Belief Systems and Partial Spaces

One important role of belief systems is to allow us to represent information about a certain domain of inquiry. This paper presents a formal framework to accommodate such information representation. Three cognitive models to represent information are discussed: conceptual spaces (Gärdenfors in Conceptual spaces: the geometry of thought. MIT Press, Cambridge, 2000), state-spaces (van Fraassen in Quantum mechanics: an empiricist view. Clarendon Press, Oxford, 1991), and the problem spaces familiar from artificial intelligence. After indicating their weakness to deal with partial information, it is argued that an alternative, formulated in terms of partial structures (da Costa and French in Science and partial truth. Oxford University Press, New York, 2003), can be provided which not only captures the positive features of these models, but also accommodates the partiality of information ubiquitous in science and mathematics.     

Spin and Wind Directions I: Identifying Entanglement in Nature and Cognition

We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions. Data are shown to violate the CHSH version of Bell’s inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics laboratories. This is the first part of a two-part article. In the second part (Aerts et al. in Found Sci, 2017) we present a symmetrized version of the same experiment for which we provide a quantum modeling of the collected data in Hilbert space.     

Artificial Diamonds are Still Diamonds

As a reply to the commentary (Lenhard in Found Sci, 2012), we stress here that structural understanding of data analysis techniques is the natural counterpart to the lack of understanding of phenomena in agnostic science. We suggest moreover that the dynamics of computational processes, and their parallels with the dynamics of natural processes, will increasingly be, possibly, the driving force of the development of data analysis.     

Social Autonomy and Heteronomy in the Age of ICT: The Digital <Emphasis Type="Italic">Pharmakon</Emphasis> and the (Dis)Empowerment of the General Intellect

‘The art of living with ICTs (information and communication technologies)’ today not only means finding new ways to cope, interact and create new lifestyles on the basis of the new digital (network) technologies individually, as ‘consumer-citizens’. It also means inventing new modes of living, producing and, not in the least place, struggling collectively, as workers and producers. As the so-called digital revolution unfolds in the context of a neoliberal cognitive and consumerist capitalism, its ‘innovations’ are predominantly employed to modulate and control both production processes and consumer behavior in view of the overall goal of extracting surplus value. Today, the digital networks overwhelmingly destroy social autonomy, instead engendering increasing social heteronomy and proletarianization. Yet it is these very networks themselves, as technical pharmaka in the sense of French ‘technophilosopher’ Bernard Stiegler, that can be employed as no other to struggle against this tendency. This paper briefly explores this possibility by reflecting upon current diagnoses of our ‘technological situation’ by some exemplary post-operaist Marxists from a Stieglerian, pharmacological perspective.     

The Abductive Loop: Tracking Irrational Sets

We argue from the Church-Turing thesis (Kleene Mathematical logic. New York: Wiley 1967) that a program can be considered as equivalent to a formal language similar to predicate calculus where predicates can be taken as functions. We can relate such a calculus to Wittgenstein’s first major work, the Tractatus, and use the Tractatus and its theses as a model of the formal classical definition of a computer program. However, Wittgenstein found flaws in his initial great work and he explored these flaws in a new thesis described in his second great work; the Philosophical Investigations. The question we address is “can computer science make the same leap?” We are proposing, because of the flaws identified by Wittgenstein, that computers will never have the possibility of natural communication with people unless they become active participants of human society. The essential difference between formal models used in computing and human communication is that formal models are based upon rational sets whereas people are not so restricted. We introduce irrational sets as a concept that requires the use of an abductive inference system. However, formal models are still considered central to our means of using hypotheses through deduction to make predictions about the world. These formal models are required to continually be updated in response to peoples’ changes in their way of seeing the world. We propose that one mechanism used to keep track of these changes is the Peircian abductive loop.     

Identifying Difference,Engaging Dissent: What is at Stake in Democratizing Knowledge?

Several prominent voices have called for a democratization of science through deliberative processes that include a diverse range of perspectives and values. We bring these scholars into conversation with extant research on democratic deliberation in political theory and the social sciences. In doing so, we identify systematic barriers to the effectiveness of inclusive deliberation in both scientific and political settings. We are particularly interested in what we call misidentified dissent, where deliberations are starkly framed at the outset in terms of dissenting positions without properly distinguishing the kinds of difference and disagreement motivating dissent.     

Spin and Wind Directions II: A Bell State Quantum Model

In the first half of this two-part article (Aerts et al. in Found Sci. doi: 10.1007/s10699-017-9528-9, 2017b), we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and showed that the data violate the CHSH version of Bell’s inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms.     

Perceiving the Infinite and the Infinitesimal World: Unveiling and Optical Diagrams in Mathematics

Many important concepts of the calculus are difficult to grasp, and they may appear epistemologically unjustified. For example, how does a real function appear in “small” neighborhoods of its points? How does it appear at infinity? Diagrams allow us to overcome the difficulty in constructing representations of mathematical critical situations and objects. For example, they actually reveal the behavior of a real function not “close to” a point (as in the standard limit theory) but “in” the point. We are interested in our research in the diagrams which play an optical role –microscopes and “microscopes within microscopes”, telescopes, windows, a mirror role (to externalize rough mental models), and an unveiling role (to help create new and interesting mathematical concepts, theories, and structures). In this paper we describe some examples of optical diagrams as a particular kind of epistemic mediator able to perform the explanatory abductive task of providing a better understanding of the calculus, through a non-standard model of analysis. We also maintain they can be used in many other different epistemological and cognitive situations.     

The Death and the Resurrection of (Psy)critique: The Case of Neuroeducation

A rapidly emerging hegemonic neuro-culture and a booming neural subjectivity signal the entry point for an inquiry into the status of the signifier neuro as a universal passe-partout. The wager of this paper is that the various (mis)appropriations of the neurosciences in the media and in academia itself point to something essential, if not structural, in connection with both the discipline of the neurosciences and the current socio-cultural and ideological climate. Starting from the case of neuroeducation (the application of neuroscience within education), the genealogy of the neurological turn is linked to the history of psychology and its inextricable bond with processes of psychologisation. If the neurological turn risks not merely neglecting the dimension of critique, but also obviating its possibility, then revivifying a psy-critique (understanding the academified modern subject as grounded in the scientific point of view from nowhere) might be necessary in order to understand today’s neural subjectivity and its place within current biopolitics.     

Computational and Biological Analogies for Understanding Fine-Tuned Parameters in Physics

In this philosophical paper, we explore computational and biological analogies to address the fine-tuning problem in cosmology. We first clarify what it means for physical constants or initial conditions to be fine-tuned. We review important distinctions such as the dimensionless and dimensional physical constants, and the classification of constants proposed by Lévy-Leblond. Then we explore how two great analogies, computational and biological, can give new insights into our problem. This paper includes a preliminary study to examine the two analogies. Importantly, analogies are both useful and fundamental cognitive tools, but can also be misused or misinterpreted. The idea that our universe might be modelled as a computational entity is analysed, and we discuss the distinction between physical laws and initial conditions using algorithmic information theory. Smolin introduced the theory of “Cosmological Natural Selection” with a biological analogy in mind. We examine an extension of this analogy involving intelligent life. We discuss if and how this extension could be legitimated.     

Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation

This paper introduces a novel mixture model-based approach to the simultaneous clustering and optimal segmentation of functional data, which are curves presenting regime changes. The proposed model consists of a finite mixture of piecewise polynomial regression models. Each piecewise polynomial regression model is associated with a cluster, and within each cluster, each piecewise polynomial component is associated with a regime (i.e., a segment). We derive two approaches to learning the model parameters: the first is an estimation approach which maximizes the observed-data likelihood via a dedicated expectation-maximization (EM) algorithm, then yielding a fuzzy partition of the curves into K clusters obtained at convergence by maximizing the posterior cluster probabilities. The second is a classification approach and optimizes a specific classification likelihood criterion through a dedicated classification expectation-maximization (CEM) algorithm. The optimal curve segmentation is performed by using dynamic programming. In the classification approach, both the curve clustering and the optimal segmentation are performed simultaneously as the CEM learning proceeds. We show that the classification approach is a probabilistic version generalizing the deterministic K-means-like algorithm proposed in Hébrail, Hugueney, Lechevallier, and Rossi (2010). The proposed approach is evaluated using simulated curves and real-world curves. Comparisons with alternatives including regression mixture models and the K-means-like algorithm for piecewise regression demonstrate the effectiveness of the proposed approach.     

<Emphasis Type="Italic">The Mathematical Intelligencer</Emphasis> Flunks the Olympics

The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and clearer system (IST). Lou Kauffman, who published an article on a grossone, places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals.     

Constructivism, Cognition, and Science – An Investigation of Its Links and Possible Shortcomings

This paper addresses the questions concerningthe relationship between scientific andcognitive processes. The fact that both,science and cognition, aim at acquiring somekind of knowledge or representationabout the “world” is the key for establishing alink between these two domains. It turns outthat the constructivist frameworkrepresents an adequate epistemologicalfoundation for this undertaking, as its focusof interest is on the (constructive)relationship between the world and itsrepresentation. More specifically, it will beshown how cognitive processes and their primaryconcern to construct a representation of theenvironment and to generate functionallyfitting behavior can act as the basis forembedding the activities and dynamics of theprocess of science in them by making use ofconstructivist concepts, such as functionalfitness, structure determinedness, etc.Cognitive science and artificiallife provide the conceptual framework of representational spaces and their interactionbetween each other and with the environmentenabling us to establish this link betweencognitive processes and thedevelopment/dynamics of scientific theories.The concepts of activation, synaptic weight,and genetic (representational) spaces arepowerful tools which can be used as“explanatory vehicles”for a cognitivefoundation of science, more specifically forthe “context of discovery” (i.e., thedevelopment, construction, and dynamics ofscientific theories and paradigms).Representational spaces do not only offer us abetter understanding of embedding science incognition, but also show, how theconstructivist framework, both, can act as anadequate epistemological foundation for theseprocesses and can be instantiated by theserepresentational concepts from cognitivescience. The final part of this paper addresses somemore fundamental questions concerning thepositivistic and constructivist understandingof science and human cognition. Among otherthings it is asked, whether a purelyfunctionalist and quantitative view of theworld aiming almost exclusively at itsprediction and control is really satisfying forour intellect (having the goal of achieving aprofound understanding of reality).     

Weighted Graphs with Distances in Given Ranges

Let \( \mathcal{G} \) = (G,w) be a weighted simple finite connected graph, that is, let G be a simple finite connected graph endowed with a function w from the set of the edges of G to the set of real numbers. For any subgraph G′ of G, we define w(G′) to be the sum of the weights of the edges of G′. For any i, j vertices of G, we define D _{i,j}(\( \mathcal{G} \)) to be the minimum of the weights of the simple paths of G joining i and j. The D _{i,j}(\( \mathcal{G} \)) are called 2-weights of \( \mathcal{G} \). Weighted graphs and their reconstruction from 2-weights have applications in several disciplines, such as biology and psychology.Let \( {\left\{{m}_I\right\}}_{I\in \left(\frac{\left\{1,\dots, n\right\}}{2}\right)} \) and \( {\left\{{M}_I\right\}}_{I\in \left(\frac{\left\{1,\dots, n\right\}}{2}\right)} \) be two families of positive real numbers parametrized by the 2-subsets of {1, …, n} with m _I ≤ M _I for any I; we study when there exist a positive-weighted graph G and an n-subset {1, …, n} of the set of its vertices such that D _I (\( \mathcal{G} \)) ∈ [m _I ,M _I ] for any \( I\in \left(\frac{\left\{1,\dots, n\right\}}{2}\right) \). Then we study the analogous problem for trees, both in the case of positive weights and in the case of general weights.     

On the Meaning of Volunteering: A Study of Worldviews in Everyday Life

This article is intended to contribute to the discussion on the meaning of volunteering by investigating voluntary work from the viewpoint of volunteers active in Swedish civil society organizations.Meaning refers both to the cognitive meaning of concepts and to the perceived meaning in life. The aim to uncover the predicates that people attribute to the concept is an attempt to anatomize volunteering as a social construct. Five predicates emerged and they make up the phenomenological structure of volunteering. By contextualizing this structure in contemporary Swedish society, it is demonstrated that the conceptual meaning of volunteering has significance for its existential meaning. The volunteers say that their authenticity is confirmed through the voluntary work since they are making themselves manifest in public. Following Hannah Arendt, the reasons for this is that authenticity demands that the volunteers conduct their actions in a public realm where their actions acquire an intrinsic value as neither coerced nor instrumental.     

On the Properties of <Emphasis Type="Italic">α</Emphasis>-Unchaining Single Linkage Hierarchical Clustering

In the election of a hierarchical clustering method, theoretic properties may give some insight to determine which method is the most suitable to treat a clustering problem. Herein, we study some basic properties of two hierarchical clustering methods: α-unchaining single linkage or SL(α) and a modified version of this one, SL?(α). We compare the results with the properties satisfied by the classical linkage-based hierarchical clustering methods.     

The Unseen Déjà-Vu: From Erkki Huhtamo’s <Emphasis Type="Italic">Topoi</Emphasis> to Ken Jacobs’ Remakes

This commentary on Edwin Carels’ essay “Revisiting Tom Tom: Performative anamnesis and autonomous vision in Ken Jacobs’ appropriations of Tom Tom the Piper’s Son” broadens up the media-archaeological framework in which Carels places his text. Notions such as Huhtamo’s topos and Zielinski’s “deep time” are brought into the discussion in order to point out the difficulty to see what there is to see and to question the position of the viewer in front of experimental films like Tom Tom the Piper’s Son and its remakes.     

自主论、还原论和计算主义

关于生命科学与物理科学之间关系的认识论和解释方式的讨论,可以大体上划分为自主论和还原论(或称之为"分支论"),两种观点在对"突现"的理解、解释方式的看法是相互对立的;而对于"突现"问题和解释方式的讨论,最终可以归结到对进化现象的解释.对进化过程给予公理化解释和动力学演化过程的计算描述是还原论的观点,但是,这种计算解释遭受到即使不是无限也是巨大的复杂性的困境.强大运算能力的计算机和计算机仿真实验成为解决计算困境的突破口,以康韦(J.Conway)证明了细胞自动机与图灵机完全等价为契机,导致了对生命过程的计算主义理解的兴起并产生了计算主义生命本质观.计算主义生命本质观带有还原论的色彩,但是,并非完全地支持还原论,实际上弱化了还原论,因为主张从部分到整体的突现过程的可计算性与可预言性是不同的.     

模块性、经典计算和意向实在论——论福多思维非模块性论题的一个本体论后果

福多将计算模块的概念运用于对心灵模块性的分析，提出心灵之负责输入分析的部分（感知觉系统、语言系统等）是模块性的，而心灵之专司信念的确立和思维之职的部分（中心系统）是非模块性的。由此，福多进一步得出心的计算理论不适用于中心系统的结论。然而，福多的结论给他的计算主义的意向实在论辩护带来了问题：如果思维不是计算，那么，福多关于常识心理学所持的意向实在论主张就成了空中楼阁。