs. Given a web query as stored in a security log, a NCD-based feature vector is created and classified using a support vector machine. The method is tested using the CSIC-2010 data set, and the results are analyzed with respect to similar proposals. (shrink)

Legal reasoning on the requirements and application of law has been studied for centuries, but in this subject area the legal profession maintains predominantly the same stance it did in the time of the Ancient Greeks. There is a gap between the standards of proof, one which has been always demonstrated by percentages and in terms of the evaluation of these standards by percentages by mathematical or statistical methods. One method to fill the gap is Bayes theorem that describes (...) an event’s probability based on conditions that might be related to an event. Bayes theorem can help to establish or confirm a relation between facts and rules if there is sufficient other evidence that connect a party in a procedure with a considered legal action. (shrink)

Many argued (Accardi and Fedullo, Pitowsky) that Kolmogorov's axioms of classical probability theory are incompatible with quantum probabilities, and that this is the reason for the violation of Bell's inequalities. Szabó showed that, in fact, these inequalities are not violated by the experimentally observed frequencies if we consider the real, “effective” frequencies. We prove in this work a theorem which generalizes this results: “effective” frequencies associated to quantum events always admit a Kolmogorovian representation, when these events are collected (...) through different experimental setups, the choice of which obeys a classical distribution. (shrink)

This article concerns efforts to see politics in web space. It is a network-topological approach in which the mappings of web space over the past decade have resulted in specific political geometries (roundtables, spheres, lists, etc.). In the web as hyperspace period, random site generators invited surfers to jumpcut through space. Mapping was performed for sites’ backlinks, showing distinctive ‘politics of association’. In the web as public sphere period, circle maps served as virtual roundtables. What if the web were to (...) decide who should sit at the table? As ideas about the shapes the web accommodated shifted from public spheres to networks, the maps displayed ‘issue spaces’ – clusters of actors engaged in the same issue area, but now central or marginal. Finally, in what is dubbed as the revenge of geography, in the current locative period, maps show the distributed geography of engagement. Actors are temporarily ‘based’ and travelling physically from event to event, with tracing and other social software showing their routes. The article treats the shift in focus away from the ‘metaphysics’ of software-enabled spaces online (the ‘virtual’ topologies) to critiques of the new ‘trace routes’ (followed by mobile network actors) now that cyberspace is grounded. (shrink)

Civic media literacy entails understanding complex topics and events that are increasingly mediated by digital sources of information and where it can be challenging to evaluate the reliability merits of these sources. The goal of this study was to discern the ways undergraduate preservice social studies teachers with different climate change beliefs read and evaluated the reliability of four diverse Web sources about the complex socioscientific topic of climate change. Findings highlight clear alignment between most participants with climate change (...) beliefs at either end of a beliefs continuum with less alignment for participants with climate change beliefs toward the middle of a continuum. Findings also point to the benefits of whole group deliberation to help participants more critically evaluate a Web source that opposed the scientific consensus about climate change. In an age of “alternative facts,” this study points to the importance of students and educators having opportunities to evaluate, discuss, and determine the credibility of a range of online sources. (shrink)