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)

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)

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)

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)

(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)

In TSCH, which is a MAC mechanism set of the IEEE 802.15.4e amendment, calculation, construction, and maintenance of the packet transmission schedules are not defined. Moreover, to ensure optimal throughput, most of the existing scheduling methods are based on the assumption that instantaneous and accurate Channel State Information (CSI) is available. However, due to the inevitable errors in the channel estimation process, this assumption cannot be materialized in many practical scenarios. In this paper, we propose two alternative and realistic approaches. (...) In our first approach, we assume that only the statistical knowledge of CSI is available a priori. Armed with this knowledge, the average packet rate on each link is computed and then, using the results, the throughput-optimal schedule for the assignment of (slot-frame) cells to links can be formulated as a max-weight bipartite matching problem, which can be solved efficiently using the well-known Hungarian algorithm. In the second approach, we assume that no CSI knowledge (even statistical) is available at the design stage. For this zero-knowledge setting, we introduce a machine learning-based algorithm by formally modeling the scheduling problem in terms of a combinatorial multi-armed bandit (CMAB) process. Our CMAB-based scheme is widely applicable to many real operational environments, thanks to its reduced reliance on design-time knowledge. Simulation results show that the average throughput obtained by the statistical CSI-based method is within the margin of 15% from the theoretical upper bound associated with perfect instantaneous CSI. The aforesaid margin is around 18% for our learning-theoretic solution. (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.

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

“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)

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)

Despite an increasing role of machine learning in science, there is a lack of results on limits of empirical exploration aided by machine learning. In this paper, we construct one such limit by proving undecidability of learnability of state spaces of physical systems. We characterize state spaces as binary hypothesis classes of the computable Probably Approximately Correct learning framework. This leads to identifying the first limit for learnability of state spaces in the agnostic setting. Further, using the fact that finiteness (...) of the combinatorial dimension of hypothesis classes is undecidable, we derive undecidability for learnability of state spaces as well. Throughout the paper, we try to connect our formal results with modern neural networks. This allows us to bring the limits close to the current practice and make a first step in connecting scientific exploration aided by machine learning with results from learning theory. (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)

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)

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)

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)

This essay examines the role of non-existent objects in "epistemological ontology" — the study of the entities that make thinking possible. An earlier revision of Meinong's Theory of Objects is reviewed, Meinong's notions of Quasisein and Außersein are discussed, and a theory of Meinongian objects as "combinatorially possible" entities is presented.

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)

We formulate the problem of permuting a matrix to block angular form as the combinatorial minimization of an objective function. We motivate the use of simulated annealing (SA) as an optimization tool. We then introduce a heuristic temperature dependent penalty function in the simulated annealing cost function, to be used instead of the real objective function being minimized. Finally we show that this temperature dependent penalty function version of simulated annealing consistently outperforms the standard simulated annealing approach, producing, with (...) smaller running times, better solutions. We believe that the use of a temperature dependent penalty function may be useful in developing SA algorithms for other combinatorial problems. -/- . (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)

It is fundamental that, in philosophy, we make sure that we are not mistaking merely verbal disputes, or “conceptual” disputes, for substantive ones. This essay presents a tripartite framework that is useful for clarifying cases where it is difficult to tell whether we are engaged in substantive or non-substantive disputes. For this purpose, the essay offers some combinatorial possibilities between the following levels: verbal, conceptual, and objectual. We need to distinguish whether we are arguing about the world, concepts, or (...) words to avoid talking at cross-purposes and to recognize when our disputes are not worth the time. Distinguishing between these three levels can also throw light and guide research on conceptual engineering, metalinguistic negotiations, metaontology, and so on. (shrink)

This paper offers a sketch of welfarist pluralism, a view that is intended to resolve a difficulty for non-derivative pluralists about normative reasons for belief. Welfarist pluralism is the view that all reasons for belief are rooted in wellbeing, and that wellbeing has as one of its components being in a positive epistemic state. The paper explores how this view can explain various pluralist intuitions and why it offers a plausible basis for combinatorial pluralists who believe that alethic and (...) pragmatic reasons for belief combine to determine what one ought to believe. The paper also considers the relationship between theoretical rationality and wellbeing, and provides a partial argument for the derivative normativity of at least some requirements of theoretical rationality. (shrink)

This essay examines the role of non-existent objects in "epistemological ontology"--the study of the entities that make thinking possible. An earlier revision of Meinong's Theory of Objects is reviewed, Meinong's notions of Quasisein and Aussersein are discussed, and a theory of Meinongian objects as "combinatorially possible" entities is presented.

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)

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.

Alsted was a foremost encyclopedist of the early seventeenth century. He provided both a complete presentation of all the subjects of philosophy (of which encyclopedia consisted) and a method to learn them. This method was an original synthesis of the dialectic of Petrus Ramus, the combinatorial art of memory of Raimond Lull and Giordano Bruno, and the method of presentation of philosophical disciplines of Bartholomäus Keckermann. Alsted’s encyclopedism was intended as a remedy to the postlapsarian condition of man and (...) was functional to the pedagogical reform pursued at the Academy of Herborn; this was, in turn, an essential part of the Calvinist state reform of the county of Nassau-Dillenburg. In theology, the importance of Alsted consists of having introduced millenarianism in the Reformed Europe, though his early, optimistic views on the imminent end of the world would change to pessimistic as a consequence of the Thirty Years’ War. (shrink)

Karl Christian Friedrich Krause and Georg Wilhelm Friedrich Hegel are two representatives of German Idealism, both of whom developed impressing category systems. At the core of both systems is the question of the relation of the Absolute to its determinations and the determinations of finite beings. Both idealists try to deduce their respective category systems from the immediacy of the Absolute. Both use combinatorial methods to get from known to new categories or constellations in the system, which then unfold (...) in the world. Krause is thereby considered the eponym of so-called panentheism, the doctrine that “Everything is in God.” Hegel is also often referred to as a panentheist. Through a comparison of the two systems of categories, in this essay the thesis will be advocated that Hegel was in no sense a panentheist. Krause is and remains the gold standard of panentheism. (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)

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)

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)

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)

According to an influential reading of his later philosophy, Wittgenstein thinks that nonsense can result from combining expressions in ways prohibited by the rules to which their use is subject. According to another influential reading, the later Wittgenstein thinks that nonsense only ever results from privation—that is, from a failure to assign a meaning to one or more of the relevant expressions. This chapter challenges Glock’s defence of the view that the later Wittgenstein allows for combinatorial nonsense. In doing (...) so, it defends a version of the privation view. According to it, Wittgenstein thinks that nonsense results, not so much from a failure to assign a meaning to an expression, as a failure to use an expression in a way that has a point or purpose. As the chapter shows, this interpretation is consistent with prominent themes in Wittgenstein’s later philosophy, such as that meaning and explanation are coordinate notions, that for a word to have a meaning is for there to be a rule-governed practice of using it, that the rules of the practice are arbitrary, and that they determine the bounds of sense. (shrink)

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)

Abstract: Many believe that, in addition to cognitive capacities, autonomous robots need something similar to affect. As in humans, affect, including specific emotions, would filter robot experience based on a set of goals, values, and interests. This narrows behavioral options and avoids combinatorial explosion or regress problems that challenge purely cognitive assessments in a continuously changing experiential field. Adding human-like affect to robots is not straightforward, however. Affect in organisms is an aspect of evolved biological systems, from the taxes (...) of single-cell organisms to the instincts, drives, feelings, moods, and emotions that focus human behavior through the mediation of hormones, pheromones, neurotransmitters, the autonomic nervous system, and key brain structures. We argue that human intelligence is intimately linked to biological affective systems and to the unique repertoire of potential behaviors, sometimes conflicting, they facilitate. Artificial affect is affect in name only and without genes and biological bodies, autonomous robots will lack the goals, interests, and value systems associated with human intelligence. We will take advantage of their general intelligence and expertise, but robots will not enter our intellectual world or apply for legal status in the community. -/- . (shrink)

Beyond the predominant paradigm of an essentially rational human cognition, based on the classical binary logic, we want to propose some reflections that are organized around the intuition that the representations we have of the world are weighted with appreciations, for example affective ones. resulting from our integration into a social environment. We see these connotations as essentially ternary in nature, depending on the concepts underlying neutrosophy: either positive, negative or neutral. This form of representation would then influence the very (...) nature of the cognitive process, which in complex real-world situations, has to deal with problems of a combinatorial nature leading to a number of cases too large for our abilities. Forced to proceed by shortcuts on the basis of heuristics, cognition would use these assessments of the representations it manipulates to decide whether partial solutions are attractive for solving the problem or on the contrary are judged negative and are then quickly rejected. There is still the case of a neutral weighting that allows processing to continue. Thus a neutrosophical conception of our representations of the world explains how our cognition functions in its treatment of combinatorial problems in the form of producing processing accelerating heuristics, both in terms of partial solutions selection and processing optimization. (shrink)

We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely (...) class='Hi'>combinatorial characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (shrink)