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

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

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

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

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

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

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

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

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

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

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

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

We present a formal theory of contextuality for a set of random variables grouped into different subsets corresponding to different, mutually incompatible conditions. Within each context the random variables are jointly distributed, but across different contexts they are stochastically unrelated. The theory of contextuality is based on the analysis of the extent to which some of these random variables can be viewed as preserving their identity across different contexts when one considers all possible joint distributions imposed on the (...) entire set of the random variables. We illustrate the theory on three systems of traditional interest in quantum physics. These are systems of the Klyachko–Can–Binicioglu–Shumovsky-type, Einstein–Podolsky–Rosen–Bell-type, and Suppes–Zanotti–Leggett–Garg-type. Listed in this order, each of them is formally a special case of the previous one. For each of them we derive necessary and sufficient conditions for contextuality while allowing for experimental errors and contextual biases or signaling. Based on the same principles that underly these derivations we also propose a measure for the degree of contextuality and compute it for the three systems in question. (shrink)

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

On March 28, 2008, the Association for Computer Machinery's Special Interest Group for Computers and Society conferred the 2008 Making a Difference Award on Dr. Jim Thatcher. Dr. Thatcher's work in the area of assistive technologies has spanned four decades, and has enabled many blind and visually impaired individuals throughout the world to expand their use of computers in their daily lives. This summer, I had the opportunity to talk with Dr. Thatcher about his extraordinary career and (...) this acknowledgement he has received from the ACM. --- MN. (shrink)

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

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

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

In lieu of an abstract, here is a brief excerpt of the content:526 BOOK REVIEWS learned how to integrate satisfaction into love (91, 113, 119, 124, 136, 186, 192, 198; cp. 37). Indeed, it is Aquinas's gradual integration of satisfaction as a motive for the Incarnation subordinate to love (166) that enables Aquinas aptly to locate satisfaction within the Christian life (cp. 47, 136, 142, 166) and accounts for Cessario's subtitle. Third, I am not clear on Ccssario's (or my own!) (...) stand on how we ought sort out the respects in which Thomas's and our perspectives merge (cp. xiv). In his conclusion Cessario is cautious, suggesting that "if the term ' satisfaction ' cannot be restored to current usage, then certainly the substance of Saint Thomas's understanding of satisfaction can and should be." (256). But, given Cessario's own persuasive display of the way satisfactio pervades the very texture of Aquinas's theology, I am not sure we can have the "substance" without the term-or vice-versa. Clearly Cessario thinks the merging is substantive. But he himself teaches us that supporting this claim involves supporting claims for exegetical, liturgical ecclesial, and other practices. Those of us who think that satisfactio is a description rather than "the guiding model or key notion" (xx, my emphasis) for thinking Christ crucified will need to see such support worked out in relation to the competing sotcriologies Cessario mentions (267) as well as ecumenical discussions of justification which were understandably outside the scope of this book (151). But a single book can only accomplish a single thing-and this book clearly succeeds in showing us how Thomas can be brought to bear on contemporary theological issues. All students of Aquinas and/or soteriology ought to read this text. Loyola College in Maryland Baltimore, Maryland JAMES J. BUCKLEY How We Know. Edited by MICHAEr, SHAFTO. San 1!1rancisco: Harper & Row. 1985. Pp. xv and 171. $14.95. How We Know is a collection of six papers delivered in 1984 at the twentieth Nobel Conference, held at Gustavus Adolphus College in St. Peter, Minnesota. Two words that came to my mind as I worked through the papers were "fascinating" and "frightening". The Conference dealt with cognitive science and a number of the authors have come up with interesting, provocative, and often orig'inal observations about how the human mind operates when it hies to remember and to understand. In his Introduction Michael Shafto, who is a Scientific Officer in the Personnel and Training Research Programs of the United States Office of Naval Research, notes that cognitive science as the work of a coalition of thinkers is barely a decade old, and he reminds the reader that the methods BOOK REVIEWS 59.7 of cognitive science are those of experimental psychology, physiology, and computer science. Though the Confermce was supposedly aimed at nonspecialists, the reader unfamiliar with cognitive science might find some of the papers a bit difficult. Certainly the backgrounds of the authors are very impressive. The first four papers in the collection are by Gerald Edelman, Brenda Milner, Roger C. Schank, and Herbert A. Simon respectively. Edelman is the Director and Scientific Chairman of the Neurosciences Research Program at Rockefeller University; Milner is Professor of Psychology in the Department of Neurology at McGill University: Schank is Professor and Chairman of the Computer Science Department at Yale; and Simon is Professor of Computer Science and Psychology at Carnegie-Mellon University. Calling his theory of the hum:m brain "Neural Darwinism," Edelman claims that the brain is Darwinian. Taking Darwin's theory of natural selections and applying it to the brain, Edelman argues that during ontogeny and behavior those groups of neurons are chosen that are adaptive for the organism. Milner explores the neurophysiological basis of that special moment when a new experience affects the brain. Insisting that memory is not merely a passive reproi!ucer but rather actively selective, Milner, relying on her studies of patients. with loss of memory, suggests that the frontal lobes of the brain hnve a special role in memory. Interested in the interface of mcmory anil percr-ption, Schank notes that, because human memory is dynamic and the memory of the computer is not, the -programming of the intelligent functions of... (shrink)

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

This book stands at the intersection of two topics: the decidability and computational complexity of hybrid logics, and the deductive systems designed for them. Hybrid logics are here divided into two groups: standard hybrid logics involving nominals as expressions of a separate sort, and non-standard hybrid logics, which do not involve nominals but whose expressive power matches the expressive power of binder-free standard hybrid logics.The original results of this book are split into two parts. This division reflects the division of (...) the book itself. The first type of results concern model-theoretic and complexity properties of hybrid logics. Since hybrid logics which we call standard are quite well investigated, the efforts focused on hybrid logics referred to as non-standard in this book. Non-standard hybrid logics are understood as modal logics with global counting operators ) whose expressive power matches the expressive power of binder-free standard hybrid logics. The relevant results comprise: 1. Establishing a sound and complete axiomatization for the modal logic K with global counting operators ), which can be easily extended onto other frame classes, 2. Establishing tight complexity bounds, namely NExpTime-completeness for the modal logic with global counting operators defined over the classes of arbitrary, reflexive, symmetric, serial and transitive frames ), MT), MD), MB), MK4) with numerical subscripts coded in binary. Establishing the exponential-size model property for this logic defined over the classes of Euclidean and equivalential frames ), MS5).Results of the second type consist of designing concrete deductive systems for standard and non-standard hybrid logics. More precisely, they include: 1. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for a rich class of binder-free standard hybrid logics. An interesting feature of indicated calculi is the nonbranching character of the rule, 2. Devising a prefixed and an internalized tableau calculi which are sound, complete and terminating for non-standard hybrid logics. The internalization technique applied to a tableau calculus for the modal logic with global counting operators is novel in the literature, 3. Devising the first hybrid algorithm involving an inequality solver for modal logics with global counting operators. Transferring the arithmetical part of reasoning to an inequality solver turned out to be sufficient in ensuring termination.The book is directed to philosophers and logicians working with modal and hybrid logics, as well as to computer scientists interested in deductive systems and decision procedures for logics. Extensive fragments of the first part of the book can also serve as an introduction to hybrid logics for wider audience interested in logic.The content of the book is situated in the areas of formal logic and theoretical computer science with some elements of the theory of computational complexity. (shrink)

BackgroundWith the emergence of Brain Computer Interfaces, clinicians have been facing a new group of patients with severe acquired brain injury who are unable to show any behavioral sign of consciousness but respond to active neuroimaging or electrophysiological paradigms. However, even though well documented, there is still no consensus regarding the nomenclature for this clinical entity.ObjectivesThis systematic review aims to 1) identify the terms used to indicate the presence of this entity through the years, and 2) promote an informed (...) discussion regarding the rationale for these names and the best candidates to name this fascinating disorder.MethodsThe Disorders of Consciousness Special Interest Group of the International Brain Injury Association launched a search on Pubmed and Google scholar following PRISMA guidelines to collect peer-reviewed articles and reviews on human adults published in English between 2006 and 2021.ResultsThe search launched in January 2021 identified 4,089 potentially relevant titles. After screening, 1,126 abstracts were found relevant. Finally, 161 manuscripts were included in our analyses. Only 58% of the manuscripts used a specific name to discuss this clinical entity, among which 32% used several names interchangeably throughout the text. We found 25 different names given to this entity. The five following names were the ones the most frequently used: covert awareness, cognitive motor dissociation, functional locked-in, non-behavioral MCS and higher-order cortex motor dissociation.ConclusionSince 2006, there has been no agreement regarding the taxonomy to use for unresponsive patients who are able to respond to active neuroimaging or electrophysiological paradigms. Developing a standard taxonomy is an important goal for future research studies and clinical translation. We recommend a Delphi study in order to build such a consensus. (shrink)

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

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

Computational implementations are special relations between what is computed and what computes it. Though the word “isomorphism” appears in philosophical discussions about the nature of implementations, it is used only metaphorically. Here we discuss computation in the precise language of abstract algebra. The capability of emulating computers is the defining property of computers. Such a chain of emulation is ultimately grounded in an algebraic object, a full transformation semigroup. Mathematically, emulation is defined by structure preserving maps (morphisms) between semigroups. (...) These are systematic, very special relationships, crucial for defining implementation. In contrast, interpretations are general functions with no morphic properties. They can be used to derive semantic content from computations. Hierarchical structure imposed on a computational structure plays a similar semantic role. Beyond bringing precision into the investigation, the algebraic approach also sheds light on the interplay between time and computation. (shrink)

"Dimensions of Shared Agency" investigates the way in which standard philosophical accounts have been dealing with the issue of collective actions. In particular, the book focuses on the 'Big Five' of analytical social ontology and their accounts of shared/collective intentions and actions. Through systematic readings of different positions in the debate, the author proposes original ways of analyzing and classifying current theories of shared agency according to whether they advance a member-level or a group-level account of shared agency. While (...) member-level accounts are theories of shared agency based on individuals' attitudes and actions, group-level accounts give attention to the group of individuals considered as a whole, i.e., as an agent itself. Criticism arises against the idea that the Big Five have proposed stable group-level accounts suitable for explaining the case of shared agency as a group-level phenomenon. The widespread tendency in the debate is to endorse a perspective called holistic individualism, which maintains that high-level explanations are objective even though social facts are ontologically reducible to facts about individuals. Lasagni argues that as long as holistic individualism is held, the GLA is reducible to the MLA because holistic individualism upholds ontological individualism based on a deep individualistic premise, fixing the special status of individual agents as natural persons. The premise makes the claim to treat groups as agents contradictory to the general framework of the theory. This book profiles an alternative interpretation according to which agency should be considered as a functional kind, which is equally instantiated by different systems, such as individual human beings and organized social groups. In this way, the author claims, the reduction of the social can be avoided. "Dimensions of Shared Agency" will be of interest to doctoral students, researchers, and scholars interested in social ontology and the philosophy of the social sciences. It can also be utilised as supplementary reading or an introduction to philosophy students and scholars who are first approaching the philosophy of collective intentionality and shared agency. (shrink)

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

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

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

Over recent decades, computer simulations have become a common tool among practitioners of the social sciences. They have been utilized to study such diverse phenomena as the integration and segregation of different racial groups, the emergence and evolution of friendship networks, the spread of gossip, fluctuations of housing prices in an area, the transmission of social norms, and many more. Philosophers of science and others interested in the methodological status of these studies have identified a number of distinctive virtues of (...) the use of computer simulations. For instance, it has been generally appreciated that as simulations require the formulation of an explicit algorithm, they foster precision and clarity about whatever conceptual issues are involved in the study. The value of computer simulations as a heuristic tool for developing hypotheses, models, and theories has also been recognized, as has been the fact that they can serve as a substitute for real experiments. This is especially useful in the social domain, given that human beings cannot be freely manipulated at the discretion of the experimenter . However, the main virtue of computer simulations is generally believed to be that they are able to deal with the complexities that arise when many elements interact in a highly dynamic system and which often evade an exact formal analysis. (shrink)

Computer simulation is shown to be philosophically interesting because it introduces a qualitatively new methodology for theory construction in science different from the conventional two components of "theory" and "experiment and/or observation". This component is "experimentation with theoretical models." Two examples from the physical sciences are presented for the purpose of demonstration but it is claimed that the biological and social sciences permit similar theoretical model experiments. Furthermore, computer simulation permits theoretical models for the evolution of physical systems (...) which use cellular automata rather than differential equations as their syntax. The great advantages of the former are indicated. (shrink)

There have been two major lines of research aimed at capturing resource-bounded players in game theory. The first, initiated by Rubinstein (), charges an agent for doing costly computation; the second, initiated by Neyman (), does not charge for computation, but limits the computation that agents can do, typically by modeling agents as finite automata. We review recent work on applying both approaches in the context of decision theory. For the first approach, we take the objects of (...) choice in a decision problem to be Turing machines, and charge players for the “complexity” of the Turing machine chosen (e.g., its running time). This approach can be used to explain well-known phenomena like first-impression-matters biases (i.e., people tend to put more weight on evidence they hear early on) and belief polarization (two people with different prior beliefs, hearing the same evidence, can end up with diametrically opposed conclusions) as the outcomes of quite rational decisions. For the second approach, we model people as finite automata, and provide a simple algorithm that, on a problem that captures a number of settings of interest, provably performs optimally as the number of states in the automaton increases. (shrink)

This Special Issue addresses a range of educational issues linked to main themes from our 2019 book The Emergence of Complexity: Rethinking Education as a Social Science. This book elaborated two major theses that raise fundamental questions for philosophy of education. First, that learning by groups is typically a distinctive kind of learning that is not reducible to learning by individuals. Second, that a degree of holism, as against a focus on individuals, is essential for achieving a convincing understanding (...) of this distinctive type of group learning. These two theses are of direct interest to philosophy of education since they challenges the resources of received theories of learning. Yet this kind of group learning characterises the vast bulk of human learning situations that occur outside of formal education systems. In this Special Issue introductory article we, firstly, introduce some basic principles of complexity theory, and demonstrate that, together with the concept of a ‘co-present group’ (between 2 and about 12 individuals), these ideas offer develop novel understandings of the distinctive learning that occurs within such groups. Secondly, we outline and illustrate with further examples the main features of co-present groups. Thirdly, we consolidate our conceptual work by showing five ways in which our account of group learning serves to refurbish the concept of ‘learning’. (shrink)

The fundamental question in reverse mathematics is to determine which set existence axioms are required to prove particular theorems of mathematics. In addition to being interesting in their own right, answers to this question have consequences in both effective mathematics and the foundations of mathematics. Before discussing these consequences, we need to be more specific about the motivating question.Reverse mathematics is useful for studying theorems of either countable or essentially countable mathematics. Essentially countable mathematics is a vague term that is (...) best explained by an example. Complete separable metric spaces are essentially countable because, although the spaces may be uncountable, they can be understood in terms of a countable basis. Simpson gives the following list of areas which can be analyzed by reverse mathematics: number theory, geometry, calculus, differential equations, real and complex analysis, combinatorics, countable algebra, separable Banach spaces, computability theory, and the topology of complete separable metric spaces. Reverse mathematics is less suited to theorems of abstract functional analysis, abstract set theory, universal algebra, or general topology.Section 2 introduces the major subsystems of second order arithmetic used in reverse mathematics: RCA0, WKL0, ACA0, ATR0 and – CA0. Sections 3 through 7 consider various theorems of ordered group theory from the perspective of reverse mathematics. Among the results considered are theorems on ordered quotient groups, groups and semigroup conditions which imply orderability, the orderability of free groups, Hölder's Theorem, Mal'tsev's classification of the order types of countable ordered groups. (shrink)

ABSTRACT I argue that this examination and appreciation for the shift to abductive reasoning should be extended to the intersection of neuroscience and novel brain-computer interfaces too. This paper highlights the implications of applying abductive reasoning to personalized implantable neurotechnologies. Then, it explores whether abductive reasoning is sufficient to justify insurance coverage for devices absent widespread clinical trials, which are better applied to one-size-fits-all treatments. INTRODUCTION In contrast to the classic model of randomized-control trials, often with a large number of (...) subjects enrolled, precision medicine attempts to optimize therapeutic outcomes by focusing on the individual.[i] A recent publication highlights the strengths and weakness of both traditional evidence-based medicine and precision medicine.[ii] Plus, it outlines a tension in the shift from evidence-based medicine’s inductive reasoning style (the collection of data to postulate general theories) to precision medicine’s abductive reasoning style (the generation of an idea from the limited data available).[iii] The paper’s main example is the application of precision medicine for the treatment of cancer.[iv] I argue that this examination and appreciation for the shift to abductive reasoning should be extended to the intersection of neuroscience and novel brain-computer interfaces too. As the name suggests, brain-computer interfaces are a significant advancement in neurotechnology that directly connects someone’s brain to external or implanted devices.[v] Among the various kinds of brain-computer interfaces, adaptive deep brain stimulation devices require numerous personalized adjustments to their settings during the implantation and computation stages in order to provide adequate relief to patients with treatment-resistant disorders. What makes these devices unique is how adaptive deep brain stimulation integrates a sensory component to initiate the stimulation. While not commonly at the level of sophistication as self-supervising or generative large language models,[vi] they currently allow for a semi-autonomous form of neuromodulation. This paper highlights the implications of applying abductive reasoning to personalized implantable neurotechnologies. Then, it explores whether abductive reasoning is sufficient to justify insurance coverage for devices absent widespread clinical trials, which are better applied to one-size-fits-all treatments.[vii] ANALYSIS I. The State of Precision Medicine in Oncology and the Epistemological Shift While a thorough overview of precision medicine for the treatment of cancer is beyond the scope of this article, its practice can be roughly summarized as identifying clinically significant characteristics a patient possesses (e.g., genetic traits) to land on a specialized treatment option that, theoretically, should benefit the patient the most.[viii] However, in such a practice of stratification patients fall into smaller and smaller populations and the quality of evidence that can be applied to anyone outside these decreases in turn.[ix] As inductive logic helps to articulate, the greater the number of patients that respond to a particular therapy the higher the probability of its efficacy. By straying from this logical framework, precision medicine opens the treatment of cancer to more uncertainty about the validity of these approaches to the resulting disease subcategories.[x] Thus, while contemporary medical practices explicitly describe some treatments as “personalized”, they ought not be viewed as inherently better founded than other therapies.[xi] A relevant contemporary case of precision medicine out of Norway focuses on the care of a patient with cancer between the ventricles of the heart and esophagus, which had failed to respond to the standard regimen of therapies over four years.[xii] In a last-ditch effort, the patient elected to pay out-of-pocket for an experimental immunotherapy (nivolumab) at a private hospital. He experienced marked improvements and a reduction in the size of the tumor. Understandably, the patient tried to pursue further rounds of nivolumab at a public hospital. However, the hospital initially declined to pay for it given the “lack of evidence from randomised clinical trials for this drug relating to this [patient’s] condition.”[xiii] In rebuttal to this claim, the patient countered that he was actually similar to a subpopulation of patients who responded in “open‐label, single arm, phase 2 studies on another immune therapy drug” (pembrolizumab).[xiv] Given this interpretation of the prior studies and the patient’s response, further rounds of nivolumab were approved. Had the patient not had improvements in the tumor’s size following a round of nivolumab, then pembrolizumab’s prior empirical evidence in isolation would have been insufficient, inductively speaking, to justify his continued use of nivolumab.[xv] The case demonstrates a shift in reasoning from the traditional induction to abduction. The phenomenon of ‘cancer improvement’ is considered causally linked to nivolumab and its underlying physiological mechanisms.[xvi] However, “the weakness of abductions is that there may always be some other better, unknown explanation for an effect. The patient may for example belong to a special subgroup that spontaneously improves, or the change may be a placebo effect. This does not mean, however, that abductive inferences cannot be strong or reasonable, in the sense that they can make a conclusion probable.”[xvii] To demonstrate the limitations of relying on the abductive standard in isolation, commentators have pointed out that side effects in precision medicine are hard to rule out as being related to the initial intervention itself unless trends from a group of patients are taken into consideration.[xviii] As artificial intelligence (AI) assists the development of precision medicine for oncology, this uncertainty ought to be taken into consideration. The implementation of AI has been crucial to the development of precision medicine by providing a way to combine large patient datasets or a single patient with a large number of unique variables with machine learning to recommend matches based on statistics and probability of success upon which practitioners can base medical recommendations.[xix] The AI is usually not establishing a causal relationship[xx] – it is predicting. So, as AI bleeds into medical devices, like brain-computer interfaces, the same cautions about using abductive reasoning alone should be carried over. II. Responsive Neurostimulation, AI, and Personalized Medicine Like precision medicine in cancer treatment, computer-brain interface technology similarly focuses on the individual patient through personalized settings. In order to properly expose the intersection of AI, precision medicine, abductive reasoning, and implantable neurotechnologies, the descriptions of adaptive deep brain stimulation systems need to deepen.[xxi] As a broad summary of adaptive deep brain stimulation, to provide a patient with the therapeutic stimulation, a neural signal, typically referred to as a local field potential,[xxii] must first be detected and then interpreted by the device. The main adaptive deep brain stimulation device with premarket approval, the NeuroPace Responsive Neurostimulation system, is used to treat epilepsy by detecting and storing “programmer-defined phenomena.”[xxiii] Providers can optimize the detection settings of the device to align with the patient’s unique electrographic seizures as well as personalize the reacting stimulation’s parameters.[xxiv] The provider adjusts the technology based on trial and error. One day machine learning algorithms will be able to regularly aid this process in myriad ways, such as by identifying the specific stimulation settings a patient may respond to ahead of time based on their electrophysiological signatures.[xxv] Either way, with AI or programmers, adaptive neurostimulation technologies are individualized and therefore operate in line with precision medicine rather than standard treatments based on large clinical trials. Contemporary neurostimulation devices are not usually sophisticated enough to be prominent in AI discussions where the topics of neural networks, deep learning, generative models, and self-attention dominate the conversation. However, implantable high-density electrocorticography arrays (a much more sensitive version than adaptive deep brain stimulation systems use) have been used in combination with neural networks to help patients with neurologic deficits from a prior stroke “speak” through a virtual avatar.[xxvi] In some experimental situations, algorithms are optimizing stimulation parameters with increasing levels of independence.[xxvii] An example of neurostimulation that is analogous to the use of nivolumab in Norway surrounds a patient in the United States who was experiencing both treatment-resistant OCD and temporal lobe epilepsy.[xxviii]Given the refractory nature of her epilepsy, implantation of an adaptive deep brain stimulation system was indicated. As a form of experimental therapy, her treatment-resistant OCD was also indicated for the off-label use of an adaptive deep brain stimulation set-up. Another deep brain stimulation lead, other than the one implanted for epilepsy, was placed in the patient’s right nucleus accumbens and ventral pallidum region given the correlation these nuclei had with OCD symptoms in prior research. Following this, the patient underwent “1) ambulatory, patient-initiated magnet-swipe storage of data during moments of obsessive thoughts; (2) lab-based, naturalistic provocation of OCD-related distress (naturalistic provocation task); and (3) lab-based, VR [virtual reality] provocation of OCD-related distress (VR provocation task).”[xxix] Such signals were used to identify when to deliver the therapeutic stimulation in order to counter the OCD symptoms. Thankfully, following the procedure and calibration the patient exhibited marked improvements in their OCD symptoms and recently shared her results publicly.[xxx] In both cases, there is a similar level of abductive justification for the efficacy of the delivered therapy. In the case study in which the patient was treated with adaptive deep brain stimulation, they at least had their neural activity tested in various settings to determine the optimum parameters for treatment to avoid them being based on guesswork. Additionally, the adaptive deep brain stimulation lead was already placed before the calibration trials were conducted, meaning that the patient had already taken on the bulk of the procedural risk before the efficacy could be determined. Such an efficacy test could have been replicated in the first patient’s cancer treatment, had it been biopsied and tested against the remaining immunotherapies in vitro. Yet, in the case of cancer with few options, one previous dose of a drug that appeared to work on the patient may justify further doses. However, as the Norwegian case presents, corroboration with known responses to a similar drug (from a clinical trial) could be helpful to validate the treatment strategy. (It should be noted that both patients were resigned to these last resort options regardless of the efficacy of treatment.) There are some elements of inductive logic seen with adaptive deep brain stimulation research in general. For example, abductively the focus could be that patient X’s stimulation parameters are different from patient Y’s and patient Z’s. In contrast, when grouped as subjects who obtained personalized stimulation, patients X, Y, and Z demonstrate an inductive aspect to this approach’s safety and/or efficacy. The OCD case holds plenty of abductive characteristics in line with precision medicine’s approach to treating cancer and as more individuals try the method, there will be additional data. With the gradual integration of AI into brain-computer interfaces in the name of efficacy, this reliance on abduction will continue, if not grow, over time. Moving forward, if a responsive deep brain stimulation treatment is novel and individualized (like the dose of nivolumab) and there is some other suggestion of efficacy (like clinical similarities to other patients in the literature), then it may justify insurance coverage for the investigative intervention, absent other unrelated reasons to deny it. III. Ethical Implications and Next Steps While AI’s use in oncology and neurology is not yet as prominent as its use in other fields (e.g., radiology), it appears to be on the horizon for both.[xxxi] AI can be found in both the functioning of the neurotechnologies as well as the implementation of precision medicine. The increasing use of AI may serve to further individualize both oncologic and neurological therapies. Given these implications and the handful of publications cited in this article, it is important to have a nuanced evaluation of how these treatments, which heavily rely on abductive justification, ought to be managed. The just use an abductive approach may be difficult as AI infused precision medicine is further pursued. At baseline, such technology relies on a level of advanced technology literacy among the general public and could exclude populations who lack access to basic technological infrastructure or know-how from participation.[xxxii] Even among nations with adequate infrastructure, as more patients seek out implantable neurotechnologies, which require robust healthcare resources, the market will favor patient populations that can afford this complex care.[xxxiii] If patients already have the means to pay for an initial dose/use of a precision medicine product out of pocket, should insurance providers be required to cover subsequent treatments?[xxxiv] That is, if a first dose of a cancer drug or a deep brain stimulator over its initial battery life is successful, patients may feel justified in having the costs of further treatments covered. The Norwegian patient’s experience implies there is a precedent for the idea that some public insurance companies ought to cover successful cancer therapies, however, insurance companies may not all see themselves as obligated to cover neurotechnologies that rely on personalized settings or that are based on precision/abductive research more than on clinical trials. CONCLUSION The fact that the cases outlined above rely on abductive style of reasoning implies that there may not be as strong a justification for coverage by insurance, as they are both experimental and individualized, when compared to the more traditional large clinical trials in which groups have the same or a standardized protocol (settings/doses). If a study is examining the efficacy of a treatment with a large cohort of patients or with different experimental groups/phases, insurance companies may conclude that the resulting symptom improvements are more likely to be coming from the devices themselves. A preference for inductive justification may take priority when ruling in favor of funding someone’s continued use of an implantable neurostimulator. There are further nuances to this discussion surrounding the classifications of these interventions as research versus clinical care that warrant future exploration, since such a distinction is more of a scale[xxxv] than binary and could have significant impacts on the “right-to-try” approach to experimental therapies in the United States.[xxxvi] Namely, given the inherent limitations of conducting large cohort trials for deep brain stimulation interventions on patients with neuropsychiatric disorders, surgically innovative frameworks that blend abductive and inductive methodologies, like with sham stimulation phases, have traditionally been used.[xxxvii] Similarly, for adaptive brain-computer interface systems, if there are no large clinical trials and instead only publications that demonstrate that something similar worked for someone else, then, in addition to the evidence that the first treatment/dose worked for the patient in question, the balance of reasoning would be valid and arguably justify insurance coverage. As precision approaches to neurotechnology become more common, frameworks for evaluating efficacy will be crucial both for insurance coverage and for clinical decision making. ACKNOWLEDGEMENT This article was originally written as an assignment for Dr. Francis Shen’s “Bioethics & AI” course at Harvard’s Center for Bioethics. I would like to thank Dr. Shen for his comments as well as my colleagues in the Lázaro-Muñoz Lab for their feedback. - [i] Jonathan Kimmelman and Ian Tannock, “The Paradox of Precision Medicine,” Nature Reviews. Clinical Oncology 15, no. 6 (June 2018): 341–42, https://doi.org/10.1038/s41571-018-0016-0. [ii] Henrik Vogt and Bjørn Hofmann, “How Precision Medicine Changes Medical Epistemology: A Formative Case from Norway,” Journal of Evaluation in Clinical Practice 28, no. 6 (December 2022): 1205–12, https://doi.org/10.1111/jep.13649. [iii] David Barrett and Ahtisham Younas, “Induction, Deduction and Abduction,” Evidence-Based Nursing 27, no. 1 (January 1, 2024): 6–7, https://doi.org/10.1136/ebnurs-2023-103873. [iv] Vogt and Hofmann, “How Precision Medicine Changes Medical Epistemology,” 1208. [v] Wireko Andrew Awuah et al., “Bridging Minds and Machines: The Recent Advances of Brain-Computer Interfaces in Neurological and Neurosurgical Applications,” World Neurosurgery, May 22, 2024, S1878-8750(24)00867-2, https://doi.org/10.1016/j.wneu.2024.05.104. [vi] Mark Riedl, “A Very Gentle Introduction to Large Language Models without the Hype,” Medium (blog), May 25, 2023, https://mark-riedl.medium.com/a-very-gentle-introduction-to-large-language-models-without-the-hype-5 f67941fa59e. [vii] David E. Burdette and Barbara E. Swartz, “Chapter 4 - Responsive Neurostimulation,” in Neurostimulation for Epilepsy, ed. Vikram R. Rao (Academic Press, 2023), 97–132, https://doi.org/10.1016/B978-0-323-91702-5.00002-5. [viii] Kimmelman and Tannock, 2018. [ix] Kimmelman and Tannock, 2018. [x] Simon Lohse, “Mapping Uncertainty in Precision Medicine: A Systematic Scoping Review,” Journal of Evaluation in Clinical Practice 29, no. 3 (April 2023): 554–64, https://doi.org/10.1111/jep.13789. [xi] Kimmelman and Tannock, “The Paradox of Precision Medicine.” [xii] Vogt and Hofmann, 1206. [xiii] Vogt and Hofmann, 1206. [xiv] Vogt and Hofmann, 1206. [xv] Vogt and Hofmann, 1207. [xvi] Vogt and Hofmann, 1207. [xvii] Vogt and Hofmann, 1207. [xviii] Vogt and Hofmann, 1210. [xix] Mehar Sahu et al., “Chapter Three - Artificial Intelligence and Machine Learning in Precision Medicine: A Paradigm Shift in Big Data Analysis,” in Progress in Molecular Biology and Translational Science, ed. David B. Teplow, vol. 190, 1 vols., Precision Medicine (Academic Press, 2022), 57–100, https://doi.org/10.1016/bs.pmbts.2022.03.002. [xx] Stefan Feuerriegel et al., “Causal Machine Learning for Predicting Treatment Outcomes,” Nature Medicine 30, no. 4 (April 2024): 958–68, https://doi.org/10.1038/s41591-024-02902-1. [xxi] Sunderland Baker et al., “Ethical Considerations in Closed Loop Deep Brain Stimulation,” Deep Brain Stimulation 3 (October 1, 2023): 8–15, https://doi.org/10.1016/j.jdbs.2023.11.001. [xxii] David Haslacher et al., “AI for Brain-Computer Interfaces,” 2024, 7, https://doi.org/10.1016/bs.dnb.2024.02.003. [xxiii] Burdette and Swartz, “Chapter 4 - Responsive Neurostimulation,” 103–4; “Premarket Approval (PMA),” https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfpma/pma.cfm?id=P100026. [xxiv] Burdette and Swartz, “Chapter 4 - Responsive Neurostimulation,” 104. [xxv] Burdette and Swartz, 126. [xxvi] Sean L. Metzger et al., “A High-Performance Neuroprosthesis for Speech Decoding and Avatar Control,” Nature 620, no. 7976 (August 2023): 1037–46, https://doi.org/10.1038/s41586-023-06443-4. [xxvii] Hao Fang and Yuxiao Yang, “Predictive Neuromodulation of Cingulo-Frontal Neural Dynamics in Major Depressive Disorder Using a Brain-Computer Interface System: A Simulation Study,” Frontiers in Computational Neuroscience 17 (March 6, 2023), https://doi.org/10.3389/fncom.2023.1119685; Mahsa Malekmohammadi et al., “Kinematic Adaptive Deep Brain Stimulation for Resting Tremor in Parkinson’s Disease,” Movement Disorders 31, no. 3 (2016): 426–28, https://doi.org/10.1002/mds.26482. [xxviii] Young-Hoon Nho et al., “Responsive Deep Brain Stimulation Guided by Ventral Striatal Electrophysiology of Obsession Durably Ameliorates Compulsion,” Neuron 0, no. 0 (October 20, 2023), https://doi.org/10.1016/j.neuron.2023.09.034. [xxix] Nho et al. [xxx] Nho et al.; Erik Robinson, “Brain Implant at OHSU Successfully Controls Both Seizures and OCD,” OHSU News, accessed March 3, 2024, https://news.ohsu.edu/2023/10/25/brain-implant-at-ohsu-successfully-controls-both-seizures-and-ocd. [xxxi] Awuah et al., “Bridging Minds and Machines”; Haslacher et al., “AI for Brain-Computer Interfaces.” [xxxii] Awuah et al., “Bridging Minds and Machines.” [xxxiii] Sara Green, Barbara Prainsack, and Maya Sabatello, “The Roots of (in)Equity in Precision Medicine: Gaps in the Discourse,” Personalized Medicine 21, no. 1 (January 2024): 5–9, https://doi.org/10.2217/pme-2023-0097. [xxxiv] Green, Prainsack, and Sabatello, 7. [xxxv] Robyn Bluhm and Kirstin Borgerson, “An Epistemic Argument for Research-Practice Integration in Medicine,” The Journal of Medicine and Philosophy: A Forum for Bioethics and Philosophy of Medicine 43, no. 4 (July 9, 2018): 469–84, https://doi.org/10.1093/jmp/jhy009. [xxxvi] Vijay Mahant, “‘Right-to-Try’ Experimental Drugs: An Overview,” Journal of Translational Medicine 18 (June 23, 2020): 253, https://doi.org/10.1186/s12967-020-02427-4. [xxxvii] Michael S. Okun et al., “Deep Brain Stimulation in the Internal Capsule and Nucleus Accumbens Region: Responses Observed during Active and Sham Programming,” Journal of Neurology, Neurosurgery & Psychiatry 78, no. 3 (March 1, 2007): 310–14, https://doi.org/10.1136/jnnp.2006.095315. (shrink)

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

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

In the present study we investigated the role of channel characteristics with regard to gender role portrayals in television advertisements. Drawing on cultivation theory and social cognitive theory, we investigated six key variables in this line of research. We sampled a total of N = 1022 advertisements from four Austrian television channels: a public service channel, a commercial channel, and one commercial special interest channel for men and for women, respectively. Our results replicate well-known stereotypic gender (...) role portrayals prevalent in television advertisements. The public service channel and the private channel did not differentiate from each other with regards to gender stereotyping. We found that a channel with a female target group aired advertisements containing the same or even amplified stereotypes compared to a male channel. The potential negative effects of stereotypic gender role portrayals in television advertisements are discussed. (shrink)

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

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

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

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

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

The explanatory power of logic is vast and therefore it has proved a valuable tool for many disciplines, including the building-blocks of cognitive science, such as philosophy, computer science, mathematics, artificial intelligence, and linguistics. Logic has a great track record in providing interesting insights by means of formalization, and as such it is very useful in disambiguating psychological theories. Logically formalized cognitive theories are not only the source of unequivocal experimental hypotheses, but they also lend themselves naturally to computational modeling. (...) Most importantly, modern logic has at its service a rich variety of tools to assess and compare such psychological theories. This toolbox can be utilized in evaluating cognitive models along the following dimensions:logical relationships, for example, incompatibility or identity of models;explanatory power, for example, what can be expressed by means of a model?computational plausibility, for example, a. (shrink)

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

This is a comprehensive discussion of complexity as it arises in physical, chemical, and biological systems, as well as in mathematical models of nature. Common features of these apparently unrelated fields are emphasised and incorporated into a uniform mathematical description, with the support of a large number of detailed examples and illustrations. The quantitative study of complexity is a rapidly developing subject with special impact in the fields of physics, mathematics, information science, and biology. Because of the variety of (...) the approaches, no comprehensive discussion has previously been attempted. This book will be of interest to graduate students and researchers in physics (nonlinear dynamics, fluid dynamics, solid-state, cellular automata, stochastic processes, statistical mechanics and thermodynamics), mathematics (dynamical systems, ergodic and probability theory), information and computer science (coding, information theory and algorithmic complexity), electrical engineering and theoretical biology. (shrink)

In her landmark book, Language, Thought, and Other Biological Categories (Millikan1984),1 Ruth Garrett Millikan utilizes the idea of a biological function to solve philosophical problems associated with the phenomena of language, thought, and meaning. Language and thought are activities of biological organisms, according to Millikan, and we should treat them as such when trying to answer related philosophical questions. Of special interest is Millikan’s treatment of intentionality. Here Millikan employs the notion of a biological function to explain what (...) it is for one thing in nature, a bee dance (43), for example, to be about another, in this case, the location of a nectar source. My concern in this paper is to understand whether Millikan’s account of intentionality adequately explains how humans achieve reference, in language or thought, to individuals and groups in their environment. In bringing her theory of intentional content to bear on human activities, Millikan focuses largely on natural language. Thus, in what follows, I begin by laying out the biology-based principles that underlie Millikan’s theory of content, then proceed with an explanation of how the theory is to apply to natural language. As it appears, Millikan’s account of how content is determined for natural language terms and sentences rests on the determinacy of intentional content at the psychological level. This leads me to take a careful look at what Millikan says about the content of mental representations, in hopes of finding a sufficient basis there for the application of Millikan’s theory of content to natural language. Ultimately, I conclude that Millikan’s theory faces a problem of vacuity. If we approach the theory as a theory of intentional content, intended to explain the nature of reference, the theory is lacking in an extremely important respect: Millikan explains how it could be one of the biological functions of a mental or natural language term to refer, without telling us precisely what in the natural order constitutes the reference relation.. (shrink)