There is currently much interest in bringing together the tradition of categorial grammar, and especially the Lambek calculus, with the recent paradigm of linear logic to which it has strong ties. One active research area is designing non-commutative versions of linear logic (Abrusci, 1995; Retoré, 1993) which can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic (Dalrymple et al., 1995). Some connections between the Lambek calculus and computations in groups have long (...) been known (van Benthem, 1986) but no serious attempt has been made to base a theory of linguistic processing solely on group structure. This paper presents such a model, and demonstrates the connection between linguistic processing and the classical algebraic notions of non-commutative free group, conjugacy, and group presentations. A grammar in this model, or G-grammar is a collection of lexical expressions which are products of logical forms, phonological forms, and inverses of those. Phrasal descriptions are obtained by forming products of lexical expressions and by cancelling contiguous elements which are inverses of each other. A G-grammar provides a symmetrical specification of the relation between a logical form and a phonological string that is neutral between parsing and generation modes. We show how the G-grammar can be oriented for each of the modes by reformulating the lexical expressions as rewriting rules adapted to parsing or generation, which then have strong decidability properties (inherent reversibility). We give examples showing the value of conjugacy for handling long-distance movement and quantifier scoping both in parsing and generation. The paper argues that by moving from the free monoid over a vocabulary V (standard in formal language theory) to the free group over V, deep affinities between linguistic phenomena and classical algebra come to the surface, and that the consequences of tapping the mathematical connections thus established can be considerable. (shrink)

Let M be a smooth, compact manifold of dimension n ≥ 5 and sectional curvature | K | ≤ 1. Let Met (M) = Riem(M)/Diff(M) be the space of Riemannian metrics on M modulo isometries. Nabutovsky and Weinberger studied the connected components of sublevel sets (and local minima) for certain functions on Met (M) such as the diameter. They showed that for every Turing machine T e , e ∈ ω, there is a sequence (uniformly effective in e) of homology (...) n-spheres {P k e } k ∈ ω which are also hypersurfaces, such that P k e is diffeomorphic to the standard n-sphere S n (denoted P k e ≈ diff S n ) iff T e halts on input k, and in this case the connected sum N k e =M ♯ P k e ≈ diff M , so N k e ∈ Met(M), and N k e is associated with a local minimum of the diameter function on Met(M) whose depth is roughly equal to the settling time σ e (k) of T e on inputs y i } ∈ ω of c.e. sets so that for all i the settling time of the associated Turing machine for A i dominates that for A i + 1 , even when the latter is composed with an arbitrary computable function. From this, Nabutovsky and Weinberger showed that the basins exhibit a "fractal" like behavior with extremely big basins, and very much smaller basins coming off them, and so on. This reveals what Nabutovsky and Weinberger describe in their paper on fractals as "the astonishing richness of the space of Riemannian metrics on a smooth manifold, up to reparametrization." From the point of view of logic and computability, the Nabutovsky-Weinberger results are especially interesting because: (1) they use c.e. sets to prove structural complexity of the geometry and topology, not merely undecidability results as in the word problem for groups, Hilbert's Tenth Problem, or most other applications; (2) they use nontrivial information about c.e. sets, the Soare sequence {A i } i ∈ ω above, not merely G öodel's c.e. noncomputable set K of the 1930's; and (3) without using computability theory there is no known proof that local minima exist even for simple manifolds like the torus T 5 (see §). (shrink)

American Academy of Pediatrics (AAP) and American College of Medical Genetics (ACMG) recently provided two recommendations about predictive genetic testing of children. The Clinical Sequencing Exploratory Research Consortium's Pediatrics Working Group compared these recommendations, focusing on operational and ethical issues specific to decision making for children. Content analysis of the statements addresses two issues: (1) how these recommendations characterize and analyze locus of decision making, as well as the risks and benefits of testing, and (2) whether the guidelines conflict (...) or come to different but compatible conclusions because they consider different testing scenarios. These statements differ in ethically significant ways. AAP/ACMG analyzes risks and benefits using best interests of the child and recommends that, absent ameliorative interventions available during childhood, clinicians should generally decline to order testing. Parents authorize focused tests. ACMG analyzes risks and benefits using the interests of the child and other family members and recommends that sequencing results be examined for additional variants that can lead to ameliorative interventions, regardless of age, which laboratories should report to clinicians who should contextualize the results. Parents must accept additional analysis. The ethical arguments in these statements appear to be in tension with each other. (shrink)

In everyday life, as well as in science, we have to deal with and act on the basis of partial (i.e. incomplete, uncertain, or even inconsistent) information. This observation is the source of a broad research activity from which a number of competing approaches have arisen. There is some disagreement concerning the way in which partial or full ignorance is and should be handled. The most successful approaches include both quantitative aspects (by means of probability theory) and qualitative aspect (...) (by means of graphical or causal models or logic). Some of these approaches have important impacts on various disciplines including philosophy, computer science, statistics, mathematics, physics, and social science. Most notably, the relation between causal and probabilistic information is a topic of interest in all of these fields. The general question of how uncertainty is related to ignorance, and the connection thereof to causality, have been the key topics of the international summer school at the University of Konstanz, Germany, in August 2004. This was the third event in a series of summer schools organized by the interdisciplinary research group “Philosophy, Probability, and Modeling”. The group was in operation from September 1st, 2001, until August 31, 2005. The first summer school, held in September 2002, focused on the application of probability theory to topics of philosophical interest. Problems and questions that arise when probabilistic models and techniques are being applied in the special sciences were then discussed during the second summer school, held in July 2003. The fourth and final event in the series, in August 2005, was devoted to philosophical questions related to the application and interpretation of probabilities in physics. Each of the four summer schools attracted 40–50 people from many different countries. It was an inspiring forum for an interdisciplinary discussion among researchers and students from many different areas. This special issue collects a selection of the invited and contributed papers presented at the summer school in 2004. We acknowledge the generous support of the Center for Junior Research Fellows at the University of Konstanz, the Gesellschaft für analytische Philosophie e.V., the Centre for Philosophy of Natural and Social Science at the London School of Economics, the Alexander von Humboldt Foundation, the Federal Ministry of Education and Research and the Program for the Investment in the Future (ZIP) of the German Government through a Sofja Kovalevskaja Award. We thank the referees of the papers for their work, and James Moor for his interest in dedicating a special issue of this journal to Causality, Uncertainty and Ignorance. (shrink)

Turing's World is a self-contained introduction to Turing machines, one of the fundamental notions of logic and computer science. The text and accompanying diskette allow the user to design, debug, and run sophisticated Turing machines in a graphical environment on the Macintosh. Turning's World introduces users to the key concpets in computability theory through a sequence of over 100 exercises and projects. Within minutes, users learn to build simple Turing machines using a convenient package of graphical functions. Exercises (...) then progress through a significant portion of elementary computability theory, covering such topics as the Halting problem, the Busy Beaver function, recursive functions, and undecidability. Version 3.0 is an extensive revision and enhancement of earlier releases of the program, allowing the construction of one-way and two-way finite state machines (finite automata), as well as nondeterministic Turing and finite-state machines. Special exercises allow users to explore these alternative machines. (shrink)

Simple Heuristics That Make Us Smart invites readers to embark on a new journey into a land of rationality that differs from the familiar territory of cognitive science and economics. Traditional views of rationality tend to see decision makers as possessing superhuman powers of reason, limitless knowledge, and all of eternity in which to ponder choices. To understand decisions in the real world, we need a different, more psychologically plausible notion of rationality, and this book provides it. It is about (...) fast and frugal heuristics--simple rules for making decisions when time is pressing and deep thought an unaffordable luxury. These heuristics can enable both living organisms and artificial systems to make smart choices, classifications, and predictions by employing bounded rationality. But when and how can such fast and frugal heuristics work? Can judgments based simply on one good reason be as accurate as those based on many reasons? Could less knowledge even lead to systematically better predictions than more knowledge? Simple Heuristics explores these questions, developing computational models of heuristics and testing them through experiments and analyses. It shows how fast and frugal heuristics can produce adaptive decisions in situations as varied as choosing a mate, dividing resources among offspring, predicting high school drop out rates, and playing the stock market. As an interdisciplinary work that is both useful and engaging, this book will appeal to a wide audience. It is ideal for researchers in cognitive psychology, evolutionary psychology, and cognitive science, as well as in economics and artificial intelligence. It will also inspire anyone interested in simply making good decisions. (shrink)

This volume contains the proceedings of three special sessions: Algebra and Computer Science, held during the Joint AMS-EMS-SPM meeting in Porto, Portugal, June 10–13, 2015; Groups, Algorithms, and Cryptography, held during the Joint Mathematics Meeting in San Antonio, TX, January 10–13, 2015; and Applications of Algebra to Cryptography, held during the Joint AMS-Israel Mathematical Union meeting in Tel-Aviv, Israel, June 16–19, 2014. Papers contained in this volume address a wide range of topics, from theoretical aspects of algebra, namely (...) class='Hi'>group theory, universal algebra and related areas, to applications in several different areas of computer science. From the computational side, the book aims to reflect the rapidly emerging area of algorithmic problems in algebra, their computational complexity and applications, including information security, constraint satisfaction problems, and decision theory. The book gives special attention to recent advances in quantum computing that highlight the need for a variety of new intractability assumptions and have resulted in a new area called group-based cryptography. (shrink)

We don't yet have adequate theories of what the human mind is representing when it represents a social group. Worse still, many people think we do. This mistaken belief is a consequence of the state of play: Until now, researchers have relied on their own intuitions to link up the concept social group on the one hand and the results of particular studies or models on the other. While necessary, this reliance on intuition has been purchased at a (...) considerable cost. When looked at soberly, existing theories of social groups are either literal, but not remotely adequate, or simply metaphorical. Intuition is filling in the gaps of an explicit theory. This paper presents a computational theory of what, literally, a group representation is in the context of conflict: It is the assignment of agents to specific roles within a small number of triadic interaction types. This “mental definition” of a group paves the way for a computational theory of social groups – in that it provides a theory of what exactly the information-processing problem of representing and reasoning about a group is. For psychologists, this paper offers a different way to conceptualize and study groups, and suggests that a non-tautological definition of a social group is possible. For cognitive scientists, this paper provides a computational benchmark against which natural and artificial intelligences can be held. (shrink)

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, (...) and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students. (shrink)

Whenever a structure with a particularly interesting computability-theoretic property is found, it is natural to ask whether similar examples can be found within well-known classes of algebraic structures, such as groups, rings, lattices, and so forth. One way to give positive answers to this question is to adapt the original proof to the new setting. However, this can be an unnecessary duplication of effort, and lacks generality. Another method is to code the original structure into a structure in the (...) given class in a way that is effective enough to preserve the property in which we are interested. In this paper, we show how to transfer a number of computability-theoretic properties from directed graphs to structures in the following classes: symmetric, irreflexive graphs; partial orderings; lattices; rings ; integral domains of arbitrary characteristic; commutative semigroups; and 2-step nilpotent groups. This allows us to show that several theorems about degree spectra of relations on computable structures, nonpreservation of computable categoricity, and degree spectra of structures remain true when we restrict our attention to structures in any of the classes on this list. The codings we present are general enough to be viewed as establishing that the theories mentioned above are computably complete in the sense that, for a wide range of computability-theoretic nonstructure type properties, if there are any examples of structures with such properties then there are such examples that are models of each of these theories. (shrink)

Since its conception nearly 20 years ago, Logic Programming - the idea of using logic as a programming language - has been developed to the point where it now plays an important role in areas such as database theory, artificial intelligence and software engineering. However, there are still many challenging research issues to be addressed and the UK branch of the Association for Logic Programming was set up to provide a forum where the flourishing research community could discuss important (...) issues of Logic Programming which were often by-passed at the large international conferences. This volume contains the twelve papers which were presented at the ALPUK's 3rd conference which was held in Edinburgh, 10-12 April 1991. The aim of the conference was to give a broad but detailed technical insight into the work currently being done in this field, both in the UK and by researchers as far afield as Canada and Bulgaria. The breadth of interest in this area of Computer Science is reflected in the range of the papers which cover - amongst other areas - massively parallel implementation, constraint logic programming, circuit modelling, algebraic proof of program properties, deductive databases, specialised editors and standardisation. The resulting volume gives a good overview of the current progress being made in the field and will be of interest to researchers and students of any aspects of logic programming, parallel computing or database techniques and management. (shrink)

Epistemic logic has grown from its philosophical beginnings to find diverse applications in computer science, and as a means of reasoning about the knowledge and belief of agents. This book provides a broad introduction to the subject, along with many exercises and their solutions. The authors begin by presenting the necessary apparatus from mathematics and logic, including Kripke semantics and the well-known modal logics K, T, S4 and S5. Then they turn to applications in the context of distributed systems and (...) artificial intelligence. These include the notions of common knowledge, distributed knowledge, explicit and implicit belief, the interplays between knowledge and time, and knowledge and action, as well as a graded (or numerical) variant of the epistemic operators. The authors also discuss extensively the problem of logical omniscience. They cover Halpern & Moses' theory of honest formulas, and they make a digression into the realm of nonmonotonic reasoning and preferential entailment. They discuss Moore's autoepistemic logic, together with Levesque's related logic of "all I know". Furthermore, they show how one can base default and counterfactual reasoning on epistemic logic. Graduate students in philosophy or in computer science, especially those with an interest in AI, will find this book useful. (shrink)

This paper was motivated by the following two questions which arise in the theory of complexity for computation over ordered rings in the now famous computational model introduced by Blum, Shub and Smale: 1. is the answer to the question P = ?NP the same in every real-closed field?2. if P ≠ NP for , does there exist a problem of which is NP but neither P nor NP-complete ?Some unclassical complexity classes arise naturally in the study of these (...) questions. They are still open, but we could obtain unconditional results of independent interest.Michaux introduced/const complexity classes in an effort to attack question . We show that , answering a question of his. Here A is the class of real problems which are algorithmic in bounded time. We also prove the stronger result: , where PAR stands for parallel polynomial time. In our terminology, we say that is A-saturated and PAR-saturated. We also prove, at the nonuniform level, the above results for every real-closed field. It is not known whether is P-saturated. In the case of the reals with addition and order we obtain P-saturation ). More generally, we show that an ordered -vector space is P-saturated at the nonuniform level ).We also study a stronger notion that we call P-stability. Blum, Cucker, Shub and Smale have shown that fields of characteristic 0 are P-stable. We show that the reals with addition and order are P-stable, but real-closed fields are not.Questions and and the/const complexity classes have some model theoretic flavor. This leads to the theory of complexity over “arbitrary” structures as introduced by Poizat. We give a summary of this theory with a special emphasis on the connections with model theory and we study/const complexity classes from this point of view. Note also that our proof of the PAR-saturation of shows that an o-minimal structure which admits quantifier elimination is A-saturated at the nonuniform level. (shrink)

We prove a number of results motivated by global questions of uniformity in computabi- lity theory, and universality of countable Borel equivalence relations. Our main technical tool is a game for constructing functions on free products of countable groups. We begin by investigating the notion of uniform universality, first proposed by Montalbán, Reimann and Slaman. This notion is a strengthened form of a countable Borel equivalence relation being universal, which we conjecture is equivalent to the usual notion. With this (...) additional uniformity hypothesis, we can answer many questions concerning how countable groups, probability measures, the subset relation, and increasing unions interact with universality. For many natural classes of countable Borel equivalence relations, we can also classify exactly which are uniformly universal. We also show the existence of refinements of Martin’s ultrafilter on Turing invariant Borel sets to the invariant Borel sets of equivalence relations that are much finer than Turing equivalence. For example, we construct such an ultrafilter for the orbit equivalence relation of the shift action of the free group on countably many generators. These ultrafilters imply a number of structural properties for these equivalence relations. (shrink)

Hilbert’s axiomatic approach to the sciences was characterized by a dynamic methodology tied to scientific and mathematical fields under investigation. In particular, it is an analytic art for choosing axioms but, at the same time, it has to include dynamically synthetic procedures and meta-theoretical reflections. Axioms have to be useful, or capture something, or help as part of explanations. The Andréka-Németi group use several formal axiomatic theories together to re-capture, predict, recover or explain the phenomena of special relativity, (...) general relativity and classical kinematics. Their scientific methodology is close to Hilbert’s conceptions of how science should be done ideally. In this paper, we compare Formica’s reading of Hilbert’s axiomatic method to the method used by the Andréka-Németi group. (shrink)

As the debate about research on foetal tissue transplantation progressed, medical scientists learned more about the procedure and its potential for helping persons with degenerative brain disorders such as Parkinson's disease. Increased scientific knowledge significantly influenced the political process, yet it did not by any means resolve the debate. Rather, increased medical evidence served as a lens which focused discourse on particular issues related to foetal research, such as the details of obtaining informed consent, as well as technical matters related (...) to tissue transplantation, for example, that the creation of a tissue bank was unreasonable, and that foetuses of certain ages were required for the procedure. This increased focus changed the character of the debate on foetal tissue transplantation research, and convinced some law-makers that they should encourage financial support for the research despite their anti-abortion political views.The heart of the stalemate on transplantation research lay in rigid attachment to particular arguments, which in turn resulted in the disunity of the participants; this was compounded by the lack of persuasive scientific evidence that foetal tissue transplantation could significantly benefit those with Parkinson's disease. Privately supported clinical studies answered several important clinical questions while the ban on federal support remained in effect, however, and increased scientific knowledge was soon followed by an increasingly clear analysis of the relevant issues. By the time federal support for the research was permitted, the arguments of all of the interest groups had been altered by the findings of privately supported studies.As research continues under the auspices of a somewhat more permissive administration, these refined arguments and attitudes may continue to contribute to a stronger and more clearly defined public policy. (shrink)

This project continues our interdisciplinary research into computational and cognitive aspects of narrative comprehension. Our ultimate goal is the development of a computational theory of how humans understand narrative texts. The theory will be informed by joint research from the viewpoints of linguistics, cognitive psychology, the study of language acquisition, literary theory, geography, philosophy, and artificial intelligence. The linguists, literary theorists, and geographers in our group are developing theories of narrative language and spatial understanding that are (...) being tested by the cognitive psychologists and language researchers in our group, and a computational model of a reader of narrative text is being developed by the AI researchers, based in part on these theories and results and in part on research on knowledge representation and reasoning. This proposal describes the knowledge-representation and natural-language-processing issues involved in the computational implementation of the theory; discusses a contrast between communicative and narrative uses of language and of the relation of the narrative text to the story world it describes; investigates linguistic, literary, and hermeneutic dimensions of our research; presents a computational investigation of subjective sentences and reference in narrative; studies children’s acquisition of the ability to take third-person perspective in their own storytelling; describes the psychological validation of various linguistic devices; and examines how readers develop an understanding of the geographical space of a story. This report is a longer version of a project description submitted to NSF. This document, produced in May 2007, is a L ATEX version of Technical Report 89-07 (Buffalo: SUNY Buffalo Department of Computer Science, August 1989), with slightly.. (shrink)

During the past few decades, the global food system has confronted new sustainability challenges related not only to public health and the environment but also to ethical concerns over the treatment of farmed animals. However, the traditional threedimensional framework of sustainable development is ill equipped to take ethical concerns related to non-human animals into account. For instance, the interests of farmed animals are often overridden by objectives associated with social, economic or environmental sustainability, despite their vast numbers and influence on (...) contemporary societies. Moreover, sustainability policies necessarily involve an element of ethical evaluation; yet this element is not explicitly incorporated in prevailing frameworks of sustainable development. Our purpose in this article is to address these shortcomings by developing a Sustainability Matrix that recognizes the need to consider food system sustainability from the perspective of all interest groups affected by the issue under consideration, from a plurality of ethical standpoints. Combing sustainability principles with the basic idea of an ethical evaluation tool, the proposed Sustainability Matrix evaluates the sustainability of food-related systems, decisions and policies from the perspectives of three major strands of ethical theory and from the perspectives of human beings, farmed animals and wildlife. In terms of policy implications, the Sustainability Matrix can be applied in deciding on the specific targets of food system sustainability that can then be utilized as a basis for designing policies and measures towards the achievement of these goals. (shrink)

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

Over the past several decades, the philosophical community has witnessed the emergence of an important new paradigm for understanding the mind.1 The paradigm is that of machine computation, and its influence has been felt not only in philosophy, but also in all of the empirical disciplines devoted to the study of cognition. Of the several strategies for applying the resources provided by computer and cognitive science to the philosophy of mind, the one that has gained the most attention from philosophers (...) has been the Computational Theory of Mind (CTM). CTM was first articulated by Hilary Putnam (1960, 1961), but finds perhaps its most consistent and enduring advocate in Jerry Fodor (1975, 1980, 1981, 1987, 1990, 1994). It is this theory, and not any broader interpretations of what it would be for the mind to be a computer, that I wish to address in this paper. What I shall argue here is that the notion of symbolic representation employed by CTM is fundamentally unsuited to providing an explanation of the intentionality of mental states (a major goal of CTM), and that this result undercuts a second major goal of CTM, sometimes refered to as the vindication of intentional psychology. This line of argument is related to the discussions of derived intentionality by Searle (1980, 1983, 1984) and Sayre (1986, 1987). But whereas those discussions seem to be concerned with the causal dependence of familiar sorts of symbolic representation upon meaning-bestowing acts, my claim is rather that there is not one but several notions of meaning to be had, and that the notions that are applicable to symbols are conceptually dependent upon the notion that is applicable to mental states in the fashion that Aristotle refered to as paronymy. That is, an analysis of the notions of meaning applicable to symbols reveals that they contain presuppositions about meaningful mental states, much as Aristotle's analysis of the sense of healthy that is applied to foods reveals that it means conducive to having a healthy body, and hence any attempt to explain mental semantics in terms of the semantics of symbols is doomed to circularity and regress. I shall argue, however, that this does not have the consequence that computationalism is bankrupt as a paradigm for cognitive science, as it is possible to reconstruct CTM in a fashion that avoids these difficulties and makes it a viable research framework for psychology, albeit at the cost of losing its claims to explain intentionality and to vindicate intentional psychology. I have argued elsewhere (Horst, 1996) that local special sciences such as psychology do not require vindication in the form of demonstrating their reducibility to more fundamental theories, and hence failure to make good on these philosophical promises need not compromise the broad range of work in empirical cognitive science motivated by the computer paradigm in ways that do not depend on these problematic treatments of symbols. (shrink)

In this paper, we present an intelligent tutoring system developed to help students in learning Computer Theory. The Intelligent tutoring system was built using ITSB authoring tool. The system helps students to learn finite automata, pushdown automata, Turing machines and examines the relationship between these automata and formal languages, deterministic and nondeterministic machines, regular expressions, context free grammars, undecidability, and complexity. During the process the intelligent tutoring system gives assistance and feedback of many types in an (...) intelligent manner according to the behavior of the student. An evaluation of the intelligent tutoring system has revealed reasonably acceptable results in terms of its usability and learning abilities are concerned. (shrink)

As quantum technologies (QT) advance, their potential impact on and relation with society has been developing into an important issue for exploration. In this paper, we investigate the topic of democratization in the context of QT, particularly quantum computing. The paper contains three main sections. First, we briefly introduce different theories of democracy (participatory, representative, and deliberative) and how the concept of democratization can be formulated with respect to whether democracy is taken as an intrinsic or instrumental value. Second, we (...) give an overview of how the concept of democratization is used in the QT field. Democratization is mainly adopted by companies working on quantum computing and used in a very narrow understanding of the concept. Third, we explore various narratives and counter-narratives concerning democratization in QT. Finally, we explore the general efforts of democratization in QT such as different forms of access, formation of grassroot communities and special interest groups, the emerging culture of manifesto writing, and how these can be located within the different theories of democracy. In conclusion, we argue that although the ongoing efforts in the democratization of QT are necessary steps towards the democratization of this set of emerging technologies, they should not be accepted as sufficient to argue that QT is a democratized field. We argue that more reflexivity and responsiveness regarding the narratives and actions adopted by the actors in the QT field and making the underlying assumptions of ongoing efforts on democratization of QT explicit, can result in a better technology for society. (shrink)

Leibniz coined the word “dynamics,” but his own dynamics has never been completed. However, there are many illuminating ideas scattered in his writings on dynamics and metaphysics. In this paper, I will present my own interpretation of Leibniz’s dynamics and metaphysics. To my own surprise, Leibniz’s dynamics and metaphysics are incredibly flexible and modern. In particular, the metaphysical part, namely Monadology, can be interpreted as a theory of information in terms of monads, which generate both physical phenomena and mental (...) phenomena. The phenomena, i.e., how the world of monads appears to each monad must be distinguished from its internal states, which Leibniz calls perceptions, and the phenomena must be understood as the results of these states and God’s coding. My distinctive claim is that most interpreters ignored this coding. His dynamics and metaphysics can provide a framework good enough for enabling Einstein’s special relativity. And finally, his dynamics and metaphysics can provide a very interesting theory of space and time. In Part 1, we will focus on the relationship between metaphysics and dynamics. Leibniz often says that dynamics is subordinated to metaphysics. We have to take this statement seriously, and we have to investigate how dynamics and metaphysics are related. To this question, I will give my own answer, based on my informational interpretation. On my view, Leibniz’s metaphysics tries, among others, to clarify the following three: How each monad is programmed. How monads are organized into many groups, each of which is governed by a dominant monad ; this can be regarded as a precursor of von Neumann’s idea of cellular automata. And how the same structure is repeated in sub-layers of the organization. This structure is best understood in terms of the hierarchy of programs, a nested structure going down from the single dominant program to subprograms, which again controls respective subprograms, and ad infinitum. If we may use a modern term, this is a sort of recursion, although Leibniz himself did not know this word. And one of my major discoveries is that the same recursive structure is repeated in the phenomenal world, the domain of dynamical investigations. Recursion of what, you may ask. I will argue that it is elastic collision. For Leibniz, aside from inertial motions, dynamical changes of motion are brought about by elastic collisions, at any level of the infinite divisibility of matter. This nicely corresponds to the recursive structure of the program of a monad, or of the program of an organized group of monads. This is the crux of his claim that dynamics is subordinated to metaphysics. Moreover, the program of any monad is teleological, whereas the phenomenal world is governed by efficient cause of dynamics. And it is natural that the pre-established harmony is there, since God is the ultimate programmer, as well as the creator. (shrink)

Proponents of the “literacy” thesis share with proponents of the “extended mind” thesis the viewpoint that communication systems such as language or writing have cognitive implications that go beyond their purely social and communicative purposes. Conceiving of media as extensions of the mind thus has the potential to bring together and cross-fertilize research programs that are currently placed in distant corners of the study of mind, language, and society. In this issue, we bring together authors with a diverse set of (...) interests to identify promising areas of overlap, blaze new trails for us to explore, but also to highlight dissonances and challenges that will have to be addressed in future work. (shrink)

This E-Special issue brings together a range of articles from the Theory, Culture, & Society archive that directly explore the relations between fiction and social theory. Each article develops a different perspective on these relations, yet they all share a common interest in probing at the different ways in which fiction might enrich and provoke our conceptual imaginations. These articles ask how theory might be used to understand or illuminate fiction, whilst also considering how (...) class='Hi'>theory might be extended, challenged or informed by fictional resources. In general terms, the articles take three types of overlapping approach. First, there are those that use fiction to extend the imagination of social theory. Second are the articles that use fiction as a documentary resource and platform for theorizing. And, finally, there are those articles that use theory to reanimate and re-examine fictional forms. In exploring these three intersecting branches the pieces illustrate the different ways in which fiction and social theory might interweave in our thinking. The articles gathered here provide frameworks, ideas and resources through which the reader might continue to think imaginatively and creatively about the social world. (shrink)

The book brings into relief the variety of approaches and disciplines that have informed the quest for a theory of cognition. The center of interest are the historical, geographical, and theoretical peripheries of classic AI's mainstream research program. The twelve chapters bring back into focus the variety of strategies and theoretical questions that researchers explored while working toward a scientific theory of cognition and pre-cognition. The volume is organized in four parts, each one including three essays. The (...) first one deals with cybernetics, the approach that may be considered as the most important periphery of classic AI research. The second part focuses on the geographical periphery of AI research. It examines how the theories and techniques developed on AI's home ground were translated into countries with different cultures and traditions: Italy, France, and the Soviet Union. The third part focuses on AI's periphery understood in the cultural and historical meaning of the term. It contains essays that locate some of the central concepts of AI, like representation and computability, within a broader philosophical (Descartes, Aristotle, Leibniz) and technical background (programming theory and practice). The fourth and final part of the volume is focused directly on the limitation of Turing's classic computability theory and its possible alternatives, some of which were studied in the early years of AI's research (e.g. Ashby's re-entrant information model), while others have been intensely studied in recent times (quantum automata). (shrink)

Prospect Theory: For Risk and Ambiguity, provides a comprehensive and accessible textbook treatment of the way decisions are made both when we have the statistical probabilities associated with uncertain future events and when we lack them. The book presents models, primarily prospect theory, that are both tractable and psychologically realistic. A method of presentation is chosen that makes the empirical meaning of each theoretical model completely transparent. Prospect theory has many applications in a wide variety of disciplines. (...) The material in the book has been carefully organized to allow readers to select pathways through the book relevant to their own interests. With numerous exercises and worked examples, the book is ideally suited to the needs of students taking courses in decision theory in economics, mathematics, finance, psychology, management science, health, computer science, Bayesian statistics, and engineering. (shrink)

The US Securities and Exchange Commission recently proposed rules relating to shareholder (independent) director nominations to publicly-traded companies. While shareholder groups, such as institutional investors, consumer groups, and shareholder activists, generally support the proxy reform, the business community, including The Business Roundtable and the US Chamber of Commerce, are critical of the proposal, arguing that it will 'open the door' to special interest directors, e.g., labour unions or other groups having a social or political agenda contrary to the (...) economic interests of the shareholder owners of the corporation. An analysis of the proposed rules, however, show that the mechanisms offered to nominate and elect independent directors offer little or no threat of any shareholder group placing special interest directors on the board of a publicly-traded company in the USA. The article concludes with a recommended managerial course of action for executives and boards to follow in the unlikely event that shareholders are seriously threatening to place a special interest director(s) on the proxy ballot. (shrink)

In both biology and the human sciences, social groups are sometimes treated as adaptive units whose organization cannot be reduced to individual interactions. This group-level view is opposed by a more individualistic one that treats social organization as a byproduct of self-interest. According to biologists, group-level adaptations can evolve only by a process of natural selection at the group level. Most biologists rejected group selection as an important evolutionary force during the 1960s and 1970s but (...) a positive literature began to grow during the 1970s and is rapidly expanding today. We review this recent literature and its implications for human evolutionary biology. We show that the rejection of group selection was based on a misplaced emphasis on genes as "replicators" which is in fact irrelevant to the question of whether groups can be like individuals in their functional organization. The fundamental question is whether social groups and other higher-level entities can be "vehicles" of selection. When this elementary fact is recognized, group selection emerges as an important force in nature and what seem to be competing theories, such as kin selection and reciprocity, reappear as special cases of group selection. The result is a unified theory of natural selection that operates on a nested hierarchy of units. The vehicle-based theory makes it clear that group selection is an important force to consider in human evolution. Humans can facultatively span the full range from self-interested individuals to "organs" of group-level "organisms." Human behavior not only reflects the balance between levels of selection but it can also alter the balance through the construction of social structures that have the effect of reducing fitness differences within groups, concentrating natural selection (and functional organization) at the group level. These social structures and the cognitive abilities that produce them allow group selection to be important even among large groups of unrelated individuals. (shrink)

This commentary is an elaboration on Schyns, Goldstone & Thibaut's proposal for flexible features in categorization in the light of three areas not explicitly discussed by the authors: connectionist models of categorization, computational learning theory, and constructivist theories of the mind. In general, the authors' proposal is strongly supported, paving the way for model extensions and for interesting novel cognitive research. Nor is the authors' proposal incompatible with theories positing some fixed set of features.

Since Darwin, the idea of psychological continuity between humans and other animals has dominated theory and research in investigating the minds of other species. Indeed, the field of comparative psychology was founded on two assumptions. First, it was assumed that introspection could provide humans with reliable knowledge about the causal connection between specific mental states and specific behaviors. Second, it was assumed that in those cases in which other species exhibited behaviors similar to our own, similar psychological causes were (...) at work. In this paper. we show how this argument by analogy is flowed with respect to the case of second-order mental states. As a test case, we focus on the question of how other species conceive of visual attention, and in particular whether chimpanzees interpret seeing as a mentalistic event involving internal states of perception, attention, and belief. We conclude that chimpanzees do not reason about seeing in this manner, and indeed, there is considerable reason to suppose that they do not harbor representations of mental states in general. We propose a reinterpretation model in which the majority of the rich social behaviors that humans and other primates share in common emerged long before the human lineage evolved the psychological means of interpreting those behaviors in mentalistic terms. Although humans, chimpanzees, and most other species may be said to possess mental states, humans alone may have evolved a cognitive specialization for reasoning about such states. (shrink)

Pietraszewski exemplifies the need for computational theory using group conflict; I complement this with an example of group cooperation. He criticizes past theories for having black boxes; I suggest his theory also has a black box – the concept of costs. He divides what mentally constitutes a group from mere ancillary attributes; I hazard that some of these attributes are essential.

Lattice representations are an important tool for computability theorists when they embed nondistributive lattices into degree-theoretic structures. In this expository paper, we present the basic definitions and results about lattice representations needed by computability theorists. We define lattice representations both from the lattice-theoretic and computability-theoretic points of view, give examples and show the connection between the two types of representations, discuss some of the known theorems on the existence of lattice representations that are of interest to (...) computability theorists, and give a simple example of the use of lattice representations in an embedding result. (shrink)

A generic computation of a subset $A$ of $\mathbb{N}$ consists of a computation that correctly computes most of the bits of $A$, and never incorrectly computes any bits of $A$, but which does not necessarily give an answer for every input. The motivation for this concept comes from group theory and complexity theory, but the purely recursion theoretic analysis proves to be interesting, and often counterintuitive. The primary result of this paper is that there are no minimal (...) pairs for generic computability, answering a question of Jockusch and Schupp. (shrink)

Why are US labor unions so weak? Union decline has had important consequences for politics, inequality, and social policy. Common explanations cite employment shifts, public opinion, labor laws, and differences in working class culture and organization. But comparing the United States with Canada challenges those explanations. After following US unionization rates for decades, Canadian rates diverged in the 1960s, and are now nearly three times higher. This divergence was due to different processes of working class political incorporation. In the United (...) States, labor was incorporated as an interest group into a labor regime governed by a pluralist idea. In Canada, labor was incorporated as a class representative into a labor regime governed by a class idea. This led to a relatively stronger Canadian labor regime that better held employers in check and protected workers’ collective bargaining rights. As a result, union density stabilized in Canada while plummeting in the United States. (shrink)

Putnam (Representations and reality. MIT Press, Cambridge, 1988) and Searle (The rediscovery of the mind. MIT Press, Cambridge, 1992) famously argue that almost every physical system implements every finite computation. This universal implementation claim, if correct, puts at the risk of triviality certain functional and computational views of the mind. Several authors have offered theories of implementation that allegedly avoid the pitfalls of universal implementation. My aim in this paper is to suggest that these theories are still consistent with a (...) weaker result, which is the nomological possibility of systems that simultaneously implement different complex automata. Elsewhere I (Shagrir in J Cogn Sci, 2012) argue that this simultaneous implementation result challenges a computational sufficiency thesis (articulated by Chalmers in J Cogn Sci, 2012). My focus here is on theories of implementation. After presenting the basic simultaneous implementation construction, I argue that these theories do not avoid the simultaneous implementation result. The conclusion is that the idea that the implementation of the right kind of automaton suffices for a possession of a mind is dubious. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Thinking with Heidegger:Rethinking Environmental Theory and PracticeKevin Michael DeLuca (bio)Environmentalism is tired. It is a movement both institutionalized and insipid. The vast majority of Americans claim to be environmentalists while buying ever more SUVs, leaf-blowers, and uncountable plastic consumer goods. Indeed, environmentalism itself has become just another practice of consumerism, a matter of buying Audubon memberships, Ansel Adams calendars, and 'biodegradable' plastic bags with one's Sierra Club credit (...) card. As a practice of everyday life, environmentalism has devolved into another lifestyle choice.On the political front, carbon-copy blow-dried presidential candidates proclaim their allegiance to the environment, an allegiance that is more a sign of fealty to opinion polls than a concern with environmental issues. In the world of real-politic, environmental regulations are gutted as corporations write legislation for the politicians they have bought. Outspent and outmaneuvered, mainstream environmental groups preach at the altar of broken promises about the potential of lobbying and insider access while awaiting the blandishments of the next candidate. As [End Page 67] a political practice, mainstream environmentalism has degenerated into a marginal special-interest group.On the intellectual front, a confusing array of reform environmentalists, deep ecologists, social ecologists, ecofeminists, wilderness advocates, social justice activists, social constructionists, and Christian ecologists offer a cacophony of competing paradigms and programs while exchanging charges and countercharges of wrong-headedness and infidelity. If on the level of practice an exhausted environmentalism has achieved both institutionalism and irrelevance, intellectually environmentalism has reached several stasis points. This is crucial, for at a level that is unusual for social movements, environmentalism has always highlighted the importance of how we think about the environment, that ideas of nature are powerful because practices follow from ideas. In other words, how we think about nature guides how we act toward nature. In the midst of this melee I want to suggest we reconsider the work of Martin Heidegger.I want to think Heidegger in distress: in the distress of machination; in the distress of the technological enframing of the earth; in the distress of the environmental crisis. In rejecting a Heideggerian hermeneutics, a piety to textual exegesis, I hope to stress Heidegger in order to stress environmental theory. With few exceptions,1 two insufficient responses typify the reception of Heidegger in environmental thinking. One is to champion Heidegger as some proto-environmentalist. Certainly, quotes from such works as Being and Time, Contributions to Philosophy: From Enowning, "The Question Concerning Technology," "Building Dwelling Thinking," and "The Age of the World Picture" inspire such a reading. Such readings, however, present a simplified Heidegger. For example, a poor reading of an essay such as "The Question Concerning Technology" produces the conclusion that Heidegger was anti-technology.2 These misreadings are not merely accidental but a result of the goal of the citation. The challenge of Heidegger is not engaged to develop environmental theory; rather, Heidegger is cited to lend some borrowed legitimacy to the fledgling enterprise. The most prominent example of this move occurs in Devall and Sessions' Deep Ecology, wherein Heidegger joins a potpourri of thinkers, including Dogen, Job, St. Francis of Assisi, Giordano Bruno, Spinoza, Thoreau, Chief Seattle, Herman Melville, John Muir, Aldous Huxley, Gandhi, Rainer Maria Rilke, Aldo Leopold, Robinson Jeffers, Mary Austin, Rachel Carson, Barry Commoner, Stanley Diamond, and [End Page 68] David Brower from a host of traditions, including Taoism, Hinduism, Zen Buddhism, Christianity, Native American thought, Romanticism, and ecological science (1985, 79–108). The result is confusion, at best.On the other hand, in a second response Heidegger serves as a kind of bogeyman, a Nazi used to tar the more radical environmental groups. The syllogism is simple and simplistic: Deep Ecologists are bio/ecocentric; Deep Ecologists quote Heidegger; Heidegger was a Nazi; Therefore, Deep Ecologists are Nazis/fascists. (To push this thinking to its logical extreme, then, all nonanthropocentric thinking is fascist.) Both responses may be useful for polemics but serve to prevent a possibly productive exploration of Heidegger for the engagement of the difficult problems that have stumped environmentalism on multiple levels.Violating HeideggerAs a prefatory word, even a cursory glance at Heidegger's work reveals him to be a thinker who... (shrink)

This paper presents the results of computer simulations with a community of actors playing a large number of voluntarily iterated two-person-PD. The simulations are designed to enable uncooperative actors to exploit partners, leave them and find a new partner who knows nothing about their previous behavioral history. Hit-and-run exploitation should thrive under these conditions. However, as Schuessler (1989; 1990) has shown, the setting is highly unfavorable to uncooperative players. The present study extends this result to a wider set of strategies (...) which can alternatively stay with defectors {and try to improve them) or leave them quickly. In addition, a class of seemingly clever strategies is introduced which try to exploit the expected dynamics of looking for a partner. Still, a high amount of egoistical cooperation can persist in the present scenario. (shrink)

Retributivism is currently a keenly debated theory of punishment. In this volume, the contributors explore its various dimensions including its implications for sentencing and evaluate it against utilitarian options. Content: Jean Hampton: An Expressive Theory of Retribution u Brian Slattery: The Myth of Retributive Justice u Tim Dare: Retributivism, Punishment and Public Values u Anthony Duff: Alternatives to Punishment - or Alternative Punishments u Jerome Bickenbach: Duff on Non-Custodial Punishment u Sandra Marshall: Harm and Punishment in the Community. (...) (Franz Steiner 1992). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Thinking with Heidegger:Rethinking Environmental Theory and PracticeKevin Michael DeLuca (bio)Environmentalism is tired. It is a movement both institutionalized and insipid. The vast majority of Americans claim to be environmentalists while buying ever more SUVs, leaf-blowers, and uncountable plastic consumer goods. Indeed, environmentalism itself has become just another practice of consumerism, a matter of buying Audubon memberships, Ansel Adams calendars, and 'biodegradable' plastic bags with one's Sierra Club credit (...) card. As a practice of everyday life, environmentalism has devolved into another lifestyle choice.On the political front, carbon-copy blow-dried presidential candidates proclaim their allegiance to the environment, an allegiance that is more a sign of fealty to opinion polls than a concern with environmental issues. In the world of real-politic, environmental regulations are gutted as corporations write legislation for the politicians they have bought. Outspent and outmaneuvered, mainstream environmental groups preach at the altar of broken promises about the potential of lobbying and insider access while awaiting the blandishments of the next candidate. As [End Page 67] a political practice, mainstream environmentalism has degenerated into a marginal special-interest group.On the intellectual front, a confusing array of reform environmentalists, deep ecologists, social ecologists, ecofeminists, wilderness advocates, social justice activists, social constructionists, and Christian ecologists offer a cacophony of competing paradigms and programs while exchanging charges and countercharges of wrong-headedness and infidelity. If on the level of practice an exhausted environmentalism has achieved both institutionalism and irrelevance, intellectually environmentalism has reached several stasis points. This is crucial, for at a level that is unusual for social movements, environmentalism has always highlighted the importance of how we think about the environment, that ideas of nature are powerful because practices follow from ideas. In other words, how we think about nature guides how we act toward nature. In the midst of this melee I want to suggest we reconsider the work of Martin Heidegger.I want to think Heidegger in distress: in the distress of machination; in the distress of the technological enframing of the earth; in the distress of the environmental crisis. In rejecting a Heideggerian hermeneutics, a piety to textual exegesis, I hope to stress Heidegger in order to stress environmental theory. With few exceptions,1 two insufficient responses typify the reception of Heidegger in environmental thinking. One is to champion Heidegger as some proto-environmentalist. Certainly, quotes from such works as Being and Time, Contributions to Philosophy: From Enowning, "The Question Concerning Technology," "Building Dwelling Thinking," and "The Age of the World Picture" inspire such a reading. Such readings, however, present a simplified Heidegger. For example, a poor reading of an essay such as "The Question Concerning Technology" produces the conclusion that Heidegger was anti-technology.2 These misreadings are not merely accidental but a result of the goal of the citation. The challenge of Heidegger is not engaged to develop environmental theory; rather, Heidegger is cited to lend some borrowed legitimacy to the fledgling enterprise. The most prominent example of this move occurs in Devall and Sessions' Deep Ecology, wherein Heidegger joins a potpourri of thinkers, including Dogen, Job, St. Francis of Assisi, Giordano Bruno, Spinoza, Thoreau, Chief Seattle, Herman Melville, John Muir, Aldous Huxley, Gandhi, Rainer Maria Rilke, Aldo Leopold, Robinson Jeffers, Mary Austin, Rachel Carson, Barry Commoner, Stanley Diamond, and [End Page 68] David Brower from a host of traditions, including Taoism, Hinduism, Zen Buddhism, Christianity, Native American thought, Romanticism, and ecological science (1985, 79–108). The result is confusion, at best.On the other hand, in a second response Heidegger serves as a kind of bogeyman, a Nazi used to tar the more radical environmental groups. The syllogism is simple and simplistic: Deep Ecologists are bio/ecocentric; Deep Ecologists quote Heidegger; Heidegger was a Nazi; Therefore, Deep Ecologists are Nazis/fascists. (To push this thinking to its logical extreme, then, all nonanthropocentric thinking is fascist.) Both responses may be useful for polemics but serve to prevent a possibly productive exploration of Heidegger for the engagement of the difficult problems that have stumped environmentalism on multiple levels.Violating HeideggerAs a prefatory word, even a cursory glance at Heidegger's work reveals him to be a thinker who... (shrink)

Originally published between 1982 and 1991 the 3 volumes in this set Reflect the diversity in Hegelianism and every branch of philosophy which he contributed to. Examine Hegel's work in relation to Marx and Wittgenstein Discuss Hegel's social theory Examine British Hegelian thinking and the lines of its development Offer an interpretation of Hegelian theory that is relevant for the understanding of modern republican constitutions.

Analyses of Theories and Methods of Physics and Psychology was first published in 1970. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions.This is Volume IV of the Minnesota Studies in the Philosophy of Science, a series published in cooperation with the Minnesota Center for Philosophy of Science at the University of Minnesota and edited by Herbert Feigl and Grover Maxwell. Dr. Feigl was the (...) director of the Center.In a preface to the first volume in the series, Professors Feigl and Michael Scriven noted the extensive concern of the Center with "the meaning of theoretical concepts as defined by their locus in the 'nomological net' and the related rejection of the reductionist forms of operationism and positivism." In this volume, several contributors are again concerned with philosophical, logical, and methodological problems of psychology. As before, some papers deal with broad philosophical issues, others with more specific problems of method or interpretation. However, a deep concern for logical and methodological problems of special relevance to the physical sciences is reflected in a number of essays.The contents are arranged in two sections, the first part being based on the papers and discussion from a conference held at the Center on the problems of correspondence rules. Contributors are Herbert Feigl, Paul K. Feyerabend, N.R. Hanson, Carl G. Hempel, Mary Hesse, Grover Maxwell, and William Rozeboom. The second group of essays, by various members of the staff of the Center and some of its visitors, reflects current issues and controversies of great interest. The contributors are William Demopoulos, Keith Gunderson, Paul E. Meehl (three essays), and Michael Radner. (shrink)

This 20 volume Routledge Revivals collection brings together a selection of groundbreaking Philosophy titles, from the rich and diverse Routledge backlist. With titles published between 1933 and 1991, this is a truly wide-ranging selection, encompassing works by distinguished authors such as: Simone Weil, Hilary Putnam, Franz Brentano, Anthony Kenny, Karl Jaspers and Israel Scheffler. Dealing with everything from the notion of freewill, to concepts of time and space, to theories of morality, this set offers a collection of the best of (...) Routledge publishing in the field of Philosophy from across the Twentieth Century. Please note that all titles have been previously available for sale individually through the Routledge Revivals programme. (shrink)

The idea behind this special theme journal issue was to continue the work we have started with the INBIOSA initiative (www.inbiosa.eu) and our small inter-disciplinary scientific community. The result of this EU funded project was a white paper (Simeonov et al., 2012a) defining a new direction for future research in theoretical biology we called Integral Biomathics and a volume (Simeonov et al., 2012b) with contributions from two workshops and our first international conference in this field in 2011. The initial (...) impulse for this effort was given a year earlier by a publication of one of the guest editors of this issue (Simeonov, 2010) in this journal. This time we wish to provide a broader forum and more space to elaborate in detail some of the most interesting concepts we have encountered in our discussions, as well as to invite some new contributions of particular interest in the field. Another goal we had in mind was to collect and review as many provocative perspectives as possible on the same key topic we are interested before making a decision to follow a more focused notion that would lead to a funded research program. Therefore we welcomed the generous suggestion of Professor Denis Noble, FRS, who is also editor of this journal to prepare a special theme issue entitled: “Can biology create a profoundly new mathematics and computation?” It has taken a while to invite and collect the contributions. Most of them had a couple of revision cycles and adjustments after having been thoroughly discussed with colleagues, incl. the editors of this issue. We think that the result we have obtained at the end is a satisfactory one, since we succeeded to integrate a diversity of original, but sometimes controversial and mutually excluding concepts organized within chapters of a self-contained volume. The task of compiling all this was not easy at all. Despite our efforts to position the articles of different authors and themes in a way allowing their easy comprehension and relation to each other within the individual chapters, some of them still require a sort of introduction to dissolve possible ambiguities. This is what we are going to do in the following few paragraphs with the hope that the reader (and some of the authors) would excuse our failures. (shrink)