We show that linear logic can serve as an expressive framework in which to model a rich variety of combinatorial auction mechanisms. Due to its resource-sensitive nature, linear logic can easily represent bids in combinatorial auctions in which goods may be sold in multiple units, and we show how it naturally generalises several bidding languages familiar from the literature. Moreover, the winner determination problem, i.e., the problem of computing an allocation of goods to bidders producing a certain (...) amount of revenue for the auctioneer, can be modelled as the problem of finding a proof for a particular linear logic sequent. (shrink)

Combinatorial behavior involves combining different elements into larger aggregates with meaning. It is generally contrasted with compositionality, which involves the combining of meaningful elements into larger constituents whose meaning is derived from its component parts. Combinatoriality is commonly considered a capacity found in primates and other animals, whereas compositionality often is considered uniquely human. Questioning the validity of this claim, this multidisciplinary special issue of the International Journal of Primatology unites papers that each study aspects of combinatoriality and compositionality (...) found in primate and bird communication systems, tool use, skills, and human language. The majority of authors conclude that compositionality is evolutionarily preceded by combinatoriality and that neither are uniquely human. This introduction briefly introduces readers to the major findings and issues raised by the contributors. -/- . (shrink)

Human language, hominin tool production modes, and multimodal communications systems of primates and other animals are currently well-studied for how they display compositionality or combinatoriality. In all cases, the former is defined as a kind of hierarchical nesting and the latter as a lack thereof. In this article, I extend research on combinatoriality and compositionality further to investigations of everyday primate skills. Daily locomotion modes as well as behaviors associated with subsistence practices, hygiene, or body modification rely on the hierarchical (...) nesting of different behavioral and cognitive actions into complex skills. I introduce a scheme which uses hierarchical organization to differentiate combinatorial from compositional skills. Combinatorial skills are defined either as aggregational or linearly hierarchical depending on whether the skill occurs momentarily in space or unfolds sequentially over time. Compositional skills are defined either as nested or interactionally hierarchical depending on whether the skill results in new constructs or in new interactions between existing constructs. The methodology I propose combines epistemological hierarchy theory with data from primatological field research and experimental and comparative psychological research and provides a means to integrate current constructionist and extended views on cognition and action with older research on behavioral logics in psychology and operational chain thinking in anthropology. The approach furthermore synchronizes with ongoing research on teleonomy, intentionality, and creativity. -/- . (shrink)

The purpose of this paper is to review and critique Wessel Reijers and Bert Gordijn’s paper Moving from value sensitive design to virtuous practice design. In doing so, it draws on recent literature on developing value sensitive design (VSD) to show how the authors’ virtuous practice design (VPD), at minimum, is not mutually exclusive to VSD. This paper argues that virtuous practice is not exclusive to the basic methodological underpinnings of VSD. This can therefore strengthen, rather than exclude the VSD (...) approach. Likewise, this paper presents not only a critique of what was offered as a “potentially fruitful alternative to VSD” but further clarifies and contributes to the VSD scholarship in extending its potential methodological practices and scope. It is concluded that VPD does not appear to offer any original contribution that more recent instantiations of VSD have not already proposed and implemented. (shrink)

The 1994 US spectrum auction is now a paradigmatic case of the successful use of microeconomic theory for policy-making. We use a detailed analysis of it to review standard accounts in philosophy of science of how idealized models are connected to messy reality. We show that in order to understand what made the design of the spectrum auction successful, a new such account is required, and we present it here. Of especial interest is the light this sheds on the issue (...) of progress in economics. In particular, it enables us to get clear on exactly what has been progressing, and on exactly what theory has – and has not – contributed to that. This in turn has important implications for just what it is about economic theory that we should value. (shrink)

Deferential Monadic Panpsychism is a view that accepts that physical science is capable of discovering the basic structure of reality. However, it denies that reality is fully and exhaustively de- scribed purely in terms of physical science. Consciousness is missing from the physical description and cannot be reduced to it. DMP explores the idea that the physically fundamental features of the world possess some intrinsic mental aspect. It thereby faces a se- vere problem of understanding how more complex mental states (...) emerge from the mental features of the fundamental features. Here I explore the idea that a new form of aggregative emergence, which I call 'combinatorial infusion', could shed light on this problem and bolster the prospects for this form of panpsychism. (shrink)

Three objections have recently been levelled at the analysis of intrinsicness offered by Rae Langton and David Lewis. While these objections do seem telling against the particular theory Langton and Lewis offer, they do not threaten the broader strategy Langton and Lewis adopt: defining intrinsicness in terms of combinatorial features of properties. I show how to amend their theory to overcome the objections without abandoning the strategy.

The Controversy over the Existence of the World (henceforth Controversy) is the magnum opus of Polish philosopher Roman Ingarden. Despite the renewed interest for Ingarden’s pioneering ontological work whithin analytic philosophy, little attention has been dedicated to Controversy's main goal, clearly indicated by the very title of the book: finding a solution to the centuries-old philosophical controversy about the ontological status of the external world. -/- There are at least three reasons for this relative indifference. First, even at the time (...) when the book was published, the Controversy was no longer seen as a serious polemical topic, whether it was disqualified as an archaic metaphysical pseudo-problem, or taken to be the last remnant of an antiscientific approach to philosophy culminating in idealism and relativism. Second, Ingarden’s reasoning on the matter is highly complex, at times misleading, and even occasionally faulty. Finally, his analysis is not only incomplete – Controversy being unachieved – but also arguably aporetic. -/- One may wonder, then, why it is still worth excavating this mammoth treatise to study an issue apparently no longer relevant to contemporary philosophy. Aside from historical and exegetical purposes, which are of course very interesting in their own right, Ingarden’s treatment of the Controversy remains one of the most detailed and ambitious ontological undertakings of the twentieth century. Not only does it lay out an incredibly detailed map of possible solutions to the Controversy, but it also tries to show why the latter is a genuine and fundamental problem that owes its hasty disqualification to various oversimplifications over the course of the history of philosophy. -/- In this chapter, I first give an overview of Ingarden’s method, which relies mainly on a combinatorial analysis. Then, I summarize his examination of possible solutions to the Controversy, and determine which ones can be ruled out on ontological grounds. Finally, I explain why this ambitious project ultimately leads to a theoretical impasse, leaving Ingarden unable to come up with a definitive solution to the Controversy – regardless of the fact that the book is unachieved. I argue that his analysis of the problem yields a more modest but nonetheless valuable result. (shrink)

This article addresses the emergence of African– European business relationships. Its focus is on the role of bargaining power and information tech- nology and its impact on the different stakeholders in (electronic) markets (sellers, market maker, buy- ers). Information technology is seen as an enabling technology that facilitates reaching a wider cus- tomer base (called reach) and providing a channel for increased customer services (called richness). The central question is how African suppliers can create bargaining power by means of information (...) technology and therefore enter and improve their position in European markets. Research is carried out in the flower industry. In this industry African flower growers create competitive advantage and develop business relationships with European buy- ers (wholesalers, retailers). In this article we inves- tigate three flower markets (Tele Flower Auction, FloraHolland Auction, and Aalsmeer Auction), the role of African flower growers, and the use and impact of information technology in these markets. The results of our research show that there are pot- entials for African flower growers to enter the Euro- pean flower markets and to increase their position of bargaining power. A first potential is using and implementing information technology for the access to new and large European markets. African flower growers use information technology to streamline transaction processes and lower transac- tion costs. A second potential is related to the qual- ity and specificity of the produced flower products. Information technology can remove the quality uncertainty of products and can provide rich infor- mation services to buyers. The results in the flower industry suggest that information technology pro- vides opportunities for the African producers to expand the reach and richness of their product and service offerings, thus creating economic value. Ó 2004 Elsevier Ltd. All rights reserved. (shrink)

(1) An introduction to the principles of conceptual modelling, combinatorial heuristics and epistemological history; (2) the examination of a number of perennial epistemological-methodological schemata: conceptual spaces and blending theory; ars inveniendi and ars demonstrandi; the two modes of analysis and synthesis and their relationship to ars inveniendi; taxonomies and typologies as two fundamental epistemic structures; extended cognition, cognitio symbolica and model-based reasoning; (3) Plato’s notions of conceptual spaces, conceptual blending and hypothetical-analogical models (paradeigmata); (4) Ramon Llull’s concept analysis and (...) combinatoric spaces; (5) Gottfried Leibniz’s development of compositional analysis and synthesis as a general modelling method and a paradigm for ars inveniendi; (6) Fritz Zwicky’s revival of the morphological method of analysis and construction, and its subsequent computerised applications. (shrink)

The aim of this paper is to show that topology has a bearing on<br><br>combinatorial theories of possibility. The approach developed in this article is “mapping account” considering combinatorial worlds as mappings from individuals to properties. Topological structures are used to define constraints on the mappings thereby characterizing the “really possible” combinations. The mapping approach avoids the well-known incompatibility problems. Moreover, it is compatible with atomistic as well as with non-atomistic ontologies.It helps to elucidate the positions of logical atomism (...) and monism with theaid of topological separation axioms. (shrink)

Economic policy decisions require comparisons of the gains and losses from policy choices to different people. If those gains can be valued in monetary terms, than all that is needed is a comparison of the value of income to different persons, which can be weights in cost-benefit analysis. An objective comparison of the value of income to different people has been long sought but never found. I propose that when money to be allocated is controlled by a group of people (...) with equal control over that money, then a hypothetical auction for transfers of income between people can produce a collective judgment about the value of income that provides suitable weights, and is morally defensible in cases where the decision is made by the group collectively, e.g. when making government policy choices. I provide a method for calculating such weights from observed choices about distributing income, and discuss several desirable properties that they have. (shrink)

The present volume is an introduction to the use of tools from computability theory and reverse mathematics to study combinatorial principles, in particular Ramsey's theorem and special cases such as Ramsey's theorem for pairs. It would serve as an excellent textbook for graduate students who have completed a course on computability theory.

Some objections to the idea that disputed territories should be auctioned.

The conventional implicature, arguably, refers to plenty of linguistic aspects with respect to episteme, metaphysics, as well as semantic criticism of language. Accordingly, the conventional implication consists of a sort of specific literal meanings, which slightly differ from the conversational implication. In addition to that, the particular taxonomy of slur words intends to utter a variety of dyslogistic, disparaging expressions in terms of bad or awful contents along with immoral conducts of a word. Hence, it is, apparently, debatable and doubtful (...) that to what extent slur words can convey unethical substance in a way of the conventional implicature? This contrastive article, therefore, attempts to examine credible reasons for clarifying the thesis: the awful essence of pejorative words comes with a conventional implicature. Correspondingly, I have emphasised a few substantial findings such as combinatorial externalism, prohibitionism alongside expressivism. However, notwithstanding this semantic analysis, it is restricted to investigate epistemic and metaphysical affiliations in this regard. (shrink)

Chiastic order is an ancient expression for cross-classification. Cross-classification, in turn, is one of many terms used for the operation of conjoining or cross-mapping one domain, class or set of concepts with another. As such, it is the primordial form of non-quantified modelling and combinatory heuristics. This article presents a brief epistemological history of non-quantified modelling: its prehistory in the form of rhetorical chiasmus; its early (pre-symbolic) use by Plato as a cross-order (paradigmatic) modelling method; and its “modern” (symbolic) use (...) by Leibniz as a calculus of concepts. It will also be shown how classification theory itself is built on a cross-classificatory construct involving two fundamental logical/structural relationships: subordination and conjunction. Finally, examples of modern computer-aided, non-quantified modal modelling are presented in the areas of design theory, operational research and decision science. (shrink)

The formal ontology here presented is what we might call a typed combinatorial Meinongian mereology. Its author seeks to formulate the laws, here called ‘canons’, regulating how entities can combine together in wholes of different sorts. The method, as in Bergmann’s earlier works, involves the construction of an ideal language of such a sort that the analysis of complex wholes can be achieved by transforming our natural-language representations of reality into what we might think of as artificial characteristic maps (...) or diagrams which allow the relevant ontological structures to be read off immediately from the symbolic representations which results. In former works Bergmann had held that the symbolic language of Principia Mathematica could serve as the appropriate diagrammatic device for the standard first-order functional calculus and develops instead a new sort diagrammatic language. (shrink)

A combinatorial analysis of intrinsicality takes intrinsic properties to be independent of accompaniment: a property is intrinsic only if it is possible for a lonely or an accompanied thing to have it or lack it (I). Cameron argues that the combinatorial analysis in Langton & Lewis (1998) faces an epistemic circularity, which makes (I) suspicious. In this paper, I examine two approaches to free the combinatorial analyses from the circularity and find them all fail. Then I provide (...) an outline of an argument for (I) by appealing to the grounding analyses of intrinsicality, which shows an advantage of the grounding analyses over the combinatorial ones. (shrink)

Combinatory logic (Curry and Feys 1958) is a “variable-free” alternative to the lambda calculus. The two have the same expressive power but build their expressions differently. “Variable-free” semantics is, more precisely, “free of variable binding”: it has no operation like abstraction that turns a free variable into a bound one; it uses combinators—operations on functions—instead. For the general linguistic motivation of this approach, see the works of Steedman, Szabolcsi, and Jacobson, among others. The standard view in linguistics is that reflexive (...) and personal pronouns are free variables that get bound by an antecedent through some coindexing mechanism. In variable free semantics the same task is performed by some combinator that identifies two arguments of the function it operates on (a duplicator). This combinator may be built into the lexical semantics of the pronoun, into that of the antecedent, or it may be a free-floating operation applicable to predicates or larger chunks of texts, i.e. a typeshifter. This note is concerned with the case of cross-sentential anaphora. It adopts Hepple’s and Jacobson’s interpretation of pronouns as identity maps and asks how this can be extended to the cross-sentential case, assuming the dynamic semantic view of anaphora. It first outlines the possibility of interpreting indefinites that antecede non-ccommanded pronouns as existential quantifiers enriched with a duplicator. Then it argues that it is preferable to use the duplicator as a type-shifter that applies “on the fly”. The proposal has consequences for two central ingredients of the classical dynamic semantic treatment: it does away with abstraction over assignments and with treating indefinites as inherently existentially quantified. However, cross-sentential anaphora remains a matter of binding, and the idea of propositions as context change potentials is retained. (shrink)

Can trust evolve on the Internet between virtual strangers? Recently, Pettit answered this question in the negative. Focusing on trust in the sense of ‘dynamic, interactive, and trusting’ reliance on other people, he distinguishes between two forms of trust: primary trust rests on the belief that the other is trustworthy, while the more subtle secondary kind of trust is premised on the belief that the other cherishes one’s esteem, and will, therefore, reply to an act of trust in kind (‘trust-responsiveness’). (...) Based on this theory Pettit argues that trust between virtual strangers is impossible: they lack all evidence about one another, which prevents the imputation of trustworthiness and renders the reliance on trust-responsiveness ridiculous. I argue that this argument is flawed, both empirically and theoretically. In several virtual communities amazing acts of trust between pure virtuals have been observed. I propose that these can be explained as follows. On the one hand, social cues, reputation, reliance on third parties, and participation in (quasi-) institutions allow imputing trustworthiness to varying degrees. On the other, precisely trust-responsiveness is also relied upon, as a necessary supplement to primary trust. In virtual markets, esteem as a fair trader is coveted while it contributes to building up one’s reputation. In task groups, a hyperactive style of action may be adopted which amounts to assuming (not: inferring) trust. Trustors expect that their virtual co-workers will reply in kind while such an approach is to be considered the most appropriate in cyberspace. In non-task groups, finally, members often display intimacies while they are confident someone else ‘out there’ will return them. This is facilitated by the one-to-many, asynchronous mode of communication within mailing lists. (shrink)

In this essay, I develop the concept of episodic value, which describes a form of value connected to a particular object or individual expressed and delivered through a narrative. Narrative can bestow special kinds of value on objects, as exemplified by auction articles or museum collections. To clarify the nature of episodic value, I show how the notion of episodic value fundamentally differs from the traditional axiological picture. I extend my discussion of episodic value to argue that the notion of (...) episodic value readily incorporates the role of narratives into the construction of identity in personal and social contexts. My main contentions are twofold. First, events or experiences from our personal narratives are episodically valuable insofar as they contribute to shaping our narrative identities. Second, when engaged in a collective action, we write a joint narrative with other participants that confers special meanings on the actions of each participant. (shrink)

This chapter discusses different perspectives and trends in social decision making, especially the actual processes used by humans when they make decisions in their everyday lives or in business situations. The chapter uses cognitive psychological techniques to break down these processes and set them in their social context. Most of our decisions are made in a social context and are therefore influenced by other people. If you are at an auction and bidding on a popular item, you will try to (...) guess how long the others will keep in the bidding race. Likewise, when you and another person have to coordinate your decision to win a card game you will also try to think about what the other person know and what s/he will do, so you can adjust your choice. In other words, you are trying to come up with a model of the person and his decision-making process. This involves the capability to think about the thoughts and intentions of others, to put yourself in another person's shoes (perspective taking), and to think recursively about your and another person's over several steps (like in a game of chess). Especially, recursive social reasoning is one of the hallmarks of social decision-making. Whereas observational, competitive and cooperative decision-making can all be seen as trying to maximize the own reward or profit, altruistic decision-making blatantly violates this axiomatic principle of behavioral economics. Yet, altruistic behavior is quite common throughout human society. -/- . (shrink)

Markets sit in places and knowledge produced in these places also constitute the very foundation of markets’ viability and market actors’ performative competitive edge. However, not all markets are created equal primarily in the context of their importance in the global economy. Thus conceived, we imagine a world economy or markets populated by people in front of wide computer screens making sense of financial algorithms and derivatives. In a way, here, we see a market that is run by codified knowledge, (...) or scientific knowledge that transcends boundaries. But what about a conception of market that recognizes the production of knowledge in the periphery, and this instance, fish markets, where place-based knowledge marks the contours of engagement of fishmongers to their wider world and yet, concomitantly, also underscores their attachment to place? In this article, in an ethnographic study of four fish markets in a small coastal town in southern Philippine, fishmongers engage with market processes via their production and deployment of vernacular knowledge which is performed in the form of public specialized knowledge, tacit knowledge and network knowledge. In these forms of vernacular knowledge, we become cognizant of the complexities of market processes even in places that are relegated to the margins, where knowledge plays a crucial role in sensing the world and making it lived and real. (shrink)

Recent investigations surprisingly indicate that single RNA "stem-loops" operate solely by chemical laws that act without selective forces, and in contrast, self-ligated consortia of RNA stem-loops operate by biological selection. To understand consortial RNA selection, the concept of single quasi-species and its mutant spectra as drivers of RNA variation and evolution is rethought here. Instead, we evaluate the current RNA world scenario in which consortia of cooperating RNA stem-loops are the basic players. We thus redefine quasispecies as RNA quasispecies consortia (...) and argue that it has essential behavioral motifs that are relevant to the inherent variation, evolution and diversity in biology. We propose that qs-c is an especially innovative force. We apply qs-c thinking to RNA stem-loops and evaluate how it yields altered bulges and loops in the stem-loop regions, not as errors, but as a natural capability to generate diversity. This basic competence-not error-opens a variety of combinatorial possibilities which may alter and create new biological interactions, identities and newly emerged self identity functions. Thus RNA stem-loops typically operate as cooperative modules, like members of social groups. From such qs-c of stem-loop groups we can trace a variety of RNA secondary structures such as ribozymes, viroids, viruses, mobile genetic elements as abundant infection derived agents that provide the stem-loop societies of small and long non-coding RNAs. (shrink)

Lady Mary Shepherd holds that the relation of cause and effect consists of the combination of two objects to create a third object. She also holds that this account implies that causes are synchronous with their effects. There is a single instant in which the objects that are causes combine to create the object which is their effect. Hume argues that cause and effect cannot be synchronous because if they were then the entire chain of successive causes and effects would (...) all collapse into a single moment, and succession would not be possible. I argue that Shepherd has a ready, although implicit response, to Hume’s argument. Since causation is combination on Shepherd’s view, she is free to hold that there are times in between those instants in which combinations occur, during which times other, non-combinatory changes occur, which changes account for succession. (shrink)

The increasing standardization, specialisation and monetarization of academic publishing is designed to foster quality in research and expression. But these tendencies also pose serious challenges to the expression of cultural difference, particularly with regard to philosophy and religious studies. Scholars from various cultural backgrounds outside of mainstream universities often find themselves marginalised when the quality of their work is judged through the metrics of mainstream academic publishing. Smaller journals which give a forum to local research are gradually disappearing or becoming (...) irrelevant. The corporate control of publishing limits the access and distribution of information making it difficult for smaller regional universities to access and conduct research. But these challenges to the expression of cultural difference also reflect the deeper tendencies of the information age. To approach this problem, we need to consider the conflict between culture and spirit on the one hand, with the flows of information and capital on the other. I will introduce this problem through an idea of hermeneutics presented by George McLean. I will then discuss the approaches to this problem by such writers as Michel Serres, Jean Francois Lyotard, Giorgio Agamben and Jacques Derrida. I will show that these latter writers devise strategies to reach something outside of the cybernetic flows of information in the media age, but that their solutions are incomplete because they rely on intellectual concepts of redemption and ignore the concrete practices of spiritual redemption. The issue that cross-cultural journals must consider is how to emphasize something beyond the merely intellectual; how to amplify practice within its expression. I will address this issue in the spirit of a poem by Emily Dickinson entitled “Publication – is the Auction” which supplies the title of this essay. (shrink)

A comprehensive introduction to the Language of Though Hypothesis (LOTH) accessible to general audiences. LOTH is an empirical thesis about thought and thinking. For their explication, it postulates a physically realized system of representations that have a combinatorial syntax (and semantics) such that operations on representations are causally sensitive only to the syntactic properties of representations. According to LOTH, thought is, roughly, the tokening of a representation that has a syntactic (constituent) structure with an appropriate semantics. Thinking thus consists (...) in syntactic operations defined over representations. Most of the arguments for LOTH derive their strength from their ability to explain certain empirical phenomena like productivity, systematicity of thought and thinking. (shrink)

Essential Microeconomics is designed to help students deepen their understanding of the core theory of microeconomics. Unlike other texts, this book focuses on the most important ideas and does not attempt to be encyclopedic. Two-thirds of the textbook focuses on price theory. As well as taking a new look at standard equilibrium theory, there is extensive examination of equilibrium under uncertainty, the capital asset pricing model, and arbitrage pricing theory. Choice over time is given extensive coverage and includes a basic (...) introduction to control theory. The final third of the book, on game theory, provides a comprehensive introduction to models with asymmetric information. Topics such as auctions, signaling and mechanism design are made accessible to students who have a basic rather than a deep understanding of mathematics. Examples and diagrams are used to illustrate issues as well as formal derivations. (shrink)

We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive (...) formulae are elementary canonical and thus extend Sahlqvist’s theorem over them. In particular, we give a simple example of an inductive formula which is not frame-equivalent to any Sahlqvist formula. Then, after a deeper analysis of the inductive formulae as set-theoretic operators in descriptive and Kripke frames, we establish a somewhat stronger model-theoretic characterization of these formulae in terms of a suitable equivalence to syntactically simpler formulae in the extension of the language with reversive modalities. Lastly, we study and characterize the elementary canonical formulae in reversive languages with nominals, where the relevant notion of persistence is with respect to discrete frames. (shrink)

Synthetic biology has a strong modal dimension that is part and parcel of its engineering agenda. In turning hypothetical biological designs into actual synthetic constructs, synthetic biologists reach towards potential biology instead of concentrating on naturally evolved organisms. We analyze synthetic biology’s goal of making biology easier to engineer through the combinatorial theory of possibility, which reduces possibility to combinations of individuals and their attributes in the actual world. While the last decades of synthetic biology explorations have shown biology (...) to be much more difficult to engineer than originally conceived, synthetic biology has not given up its combinatorial approach. (shrink)

Boltzmannian statistical mechanics partitions the phase space of a sys- tem into macro-regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the Maxwell-Boltzmann distribution, and maxi- mum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macrostate in which a system spends most of its time and prove a new theorem establishing that equilib- rium thus defined corresponds to the (...) largest macro-region. Our derivation is completely general in that it does not rely on assumptions about a system’s dynamics or internal interactions. (shrink)

In this article, network science is discussed from a methodological perspective, and two central theses are defended. The first is that network science exploits the very properties that make a system complex. Rather than using idealization techniques to strip those properties away, as is standard practice in other areas of science, network science brings them to the fore, and uses them to furnish new forms of explanation. The second thesis is that network representations are particularly helpful in explaining the properties (...) of non-decomposable systems. Where part-whole decomposition is not possible, network science provides a much-needed alternative method of compressing information about the behavior of complex systems, and does so without succumbing to problems associated with combinatorial explosion. The article concludes with a comparison between the uses of network representation analyzed in the main discussion, and an entirely distinct use of network representation that has recently been discussed in connection with mechanistic modeling. (shrink)

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...) computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

Fodor and Pylyshyn's critique of connectionism has posed a challenge to connectionists: Adequately explain such nomological regularities as systematicity and productivity without postulating a "language of thought" (LOT). Some connectionists like Smolensky took the challenge very seriously, and attempted to meet it by developing models that were supposed to be non-classical. At the core of these attempts lies the claim that connectionist models can provide a representational system with a combinatorial syntax and processes sensitive to syntactic structure. They are (...) not implementation models because, it is claimed, the way they obtain syntax and structure sensitivity is not "concatenative," hence "radically different" from the way classicists handle them. In this paper, I offer an analysis of what it is to physically satisfy/realize a formal system. In this context, I examine the minimal truth-conditions of LOT Hypothesis. From my analysis it will follow that concatenative realization of formal systems is irrelevant to LOTH since the very notion of LOT is indifferent to such an implementation level issue as concatenation. I will conclude that to the extent to which they can explain the law-like cognitive regularities, a certain class of connectionist models proposed as radical alternatives to the classical LOT paradigm will in fact turn out to be LOT models, even though new and potentially very exciting ones. (shrink)

According to the Computational/Representational Theory of Thought (CRTT ? Language of Thought Hypothesis, or LOTH), propositional attitudes, such as belief, desire, and the like, are triadic relations among subjects, propositions, and internal mental representations. These representations form a representational _system_ physically realized in the brain of sufficiently sophisticated cognitive organisms. Further, this system of representations has a combinatorial syntax and semantics, but the processes that operate on the representations are causally sensitive only to their syntax, not to their semantics. (...) On this approach, a first pass account of propositional attitudes is the following (cf. Field 1978: 37 and Fodor 1987: 17). (shrink)

This book’s goal is to give an intellectual context for the following manuscript. -/- Includes bibliographical references and an index. Pages 1-123. 1). Philosophy. 2). Metaphysics. 3). Philosophy, German. 4). Philosophy, German -- 18th century. 5). Philosophy, German and Greek Influences Metaphysics. I. Hegel, Georg Wilhelm Friedrich -- 1770-1831 -- Das älteste Systemprogramm des deutschen Idealismus. II. Rosenzweig, Franz, -- 1886-1929. III. Schelling, Friedrich Wilhelm Joseph von, -- 1775-1854. IV. Hölderlin, Friedrich, -- 1770-1843. V. Ferrer, Daniel Fidel, 1952-. [Translation from (...) German into English of the-- Das älteste Systemprogramm des deutschen Idealismus.]. -/- Note: the manuscript is in the handwriting of G.W.F. Hegel, but the actual authorship is disputed. No date is given. Franz Rosenzweig made up the title as it is known today. He published the text in 1917. At that time, F. Rosenzweig thought F.W.J. Schelling was the author. No one has read this book for errors. As always, any errors, mistakes or oversights etc. are mine alone. Given a couple more years, I could improve this book. This is a philosophical translation and not a philological translation. Martin Luther who did the famous early translation of the Bible into German wrote in a letter, “If anyone does not like my translation, they can ignore it… (September 15, 1530)”. There are no ‘correct’ translations. Some are just better than other translations. -/- The Oldest Systematic Program of German Idealism. The German title is: Das Älteste Systemprogramm Des Deutschen Idealismus. This title was made up by Franz Rosenzweig in 1917, when he first published the manuscript. He found the manuscript in the Royal Library in Berlin in 1913. The manuscript suggested date is around 1796 and was done by handwriting research. However, the manuscript is not dated. The Prussian State Library auctioned in March 1913 from the auction of the house Liepmannssohn in Berlin a single sheet on the front and back with Hegel's cursive handwriting. The manuscript was lost during WWII. But Dieter Henrich found it again in 1979 in the “Biblioteka Jagiellonska” in Krakow (Poland), where it is today. Address: Jagiellonian Library, Jagiellonian University, al. Mickiewicza 22, 30-059 Cracow, Poland. Later research suggests that manuscript had come from the estate of Hegel’s student Friedrich Christoph Förster (1791-1868). He was one of the editors of Hegel’s posthumous works and most likely had access to a number of Hegel’s manuscripts. This text actually being one of them. Hegel traveled around Bohemia with Marie and Friedrich Christoph Förster around the year 1820-21 (see Klaus Vieweg). -/- Philosophical mystery -- who is the author or authors of this text? -/- Take a plunge into the deep and cold waters. Maybe a quagmire or quandary, but decidedly interesting. This project is to contextualize an old handwritten manuscript which is about 225 years old. The actual author is a mystery. I offer my own assessment. You can make your own assessments. The mystery has continued to unfold since 1917. There is plenty to read. Otherwise, think about the authorship and read more of the German philosophers and authors from this period and enjoy the depth of thinking and philosophizing. On one hand, there is just the sheer fun in the puzzle of the authorship questions; and on the other hand, these are the alluring thoughts that lead to the nascent stage of German Idealism and our intellectual heritage. There is no end to the accolades for this group of philosophers. A heritage that we still hear in in our attempts to move forward into our future. -/- Do your own astute exegesis (ἐξήγησις) as all paths are still open. Let your thought take to the wings of what is called thinking with this text. Critical encounters (Auseinandersetzung, or a Gegenüberstellung) with at least: Friedrich Hölderlin (1770-1843) Friedrich Wilhelm Joseph Schelling (1775-1854), and Georg Wilhelm Friedrich Hegel (1770-1831) --- starts here! German Idealism. We are not going to study this situation endlessly, instead we make some broad strokes and provide you a general context. You are allowed to read between the lines too. Goal: to understand the overall affinity and differences between the intellectuals of this period in German history; and to come to grips with this demanding text within its large scholarly context in the last 100 years. There are no final answers. (shrink)

This paper argues that general skills and the varieties of subject-specific discourse are both important for teaching, learning and practising critical thinking. The former is important because it outlines the principles of good reasoning simpliciter (what constitutes sound reasoning patterns, invalid inferences, and so on). The latter is important because it outlines how the general principles are used and deployed in the service of ‘academic tribes’. Because critical thinking skills are—in part, at least—general skills, they can be applied to all (...) disciplines and subject-matter indiscriminately. General skills can help us assess reasoning independently of the vagaries of the linguistic discourse we express arguments in. The paper looks at the debate between the ‘specifists’—those who stress the importance of critical thinking understood as a subject-specific discourse—and the ‘generalists’—those that stress the importance of critical thinking understood independently of disciplinary context. The paper suggests that the ‘debate’ between the specifists and the generalists amounts to a fallacy of the false alternative, and presents a combinatory-‘infusion’ approach to critical thinking. (shrink)

In this paper I argue for an association between impurity and explanatory power in contemporary mathematics. This proposal is defended against the ancient and influential idea that purity and explanation go hand-in-hand (Aristotle, Bolzano) and recent suggestions that purity/impurity ascriptions and explanatory power are more or less distinct (Section 1). This is done by analyzing a central and deep result of additive number theory, Szemerédi’s theorem, and various of its proofs (Section 2). In particular, I focus upon the radically impure (...) (ergodic) proof due to Furstenberg (Section 3). Furstenberg’s ergodic proof is striking because it utilizes intuitively foreign and infinitary resources to prove a finitary combinatorial result and does so in a perspicuous fashion. I claim that Furstenberg’s proof is explanatory in light of its clear expression of a crucial structural result, which provides the “reason why” Szemerédi’s theorem is true. This is, however, rather surprising: how can such intuitively different conceptual resources “get a grip on” the theorem to be proved? I account for this phenomenon by articulating a new construal of the content of a mathematical statement, which I call structural content (Section 4). I argue that the availability of structural content saves intuitive epistemic distinctions made in mathematical practice and simultaneously explicates the intervention of surprising and explanatorily rich conceptual resources. Structural content also disarms general arguments for thinking that impurity and explanatory power might come apart. Finally, I sketch a proposal that, once structural content is in hand, impure resources lead to explanatory proofs via suitably understood varieties of simplification and unification (Section 5). (shrink)

Slurs are derogatory, and theories of slurs aim at explaining their “derogatory force”. This paper draws a distinction between the type derogatory force and the token derogatory force of slurs. To explain the type derogatory force is to explain why a slur is a derogatory word. By contrast, to explain the token derogatory force is to explain why an utterance of a slur is derogatory. This distinction will be defended by examples in which the type and the token derogatory force (...) come apart. Because of the distinction, an adequate theory of slurs must be plausible for both the type and the token derogatory force. However, I will argue that many theories fail to be plausible for both. In particular, Hom’s combinatorial externalism and the conventional implicature theory offer implausible accounts of the token derogatory force, whereas the prohibitionist theory is insufficient to explain the type derogatory force. (shrink)

When one has both epistemic and practical reasons for or against some belief, how do these reasons combine into an all-things-considered reason for or against that belief? The question might seem to presuppose the existence of practical reasons for belief. But we can rid the question of this presupposition. Once we do, a highly general ‘Combinatorial Problem’ emerges. The problem has been thought to be intractable due to certain differences in the combinatorial properties of epistemic and practical reasons. (...) Here we bring good news: if we accept an independently motivated version of epistemic instrumentalism—the view that epistemic reasons are a species of instrumental reasons—we can reduce The Combinatorial Problem to the relatively benign problem of how to weigh different instrumental reasons against each other. As an added benefit, the instrumentalist account can explain the apparent intractability of The Combinatorial Problem in terms of a common tendency to think and talk about epistemic reasons in an elliptical manner. (shrink)

One of the main obstacles for panpsychism, the view that consciousness is fundamental and ubiquitous, is the difficulty of explaining how simple subjects could combine to form complex subjects. Known as the subject combination problem, it poses a possibly insurmountable challenge to the view. In this paper, I will assume that this challenge cannot be overcome and instead present a version of panpsychism that completely avoids talk of combination. Inspired by Gottfried Wilhelm Leibniz’s metaphysics of monads, I will focus on (...) a relational explanation of how simple subjects could constitute complex experiences, without them having to combine in virtue of their subjectivity. I call this view _monadic panpsychism_. Additionally, my proposal will not rely on emergence and so it will circumvent problems commonly faced by emergentist accounts. As I will argue, monadic panpsychism is preferable to combinatory and emergentist panpsychism because it faces a significantly less worrisome set of objections. Apart from being unaffected by the seemingly insuperable issue of subject combination, I will demonstrate that monadic panpsychism also has tools to address other kinds of the combination problem. That alone justifies the need for a new formulation of panpsychism, one which faces unique difficulties but also offers unique solutions. (shrink)

“There are no gaps in logical space,” David Lewis writes, giving voice to sentiment shared by many philosophers. But different natural ways of trying to make this sentiment precise turn out to conflict with one another. One is a *pattern* idea: “Any pattern of instantiation is metaphysically possible.” Another is a *cut and paste* idea: “For any objects in any worlds, there exists a world that contains any number of duplicates of all of those objects.” We use resources from model (...) theory to show the inconsistency of certain packages of combinatorial principles and the consistency of others. (shrink)

Since at least 2008 linguists and philosophers of language have started paying more serious attention to issues concerning the meaning or use of racial epithets and slurs. In an influential article published in The Journal of Philosophy, for instance, Christopher Hom (2008) offered a semantic account of racial epithets called Combinatorial Externalism (CE) that advanced a novel argument for the exclusion of certain epithets from freedom of speech protection under the First Amendment (p. 435). Also in more recent work, (...) “The Expressive Meaning of Racial Epithets: Towards A Non-Unitary Account of Expressive Meaning,” Diane Blakemore (2013) offered an alternative pragmatic account of racial epithets rooted in Dan Sperber and Deirdre Wilson’s (1986) relevance theory. Adam Croom (2008) has also discussed epithets before in prior work, through a consideration of a paradigmatic racial epithet directed towards Native Americans, but then moved on in subsequent work to focus on developing a more nuanced account of paradigmatic slurring terms instead (Croom 2010; Croom 2011; Croom 2012; Croom 2013; Croom 2014a; Croom 2014b; Croom under review). So the purpose of this article is to return to and extend the previous account of racial epithets provided by Croom (2008) through a consideration of another paradigmatic racial epithet, but this time one directed towards Asian Americans instead of Native Americans. Here I also offer a novel suggestion for how to differentiate between epithets and slurs, offering new insight into how epithets and slurs are both similar and different. A sample list of over 100 other racial epithets that can be accounted for by the kind of analysis presented here is provided in Croom (2008, p. 44-45). (shrink)

We propose a generalization of Sahlqvist formulae to polyadic modal languages by representing modal polyadic languages in a combinatorial style and thus, in particular, developing what we believe to be the right approach to Sahlqvist formulae at all. The class of polyadic Sahlqvist formulae PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.

Natural languages exhibit a great variety of grammatical paradigms. For instance, in English verbs are grammatically marked for tense, whereas in the tenseless Eskimo-Aleut language Kalaallisut they are marked for illocutionary mood. Although time is a universal dimension of the human experience and speaking is part of that experience, some languages encode reference to time without any grammatical tense morphology, or reference to speech acts without any illocutionary mood morphology. Nevertheless, different grammatical systems are semantically parallel in certain respects. Specifically, (...) I propose that English tenses form a temporal centering system, which monitors and updates topic times, whereas Kalaallisut moods form a modal centering system, which monitors and updates modal discourse referents. To formalize these centering parallels I define a dynamic logic that represents not only changing information but also changing focus of attention in discourse (Update with Centering, formalizing Grosz et al 1995). Different languages can be translated into this typed logic by directly compositional universal rules of Combinatory Categorial Grammar (CCG) The resulting centering theory of tense and illocutionary mood draws semantic parallels across different grammatical systems. The centering generalizations span the extremes of the typological spectrum, so they are likely to be universal. In addition, the theory accounts for the translation equivalence of tense and illocutionary mood in a given utterance context. Following Stalnaker (1978) I assume that the very act of speaking up has a ‘commonplace effect’ on the context. It focuses attention on the speech act and thereby introduces default modal and temporal topics. These universal defaults complement language-specific grammars, e.g. English tenses and Kalaallisut moods. In a given utterance context the universal discourse-initial defaults plus language-specific grammatical marking may add up to the same truth conditions.. (shrink)

If possible worlds are conjunctions of states of affairs, as in David Armstrong’s combinatorial theory, then is the empty world to be thought of as the null conjunction of states of affairs? The proposal seems plausible, and has received support from David Efird, Tom Stoneham, and Armstrong himself. However, in this paper, it is argued that the proposal faces a trilemma: either it leads to the absurd conclusion that the actual world is empty; or it reduces to a familiar (...) representation of the empty world in which the concept of a null conjunction plays no role; or it needs to make room for the null individual of certain non-classical mereologies. (shrink)

Many collective decision making problems have a combinatorial structure: the agents involved must decide on multiple issues and their preferences over one issue may depend on the choices adopted for some of the others. Voting is an attractive method for making collective decisions, but conducting a multi-issue election is challenging. On the one hand, requiring agents to vote by expressing their preferences over all combinations of issues is computationally infeasible; on the other, decomposing the problem into several elections on (...) smaller sets of issues can lead to paradoxical outcomes. Any pragmatic method for running a multi-issue election will have to balance these two concerns. We identify and analyse the problem of generating an agenda for a given election, specifying which issues to vote on together in local elections and in which order to schedule those local elections. (shrink)

Laws of nature seem to take two forms. Fundamental physics discovers laws that hold without exception, ‘strict laws’, as they are sometimes called; even if some laws of fundamental physics are irreducibly probabilistic, the probabilistic relation is thought not to waver. In the nonfundamental, or special, sciences, matters differ. Laws of such sciences as psychology and economics hold only ceteris paribus – that is, when other things are equal. Sometimes events accord with these ceteris paribus laws (c.p. laws, hereafter), but (...) sometimes the laws are not manifest, as if they have somehow been placed in abeyance: the regular relation indicative of natural law can fail in circumstances where an analogous outcome would effectively refute the assertion of strict law. Many authors have questioned the supposed distinction between strict laws and c.p. laws. The brief against it comprises various considerations: from the complaint that c.p. clauses are void of meaning to the claim that, although understood well enough, they should appear in all law-statements. These two concerns, among others, are addressed in due course, but first, I venture a positive proposal. I contend that there is an important contrast between strict laws and c.p. laws, one that rests on an independent distinction between combinatorial and noncombinatorial nomic principles.2 Instantiations of certain properties, e.g., mass and charge, nomically produce individual forces, or more generally, causal influences,3 in accordance with noncombinatorial.. (shrink)

Ultrafilters are very important mathematical objects in mathematical research [6, 22, 23]. There are a wide variety of classical theorems in various branches of mathematics where ultrafilters are applied in their proof, and other classical theorems that deal directly with ultrafilters. The objective of this article is to contribute (in a divulgative way) to ultrafilter research by describing the demonstrations of some such theorems related (uniquely or in combination) to topology, Measure Theory, algebra, combinatorial infinite, set theory and first-order (...) logic, also formulating some updated open problems of set theory that refer to non-principal ultrafilters on N, the Mathias’s model and the Solovay’s model. -/- Resumen: Los ultrafiltros son objetos matemáticos muy importantes en la investigación matemática [6, 22, 23]. Existen una gran variedad de teoremas clásicos en diversas ramas de la matemática donde se aplican ultrafiltros en su demostración, y otros teoremas clásicos que tratan directamente sobre ultrafiltros. El objetivo de este artículo es contribuir (de una manera divulgativa) con la investigación sobre ultrafiltros describiendo las demostraciones de algunos de tales teoremas relacionados (de manera única o combinada) con topología, teoría de la medida, álgebra, combinatoria infinita, teoría de conjuntos y lógica de primer orden, formulando además algunos problemas abiertos actuales de la teoría de conjuntos que se refieren a ultrafiltros no principales sobre N, al Modelo de Mathias y al Modelo de Solovay. (shrink)

In a time which it is not amiss to term “the Dark Ages of logic”, Karl Christian Friedrich Krause stayed not only true to logic but actually did something for its advancement. Besides making systematic use of Venn-diagrams long before Venn, Krause — once more taking his inspiration from Leibniz — propounded what appears to be the first completely symbolic systematic representation of logical forms, strongly suggestive of the powerful symbolic languages that have become the mainstay of logic since the (...) beginning of the 20th century. However, Krause’s limits in logic are also clearly visible: Krause’s method in logic is, in the main, not axiomatic; it is combinatorial. More importantly, Krause remained entirely within the confines of traditional syllogistics, neglecting propositional logic and, of course, first-order relational terms. (shrink)