Computational neuroscientists not only employ computer models and simulations in studying brain functions. They also view the modeled nervous system itself as computing. What does it mean to say that the brain computes? And what is the utility of the ‘brain-as-computer’ assumption in studying brain functions? In previous work, I have argued that a structural conception of computation is not adequate to address these questions. Here I outline an alternative conception of computation, which I call the analog-model. The term (...) ‘analog-model’ does not mean continuous, non-discrete or non-digital. It means that the functional performance of the system simulates mathematical relations in some other system, between what is being represented. The brain-as-computer view is invoked to demonstrate that the internal cellular activity is appropriate for the pertinent information-processing task.Keywords: Computation; Computational neuroscience; Analog computers; Representation; Simulation. (shrink)

The problem of epistemic opacity in Artificial Intelligence is often characterised as a problem of intransparent algorithms that give rise to intransparent models. However, the degrees of transparency of an AI model should not be taken as an absolute measure of the properties of its algorithms but of the model’s degree of intelligibility to human users. Its epistemically relevant elements are to be specified on various levels above and beyond the computational one. In order to elucidate this claim, (...) I first contrast computer models and their claims to algorithm-based universality with cybernetics-style analogue models and their claims to structural isomorphism between elements of model and target system. While analogue models aim at perceptually or conceptually accessible model-target relations, computer models give rise to a specific kind of underdetermination in these relations that needs to be addressed in specific ways. I then undertake a comparison between two contemporary AI approaches that, although related, distinctly align with the above modelling paradigms and represent distinct strategies towards model intelligibility: Deep Neural Networks and Predictive Processing. I conclude that their respective degrees of epistemic transparency primarily depend on the underlying purposes of modelling, not on their computational properties. (shrink)

Summary Analogue models are actual physical setups used to model something else. They are especially useful when what we wish to investigate is difficult to observe or experiment upon due to size or distance in space or time: for example, if the thing we wish to investigate is too large, too far away, takes place on a time scale that is too long, does not yet exist or has ceased to exist. The range and variety of analogue (...) models is too extensive to attempt a survey. In this article, I describe and discuss several different analogue model experiments, the results of those model experiments, and the basis for constructing them and interpreting their results. Examples of analogue models for surface waves in lakes, for earthquakes and volcanoes in geophysics, and for black holes in general relativity, are described, with a focus on examining the bases for claims that these analogues are appropriate analogues of what they are used to investigate. A table showing three different kinds of bases for reasoning using analogue models is provided. Finally, it is shown how the examples in this article counter three common misconceptions about the use of analogue models in physics. (shrink)

We argue that living systems process information such that functionality emerges in them on a continuous basis. We then provide a framework that can explain and model the normativity of biological functionality. In addition we offer an explanation of the anticipatory nature of functionality within our overall approach. We adopt a Peircean approach to Biosemiotics, and a dynamical approach to Digital-Analog relations and to the interplay between different levels of functionality in autonomous systems, taking an integrative approach. We then (...) apply the underlying biosemiotic logic to a particular biological system, giving a model of the B-Cell Receptor signaling system, in order to demonstrate how biosemiotic concepts can be used to build an account of biological information and functionality. Next we show how this framework can be used to explain and model more complex aspects of biological normativity, for example, how cross-talk between different signaling pathways can be avoided. Overall, we describe an integrated theoretical framework for the emergence of normative functions and, consequently, for the way information is transduced across several interconnected organizational levels in an autonomous system, and we demonstrate how this can be applied in real biological phenomena. Our aim is to open the way towards realistic tools for the modeling of information and normativity in autonomous biological agents. (shrink)

1.1 The predominant approach to cognitive modeling is still what has come to be called "computationalism" (Dietrich 1990, Harnad 1990b), the hypothesis that cognition is computation. The more recent rival approach is "connectionism" (Hanson & Burr 1990, McClelland & Rumelhart 1986), the hypothesis that cognition is a dynamic pattern of connections and activations in a "neural net." Are computationalism and connectionism really deeply different from one another, and if so, should they compete for cognitive hegemony, or should they collaborate? These (...) questions will be addressed here, in the context of an obstacle that is faced by computationalism (as well as by connectionism if it is either computational or seeks cognitive hegemony on its own): The symbol grounding problem (Harnad 1990). (shrink)

This paper revisits one of the first models of analog computation, the General Purpose Analog Computer . In particular, we restrict our attention to the improved model presented in [11] and we show that it can be further refined. With this we prove the following: the previous model can be simplified; it admits extensions having close connections with the class of smooth continuous time dynamical systems. As a consequence, we conclude that some of these extensions achieve Turing universality. (...) Finally, it is shown that if we introduce a new notion of computability for the GPAC, based on ideas from computable analysis, then one can compute transcendentally transcendental functions such as the Gamma function or Riemann's Zeta function. (shrink)

We examine the interrelationships between analog computational modelling and analogue (physical) modelling. To this end, we attempt a regimentation of the informal distinction between analog and digital, which turns on the consideration of computing in a broader context. We argue that in doing so one comes to see that (scientific) computation is better conceptualised as an epistemic process relative to agents, wherein representations play a key role. We distinguish between two, conceptually distinct, kinds of representation that, we argue, are (...) both involved in each case of computing. Based on the semantic and syntactic properties of each of these representations, we put forward a new account of the distinction between analog and digital computing. We discuss how the developed account is able to explain various properties of different models of computation, and we finish by conceptually comparing analog computational modelling to analogue (scale) modelling. It is concluded that, contrary to the standard view, the two practices are orthogonal, differing both in their foundations and in the epistemic functions they fulfil. (shrink)

Through an examination of the actual research strategies and assumptions underlying the Human Genome Project (HGP), it is argued that the epistemic basis of the initial model organism programs is not best understood as reasoning via causal analog models (CAMs). In order to answer a series of questions about what is being modeled and what claims about the models are warranted, a descriptive epistemological method is employed that uses historical techniques to develop detailed accounts which, in turn, help to (...) reveal forms of reasoning that are explicit, or more often implicit, in the practice of a particular field of scientific study. It is suggested that a more valid characterization of the reasoning structure at work here is a form of case-based reasoning. This conceptualization of the role of model organisms can guide our understanding and assessment of these research programs, their knowledge claims and progress, and their limitations, as well as how we educate the public about this type of biomedical research. (shrink)

This paper introduces the real core model K() and determines the extent of scales in this inner model. K() is an analog of Dodd-Jensen's core model K and contains L(), the smallest inner model of ZF containing the reals R. We define iterable real premice and show that Σ1∩() has the scale property when vR AD. We then prove the following Main Theorem: ZF + AD + V = K() DC. Thus, we obtain the Corollary: If (...) ZF + AD +()L() is consistent, then ZF + AD + DC + α < ω2 -AD is also consistent. (shrink)

The traditional model theory of first-order logic assumes that the interpretation of a formula can be given without reference to its deductive context. This paper investigates an interpretation which depends on a formula's location within a derivation. The key step is to drop the assumption that all quantified variables must have the same range and to require only that the ranges of variables in a derivation must be related in such way as to preserve the soundness of the inference (...) rules. With each (consistent) derivation there is associated a Buridan-Volpin (orBV) structure [M, {r(x)}] which is simply a Tarski structureM for the language and a map giving the ranger(x) of each variablex in the derivation. IfLK* is (approximately) the classical sequent calculusLK of Gentzen from which the structural contraction rules have been dropped, then our main result reads: If a set of first-ordered formulas has a Tarski modelM, then from any normal derivationD inLK* of can be constructed aBV modelM D=[M, {r(x)}] of where each ranger(x) is finite. (shrink)

There are many important connections between epistemic justification and moral justification. A recent example of such connections is offered by Sosa’s AAA model for the normative evaluation of epistemic performances. In order to count as knowledge, a belief has to be Accurate in attaining the truth, the subject has to be Adroit or competent for such task, and the belief has to be Apt in the sense that the accuracy of the belief has to manifest the adroitness of the (...) subject. In addition, full knowledge would require full-aptness, which is obtained when the aim of aptness is achieved in an apt way. We have here a clear definition of the model. But the application of the model to particular performances is not so clear. Both the identification of a particular performance as a case of epistemic performance and the assessment of its aptness, or full-aptness, are strongly relative to intentional descriptions paying attention to contextual factors and personal aspects. Here is where we can find close proximity with ethics. An epistemic analog to the ethical problem of double effects appears. In our paper, we analyze that problem in detail, extracting some consequences. (shrink)

So far this has been a lonely and unrewarding quest. New experiments occasionally come along which point to a breakdown of the Standard Model, but up to now they have invariably been proved wrong by more careful analysis or subsequent experiments with better data. A case in point is the energetic jet data from the CDF experiment at FermiLab which suggested possible substructure of the quark. (See my AV column "Inside the Quark" in the September-1996 issue of Analog.) The (...) CDF group found an unexpected excess of "jets" (clumps of energetic particles moving in the same direction) with energies above 200 GeV in their data. They found that they could not explain this excess of high energy jets using the Standard Model, as interpreted by standard theoretical procedures, and they pointed out that the data might represent new physics, possibly an indication that the quark is a composite object made of even more fundamental particles. (shrink)

In this article we argue for the existence of ‘analogue simulation’ as a novel form of scientific inference with the potential to be confirmatory. This notion is distinct from the modes of analogical reasoning detailed in the literature, and draws inspiration from fluid dynamical ‘dumb hole’ analogues to gravitational black holes. For that case, which is considered in detail, we defend the claim that the phenomena of gravitational Hawking radiation could be confirmed in the case that its counterpart is (...) detected within experiments conducted on diverse realizations of the analogue model. A prospectus is given for further potential cases of analogue simulation in contemporary science. 1 Introduction2 Physical Background2.1 Hawking radiation in semi-classical gravity2.2 Modelling sound in fluids2.3 The acoustic analogue model of Hawking radiation3 Simulation and Analogy in Physical Theory3.1 Analogical reasoning and analogue simulation3.2 Confirmation via analogue simulation3.3 Recapitulation4 The Sound of Silence: Analogical Insights into Gravity4.1 Experimental realization of analogue models4.2 Universality and the Hawking effect4.3 Confirmation of gravitational Hawking radiation5 Prospectus. (shrink)

This article presents a model and a case study of the narrative structures that are present in the interactive media design of multimedia applications in the mass media. As basic categories for the history and structure of media, we employ the model of the modes of the physical, analog, and digital presentation/representation. In this case study of the online edition of the New York Times, we have the case of a newspaper that in the digital edition employs multi-media (...) applications. Contrasting the traditional concept of “narrativity” with the current status quo of the digital media outlets, we will examine the specific conditions of the multimedia applications in the mass media with this sample case of the New York Times. As narrative structure of interactive design in multimedia for mass communication, we analyze the types of narrative media and general narrativity in the New York Times with the background of its processes of interactivity and media convergence. (shrink)

This article examines how modern Chinese Buddhism has been influenced by Christianity. For our purposes ‘modern Chinese Buddhism’ refers to a form of what has become known in the West as ‘Engaged Buddhism’, but in Chinese is known by titles which can be translated ‘Humanistic Buddhism’ or ‘Buddhism for Human Life’. This tradition was initiated on the Chinese mainland between the two World Wars by the monk Tài X?, and Part one of the article is devoted to him. Since the (...) communist conquest of China, its main branches have flourished in Taiwan, whence two of them have spread worldwide. The most successful, at least in numerical terms, has been Fo Guang Shan, founded by a personal disciple of Tài X?, Hsing Yun, now very old, and it is on this movement that we concentrate in Parts two and three. We differentiate between conscious imitation and analogous development due to similar social circumstances, and show how Protestant Christianity and Roman Catholicism have had different effects. In Part four, we examine Fo Guang Shan as a missionary religion. (shrink)

In this article I give a critical evaluation of the use and limitations of null-model-based hypothesis testing as a research strategy in the biological sciences. According to this strategy, the null model based on a randomization procedure provides an appropriate null hypothesis stating that the existence of a pattern is the result of random processes or can be expected by chance alone, and proponents of other hypotheses should first try to reject this null hypothesis in order to demonstrate (...) their own hypotheses. Using as an example the controversy over the use of null hypotheses and null models in species co-occurrence studies, I argue that null-model-based hypothesis testing fails to work as a proper analog to traditional statistical null-hypothesis testing as used in well-controlled experimental research, and that the random process hypothesis should not be privileged as a null hypothesis. Instead, the possible use of the null model resides in its role of providing a way to challenge scientists’ commonsense judgments about how a seemingly unusual pattern could have come to be. Despite this possible use, null-model-based hypothesis testing still carries certain limitations, and it should not be regarded as an obligation for biologists who are interested in explaining patterns in nature to first conduct such a test before pursuing their own hypotheses. (shrink)

Climate models calibrated exclusively with observations from the 19th through 21st centuries are unsuitable for assessing many important hypotheses about the future. Many systems in the modern climate are expected to cross dynamic thresholds in the near future, requiring more than the instrumental record for adequate calibration. In this paper I argue that paleoclimate analogues from earth’s past can mitigate this threshold problem, even if the modern climate exhibits features that make it historically unique. While this requires that paleoclimatologists be (...) increasingly discriminate in the past systems they target for modern analogues, the upshot is a practice of climate model construction that improves the reliability of future projections. All of this is achieved by integrating features of past climate systems discovered by the study of earth deep in the past. My analysis synthesizes important empirical work done by climate modelers and paleoclimatologists with relevant philosophical work on analogical reasoning in science. (shrink)

Analogue Gravity Phenomenology is a collection of contributions that cover a vast range of areas in physics, ranging from surface wave propagation in fluids to nonlinear optics. The underlying common aspect of all these topics, and hence the main focus and perspective from which they are explained here, is the attempt to develop analogue models for gravitational systems. The original and main motivation of the field is the verification and study of Hawking radiation from a horizon: the enabling (...) feature is the possibility to generate horizons in the laboratory with a wide range of physical systems that involve a flow of one kind or another. The years around 2010 and onwards witnessed a sudden surge of experimental activity in this expanding field of research. However, building an expertise in analogue gravity requires the researcher to be equipped with a rather broad range of knowledge and interests. The aim of this book is to bring the reader up to date with the latest developments and provide the basic background required in order to appreciate the goals, difficulties and success stories in the field of analogue gravity. Each chapter of the book treats a different topic explained in detail by the major experts for each specific discipline. The first chapters give an overview of black hole spacetimes and Hawking radiation before moving on to describe the large variety of analogue spacetimes that have been proposed and are currently under investigation. This introductory part is then followed by an in-depth description of what are currently the three most promising analogue spacetime settings, namely surface waves in flowing fluids, acoustic oscillations in Bose-Einstein condensates and electromagnetic waves in nonlinear optics. Both theory and experimental endeavours are explained in detail. The final chapters refer to other aspects of analogue gravity beyond the study of Hawking radiation, such as Lorentz invariance violations and Brownian motion in curved spacetimes, before concluding with a return to the origins of the field and a description of the available observational evidence for horizons in astrophysical black holes. (shrink)

We describe a dual-process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non-numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for single events, (...) for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non-numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P, P, P, disjunctions: P, P, P, and conditional probabilities P, P, P. They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning. (shrink)

We present a Bayesian analysis of the epistemology of analogue experiments with particular reference to Hawking radiation. Provided such experiments can be externally validated via universality arguments, we prove that they are confirmatory in Bayesian terms. We then provide a formal model for the scaling behaviour of the confirmation measure for multiple distinct realisations of the analogue system and isolate a generic saturation feature. Finally, we demonstrate that different potential analogue realisations could provide different levels of (...) confirmation. Our results thus provide a basis both to formalise the epistemic value of analogue experiments that have been conducted and to advise scientists as to the respective epistemic value of future analogue experiments. (shrink)

The relationship between humans and animals is complex and influenced by multiple variables. Humans display a remarkably flexible and rich array of social competencies, demonstrating the ability to interpret, predict, and react appropriately to the behavior of others, as well as to engage others in a variety of complex social interactions. Developing computational systems that have similar social abilities is a critical step in designing robots, animated characters, and other computer agents that appear intelligent and capable in their interactions with (...) humans and each other. Further, it will improve their ability to cooperate with people as capable partners, learn from natural instruction, and provide intuitive and engaging interactions for human partners. Thus, human−animal team analogs can be one means through which to foster veridical mental models of robots that provide a more accurate representation of their near-future capabilities. Some digital twins of human−animal teams currently exist but are often incomplete. Therefore, this article focuses on issues within and surrounding the current models of human−animal teams, previous research surrounding this connection, and the challenges when using such an analogy for human−autonomy teams. (shrink)

This paper explores the epistemology of extrapolation from model organisms to humans in molecular medicine. We take into account two common views on the issue, the homology view and the disanalogy view. In response to both interpretations, we argue that the foundational basis of extrapolations cannot simply be provided by homology and that relevant disanalogies can, thanks to the techniques of molecular biology, be experimentally controlled and exploited to allow useful and reliable extrapolations. The case of "humanised mice" in (...) the context of cancer stem cell research provides evidence of how animal models can be construed to approximate bona fide causal analogue models of human diseases. To supplement this view we show how the epistemology of model organisms needs to take into account the engineering side of molecular medicine. Model organisms are often manipulated to create analogies or remove disanalogies with the target system. We maintain that highlighting this feature is fundamental to explain what warrants extrapolation in the search for the molecular causes of disease. (shrink)

Background: Pain has been associated with structural changes of the brain. However, evidence regarding white matter changes in response to acute pain protocols is still scarce. In the present study, we assess the existence of differences in brain white matter related to pain intensity reported by patients undergoing surgical removal of a mandibular impacted third molar using diffusion tensor imaging analysis.Methods: 30 participants reported their subjective pain using a visual analog scale at three postsurgical stages: under anesthesia, in pain, and (...) after the administration of an analgesic. The diffusion data were acquired prior to surgery.Results: DTI analysis yielded significant positive associations of fractional anisotropy in white matter areas related to pain processing with the differences in pain between the three postsurgery stages. Extent and location of these associations depended on the magnitude of the subjective pain differences. Tractography analysis indicated that some pain–tract associations are significant only when pain stage is involved in the contrast, while others are only when anesthesia is involved in the contrast.Conclusions: The association of white matter fractional anisotropy and connectivity, measured before the pain stages, with subjective pain depends on the magnitude of the differences in pain scores. (shrink)

We investigate the relationship between two approaches to modeling physical systems. On the first approach, simplifying assumptions are made about the level of detail we choose to represent in a computational simulation with an eye toward tractability. On the second approach simpler, analogue physical systems are considered that have more or less well-defined connections to systems of interest that are themselves too difficult to probe experimentally. Our interest here is in the connections between the artifacts of modeling that appear (...) in these two approaches. We begin by outlining an important respect in which the two are essentially dissimilar and then propose a method whereby overcoming that dissimilarity by hand results in usefully analogous behavior. We claim that progress can be made if we think of artifacts as clues to the projectible predicates proper to the models themselves. Our degree of control over the connection between interesting analogue physical systems and their targets arises from determining the projectible predicates in the analogue system through a combination of theory and experiment. To obtain a similar degree of control over the connection between large-scale, distributed simulations of complex systems and their targets we must similarly determine the projectible predicates of the simulations themselves. In general theory will be too intractable to be of use, and so we advocate an experimental program for determining these predicates. the object of the natural history which I propose is...to give light to the discovery of causes and supply a suckling philosophy with its first food . Francis Bacon, The Great Instauration. (shrink)

Analogue experiments have attracted interest for their potential to shed light on inaccessible domains. For instance, ‘dumb holes’ in fluids and Bose–Einstein condensates, as analogues of black holes, have been promoted as means of confirming the existence of Hawking radiation in real black holes. We compare analogue experiments with other cases of experiment and simulation in physics. We argue—contra recent claims in the philosophical literature—that analogue experiments are not capable of confirming the existence of particular phenomena in (...) inaccessible target systems. As they must assume the physical adequacy of the modelling framework used to describe the inaccessible target system, arguments to the conclusion that analogue experiments can yield confirmation for phenomena in those target systems, such as Hawking radiation in black holes, beg the question. (shrink)

Philosophers of science have paid close attention to climate simulations as means of projecting the severity and effects of climate change, but have neglected the full diversity of methods in climate science. This paper shows the philosophical richness of another method in climate science: the practice of using paleoclimate analogues to inform our climate projections. First, I argue that the use of paleoclimate analogues can offer important insights to philosophers of the historical sciences. Rather than using the present as a (...) guide to the past, as is common in the historical sciences, paleoclimate analogues involve using the past as a guide to the future. I thereby distinguish different methods in the historical sciences and argue that these distinctions bear on debates over whether the historical sciences can produce generalizations or predictions. Second, I suggest that paleoclimate analogues might actually be considered a type of climate model, and, as such, their use expands on common characterizations of models to include those that are full-scale, naturally occurring, and non-manipulable. (shrink)

Mirrored-self misidentification is the delusional belief that one's own reflection in the mirror is a stranger. In two experiments, we tested the ability of hypnotic suggestion to model this condition. In Experiment 1, we compared two suggestions based on either the delusion's surface features (seeing a stranger in the mirror) or underlying processes (impaired face processing). Fifty-two high hypnotisable participants received one of these suggestions either with hypnosis or without in a wake control. In Experiment 2, we examined the (...) extent to which social cues and role-playing could account for participants' behaviour by comparing the responses of 14 hypnotised participants to the suggestion for impaired face processing (reals) with those of 14 nonhypnotised participants instructed to fake their responses (simulators). Overall, results from both experiments confirm that we can use hypnotic suggestion to produce a compelling analogue of mirrored-self misidentification that cannot simply be attributed to social cues or role-playing. (shrink)

Models are of central importance in many scientific contexts. The centrality of models such as the billiard ball model of a gas, the Bohr model of the atom, the MIT bag model of the nucleon, the Gaussian-chain model of a polymer, the Lorenz model of the atmosphere, the Lotka-Volterra model of predator-prey interaction, the double helix model of DNA, agent-based and evolutionary models in the social sciences, or general equilibrium models of markets in (...) their respective domains are cases in point. Scientists spend a great deal of time building, testing, comparing and revising models, and much journal space is dedicated to introducing, applying and interpreting these valuable tools. In short, models are one of the principal instruments of modern science. -/- Philosophers are acknowledging the importance of models with increasing attention and are probing the assorted roles that models play in scientific practice. The result has been an incredible proliferation of model-types in the philosophical literature. Probing models, phenomenological models, computational models, developmental models, explanatory models, impoverished models, testing models, idealized models, theoretical models, scale models, heuristic models, caricature models, didactic models, fantasy models, toy models, imaginary models, mathematical models, substitute models, iconic models, formal models, analogue models and instrumental models are but some of the notions that are used to categorize models. While at first glance this abundance is overwhelming, it can quickly be brought under control by recognizing that these notions pertain to different problems that arise in connection with models. For example, models raise questions in semantics (what is the representational function that models perform?), ontology (what kind of things are models?), epistemology (how do we learn with models?), and, of course, in philosophy of science (how do models relate to theory?; what are the implications of a model based approach to science for the debates over scientific realism, reductionism, explanation and laws of nature?). (shrink)

In this paper I propose a cognitive interpretation of the emergence of monotheism. I first distinguish between two fundamentally different conceptions of representation: one intuitive, which favors an analog model of rational cognition, and one discursive, which favors a digital model. While both Hellenism and Judaism may have been instrumental in setting civilization on the path to reason and law, it is the discursive or digital conception of God as a single universal Judge, I argue, that provides the (...) foundational axiom of the moral logic of the Hebrew Scriptures. That is, in monotheism, God came to be represented differently. (shrink)

We study the wisdom of the crowd in three sequential decision‐making tasks: the Balloon Analogue Risk Task (BART), optimal stopping problems, and bandit problems. We consider a behavior‐based approach, using majority decisions to determine crowd behavior and show that this approach performs poorly in the BART and bandit tasks. The key problem is that the crowd becomes progressively more extreme as the decision sequence progresses, because the diversity of opinion that underlies the wisdom of the crowd is lost. We (...) also consider model‐based approaches to each task. This involves inferring cognitive models for each individual based on their observed behavior, and using these models to predict what each individual would do in any possible task situation. We show that this approach performs robustly well for all three tasks and has the additional advantage of being able to generalize to new problems for which there are no behavioral data. We discuss potential applications of the model‐based approach to real‐world sequential decision problems and discuss how our approach contributes to the understanding of collective intelligence. (shrink)

Causal modelling provides a powerful set of tools for identifying causal structure from observed correlations. It is well known that such techniques fail for quantum systems, unless one introduces 'spooky' hidden mechanisms. Whether one can produce a genuinely quantum framework in order to discover causal structure remains an open question. Here we introduce a new framework for quantum causal modelling that allows for the discovery of causal structure. We define quantum analogues for core features of classical causal modelling techniques, including (...) the causal Markov condition and faithfulness. Based on the process matrix formalism, this framework naturally extends to generalised structures with indefinite causal order. (shrink)

In analogical reasoning, observations about one or more source domains provide varying degrees of support for a conjecture about a target domain. Norton (2021) challenges the usefulness of formal models of analogical inference. Other philosophers (Dardashti et al. 2019) develop just such formal models in order to show how analogue experiments can confirm a hypothesis, even when the target domain is inaccessible. This paper defends the value of quasi-formal models of analogical reasoning. Such models are broadly compatible with Norton’s (...) position, but help to clarify the structure of analogical reasoning and to identify basic requirements for a good analogical inference. (shrink)

A notion called Herbrand saturation is shown to provide the model-theoretic analogue of a proof-theoretic method, Herbrand analysis, yielding uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet a third approach, which is finitary but retains the semantic flavor of the model-theoretic version.

In this article we find some sufficient and some necessary ${\Sigma^1_1}$ -conditions with oracles for a model to be resplendent or chronically resplendent. The main tool of our proofs is internal arguments, that is analogues of classical theorems and model-theoretic constructions conducted inside a model of first-order Peano Arithmetic: arithmetised back-and-forth constructions and versions of the arithmetised completeness theorem, namely constructions of recursively saturated and resplendent models from the point of view of a model of arithmetic. (...) These internal arguments are used in conjunction with Pabion’s theorem that ensures that certain oracles are coded in a sufficiently saturated model of arithmetic. Examples of applications are provided for the theories of dense linear orders and of discrete linear orders. These results are then generalised to other ω-categorical theories and theories with a unique countable recursively saturated model. (shrink)

We continue the study of a theory which is a valued analogue of the theory of regular rings studied by Carson, Lipshitz and Saracino, characterize it as the model companion of the theory of Prüfer rings, and prove its decidability. We then link it to the theory of p.p. rings developed by Weispfenning and show that it admits quantifier elimination in a related language.

Recent accounts of scientific method suggest that a model, or analogy, for an axiomatized theory is another theory, or postulate set, with an identical calculus. The present paper examines five central theses underlying this position. In the light of examples from physical science it seems necessary to distinguish between models and analogies and to recognize the need for important revisions in the position under study, especially in claims involving an emphasis on logical structure and similarity in form between theory (...) and analogy. While formal considerations are often relevant in the employment of an analogy they are neither as extensive as proponents of this viewpoint suggest, nor are they in most cases sufficient for allowing analogies to fulfill the roles imputed to them. Of major importance, and what these authors generally fail to consider, are physical similarities between analogue and theoretical object. Such similarities, which are characteristic in varying degrees of most analogies actually employed, play an important role in affording a better understanding of concepts in the theory and also in the development of the theoretical assumptions. (shrink)

This paper, a sequel to Models for normal intuitionistic modal logics by M. Boi and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of S4 and S5. For these prepositional logics Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given, and soundness and completeness are proved with respect to these models. It is shown how the holding of (...) formulae characteristic for particular logics is equivalent to conditions for the relations of the models. Modalities in these logics are also investigated. (shrink)

This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF ${(\mathcal{L})}$ (the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here ${\mathcal{L}}$ is a language with a distinguished linear order <, and REF ${(\mathcal {L})}$ consists of formulas of the form $$\exists x \forall y_{1} < x \ldots \forall y_{n} < x \varphi (y_{1},\ldots ,y_{n})\leftrightarrow \varphi^{ < x}(y_1, \ldots ,y_n),$$ where φ is an ${\mathcal{L}}$ (...) -formula, φ model of T has an elementary end extension with a first new element.T ⊢ REF ${(\mathcal{L})}$ .T has an ω 1-like model that continuously embeds ω 1.For some regular uncountable cardinal κ, T has a κ-like model that continuously embeds a stationary subset of κ.For some regular uncountable cardinal κ, T has a κ-like model ${\mathfrak{M}}$ that has an elementary extension in which the supremum of M exists.Moreover, if κ is a regular cardinal satisfying κ = κ <κ , then each of the above conditions is equivalent to: T has a κ + -like model that continuously embeds a stationary subset of κ. (shrink)

I analyse three most interesting and extensive approaches to theoretical models: classical ones—proposed by Peter Achinstein and Michael Redhead, and the rela-tively rareanalysed approach of Ryszard Wójcicki, belonging to a later phase of his research where he gave up applyingthe conceptual apparatus of logical semantics. I take into consideration the approaches to theoretical models in which they are qualified as models representing the reality. That is why I omit Max Black’s and Mary Hesse’s concepts of such models, as those two (...) concepts belong to the analogue model group if we consider the main function of the model of a given class as its classification criterion. My main focus is on theoretical models with representative functions as these very models and, in a broader context, the question of representation. (shrink)

We study the relations of being substructure and elementary substructure between Kripke models of intuitionistic predicate logic with the same arbitrary frame. We prove analogues of Tarski's test and Löwenheim-Skolem's theorems as determined by our definitions. The relations between corresponding worlds of two Kripke models [MATHEMATICAL SCRIPT CAPITAL K] ⪯ [MATHEMATICAL SCRIPT CAPITAL K]′ are studied.

“Teleosemantic” or “biosemantic” theories form a strong naturalistic programme in the philosophy of mind and language. They seek to explain the nature of mind and language by recourse to a natural history of “proper functions” as selected-for effects of language- and thought-producing mechanisms. However, they remain vague with respect to the nature of the proposed analogy between selected-for effects on the biological level and phenomena that are not strictly biological, such as reproducible linguistic and cultural forms. This essay critically explores (...) various interpretations of this analogy. It suggests that these interpretations can be explicated by contrasting adaptationist with pluralist readings of the evolutionary concept of adaptation. Among the possible interpretations of the relations between biological adaptations and their analogues in language and culture, the two most relevant are a linear, hierarchical, signalling-based model that takes its cues from the evolution of co-operation and joint intentionality and a mutualistic, pluralist model that takes its cues from mimesis and symbolism in the evolution of human communication. Arguing for the merits of the mutualistic model, the present analysis indicates a path towards an evolutionary pluralist version of biosemantics that will align with theories of cognition as being environmentally “scaffolded”. Language and other cultural forms are partly independent reproducible structures that acquire proper functions of their own while being integrated with organism-based cognitive traits in co-evolutionary fashion. (shrink)

We develop positive model theory, which is a non first order analogue of classical model theory where compactness is kept at the expense of negation. The analogue of a first order theory in this framework is a compact abstract theory: several equivalent yet conceptually different presentations of this notion are given. We prove in particular that Banach and Hilbert spaces are compact abstract theories, and in fact very well-behaved as such.

Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given for analogues of the modal systemK based on Heyting's prepositional logic. It is shown that these two relations can combine with each other in various ways. Soundness and completeness are proved for systems with only the necessity operator, or only the possibility operator, or both. Embeddings in modal systems with several modal operators, based on classical propositional logic, are also considered. This paper lays the ground for (...) an investigation of intuitionistic analogues of systems stronger thanK. A brief survey is given of the existing literature on intuitionistic modal logic. (shrink)