In lieu of an abstract, here is a brief excerpt of the content:Ethics & the Environment 7.1 (2002) 102-108 [Access article in PDF] Symposium IntroductionEric Katz's Nature As Subject Andrew Light Can and should we distinguish between nature and culture? The question has become a perennial one in environmental ethics, as well as in allied fields in environmental history, sociology, and politics. And just when we think it is settled—as many did after William Cronon's famous deconstruction of wilderness in (...) 1995—and it feels safe to go back into the metaphysical waters of environmental philosophy, such issues pop up again to send us running.What follows extends this debate in the context of Eric Katz's well-known work in environmental ethics. Brought together here are Katz and two critics sympathetic to his positions, Wayne Ouderkirk and Ned Hettinger. While the occasion for the exchange was the publication of Katz's book, Nature as Subject: Human Obligation and Natural Community (1997), which collects his papers from 1979 to 1996, the focus quickly became somewhat narrower, centering on possible problems with Katz's ontological dualism between natural and artifactual entities.Katz has exerted a strong influence on the development of environmental ethics, particularly through his persistent arguments for a distinction between individualist and holist approaches to obligations to the nonhuman natural world and his metaphysical and moral critique of attempts [End Page 102] by humans to create, repair, or restore nature. While these positions continue to be on display here, there is also something more. In this exchange Katz throws down the gauntlet on his nature-culture dualism, admitting at the start that the accusation is true. Like the Protestants in Monty Python's The Meaning of Life, he is a dualist—and fiercely proud of it! Despite whatever misgivings I or others may have about this position, I believe that in making this claim, Katz, similar to David Chalmers's open embrace and resuscitation of dualism in philosophy of mind, has done us a great service. For it is arguably true that many environmental philosophers, along with other academics, have settled into a complacent "labeling as argument" pattern. If we can label a position as "dualist" or "essentialist," then our work is done. But surely not every form of dualism is necessarily wrong, even if, as Ouderkirk reminds us in his reading of Val Plumwood's work, the logic of many forms of dualism has tended toward a pernicious pattern. Arguments are needed in both directions. If nature-culture dualism is mistaken or wrongheaded, or leads to unfortunate conclusions, then we must know why; if dualism is the only way to make sense of the hurdles presented to us in coming to a better understanding of the value of nature and culture then we must know why as well. And further, because many in the field have assumed a nature-culture dualism without admitting to it, we can admire that Katz chooses to "fess up" and finally put the issue squarely on the table.If this is the road we are heading down with this particular exchange, then we are off to a good start. Both critics of Katz do a thorough job of pressing home their arguments, rather than only pointing accusatory fingers. Ned Hettinger, in "The Problem of Finding a Positive Role for Humans in the Natural World," avoids using the term "dualism," but nonetheless argues that Katz has a tendency to "rigidly dichotomize the natural/artifactual distinction." Additionally, Hettinger argues that Katz tends to overlook his own admission that the differences between nature and artifacts admit to degrees rather than a strict dualism. Hettinger focuses the bulk of his critique on the unfortunate upshot of such a position: given such a distinction, there is little if any place for a positive role for human intervention in nature, or for a philosophical contribution to the formation of better environmental policies.Wayne Ouderkirk, in "Katz's Problematic Dualism and its 'Seismic' Effects on His Theory," is sympathetic with Katz's intuitions that some distinction is needed between artifacts and natural entities. The problem [End Page 103] he sees is that such... (shrink)

The ethical and social implications of data mining, algorithmic curation and automation in the context of social media have been of heightened concern for a range of researchers with interests in digital media in recent years, with particular concerns about privacy arising in the context of mobile and locative media. Despite their wide adoption and economic importance, mobile dating apps have received little scholarly attention from this perspective – but they are intense sites of data generation, algorithmic processing, and cross-platform (...) data-sharing; bound up with competing cultures of production, exploitation and use. In this paper, we describe the ways various forms of data are incorporated into, and emerge from, hook-up apps’ business logics, socio-technical arrangements, and cultures of use to produce multiple and intersecting data cultures. We propose a multi-layered research agenda for critical and empirical inquiry into this field, and suggest appropriate conceptual and methodological frameworks for exploring the social and political challenges of data cultures. (shrink)

For thirty years at least, I have designated myself as a zoologist interested in the “philosophical aspects of biology”. But I have now to admit that not until within the last two or three years have I recognized that logic, particularly in its inductive aspect, is involved in such interest.For me as a zoologist with a predilection for natural history, observation has had a place of wide application and of implicit confidence. Until recently, I had rested in the supposition that (...) after all of the devices practiced by naturalists to insure certainty of their observations, nothing further was needed so far as the information and understanding they gained was concerned. I had gone ahead with my reasoning, my logic, with no more qualms about the trustworthiness of the “inductive” than of the “deductive” side of it. I had not taken seriously the assertion, made years ago in my hearing by an eminent philosopher, that no one can be a philosopher without being skeptical and critical of the use of his senses in getting knowledge. Latterly, however, I have come to see that traditional philosophers take themselves very seriously in such assertions. This realization has been due to the discovery that the recent advances in physics and mathematics have led most of the leaders in these fields to believe that observation and the inductive side of logic may be left where they were a hundred years ago. These scientists seem to be about where John Stuart Mill was in his effort to improve Lord Bacon's effort for a better understanding of both observation and induction. (shrink)

There seems to be something mysterious about applications of for- mal systems, including those of logic, to empirical reality 1 . If logic is to be applied to empirical situations, like those described in an ordinary lan- guage, then { it seems to some people { its statements cannot be necessary, or analytic, propositions. However, they are both applicable and necessary. This supposed puzzle constitutes a signicant part of the problem of philo- sophical foundations of logic 2 . To this (...) mind of the present writer, there is no mystery of applications, since any empirical, or even ostensive, predicate can be involved in cer- tain meaning postulates, e.g. \No red is green", which are both empirical and necessary propositions; empirical as they involve ostensibly dened predicated; necessary, as it is enough to know their meaning to state, their validity. The case of logical theorems can be considered at the same footing, logical constants being treated as dened ostensively. Nevertheless, not an individual state of mind but the actual state of scholarly discussions makes something a problem; in the present state of foundational discussions on logic, the \mystery of applications" preserves its vitality, hence any new way of dealing with it proves welcome. (shrink)

In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the (...) freedom provided by Cantorian set theory was purchased at a heavy philosophical price, namely adherence to a form of mathematical platonism that is difficult to support. -/- Beginning with a previously unpublished lecture for a general audience, Deciding the Undecidable, Feferman examines the famous list of twenty-three mathematical problems posed by David Hilbert, concentrating on three problems that have most to do with logic. Other chapters are devoted to the work and thought of Kurt Gödel, whose stunning results in the 1930s on the incompleteness of formal systems and the consistency of Cantors continuum hypothesis have been of utmost importance to all subsequent work in logic. Though Gödel has been identified as the leading defender of set-theoretical platonism, surprisingly even he at one point regarded it as unacceptable. -/- In his concluding chapters, Feferman uses tools from the special part of logic called proof theory to explain how the vast part--if not all--of scientifically applicable mathematics can be justified on the basis of purely arithmetical principles. At least to that extent, the question raised in two of the essays of the volume, Is Cantor Necessary?, is answered with a resounding no. -/- This volume of important and influential work by one of the leading figures in logic and the foundations of mathematics is essential reading for anyone interested in these subjects. (shrink)

This book analyses and defends the deflationist claim that there is nothing deep about our notion of truth. According to this view, truth is a 'light' and innocent concept, devoid of any essence which could be revealed by scientific inquiry. Cezary Cieśliński considers this claim in light of recent formal results on axiomatic truth theories, which are crucial for understanding and evaluating the philosophical thesis of the innocence of truth. Providing an up-to-date discussion and original perspectives on this (...) central and controversial issue, his book will be important for those with a background in logic who are interested in formal truth theories and in current philosophical debates about the deflationary conception of truth. (shrink)

Logical theory codifies rules of correct inferences. On the other hand, logical reasoning is typically considered as one of the most fundamental cognitive activities. Thus, cognitive science is a natural meeting-point for investigations about the place of logic in human cognition. Investigations in this perspective strongly depend on a possible understanding of logic. This paper focuses on logic in the strict sense; that is, the theory of deductive inferences. Two problems are taken into account, namely: do humans apply logical rules (...) in ordinary reasoning?; the genesis of logic. The second issue is analyzed from the naturalistic point of view. (shrink)

We investigate a subsystem of minimal logic related to D. Vakarelov’s logic \, using the framework of subminimal logics by A. Colacito, D. de Jongh and A. L. Vargas. In the course of it, the relationship between the two semantics in the respective frameworks is clarified. In addition, we introduce a sequent calculus for the investigated subsystem, and some proof-theoretic properties are established. Lastly, we formulate a new infinite class of subsystems of minimal logics.

Previous discussions of Robb’s work on space and time have offered a philosophical focus on causal interpretations of relativity theory or a historical focus on his use of non-Euclidean geometry, or else ignored altogether in discussions of relativity at Cambridge. In this paper I focus on how Robb’s work made contact with those same foundational developments in mathematics and with their applications. This contact with applications of new mathematical logic at Göttingen and Cambridge explains the transition from his electron research (...) to his treatment of relativity in 1911 and finally to the axiomatic presentation in 1914 in terms of postulates. At the heart of Robb’s physical optics was the model of the light cone. The model underwent a transition from a working mechanical model in the Maxwellian Cambridge sense of a pedagogical and research tool to the semantic model, in the logical, model-theoretic sense. Robb tracked this transition from the 19th- to the 20th-century conception with the earliest use of the term ‘model’ in the new sense. I place his cone models in a genealogy of similar models and use their evolution to track how Robb’s physical researches were informed by his interest in geometry, logic and the foundations of mathematics. (shrink)

Uses erotetic logic to model the courtroom objection "Asked and Answered!".

Light Linear Logic (LLL) and Intuitionistic Light Affine Logic (ILAL) are logics that capture polynomial time computation. It is known that every polynomial time function can be represented by a proof of these logics via the proofs-as-programs correspondence. Furthermore, there is a reduction strategy which normalizes a given proof in polynomial time. Given the latter polynomial time “weak” normalization theorem, it is natural to ask whether a “strong” form of polynomial time normalization theorem holds or not. (...) In this paper, we introduce an untyped term calculus, called Light Affine Lambda Calculus (λLA), which corresponds to ILAL. λLA is a bi-modal λ-calculus with certain constraints, endowed with very simple reduction rules. The main property of LALC is the polynomial time strong normalization: any reduction strategy normalizes a given λLA term in a polynomial number of reduction steps, and indeed in polynomial time. Since proofs of ILAL are structurally representable by terms of λLA, we conclude that the same holds for ILAL. (shrink)

The aim of this paper is to strengthen the point made by Horty about the relationship between reason holism and moral particularism. In the literature prima facie obligations have been considered as the only source of reason holism. I strengthen Horty’s point in two ways. First, I show that contrary-to-duties provide another independent support for reason holism. Next I outline a formal theory that is able to capture these two sources of holism. While in simple settings the proposed account coincides (...) with Horty’s one, this is not true in more complicated or “realistic” settings in which more than two norms collide. My chosen formalism is so-called input/output logic. A bottom-line example is introduced. It raises the issue of whether the conventional wisdom is right in assuming that normative reasons run parallel to epistemic ones. (shrink)

I urge return by the lights of logic and commonsense to a dialectical tabula rasa – according to which: (1) consciousness, in the ordinary pre-analytic sense of the term, is identified with P-consciousness, and “A-consciousness” is supplanted by suitably configured terms from its Blockian definition; (2) the supposedly fallacious Searlean argument for the view that a function of P-consciousness is to allow flexible and creative cognition is enthymematic and, when charitably specified, quite formidable.

There are still on-going debates on what exactly is wrong with Prior’s pathological “tonk.” In this article I argue, on the basis of categorical inferentialism, that two notions of inconsistency ought to be distinguished in an appropriate account of tonk; logic with tonk is inconsistent as the theory of propositions, and it is due to the fallacy of equivocation; in contrast to this diagnosis of the Prior’s tonk problem, nothing is actually wrong with tonk if logic is viewed as the (...) theory of proofs rather than propositions, and tonk perfectly makes sense in terms of the identity of proofs. Indeed, there is fully complete semantics of proofs for tonk, which allows us to link the Prior’s old philosophical idea with contemporary issues at the interface of categorical logic, computer science, and quantum physics, and thereby to expose commonalities between the laws of Reason and the laws of Nature, which are what logic and physics are respectively about. I conclude the article by articulating the ideas of categorical logical positivism and pluralistic unified science as its goal, including the unification of realist and antirealist conceptions of meaning by virtue of the categorical logical basis of metaphysics. (shrink)

The unique relation between logic and truth is crucial for understanding Fregean conception of logic. Frege has an insight that the nature of logic resides in the “truth“, which he finally locates in the assertoric-force of a sentence. Though Frege admits that assertoric-force is ineffable in ordinary language, he coins in his conceptual notation for such a force a much-disputed sign, i.e., judgment-stroke. In this paper, I will try to demonstrate that judgment-stroke is not adequate for the task its inventor (...) has assigned to it. Accordingly, it is misconceived and inconducive to clarify Frege’s vague insight into the protorelation. The mistake of judgment-stroke for the sign of assertoric-force has its root in Frege’s ignorance of the significant difference between “judgment” and assertion”, which will be elucidated at length in the light of Husserl’s theory of “doxic-modification“. In the end, based on a further elucidation of the activity of assertion, I will advance a tentative interpretation of the vague insight Frege has concerning the protorelation. (shrink)

논리적 귀추주의란 논리학의 형이상학적, 인식론적 예외성을 인정하지 않고, 논리학 또한 과학과 유사하게 귀추적으로 평가되어야 한다는 주장이다. 필자는 이 글에서, 고전논리학과 양진주의의 사례를 통해, 귀추주의가 성립하지 않음을 보일 것이다. 이러한 필자의 주장은 ‘이론적 폐쇄성’에 기초한다. 이론적 폐쇄성이란, 논리학 이론은 형식적인 연산체계뿐 아니라 논리철학적 주장을 포함하는데, 이러한 논리철학적 주장은 논리학을 평가하는 귀추적 기준을 함축한다는 것이다. 간단히 말해, 논리이론은 귀추적 평가기준을 포함하는 폐쇄적 구조를 갖기 때문에, 경쟁하는 논리이론을 평가하는 독립적 기준을 제시할 수 없다는 것이다. 물론, 이러한 귀추주의의 문제점을 필자가 처음 제시한 것은 아니다. (...) 귀추주의에 대한 기존의 비판과의 차이점은, 필자의 논의는 귀추주의의 문제를 ‘이론적 폐쇄성’이라는 논리학의 특성에 기초해서 제시한다는 것 그리고 그것에 기초해서 귀추주의자들의 가능한 반박에 대응한다는 것이다. (shrink)

Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no such thing as (...) a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language. (shrink)

Excerpt from Logic, Vol. 1: Deduction The present work aims at embracing a full course of Logic, both Formal and Inductive. In an introductory chapter, are set forth such doctrines of psychology as have a bearing on Logic, the nature of knowledge in general, and the classification of the sciences the intention being to avoid doctrinal digressions in the course of the work. Although preparatory to the under standing of what follows, this chapter may be passed over lightly on a (...) first perusal of the work. The part on Deduction contains the usual doctrines of the Syllogism, with the additions of Hamilton, and a full abstract of the novel and elaborate schemes of De Morgan and Boole. The Inductive portion comprises the methods of induc tive research, and all those collateral topics brought for ward by Mr. Mill, as part of the problem of Induction; various modifications being made in the manner of state ment, the order of topics, and the proportion of the hand ling. The greatest innovation is the rendering of Cause by the new doctrine called the Conservation, Persistence, or Correlation of Force. Mr. Mill's view of the relation of Deduction and Induc tion is fully adopted, as being the solution of the otherwise inextricable puzzle of the syllogism, and the means of giving unity and comprehensiveness to Logic. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Light version of DEMO for composing epistemic models, based on the code for the ESSLLI 2008 course on Dynamic Epistemic Logic (see http:// homepages.cwi.nl/~jve/courses/esslli08/) extended with vocabulary information [EWS10]. Factual change is also treated. The piece ends with some examples: the muddy children, and hat puzzles, dealing with the interaction of perception and change [Eijar].

Logical anti‐exceptionalism is the view that logic is not special, it is continuous with science. This continuity is typically understood in terms of the use of the abductive method in logical theory choice, with logical knowledge resulting from our choice of the theory best accounting for the data. In this paper, we argue for two related claims: (i) that this understanding of the continuity between logic and science faces considerable challenges; and (ii) that such challenges may be avoided by elaborating (...) the continuity of logic with science in terms of the “logic‐as‐models” approach. More specifically, we defend that logical theories should be seen in the lights of the “models‐as‐epistemic‐tools” approach, an approach to the nature of models in empirical science more closely connected with current scientific practice. The result is a version of logical anti‐exceptionalism opening new perspectives for the philosophical understanding of logic. (shrink)

This paper propounds a systematic examination of the link between the Knower Paradox and provability interpretations of modal logic. The aim of the paper is threefold: to give a streamlined presentation of the Knower Paradox and related results; to clarify the notion of a syntactical treatment of modalities; finally, to discuss the kind of solution that modal provability logic provides to the Paradox. I discuss the respective strength of different versions of the Knower Paradox, both in the framework of first-order (...) arithmetic and in that of modal logic with fixed point operators. It is shown that the notion of a syntactical treatment of modalities is ambiguous between a self-referential treatment and a metalinguistic treatment of modalities, and that these two notions are independent. I survey and compare the provability interpretations of modality respectively given by Skyrms, B. (1978, The Journal of Philosophy 75: 368–387) Anderson, C.A. (1983, The Journal of Philosophy 80: 338–355) and Solovay, R. (1976, Israel Journal of Mathematics 25: 287–304). I examine how these interpretations enable us to bypass the limitations imposed by the Knower Paradox while preserving the laws of classical logic, each time by appeal to a distinct form of hierarchy. (shrink)

What really makes the concepts of obligation or permission so important for practical philosophy? What if we could find a better concept, one that, despite the simplicity, could show itself as intuitive and rich as possible? Could justifications be used in common language and practice as a sign of ethical judgment and as a strong motive for action? In most scenarios, for example, it really doesn’t matter if a given action is obliged, permitted or forbidden, one may perform the action (...) as long as a justification for doing it is present. In this sense, the notion of justification seems to be more basic and powerful than other concepts used in the philosophical discourse. The existence of formal systems based on the epistemological side of justification, created by Artemov, led us primarily to think that justification could make the formal discourse much more accurate for ethics than the ones using deontological concepts. In the semantical and syntactical aspects, almost all of Artemov’s systems directly proved to be fruitful for ethical purposes. We also developed combinations between the standard deontic logic and logics of justification, resulting in what whe called the Logics of Normative Justification. These systems were able to change the object of the justification formulas and shed some light in ethics as a whole, normative and metaethics. Metaethics were a forgotten subject in formal ethics. We were also able to deal with some known problems in deontic logic, like the famous Ross’s paradox and the expressiveness of prima facie and all-things-considered obligations. (shrink)

For many recent readers of Hegel, Wilfrid Sellars’s 1956 London lectures on the “Myth of the Given” have signaled an important rapprochement between Hegelian and analytic traditions in philosophy. Here I want to explore the ideas of another philosopher, also active in London in the 1950s, who consciously pursued such a goal: John N. Findlay. The ideas that Findlay brought to Hegel—sometimes converging with, sometimes diverging from those of Sellars—had been informed by his earlier study of the Austrian philosopher Alexius (...) Meinong, and transformations of Meinong’s ideas by his student, the logician Ernst Mally. These ideas that Findlay found Hegel-friendly are ones that have had a particular bearing on more recent analytic modal metaphysics, especially via the work of Findlay’s own former student, Arthur Prior. Given this, we might not be surprised at the similarities between the type of actualist interpretation of modal logic that Prior offered in opposition to David Lewis’s variant on Leibnizian possibilism, and Hegel’s approach to the category of “Actuality” [Wirklichkeit] at the end of the Objective Logic of The Science of Logic. But the similarities, I suggest, do not end there, as elements of Hegel treatment of predication in the Subjective Logic parallel similar elements found in the work of Mally and, more recently, “modal actualists” such as Prior and Stalnaker. In this paper I explore some puzzling features of Hegel’s treatment of predication in the Subjective Logic from the point of view of the need for a logic for thought about the modally complex actual world, as Hegel conceived it. (shrink)

When my son Maxwell was a toddler, he did not believe he was ever an infant. This skepticism became manifest when he started identifying himself in photographs. Maxwell was accurate with photographs that were taken after age six months. But he dismissed earlier pictures as photographs of "BABIES".

Broadly speaking, two views of modernity are prevalent in contemporary debates. According to the first view, i.e. “modernization theory,” there is one single form of modernity, which is tantamount to liberal, capitalist modernity. The West has already and fully achieved modernity; non-Western societies have lagged behind and must simply catch up with the West. In contrast, according to the second view, “post-colonial theory,” there is no such thing as modernity. What the West erroneously calls “modernity” is nothing but a highly (...) parochial way of thought, and of economic and political organization, that developed by accident first in the West and then by the exercise of military violence or economic power was subsequently “universalized.” In this chapter, I argue that Hegel, read properly, provides a third conception of modernity, one which, contrary to the modernization theory, respects differences between societies, and yet, contrary to post-colonial theory, does not engage in dividing the human species into fundamentally different or incommensurate groups. I argue that Hegel’s theory of modernity must be sought at the conjunction of the Science of Logic (specifically the logic of the Concept) and the Philosophy of Right. I then elaborate on Hegel’s theory of modernity, thus construed. (shrink)

Throughout this century many philosophers and physicists have gone for thc ‘big ki11’ regarding tenses. They have tried to show via McTaggart’s paradox and special relativity that tcnscs arc logically and physically impossible, rcspcctivcly. Ncithcr attempt succccds, though as I argue, both lcavc their mark. In thc iirst two sections of thc paper I introduce some conceptual difficulties for the tensed theory of time. The next section then discusses the standing 0f tenses in light of special relativity, cspccially rcccnt (...) work by Stcin on thc topic. I argue that, Stcin’s possibility thcorcm notwithstanding, special relativity is inconsistent with any philosophicully interesting conception of tense. Finally, I search for help for tenses in the broader context of quantum theory, Lorcntzian interpretations 0f time dilation/length contraction, and gcncral relativistic spacctimcs. I suggest that these avenues d0 not provide tenses the home for which some have hoped. (shrink)

This book, written by one of the most distinguished of contemporary philosophers of mathematics, is a fully rewritten and updated successor to the author's earlier The Unprovability of Consistency. Its subject is the relation between provability and modal logic, a branch of logic invented by Aristotle but much disparaged by philosophers and virtually ignored by mathematicians. Here it receives its first scientific application since its invention. Modal logic is concerned with the notions of necessity and possibility. What George Boolos does (...) is to show how the concepts, techniques, and methods of modal logic shed brilliant light on the most important logical discovery of the twentieth century: the incompleteness theorems of Kurt Godel and the 'self-referential' sentences constructed in their proof. The book explores the effects of reinterpreting the notions of necessity and possibility to mean provability and consistency. (shrink)

ASSERTIONS ARE A SYMBOLIC FORM that exists only within species--specifically human language. Language, of course, allows for many other conventions of symbolic expression: greetings, exclamations, commands, exhortations, imprecations, interrogatives, and so forth. But assertions are unique in possessing, of themselves, a truth-value--that is to say, in being adjudicable as true or false. All other varieties of discourse are adjudicable as true or false by reason of assertions they presuppose, contain, or imply. But the assertion as such is what is directly (...) so adjudicable. (shrink)

In [7], a naive set theory is introduced based on a polynomial time logical system, Light Linear Logic (LLL). Although it is reasonably claimed that the set theory inherits the intrinsically polytime character from the underlying logic LLL, the discussion there is largely informal, and a formal justification of the claim is not provided sufficiently. Moreover, the syntax is quite complicated in that it is based on a non-traditional hybrid sequent calculus which is required for formulating LLL.In this paper, (...) we consider a naive set theory based on Intuitionistic Light Affine Logic (ILAL), a simplification of LLL introduced by [1], and call it Light Affine Set Theory (LAST). The simplicity of LAST allows us to rigorously verify its polytime character. In particular, we prove that a function over {0, 1}* is computable in polynomial time if and only if it is provably total in LAST. (shrink)

The barriers to responsiveness and the initiation of communication are the two key problems encountered by children with autism spectrum disorders. Prior interventions based on behavioral reinforcement have had an obvious effect on responsive communication but a weak effect on the initiation of communication. Based on psychological development theory, we designed ultra-light clay interventions involving hands-on production or multi-interaction around key concepts and themes, teaching children about basic concepts, relationships, and logic, making abstract knowledge concrete and experience. Two studies (...) showed that ultra-light clay intervention improved both the initiation of and response to communication among children with ASD, but that such improvements show a peer-generalization effect in initiation communication, not in responsive communication. These findings provide a set of ultra-light clay interventions for communication in children with ASD and suggest a relationship between endogenous interventions and the initiation of communication. (shrink)