Computational Philosophy

Computers may help us to better understand (not just verify) arguments. In this article we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language ar- gument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the existence of God. Our new method, which we call computational hermeneutics, has been particularly conceived for use in interactive-automated proof assistants. It aims at shedding light on the (...) meanings of words and sentences by framing their inferential role in a given argument. By employing automated theorem reasoning technology within interactive proof assistants, we are able to drastically reduce (by several orders of magnitude) the time needed to test the logical validity of an argu- ment’s formalization. As a result, a new approach to logical analysis, inspired by Donald Davidson’s account of radical interpretation, has been enabled. In computational hermeneutics, the utilization of automated reasoning tools ef- fectively boosts our capacity to expose the assumptions we indirectly commit ourselves to every time we engage in rational argumentation and it fosters the explicitation and revision of our concepts and commitments. (shrink)

Philosophers of science regularly use scientific publications in their research. To make their analyses of the literature more thorough, some have begun to use computational methods from the digital humanities. Yet this creates a tension: it’s become a truism in science studies that the contents of scientific publications do not accurately reflect the complex realities of scientific investigation. In this paper, we outline existing views on how scientific publications fit into the broader picture of science as a system of practices, (...) and find that none of these views exclude articles as valuable sources for philosophical inquiry. Far from ignoring the gap between texts and practice, proper use of DH tools requires, and can even contribute to, our understanding of that gap and its implications. (shrink)

Philosophers have long tried to understand scientific change in terms of a dynamics of revision within ‘theoretical frameworks,’ ‘disciplinary matrices,’ ‘scientific paradigms’ or ‘conceptual schemes.’ No-one, however, has made clear precisely how one might model such a conceptual scheme, nor what form change dynamics within such a structure could be expected to take. In this paper we take some first steps in applying network theory to the issue, modeling conceptual schemes as simple networks and the dynamics of change as cascades (...) on those networks. The results allow a new understanding of two traditional approaches—Popper and Kuhn—as well as introducing the intriguing prospect of viewing scientific change using the metaphor of selforganizing criticality. (shrink)

It is a common view among philosophers of science that theoretical virtues (also known as epistemic or cognitive values), such as simplicity and consistency, play an important role in scientific practice. In this paper, I set out to study the role that theoretical virtues play in scientific practice empirically. I apply the methods of data science, such as text mining and corpus analysis, to study large corpora of scientific texts in order to uncover patterns of usage. These patterns of usage, (...) in turn, might shed some light on the role that theoretical virtues play in scientific practice. Overall, the results of this empirical study suggest that scientists invoke theoretical virtues explicitly, albeit rather infrequently, when they talk about models (less than 30%), theories (less than 20%), and hypotheses (less than 15%) in their published works. To the extent that they are mentioned in scientific publications, the results of this study suggest that accuracy, consistency, and simplicity are the theoretical virtues that scientists invoke more frequently than the other theoretical virtues tested in this study. Interestingly, however, depending on whether they talk about hypotheses, theories, or models, scientists may invoke one of those theoretical virtues more than the others. (shrink)

We motivate a picture of social epistemology that sees forgetting as subject to epistemic evaluation. Using computer simulations of a simple agent-based model, we show that how agents forget can have as large an impact on group epistemic outcomes as how they share information. But, how we forget, unlike how we form beliefs, isn’t typically taken to be the sort of thing that can be epistemically rational or justified. We consider what we take to be the most promising argument for (...) this claim and find it lacking. We conclude that understanding how agents forget should be as central to social epistemology as understanding how agents form beliefs and share information with others. (shrink)

While scientific inquiry crucially relies on the extraction of patterns from data, we still have a very imperfect understanding of the metaphysics of patterns—and, in particular, of what it is that makes a pattern real. In this paper we derive a criterion of real-patternhood from the notion of conditional Kolmogorov complexity. The resulting account belongs in the philosophical tradition, initiated by Dennett, that links real-patternhood to data compressibility, but is simpler and formally more perspicuous than other proposals defended heretofore in (...) the literature. It also successfully enforces a non-redundancy principle, suggested by Ladyman and Ross, that aims at excluding as real those patterns that can be ignored without loss of information about the target dataset, and which their own account fails to enforce. (shrink)

This study shows firstly that it is necessary to characterize a computer simulation at a finer level than that of formal models: that of symbols and their various modes of reference. This is particularly true for those that integrate models and formalisms of a heterogeneous nature. This study then examines the ontological causes that, consequently, could explain their epistemic success. It is argued that they can be conveniently explained if one adopts a conception of nature that is both discontinuous and (...) finite. The latter thesis supports a naturalistic metaphysical position by invalidating, at its root, the argument made by speculative materialism against a scientific approach to the physical world that proceeds, like simulations, by finite representations and operations. (shrink)

The principle of self-organization has acquired a fundamental significance in the newly emerging field of computational philosophy. Self-organizing systems have been described in various domains in science and philosophy including physics, neuroscience, biology and medicine, ecology, and sociology. While system architecture and their general purpose may depend on domain-specific concepts and definitions, there are (at least) seven key properties of self-organization clearly identified in brain systems: 1) modular connectivity, 2) unsupervised learning, 3) adaptive ability, 4) functional resiliency, 5) functional plasticity, (...) 6) from-local-to-global functional organization, and 7) dynamic system growth. These are defined here in the light of insight from neurobiology, cognitive neuroscience and Adaptive Resonance Theory (ART), and physics to show that self-organization achieves stability and functional plasticity while minimizing structural system complexity. A specific example informed by empirical research is discussed to illustrate how modularity, adaptive learning, and dynamic network growth enable stable yet plastic somatosensory representation for human grip force control. Implications for the design of “strong” artificial intelligence in robotics are brought forward. (shrink)

Epistemic justifications for democracy have been offered in terms of two different aspects of decision-making: voting and deliberation, or ‘votes’ and ‘talk.’ The Condorcet Jury Theorem is appealed to as a justification in terms votes, and the Hong-Page “Diversity Trumps Ability” result is appealed to as a justification in terms of deliberation. Both of these, however, are most plausibly construed as models of direct democracy, with full and direct participation across the population. In this paper, we explore how these results (...) hold up if we vary the model so as to reflect the more familiar democratic structure of a representative hierarchy. We first recount extant analytic work that shows that representation inevitably weakens the voting results of the Condorcet Jury Theorem, but we question the ability of that result to shine light on real representative systems. We then show that, when we move from votes to talk, as modeled in Hong-Page, representation holds its own and even has a slight edge. (shrink)

It is generally accepted among philosophers of science that hypothesis testing is a key methodological feature of science. As far as philosophical theories of confirmation are con...

In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of (...) this empirical study suggest that mathematical explanations do occur in research articles published in mathematics journals, as indicated by the occurrence of explanation indicators. When compared with the use of justification indicators, however, the data suggest that justifications occur much more frequently than explanations in scholarly mathematical practice. The results also suggest that justificatory proofs occur much more frequently than explanatory proofs, thus suggesting that proof may be playing a larger justificatory role than an explanatory role in scholarly mathematical practice. (shrink)

Turner argues that computer programs must have purposes, that implementation is not a kind of semantics, and that computers might need to understand what they do. I respectfully disagree: Computer programs need not have purposes, implementation is a kind of semantic interpretation, and neither human computers nor computing machines need to understand what they do.

How can we best reconstruct the origin of a notion, its development, and possible spread to multiple fields? We present a pilot study on the spread of the notion of conceptual scheme. Though the notion is philosophically important, its origin, development, and spread are unclear. Several purely qualitative and competing historical hypotheses have been offered, which rely on disconnected disciplinary traditions, and have never been tested all at once in a single comprehensive investigation fitting the scope of its subject matter. (...) As a step toward such an investigation, we trace the use of the bigram “conceptual scheme” in about 42,000 US journal articles in social sciences from 1888-1959 by using a novel method combining a quantitative procedure aided by basic computational techniques with qualitative elements informed by Betti and van den Berg (2014)’s ‘model approach to the history of ideas’. (shrink)

What structure of scientific communication and cooperation, between what kinds of investigators, is best positioned to lead us to the truth? Against an outline of standard philosophical characteristics and a recent turn to social epistemology, this paper surveys highlights within two strands of computational philosophy of science that attempt to work toward an answer to this question. Both strands emerge from abstract rational choice theory and the analytic tradition in philosophy of science rather than postmodern sociology of science. The first (...) strand of computational research models the effect of communicative networks within groups, with conclusions regarding the potential benefit of limited communication. The second strand models the potential benefits of cognitive diversity within groups. Examples from each strand of research are used in analyzing what makes modeling of this sort both promising and distinctly philosophical, but are also used to emphasize possibilities for failure and inherent limitations as well. (shrink)

The Hong and Page ‘diversity trumps ability’ result has been used to argue for the more general claim that a diverse set of agents is epistemically superior to a comparable group of experts. Here we extend Hong and Page’s model to landscapes of different degrees of randomness and demonstrate the sensitivity of the ‘diversity trumps ability’ result. This analysis offers a more nuanced picture of how diversity, ability, and expertise may relate. Although models of this sort can indeed be suggestive (...) for diversity policies, we advise against interpreting such results overly broadly. (shrink)

Computational neuroscience attributes coloured areas and other perceptual qualia to calculations that are realizable in multiple cellular forms. This faces serious issues in explaining how the various qualia arise and how they bind to form overall perceptions. Qualia may instead be neuroelectrical. Growing evidence indicates that perceptions correlate with neuroelectrical activity spotted by locally activated EEGs, the different qualia correlate with the different electrochemistries of unique detector cells, a unified neural-electromagnetic field binds this activity to form overall perceptions, and this (...) field interacts with sensory circuits to help attentively guide perception. The coloured areas in images may thus be seated in the electrochemistry of unique cells, while constancy mechanisms and other multiply realizable computations just help refine these images behind the scenes. This theory is ultimately testable. (shrink)

This article aims to describe the last 10 years of the collaborative scientific endeavors on polarization in particular and collective problem-solving in general by our multidisciplinary research team. We describe the team’s disciplinary composition—social psychology, political science, social philosophy/epistemology, and complex systems science— highlighting the shared and unique skill sets of our group members and how each discipline contributes to studying polarization and collective problem-solving. With an eye to the literature on team dynamics, we describe team logistics and processes that (...) we believe make our multidisciplinary team persistent and productive. We emphasize challenges and difficulties caused by disciplinary differences in terms of terminology, units/levels of analysis, methodology, and theoretical assumptions. We then explain how work disambiguating the concepts of polarization and developing an integrative theoretical and methodological framework with complex systems perspectives has helped us overcome these challenges. We summarize the major findings that our research has produced over the past decade, and describe our current research and future directions. Last, we discuss lessons we have learned, including difficulties in a “three models” project and how we addressed them, with suggestions for effective multidisciplinary team research. (shrink)

It is often said that ‘every logical truth is obvious’ (Quine 1970: 82), that the ‘axioms and rules of logic are true in an obvious way’ (Murawski 2014: 87), or that ‘logic is a theory of the obvious’ (Sher 1999: 207). In this chapter, I set out to test empirically how the idea that logic is obvious is reflected in the scholarly work of logicians and philosophers of logic. My approach is data-driven. That is to say, I propose that systematically (...) searching for patterns of usage in databases of scholarly works, such as JSTOR, can provide new insights into the ways in which the idea that logic is obvious is reflected in logical and philosophical practice, i.e., in the arguments that logicians and philosophers of logic actually make in their published work. (shrink)

En ' Godel’s Way ', tres eminentes científicos discuten temas como la indecisión, la incompleta, la aleatoriedad, la computabilidad y la paracoherencia. Me acerco a estas cuestiones desde el punto de vista de Wittgensteinian de que hay dos cuestiones básicas que tienen soluciones completamente diferentes. Existen las cuestiones científicas o empíricas, que son hechos sobre el mundo que necesitan ser investigados Observacionalmente y cuestiones filosóficas en cuanto a cómo el lenguaje se puede utilizar inteligiblemente (que incluyen ciertas preguntas en matemáticas (...) y lógica), que necesitan decidirse por unt cómo realmente usar palabras en contextos concretos. Cuando tenemos claro sobre qué juego de idiomas estamos jugando, estos temas son vistos como preguntas científicas y matemáticas ordinarias como cualquier otra. Las percepciones de Wittgenstein rara vez se han igualado y nunca superado y son tan pertinentes hoy como lo fueron hace 80 años cuando dictó los libros azul y marrón. A pesar de sus fallas — realmente una serie de notas en lugar de un libro terminado —, esta es una fuente única de la obra de estos tres eruditos famosos que han estado trabajando en los bordes sangrantes de la física, las matemáticas y la filosofía durante más de medio siglo. Da Costa y Doria son citados por Wolpert (ver abajo o mis artículos sobre Wolpert y mi reseña de ' los límites de la razón ' de Yanofsky) desde que escribieron en el cómputo universal, y entre sus muchos logros, da Costa es pionera en paraconsistencia. -/- Aquellos que deseen un marco completo hasta la fecha para el comportamiento humano de la moderna dos sistemas punta da vista puede consultar mi libro 'La estructura lógica de la filosofía, la psicología, la mente y lenguaje en Ludwig Wittgenstein y John Searle ' 2a ED (2019). Los interesados en más de mis escritos pueden ver 'Monos parlantes--filosofía, psicología, ciencia, religión y política en un planeta condenado--artículos y reseñas 2006-2019 3rd ED (2019) y Delirios utópicos suicidas en el siglo 21 4a Ed (2019) y otras. (shrink)

The “received wisdom” in contemporary analytic philosophy is that intuition talk is a fairly recent phenomenon, dating back to the 1960s. In this paper, we set out to test two interpretations of this “received wisdom.” The first is that intuition talk is just talk, without any methodological significance. The second is that intuition talk is methodologically significant; it shows that analytic philosophers appeal to intuition. We present empirical and contextual evidence, systematically mined from the JSTOR corpus and HathiTrust’s Digital Library, (...) which provide some empirical support for the second rather than the first hypothesis. Our data also suggest that appealing to intuition is a much older philosophical methodology than the “received wisdom” alleges. We then discuss the implications of our findings for the contemporary debate over philosophical methodology. (shrink)

Many philosophers subscribe to the view that philosophy is a priori and in the business of discovering necessary truths from the armchair. This paper sets out to empirically test this picture. If this were the case, we would expect to see this reflected in philosophical practice. In particular, we would expect philosophers to advance mostly deductive, rather than inductive, arguments. The paper shows that the percentage of philosophy articles advancing deductive arguments is higher than those advancing inductive arguments, which is (...) what we would expect from the vantage point of the armchair philosophy picture. The results also show, however, that the percentages of articles advancing deductive arguments and those advancing inductive arguments are converging over time and that the difference between inductive and deductive ratios is declining over time. This trend suggests that deductive arguments are gradually losing their status as the dominant form of argumentation in philosophy. (shrink)

Various moral conundrums plague population ethics: the Non-Identity Problem, the Procreation Asymmetry, the Repugnant Conclusion, and more. I argue that the aforementioned moral conundrums have a structure neatly accounted for, and solved by, some ideas in computability theory. I introduce a mathematical model based on computability theory and show how previous arguments pertaining to these conundrums fit into the model. This paper proceeds as follows. First, I do a very brief survey of the history of computability theory in moral philosophy. (...) Second, I follow various papers, and show how their arguments fit into, or don't fit into, our model. Third, I discuss the implications of our model to the question why the human race should or should not continue to exist. Finally, I show that our model may be interpreted according to a Confucian-Taoist moral principle. (shrink)

This paper argues that the idea of a computer is unique. Calculators and analog computers are not different ideas about computers, and nature does not compute by itself. Computers, once clearly defined in all their terms and mechanisms, rather than enumerated by behavioral examples, can be more than instrumental tools in science, and more than source of analogies and taxonomies in philosophy. They can help us understand semantic content and its relation to form. This can be achieved because they have (...) the potential to do more than calculators, which are computers that are designed not to learn. Today’s computers are not designed to learn; rather, they are designed to support learning; therefore, any theory of content tested by computers that currently exist must be of an empirical, rather than a formal nature. If they are designed someday to learn, we will see a change in roles, requiring an empirical theory about the Turing architecture’s content, using the primitives of learning machines. This way of thinking, which I call the intensional view of computers, avoids the problems of analogies between minds and computers. It focuses on the constitutive properties of computers, such as showing clearly how they can help us avoid the infinite regress in interpretation, and how we can clarify the terms of the suggested mechanisms to facilitate a useful debate. Within the intensional view, syntax and content in the context of computers become two ends of physically realizing correspondence problems in various domains. (shrink)

Agent-based models have played a prominent role in recent debates about the merits of democracy. In particular, the formal model of Lu Hong and Scott Page and the associated “diversity trumps ability” result has typically been seen to support the epistemic virtues of democracy over epistocracy (i.e., governance by experts). In this paper we first identify the modeling choices embodied in the original formal model and then critique the application of the Hong-Page results to philosophical debates on the relative merits (...) of democracy. In particular we argue that the “best-performing agents” in Hong-Page model should not be interpreted as experts. We next explore a closely related model in which best-performing agents are more plausibly seen as experts and show that the diversity trumps ability result fails to hold. However, with changes in other parameters (such as the deliberation dynamic) the diversity trumps ability result is restored. The sensitivity of this result to parameter choices illustrates the complexity of the link between formal modeling and more general philosophical claims; we use this debate as a platform for a more general discussion of when and how agent-based models can contribute to philosophical discussions. (shrink)

Philosophy of science is beginning to be expanded via the introduction of new digital resources—both data and tools for its analysis. The data comprise digitized published books and journal articles, as well as heretofore unpublished and recently digitized material, such as images, archival text, notebooks, meeting notes, and programs. This growing bounty of data would be of little use, however, without quality tools with which to analyze it. Fortunately, the growth in available data is matched by the extensive development of (...) automated analysis tools. For the beginner, this wide variety of data sources and tools can be overwhelming. In this essay, we survey the state of digital work in the philosophy of science, showing what kinds of questions can be answered and how one can go about answering them. (shrink)

In this position paper, we describe a number of methodological and philosophical challenges that arose within our interdisciplinary Digital Humanities project CatVis, which is a collaboration between applied geometric algorithms and visualization researchers, data scientists working at OCLC, and philosophers who have a strong interest in the methodological foundations of visualization research. The challenges we describe concern aspects of one single epistemic need: that of methodologically securing (an increase in) trust in visualizations. We discuss the lack of ground truths in (...) the (digital) humanities and argue that trust in visualizations requires that we evaluate visualizations on the basis of ground truths that humanities scholars themselves create. We further argue that trust in visualizations requires that a visualization provides provable guarantees on the faithfulness of the visual representation and that we must clearly communicate to the users which part of the visualization can be trusted and how much. Finally, we discuss transparency and accessibility in visualization research and provide measures for securing transparency and accessibility. (shrink)

On edge computing, mobile devices can offload some computing intensive tasks to the cloud so that the time delay and battery losses can be reduced. Different from cloud computing, an edge computing model is under the constraint of radio transmitting bandwidth, power and etc. With regard to most models in presence, each user is assigned to a single mission, transmitting power or local CPU frequency on mobile terminals is deemed to be a constant. Furthermore, energy consumption has a positive correlation (...) with the above two parameters. In a context of multitask, such values could be increased or reduced according to workload to save energy. Additionally, the existing offloading methods are inappropriate if all the compute densities of multiple tasks are high. In this paper, a single-user multi-task with high computing density model is proposed and partial task is offloaded when use the different offload algorithm. Simulated annealing algorithm is the best method to select offloading tasks, which can enhance the offloading ratio and save energy consumption. (shrink)

The step to e-research in philosophy depends on the availability of high quality, easily and freely accessible corpora in a sustainable format composed from multi-language, multi-script books from different historical periods. Corpora matching these needs are at the moment virtually non-existing. Within @PhilosTei, we have addressed this corpus building problem by developing an open source, web-based, user-friendly workflow from textual images to TEI, based on state-of-the-art open source OCR software, to wit Tesseract, and a multi-language version of TICCL, a powerful (...) OCR post-correction tool. We have demonstrated the utility of the tool by applying it to a multilingual, multi-script corpus of important eighteenth to twentieth-century European philosophical texts. (shrink)

Paul Oppenheimer and Edward Zalta's formalisation of Anselm's ontological argument for the existence of God is automated by embedding a free logic for definite descriptions within Isabelle/HOL.

Data-driven historiography of philosophy looks to objective modeling tools for illumination of the propagation of influence. While the system of David Lewis, the most influential philosopher of our time, raises historiographic puzzles to stymie conventional analytic methods, it proves amenable to data-driven analysis. A striking result is that Lewis only becomes the metaphysician of current legend following the midpoint of his career: his initial project is to frame a descriptive science of mind and meaning; the transition to metaphysics is a (...) rhetorically breathtaking escape from this program's (inevitable) collapse. Understanding this process both aids a more focused debate whether it counts as progress, and also presents novel affordances for partisans on both sides to learn from Lewis's right and wrong steps. (shrink)

Search in an environment with an uncertain distribution of resources involves a trade-off between exploitation of past discoveries and further exploration. This extends to information foraging, where a knowledge-seeker shifts between reading in depth and studying new domains. To study this decision-making process, we examine the reading choices made by one of the most celebrated scientists of the modern era: Charles Darwin. From the full-text of books listed in his chronologically-organized reading journals, we generate topic models to quantify his local (...) (text-to-text) and global (text-to-past) reading decisions using Kullback-Liebler Divergence, a cognitively-validated, information-theoretic measure of relative surprise. Rather than a pattern of surprise-minimization, corresponding to a pure exploitation strategy, Darwin’s behavior shifts from early exploitation to later exploration, seeking unusually high levels of cognitive surprise relative to previous eras. These shifts, detected by an unsupervised Bayesian model, correlate with major intellectual epochs of his career as identified both by qualitative scholarship and Darwin’s own self-commentary. Our methods allow us to compare his consumption of texts with their publication order. We find Darwin’s consumption more exploratory than the culture’s production, suggesting that underneath gradual societal changes are the explorations of individual synthesis and discovery. Our quantitative methods advance the study of cognitive search through a framework for testing interactions between individual and collective behavior and between short- and long-term consumption choices. This novel application of topic modeling to characterize individual reading complements widespread studies of collective scientific behavior. (shrink)

It has been argued that the fundamental laws of physics do not face a ‘problem of provisos’ equivalent to that found in other scientific disciplines (Earman, Roberts and Smith 2002) and there is only the appearance of exceptions to physical laws if they are confused with differential equations of evolution type (Smith 2002). In this paper I argue that even if this is true, fundamental laws in physics still pose a major challenge to standard Humean approaches to lawhood, as they (...) are not in any obvious sense about regularities in behaviour. A Humean approach to physical laws with exceptions is possible, however, if we adopt a view of laws that takes them to be the algorithms in the algorithmic compressions of empirical data. When this is supplemented with a distinction between lossy and lossless compression, we can explain exceptions in terms of compression artefacts present in the application of the lossy laws. (shrink)

The History of Ideas is presently enjoying a certain renaissance after a long period of disrepute. Increasing quantities of digitally available historical texts and the availability of computational tools for the exploration of such masses of sources, it is suggested, can be of invaluable help to historians of ideas. The question is: how exactly? In this paper, we argue that a computational history of ideas is possible if the following two conditions are satisfied: (i) Sound Method . A computational history (...) of ideas must be built upon a sound theoretical foundation for its methodology, and the only such foundation is given by the use of models , i.e., fully explicit and revisable interpretive frameworks or networks of concepts developed by the historians of ideas themselves. (ii) Data Organisation. Interpretive models in our sense must be seen as topic-specific knowledge organisation systems (KOS) implementable (i.e. formalisable) as e.g. computer science ontologies. We thus require historians of ideas to provide explicitly structured semantic framing of domain knowledge before investigating texts computationally, and to constantly re-input findings from the interpretive point of view. In this way, a computational history of ideas maximally profits from computer methods while also keeping humanities experts in the loop. We elucidate our proposal with reference to a model of the notion of axiomatic science in 18th -19th century Europe. (shrink)

This is an attempt to develop a universal socio-technical computing machine that captures and coordinates human input to let collective problem solving activities emerge on the Web without the need for an a priori composition of a dedicated task or human collective.

In the age of big data and a machine epistemology that can anticipate, predict, and intervene on events in our lives, the problem once again is that a few individuals possess the knowledge of how to regulate these activities. But the question we face now is not how to share such knowledge more widely, but rather of how to enjoy the public benefits bestowed by this knowledge without freely sharing it. It is not merely personal privacy that is at stake (...) but a range of unsung benefits that come from ignorance and forgetting, traits that are inherently human and integral to the functioning of our society. (shrink)

This article offers an explanation of perhaps Wittgenstein’s strangest and least intuitive thesis – the semantical mutation thesis – according to which one can never answer a mathematical conjecture because the new proof alters the very meanings of the terms involved in the original question. Instead of basing our justification on the distinction between mere calculation and proofs of isolated propositions, characteristic of Wittgenstein’s intermediary period, we generalize it to include conjectures involving effective procedures as well.

The Emergic Cognitive Model (ECM) is a unified computational model of visual filling-in based on the Emergic Network architecture. The Emergic Network was designed to help realize systems undergoing continuous change. In this thesis, eight different filling-in phenomena are demonstrated under a regime of continuous eye movement (and under static eye conditions as well). -/- ECM indirectly demonstrates the power of unification inherent with Emergic Networks when cognition is decomposed according to finer-grained functions supporting change. These can interact to raise (...) additional emergent behaviours via cognitive re-use, hence the Emergic prefix throughout. Nevertheless, the model is robust and parameter free. Differential re-use occurs in the nature of model interaction with a particular testing paradigm. -/- ECM has a novel decomposition due to the requirements of handling motion and of supporting unified modelling via finer functional grains. The breadth of phenomenal behaviour covered is largely to lend credence to our novel decomposition. -/- The Emergic Network architecture is a hybrid between classical connectionism and classical computationalism that facilitates the construction of unified cognitive models. It helps cutting up of functionalism into finer-grains distributed over space (by harnessing massive recurrence) and over time (by harnessing continuous change), yet simplifies by using standard computer code to focus on the interaction of information flows. Thus while the structure of the network looks neurocentric, the dynamics are best understood in flowcentric terms. Surprisingly, dynamic system analysis (as usually understood) is not involved. An Emergic Network is engineered much like straightforward software or hardware systems that deal with continuously varying inputs. Ultimately, this thesis addresses the problem of reduction and induction over complex systems, and the Emergic Network architecture is merely a tool to assist in this epistemic endeavour. -/- ECM is strictly a sensory model and apart from perception, yet it is informed by phenomenology. It addresses the attribution problem of how much of a phenomenon is best explained at a sensory level of analysis, rather than at a perceptual one. As the causal information flows are stable under eye movement, we hypothesize that they are the locus of consciousness, howsoever it is ultimately realized. (shrink)

There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y′(x) = f(x,y) starting from an initial value y_0=y(x_0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a computer – the Infinity Computer (it has been patented and its working prototype exists). The new computer is (...) able to work numerically with finite, infinite, and infinitesimal numbers giving so the possibility to use different infinitesimals numerically and, in particular, to take advantage of infinitesimal values of h. To show the potential of the new framework a number of results is established. It is proved that the Infinity Computer is able to calculate derivatives of the solution y(x) and to reconstruct its Taylor expansion of a desired order numerically without finding the respective derivatives analytically (or symbolically) by the successive derivation of the ODE as it is usually done when the Taylor method is applied. Methods using approximations of derivatives obtained thanks to infinitesimals are discussed and a technique for an automatic control of rounding errors is introduced. Numerical examples are given. (shrink)

The paper investigates how the mathematical languages used to describe and to observe automatic computations influence the accuracy of the obtained results. In particular, we focus our attention on Single and Multi-tape Turing machines which are described and observed through the lens of a new mathematical language which is strongly based on three methodological ideas borrowed from Physics and applied to Mathematics, namely: the distinction between the object (we speak here about a mathematical object) of an observation and the instrument (...) used for this observation; interrelations holding between the object and the tool used for the observation; the accuracy of the observation determined by the tool. Results of the observation executed by the traditional and new languages are compared and discussed. (shrink)

Architecture often relies on mathematical models, if only to anticipate the physical behavior of structures. Accordingly, mathematical modeling serves to find an optimal form given certain constraints, constraints themselves translated into a language which must be homogeneous to that of the model in order for resolution to be possible. Traditional modeling tied to design and architecture thus appears linked to a topdown vision of creation, of the modernist, voluntarist and uniformly normative type, because usually (mono)functionalist. One available instrument of calculation/representation/prescription (...) orders this conception of architecture: indeed the search for an optimal solution through mathematical calculation of a model itself mathematical, thus homogeneous and simple, is only possible when one or two functions or functional constraints are formulated, never more, and this, on a global level, therefore starting from a unique and homogenizing viewpoint. It is essential to grasp that, even applied to material and its properties or towards a particular esthetic or functional dimension, this viewpoint is thus abstractive and generalizing: disregarding singularity of context, insertion and relationship to the environment or local, social behavior. It leaves aside functional specificity and heterogeneousness – re-contextualized each time – of functions that the object or edifice are required to fulfill and optimize under diverse constraints, in their different parts. The computational turning point today’s digital design and computational architecture embody modifies these instrumental, original prescriptions, rendering them more flexible. Perhaps in light of this turnabout we should retrospectively interpret 20th century calls for modernism, functionalism and even biomorphism as being just as many ex post rationalizations in respect to techniques of strongly prescriptive modeling since our only instrument is a monolithic language, and so being, incites a top-down conception, (naturally weakly reactive to contexts), including forms whose overall appearance resembles in fine a living form. In order to liberate oneself from this and despite everything, emerge as its initiators, one has constructed from ideology and philosophy (of object, habitat, the urban) ex post, even while it is the instrument of modeling and conception that largely determines, normalizes and dictates ex ante, the possibilities and limitations of the creation of forms and living experiments4 in a given time. (shrink)

Michael Dummett famously maintained that analytic philosophy was simply philosophy that followed Frege in treating the philosophy of language as the basis for all other philosophy (1978, 441). But one important insight to emerge from computer science is how difficult it is to animate the linguistic artifacts that the analysis of thought produces. Yet, modeling the effects of thought requires a new skill that goes beyond analysis: procedural literacy. Some of the most promising research in philosophy makes use of a (...) variety of modeling techniques that go beyond basic logic and elementary probability theory. What unifies this approach is a focus on what Alan Perlis called procedural literacy. This essay argues that the future spoils in philosophical research will disproportionally go to those who are procedurally literate. (shrink)

One feature of vague predicates is that, as far as appearances go, they lack sharp application boundaries. I argue that we would not be able to locate boundaries even if vague predicates had sharp boundaries. I do so by developing an idealized cognitive model of a categorization faculty which has mobile and dynamic sortals (`classes', `concepts' or `categories') and formally prove that the degree of precision with which boundaries of such sortals can be located is inversely constrained by their flexibility. (...) Given the literature, it is plausible that we are appropriately like the model. Hence, an inability to locate sharp boundaries is not necessarily because there are none; boundaries could be sharp and it is plausible that we would nevertheless be unable to locate them. (shrink)

In this paper we shed new light on the Argument from Disagreement by putting it to test in a computer simulation. According to this argument widespread and persistent disagreement on ethical issues indicates that our moral opinions are not influenced by any moral facts, either because no such facts exist or because they are epistemically inaccessible or inefficacious for some other reason. Our simulation shows that if our moral opinions were influenced at least a little bit by moral facts, we (...) would quickly have reached consensus, even if our moral opinions were affected by factors such as false authorities, external political shifts, and random processes. Therefore, since no such consensus has been reached, the simulation gives us increased reason to take seriously the Argument from Disagreement. Our conclusion is however not conclusive; the simulation also indicates what assumptions one has to make in order to reject the Argument from Disagreement. The simulation algorithm we use builds on the work of Hegselmann and Krause (J Artif Soc Social Simul 5(3); 2002, J Artif Soc Social Simul 9(3), 2006). (shrink)