In this article, we endeavour to lay the theoretical fundaments of a phenomenologically based project regarding the origins of conscious experience in the natural world. We assume that a phenomenological analysis (based upon Edmund Husserl’s philosophy) of first-person experience could substantially contribute to related empirical research. In this regard, two phenomenological conceptions provided by Husserl are of fundamental importance. The first relates to the essential and necessary _embodiment_ of every subjective experience; the second concerns the intrinsically _holistic and concrete character (...) of consciousness_. These considerations have two crucial implications. First, every mental content and capability ultimately refers to a bodily basis as its carrier and realizer (‘embodied manifestation thesis’). Second, there is a minimal set of bodily structures that carries and realizes the minimal mind (‘minimal context thesis’). Based upon these assumptions, _we can use phenomenology to select from the empirical theories of consciousness_. We argue that currently, Bjorn Merker’s _subcortical theory of consciousness_ appears to be the best candidate for a phenomenological approach. In phenomenological regard, however, it is highly challenging to test a subcortical theory; therefore, we suggest that certain experiments based upon emergence from general anaesthesia might help test such a theory in a phenomenologically legitimate way. (shrink)

Exploring and reassessing the philosophical notion of relation, Of Minimal Things views relation as the minimal and elemental theme and structure of philosophy, in contrast to the scholastic, ontological conception of relation as a thing of diminished being. Drawing radical conclusions from the classical understanding of relation as a being-toward-another, it argues that rethinking relation engages the very possibility and limits of philosophical discourse. In the author's studies of Nietzsche, Benjamin, Husserl, Heidegger, Derrida and Blanchot, relation is shown (...) to be central to their thought and to undergo elaborations that escape the ontological, categorial, and formalist ways in which the concept has traditionally been interpreted. Studying the writings of Mallarme; and Kafka, the author argues that philosophy necessarily opens up to and is implicated in its others, one such possible other being literature. (shrink)

According to one influential view, model-building in science is primarily a matter of simplifying theoretical descriptions of real-world target systems using abstraction and idealization. This view, however, does not adequately capture all types of models. Many contemporary models in the natural and social sciences – from physics to biology to economics – stand in a more tenuous relationship with real-world target systems and have a decidedly stipulative element, in that they create, by fiat, ‘model worlds’ that operate according to (...) some set of specified rules. While such models may be motivated by an interest in actual target phenomena, their validity is not – at least not primarily – to be judged by whether they constitute an empirically adequate representation of any particular empirical system. The present paper compares and contrasts three such types of models: minimal models, toy models, and exploratory models. All three share some characteristics and thus overlap in interesting ways, yet they also exhibit significant differences. It is argued that, in all three cases, modal considerations have an important role to play: by exploring the modal structure of theories and phenomena – that is, by probing possibilities in various ways – such models deepen our understanding and help us gain knowledge not only about what there is in the world, but also about what there could be. (shrink)

The ways in which space-time points and elementary particles are modeled share a curious feature: neither seems to specify which basic object has which properties. This chapter sketches the motivation for this claim and searches for an explanation for it. After reviewing several proposals, it argues for a view according to which objects occupy their place in a given relational structure essentially. This view, which is termed minimal structural essentialism, provides a metaphysical grounding for the physical equivalence of models (...) related by permutation. An interesting consequence of this position is that space-time points and elemental particles turn out to be individuals, albeit of a rather different sort than has traditionally been considered. (shrink)

Classifying research proposals by risk of harm is fundamental to the approval process and the most pivotal risk category in most regulations is that of “minimal risk.” If studies have no more than a minimal risk, for example, a nearly worldwide consensus exists that review boards may sometimes: (1) expedite review, (2) waive or modify some or all elements of informed consent, or (3) enroll vulnerable subjects including healthy children, incapacitated persons and prisoners even if studies do not (...) hold out direct benefits to them. The moral and social purposes behind this threshold are discussed along with relevant views from the National Commission, NBAC, NHRPAC, Grimes v. Kennedy Krieger Institute, The Nuremberg Code, and The WMA's Declaration of Helsinki. Representative policies from Australia, Canada, South Africa, the U.S., and CIOMS are reviewed revealing different understandings of this sorting threshold. Six of nine frequently cited interpretations of “minimal risk” are untenable. The “absolute” interpretation of the “routine examination” standard is defended as best. (shrink)

We present a formalization of collections that Cornelius Castoriadis calls “magmas”, especially the property which mainly characterizes them and distinguishes them from the usual cantorian sets. It is the property of their elements to _depend_ on other elements, either in a one-way or a two-way manner, so that one cannot occur in a collection without the occurrence of those dependent on it. Such a dependence relation on a set _A_ of atoms (or urelements) can be naturally represented by a pre-order (...) relation \(\preccurlyeq \) of _A_ with the extra condition that it contains no minimal elements. Then, working in a mild strengthening of the theory \(\textrm{ZFA}\), where _A_ is an infinite set of atoms equipped with a primitive pre-ordering \(\preccurlyeq \), the class of magmas over _A_ is represented by the class \(LO(A,\preccurlyeq )\) of nonempty open subsets of _A_ with respect to the lower topology of \(\langle A,\preccurlyeq \rangle \). The non-minimality condition for \(\preccurlyeq \) implies that all sets of \(LO(A,\preccurlyeq )\) are infinite and none of them is \(\subseteq \) -minimal. Next the pre-ordering \(\preccurlyeq \) is shifted (by a kind of simulation) to a pre-ordering \(\preccurlyeq ^+\) on \({{\mathcal {P}}}(A)\), which turns out to satisfy the same non-minimality condition as well, and which, happily, when restricted to \(LO(A,\preccurlyeq )\) coincides with \(\subseteq \). This allows us to define a hierarchy \(M_\alpha (A)\), along all ordinals \(\alpha \ge 1\), the“magmatic hierarchy”, such that \(M_1(A)=LO(A,\preccurlyeq )\), \(M_{\alpha +1}(A)=LO(M_\alpha (A),\subseteq )\), and \(M_\alpha (A)=\bigcup _{\beta, for a limit ordinal \(\alpha \). For every \(\alpha \ge 1\), \(M_\alpha (A)\subseteq V_\alpha (A)\), where \(V_\alpha (A)\) are the levels of the universe _V_(_A_) of \(\textrm{ZFA}\). The class \(M(A)=\bigcup _{\alpha \ge 1}M_\alpha (A)\) is the “magmatic universe above _A_.” The axioms of Powerset and Union (the latter in a restricted version) turn out to be true in \(\langle M(A),\in \rangle \). Besides it is shown that three of the five principles about magmas that Castoriadis proposed in his writings (mildly modified and adapted to the needs of formalization), \(M2^*\), \(M3^*\) and \(M5^*\), are true of _M_(_A_). A selection of excerpts from these writings, in which the concept of magma was first introduced and elaborated, is presented in the Introduction. (shrink)

To the best of our current understanding, quantum mechanics is part of the most fundamental picture of the universe. It is natural to ask how pure and minimal this fundamental quantum description can be. The simplest quantum ontology is that of the Everett or Many-Worlds interpretation, based on a vector in Hilbert space and a Hamiltonian. Typically one also relies on some classical structure, such as space and local configuration variables within it, which then gets promoted to an algebra (...) of preferred observables. We argue that even such an algebra is unnecessary, and the most basic description of the world is given by the spectrum of the Hamiltonian and the components of some particular vector in Hilbert space. Everything else—including space and fields propagating on it—is emergent from these minimal elements. (shrink)

Operators which map subsets of a given set to the set of their minimal elements with respect to some relation R form the basis of a semanticapproach in non-monotonic logic, belief revision, conditional logic and updating. In this paper we investigate operators of this type from an algebraicviewpoint. A representation theorem is proved and various properties of theresulting algebras are investigated. It is shown that they behave quite differently from known algebras related to logics, e.g. modal algebras and Heytingalgebras.

We establish the existence uncountably many atoms in the subvariety lattice of the variety of involutive residuated lattices. The proof utilizes a construction used in the proof of the corresponding result for residuated lattices and is based on the fact that every residuated lattice with greatest element can be associated in a canonical way with an involutive residuated lattice.

Saba Bazargan proposes a novel “hybrid” justification for the killing of minimally responsible threats (MRTs). His account allegedly combines two elements, namely “the complex account of liability” and “the lesser-evil discounting view.” I argue that Bazargan’s conclusion that minimally responsible threats can sometimes be killed as well as certain other conclusions that Bazargan regards as a particular advantage of his hybrid account are single-handedly generated by one element of the “hybrid account,” namely by the lesser-evil discounting view. The lesser-evil (...) discounting view therefore does not need to be combined with “the complex account of liability,” nor, indeed, with any account of liability. Thus, Bazargan’s hybrid view is redundant. Moreover, I will argue that both the hybrid view and the lesser evil discounting view of killing MRTs have strongly counter-intuitive implications and should therefore be rejected. (shrink)

We study o-minimal expansions of Archimedean totally ordered groups. We first prove that any such expansion must be elementarily embeddable via a unique (provided some nonzero element is 0-definable) elementary embedding into a unique o-minimal expansion of the additive ordered group of real numbers R. We then show that a definable function in an o-minimal expansion of R enjoys good differentiability properties and use this to prove that an Archimedean real closed field is definable in any (...) nonsemilinear expansion of R. Combining these results, we obtain several restrictions on possible o-minimal expansions of arbitrary Archimedean ordered groups and in particular of the rational ordered group. (shrink)

Among the virtues of relationist approaches to Frege’s puzzle is that they put us in a position to outline structural features of the puzzle that were only implicit in earlier work. In particular, they allow us to frame questions about the relation between the explanatory roles of sense and sameness of sense. In this paper, I distinguish a number of positions about that relation which have not been clearly distinguished. This has a few pay-offs. It allows us to shed light (...) on recent controversies about the ‘essential indexical’, and it also allows us to see what’s at stake between relationists and their opponents. When we see what’s at stake, we can see that we have reason to adopt an account of cognitive significance that incorporates elements of both relationist and Fregean approaches. (shrink)

Sections 1, 2 and 3 contain the main result, the strong finite axiomatizability of all 2-valued matrices. Since non-strongly finitely axiomatizable 3-element matrices are easily constructed the result reveals once again the gap between 2-valued and multiple-valued logic. Sec. 2 deals with the basic cases which include the important F i from Post's classification. The procedure in Sec. 3 reduces the general problem to these cases. Sec. 4 is a study of basic algebraic properties of 2-element algebras. In (...) particular, we show that equational completeness is equivalent to the Stone-property and that each 2-element algebra generates a minimal quasivariety. The results of Sec. 4 will be applied in Sec. 5 to maximality questions and to a matrix free characterization of 2-valued consequences in the lattice of structural consequences in any language. Sec. 6 takes a look at related axiomatization. problems for finite algebras and matrices. We study the notion of a propositional consequence with equality and, among other things, present explicit axiomatizations of 2-valued consequences with equality. (shrink)

We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally complete (PS I-complete) POVM. We show that a measurement with 2D−1 outcomes cannot be PS I-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PS I-complete POVM has 2D outcomes. We also consider PS I-complete POVMs that have only rank-one POVM elements (...) and construct an example with 3D−2 outcomes, which is a generalization of the tetrahedral measurement for a qubit. The question of the minimal number of elements in a rank-one PS I-complete POVM is left open. (shrink)

In this paper, I present a new framework supporting the claim that some elements in science play a constitutive function, with the aim of overcoming some limitations of Friedman's (2001) account. More precisely, I focus on what I consider to be the gradualism implicit in Friedman's interpretation of the constitutive a priori, that is, the fact that it seems to allow for degrees of 'constitutivity'. I tease out such gradualism by showing that the constitutive character Friedman aims to track can (...) be captured by three features - namely, quasi-axiomaticity (QA), generative potential (GP), and empirical shielding (ES) - which are exhibited to a maximal degree by the examples Friedman deploys, particularly in his analysis of Newtonian mechanics. I argue that not all varieties of 'constitutivity' can be captured by the kind of gradualism implicit in Friedman's view, although developing the gradualism itself might provide useful insights. To show this, I analyse the function of the Hardy-Weinberg principle (HWP) in population genetics in terms of its QA, GP, and ES. Whereas the HWP does not count as constitutive in classical philosophical interpretations (Sober 1984), nor does it within Friedman's framework, it does nonetheless perform a minimally constitutive function. By means of historical details and considerations on the prospects of replacing the HWP, I show that the HWP is minimally constitutive by being a counterfactual instantiation of a paradigmatically constitutive stability principle, where the latter might itself be regarded as an enabling condition for a variety of modelling practices across the sciences. (shrink)

This paper argues that severe and ongoing trauma (SOT) can lead to impairment at the level of the minimal self (MS), which is the core element in the structure of subjectivity. In the long-term, such impairments can result in complex post-traumatic stress disorder (CPTSD) and schizophrenia. The paper tackles this issue while trying to create meaningful bridges between phenomenology and neuroscience.

Two approaches to understanding the idealizations that arise in the Aharonov–Bohm effect are presented. It is argued that a common topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory role (...) of said idealizations is examined via a minimal model explanatory scheme. Last, the idealizations involved in the AB effect are placed in a wider philosophical context via a short survey of part of the literature on infinite and essential idealizations. (shrink)

LetL(K) denote the lattice (ordered by inclusion) of quasivarieties contained in a quasivarietyK and letD 2 denote the variety of distributive (0, 1)-lattices with 2 additional nullary operations. In the present paperL(D 2) is described. As a consequence, ifM+N stands for the lattice join of the quasivarietiesM andN, then minimal quasivarietiesV 0,V 1, andV 2 are given each of which is generated by a 2-element algebra and such that the latticeL(V 0+V1), though infinite, still admits an easy and (...) nice description (see Figure 2) while the latticeL(V 0+V1+V2), because of its intricate inner structure, does not. In particular, it is shown thatL(V 0+V1+V2) contains as a sublattice the ideal lattice of a free lattice with free generators. Each of the quasivarietiesV 0,V 1, andV 2 is generated by a 2-element algebra inD 2. (shrink)

We give several characterizations of weakly minimal abelian structures. In two special cases, dual in a sense to be made explicit below, we give precise structure theorems: 1. When the only finite 0-definable subgroup is {0}, or equivalently 0 is the only algebraic element (the co-strongly minimal case); 2. When the theory of the structure is strongly minimal. In the first case, we identify the abelian structure as a "near-subspace" A of a vector space V over (...) a division ring D with its induced structure, with possibly some collection of distinguished subgroups of A of finite index in A and (up to $acl(\emptyset)$ ) no further structure. In the second, the structure is that of V/A for a vector space and near-subspace as above, with the only further possible structure some collection of distinguished points. Here a near-subspace of V is a subgroup A such that for any nonzero d ∈ D, the index of $A\cap dA$ in A is finite. We also show that any weakly minimal abelian structure is a reduct of a weakly minimal module. (shrink)

Contemporary phenomenological psychopathology has raised questions concerning selfhood and its possible alterations in schizophrenia spectrum disorders. Although the notion of the self is central to several accounts of anomalies, it remains a question how exactly the radically minimal experiential features of selfhood can be altered. Indeed, the risk is to reduce the notion of selfhood so drastically, that it can no longer account for alterations of experience. Here we propose to give thickness to the minimal self. To do (...) this we first discuss Sartre’s phenomenological definition of coenesthesia as the translucent matter of consciousness articulating it with the notion of existential feelings. We then draw on the historical research on coenesthesia to dig deeper in this translucent materiality identified as the element of the body. We show that selfhood, even in its most minimal level, must be conceived of with a specific elemental thickness, corresponding to a phenomenological materiality of embodiment. We argue that a phenomenological reading of coenesthesia as the bodily element of ipseity can shed a new light on the anomalies of self-experience. (shrink)

We describe a recent program from the study of definable groups in certain o-minimal structures. A central notion of this program is that of a lattice. We propose a definition of a lattice in an arbitrary first-order structure. We then use it to describe, uniformly, various structure theorems for o-minimal groups, each time recovering a lattice that captures some significant invariant of the group at hand. The analysis first goes through a local level, where a pertinent notion of (...) pregeometry and generic elements is each time introduced. (shrink)

We prove that a function definable with parameters in an o-minimal structure is bounded away from ∞ as its argument goes to ∞ by a function definable without parameters, and that this new function can be chosen independently of the parameters in the original function. This generalizes a result in [1]. Moreover, this remains true if the argument is taken to approach any element of the structure , and the function has limit any element of the structure.

The account of causal regularities in the influential INUS theory of causation has been refined in the recent developments of the regularity approach to causation and of the Boolean methods for inference of deterministic causal structures. A key element in the refinement is to strengthen the minimality or non-redundancy condition in the original INUS account. In this paper, we argue that the Boolean framework warrants a further strengthening of the minimality condition. We motivate our stronger condition by showing, first, (...) that a rationale for strengthening the original minimality condition in the INUS theory is also applicable to our proposal to go further, and second, that the new element of the stronger condition is a counterpart to a well-established minimality condition for probabilistic causal models. We also compare the various minimality conditions in terms of the difference-making criteria they imply and argue for the criterion implied by our condition. Finally, we show that putative counterexamples to our proposal can be addressed in the same way that the Boolean theorists defend the current minimality conditions in their framework. (shrink)

Electronegativity, described by Linus Pauling described as “The power of an atom in a molecule to attract electrons to itself” (Pauling in The nature of the chemical bond, 3rd edn, Cornell University Press, Ithaca, p 88, 1960), is used to predict bond polarity. There are dozens of methods for empirically quantifying electronegativity including: the original thermochemical technique (Pauling in J Am Chem Soc 54:3570–3582, 1932), numerical averaging of the ionisation potential and electron affinity (Mulliken in J Chem Phys 2:782–784, 1934), (...) effective nuclear charge and covalent radius analysis (Sanderson in J Chem Phys 23:2467, 1955) and the averaged successive ionisation energies of an element’s valence electrons (Martynov and Batsanov in Zhurnal Neorganicheskoi Khimii 5:3171–3175, 1980), etc. Indeed, there are such strong correlations between numerous atomic parameters—physical and chemical—that the term “electronegativity” integrates them into a single dimensionless number between 0.78 and 4.00 that can be used to predict/describe/model much of an element’s physical character and chemical behaviour. The design of the common and popular medium form of the periodic table is in large part determined by four quantum numbers and four associated rules. However, adding electronegativity completes the construction so that it displays the multi-parameter periodic law operating in two dimensions, down the groups and across the periods, with minimal ambiguity. (shrink)

In this article, I argue that the artificial components of hybrid bionic systems do not play a direct explanatory role, i.e., in simulative terms, in the overall context of the systems in which they are embedded in. More precisely, I claim that the internal procedures determining the output of such artificial devices, replacing biological tissues and connected to other biological tissues, cannot be used to directly explain the corresponding mechanisms of the biological component(s) they substitute (and therefore cannot be used (...) to explain the local mechanisms determining an overall biological or cognitive function replicated by such bionic models). I ground this analysis on the use of the Minimal Cognitive Grid (MCG), a novel framework proposed in Lieto (Cognitive design for artificial minds, 2021) to rank the epistemological and explanatory status of biologically and cognitively inspired artificial systems. Despite the lack of such a direct mechanistic explanation from the artificial component, however, I also argue that the hybrid bionic systems can have an indirect explanatory role similar to the one played by some AI systems built by using an overall structural design approach (but including the partial adoption of functional components). In particular, the artificial replacement of part(s) of a biological system can provide i) a local functional account of that part(s) in the context of the overall functioning of the hybrid biological–artificial system and ii) global insights about the structural mechanisms of the biological elements connected to such artificial devices. (shrink)

For a signature L with at least one constant symbol, an L‐structure is called minimal if it has no proper substructures. Let be the set of isomorphism types of minimal L‐structures. The elements of can be identified with ultrafilters of the Boolean algebra of quantifier‐free L‐sentences, and therefore one can define a Stone topology on. This topology on generalizes the topology of the space of n‐marked groups. We introduce a natural ultrametric on, and show that the Stone topology (...) on coincides with the topology of the ultrametric space iff the ultrametric space is compact iff L is locally finite (that is, L contains finitely many n‐ary symbols for any ). As one of the applications of compactness of the Stone topology on, we prove compactness of certain classes of metric spaces in the Gromov‐Hausdorff topology. This slightly refines the known result based on Gromov's ideas that any uniformly totally bounded class of compact metric spaces is precompact. (shrink)

We prove weak elimination of imaginary elements for Boolean orderings with finitely many atoms. As a consequence we obtain equivalence of the two notions of o-minimality for Boolean ordered structures, introduced by C. Toffalori. We investigate atoms in Boolean algebras induced by algebraically closed subsets of Boolean ordered structures. We prove uniqueness of prime models in strongly o-minimal theories of Boolean ordered structures.

The spiral form of the Periodic Law is proposed as its fundamental graphic representation. This idea is based on the fact that the spiral is the most appropriate form in description transitions from simple to complicated. The spiral is easily obtained from the linear succession of the elements when they are ranged by growing nuclear charge. The spiral can be simply transformed into many other graphic representations, including tables. This paper suggests the conception of the autonomy of blocks. This autonomy (...) is clearly seen in the variation of the outer electronic shells, in the width and the height of the blocks, as well as the number and properties of elements included therein. The regularities in the changes of element properties are pronounced in certain blocks but actually absent in others. The blocks can be permuted to obtain full-fledged versions of Periodic Table. The new stage of the verification of the blocks autonomy is the use of the total number of the differentiating electrons as an independent variable in describing the properties of the elements and their compounds. Consideration of individual blocks made it possible to deduce the periodic equations valid for all the elements within each block. Formulation of the Periodic Law is advanced: while describing characteristic determining the properties of the elements, the nuclear charge is replaced by the total number of differentiating electrons. Two modifications of the conventional Periodic Table are obtained by minimal changes. The first one shows the secondary and the additional periodicites. Another table shows the total number of differentiating electrons for each element. (shrink)

Given a weakly o-minimal theory T, the T-height of an element of a model of T is defined as a means of classifying the order of magnitude of the element. If T satisfies some easily met technical conditions, then this classification is coarse enough for a Wilkie-type inequality: given a set of elements of a model of T, each of which has a different T-height, the cardinality of this set is at most 1 plus the minimum cardinality (...) of a set that generates the structure. (shrink)

This paper shows how key aspects of Aristotle’s core concepts of matter and motion, some of which have recently been shown to help make sense of quantum mechanical indeterminacy, align with some important results of the energy-momentum relationship of special relativity. In this conception, mobility and indeterminacy are inherently linked to each other and to materiality. Applying these ideas to massless particles, which relativity tells us move at the maximal cosmic speed, allows us to draw the conclusion that they must (...) be the most basic physical bodies, that is, mobile substances. The most familiar massless particle, the photon, constitutes light. Furthermore, because the photon composes luminous matter but cannot be decomposed into anything else more basic, it fulfills the definition of element. (shrink)

In this paper we attempt to advance the enactive discourse on perception by highlighting the role of bodily affects as prenoetic constraints on perceptual experience. Enactivists argue for an essential connection between perception and action, where action primarily means skillful bodily intervention in one’s surroundings. Analyses of sensory-motor contingencies (as in Noë 2004) are important contributions to the enactive account. Yet this is an incomplete story since sensory-motor contingencies are of no avail to the perceiving agent without motivational pull in (...) one direction or another or a sense of the pertinent affective contingencies. Before directly addressing the issue of affect in perception, we explain our peculiar, low-level conception of affect as a form of world-involving intentionality that modulates (minimally) bodily behavior without necessarily possessing informational value of any kind. We then address the deficiency concerning affect in enactive accounts of perception by examining some exemplary forms of bodily affect that constrain perception. We show that bodily affect significantly contributes to (either limiting or enabling) our contact with the world in our perceptually operative attentive outlook, in a kind of perceptual interest or investment, and in social perception. (shrink)

Despite the lack of invariance problem (the many‐to‐many mapping between acoustics and percepts), human listeners experience phonetic constancy and typically perceive what a speaker intends. Most models of human speech recognition (HSR) have side‐stepped this problem, working with abstract, idealized inputs and deferring the challenge of working with real speech. In contrast, carefully engineered deep learning networks allow robust, real‐world automatic speech recognition (ASR). However, the complexities of deep learning architectures and training regimens make it difficult to use them to (...) provide direct insights into mechanisms that may support HSR. In this brief article, we report preliminary results from a two‐layer network that borrows one element from ASR, long short‐term memory nodes, which provide dynamic memory for a range of temporal spans. This allows the model to learn to map real speech from multiple talkers to semantic targets with high accuracy, with human‐like timecourse of lexical access and phonological competition. Internal representations emerge that resemble phonetically organized responses in human superior temporal gyrus, suggesting that the model develops a distributed phonological code despite no explicit training on phonetic or phonemic targets. The ability to work with real speech is a major advance for cognitive models of HSR. (shrink)

Let M be a countable saturated structure, and assume that D(ν) is a strongly minimal formula (without parameter) such that M is the algebraic closure of D(M). We will prove the two following theorems: Theorem 1. If G is a subgroup of $\operatorname{Aut}(\mathfrak{M})$ of countable index, there exists a finite set A in M such that every A-strong automorphism is in G. Theorem 2. Assume that G is a normal subgroup of $\operatorname{Aut}(\mathfrak{M})$ containing an element g such that (...) for all n there exists $X \subseteq D(\mathfrak{M})$ such that $\operatorname{Dim}(g(X)/X) > n$. Then every strong automorphism is in G. (shrink)

We evaluate people all the time for a wide variety of activities. We blame them for miscalculations, uninspired art, and committing crimes. We praise them for detailed brushwork, a superb pass, and their acts of kindness. We accomplish things, from solving crosswords to mastering guitar solos. We bungle our endeavors, whether this is letting a friend down or burning dinner. Sometimes these deeds are morally significant, but many times they are not. Simply Responsible defends the radical proposal that the blameworthy (...) artist is responsible in just the same way that the blameworthy thief is. We can be responsible for all kinds of different activities, from lip-synching to long division, from murders to meringues, but the relation involved, what author Matt King calls the basic responsibility relation, is the same in every case. We are responsible for the things we do first, then blameworthy or praiseworthy for having done them in light of whether they're good or bad, according to a variety of standards. Why is this a radical proposal? Firstly, because so much of the contemporary literature on moral responsibility has moralized its nature. According to most accounts, moral responsibility is either a special species of responsibility or else depends on moralized capacities. In contrast, King argues that we get a more complete and unifying picture of responsible agency from a more general theory of responsibility. Secondly, the proposal is radical due to its drastic simplicity. King foregoes many of the complications that feature in other accounts of responsibility, arguing that we can make do with less demanding theoretical elements. (shrink)

This article examines the research of Louis J. Mordell on the Diophantine equation y2-k=x3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y^2-k=x^3$$\end{document} as it appeared in one of his first papers, published in 1914. After presenting a number of elements relating to Mordell’s mathematical youth and his (problematic) writing, we analyze the 1914 paper by following the three approaches he developed therein, respectively, based on the quadratic reciprocity law, on ideal numbers, and on binary cubic forms. This analysis (...) allows us to describe many of the difficulties in reading and understanding Mordell’s proofs, difficulties which we make explicit and comment on in depth. (shrink)

Small and medium-sized enterprises (SMEs) play a crucial role in national economic growth and contribute significantly to GDP, acting as the backbone of economies in competitive markets. However, ethical issues in SMEs are often overlooked compared to those in large organisations due to limited public financial exposure and minimal media coverage. Research on ethical culture is still limited, particularly in SMEs, as past studies have predominantly focused on large organisations. To gain deeper insights into the ethical culture of SMEs, (...) more qualitative research is needed to uncover the complexities of ethical conduct and organisational dynamics in SMEs. Therefore, this study employs a qualitative approach to explore the elements of ethical culture implemented in Malaysian SMEs. The data, gathered through in-depth interviews with eleven SME managers in Malaysia, revealed that ethical culture is reflected through formal systems, informal systems, leadership, and the newly highlighted element of religiosity. These four elements were explained with three goals for each element: communication, training, and management. The ethical issues faced by SMEs (favouritisms, selling company inventories, and disrespect towards female-led managers) were also highlighted. Accelerators (family influence, customer retention) and barriers (financial constraints) in implementing ethical culture were identified. Interestingly, this study highlights the significant role of religiosity in the ethical culture of SMEs, contributing to the literature and serving as a framework for future research. It aims to provide valuable insights for policymakers, business leaders, and stakeholders seeking to promote a robust ethical culture within the context of Malaysian SMEs. (shrink)

Throughout my investigation into abductive cognition, which is also associated with the endeavor to naturalize logic of its special consequence relation, I stressed the relevance of the following key elements: ‘optimization of eco-cognitive situatedness’, ‘maximization of changeability’ of both input and output of the general form of an inferential abductive problem and high ‘information-sensitiveness’. These elements will be summarized and further deepened in this article. In addition, I will demonstrate how, in contrast to traditional demonstrative logical ideal systems, which are (...) typified by what I refer to as the ‘maximization of memorylessness’, a naturalized logic of abduction demonstrates the necessity of recording the ‘past life’ of abductive inferential praxes. Lastly, I will analyze the significance and nature of the maximization of eco-cognitive openness, which characterizes abduction in science and describes how the many above-mentioned elements are relevant to the aims of new eco-cognitive epistemology. (shrink)

An important factor in judging whether two retinal images arise from the same object viewed from different positions may be the presence of certain properties or cues that are 'qualitative invariants' with respect to the natural transformations, particularly affine transformations, associated with changes in viewpoint. To test whether observers use certain affine qualitative cues such as concavity, convexity, collinearity, and parallelism of the image elements, a 'same-different' discrimination experiment was carried out with planar patterns that were defined by four points (...) either connected by straight line segments (line patterns) or marked by dots (dot patterns). The first three points of each pattern were generated randomly; the fourth point fell on their diagonal bisector. According to the position of that point, the patterns were concave, triangular (three points being collinear), convex, or parallel sided. In a 'same' trial, an affine transformation was applied to one of two identical patterns; in a 'different' trial, the affine transformation was applied after the point lying on the diagonal bisector was perturbed a short, fixed distance along the bisector, inwards for one pattern and outwards for the other. Observers' ability to discriminate 'same' from 'different' pairs of patterns depended strongly on the position of the fourth, displaced, point: performance varied rapidly when the position of the displaced point was such that the patterns were nearly triangular or nearly parallel sided, consistent with observers using the hypothesised qualitative cues. The experimental data were fitted with a simple probabilistic model of discrimination performance that used a combination of these qualitative cues and a single quantitative cue. (shrink)

A generic extension L[x]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{L}[x]}$$\end{document} by a real x is defined, in which the E0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{E}_0}$$\end{document}-class of x is a lightface Π21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\it \Pi}^1_2}$$\end{document} set containing no ordinal-definable reals.

This paper presents two possibility results and one impossibility result about a situation with three voters under a pairwise majoritarian aggregation function voting on a countably infi nite number of candidates. First, from individual orders with no maximal or minimal element, it is possible to generate an aggregate order with a maximal or minimal element. Second, from dense individual orders, it is possible to generate a discrete aggregate order. Finally, I show that, from discrete orders with (...) a particular property, namely the finite-distance property, it is not possible to generate a dense aggregate order. (shrink)

We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations \ and \. The set of its minimal elements proves to be very rich, and the \-hierarchy is used to get a better intuition of this richness. We find the place of the set of \-maximal ultrafilters among some known families of ultrafilters. Finally, we introduce new notions of largeness of (...) subsets of \, and compare it to other such notions, important for infinite combinatorics and topological dynamics. (shrink)

This paper investigates the semantics of measure phrases in Japanese. Based on new data, we argue that the interpretation of measure phrases in Japanese is sensitive to scale structure such that (i) measure phrases are introduced by a degree morpheme that selects only for gradable predicates whose scale contains a minimal element (i.e., a lower closed scale) and (ii) violations to this restriction are repaired via coercion, which forces a comparative interpretation with a contextually determined standard and hence (...) a minimal element. We compare the Japanese facts to data in other languages and argue that the requirement of having a minimal element is not specific to Japanese, but universal. We show that languages may vary in how they deal with potential violations of this universal constraint, including coercion of a contextually recoverable derived minimal element (Japanese), ungrammaticality (e.g., Spanish, Korean, Russian), and a hybrid system of ungrammaticality for some adjectives and allowed constraint violation for others (e.g., English, German, Italian). (shrink)

A relational structure \ is called reversible iff each bijective homomorphism from \ onto \ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible structures of a given relational language L is to notice that the maximal or minimal elements of isomorphism-invariant sets of interpretations of the language L on a fixed domain X determine reversible structures. We isolate certain syntactical conditions providing that a satisfiable \-theory defines a class of (...) interpretations having extreme elements on a fixed domain and detect several classes of reversible structures. For some of these classes, we characterize the corresponding reversible extreme interpretations. In particular, we characterize the reversible countable ultrahomogeneous graphs. (shrink)

We study the classes of hypersimple and semicomputable sets as well as their intersection in the weak truth table degrees. We construct degrees that are not bounded by hypersimple degrees outside any non-trivial upper cone of Turing degrees and show that the hypersimple-free c.e. wtt degrees are downwards dense in the c.e. wtt degrees. We also show that there is no maximal (w.r.t. ≤wtt) hypersimple wtt degree. Moreover, we consider the sets that are both hypersimple and semicomputable, characterize them as (...) the (bi-infinite) c.e. cuts of computable orderings of ℕ of order type ω+ω* and study their wtt degrees. We show that there are hypersimple degrees that are not bounded by any hypersimple semicomputable degree, investigate relationships with the join and look for maximal and minimal elements of related classes. (shrink)

The paper focusses on two claims about metaphysical structure: Atomism and Fundamentalism. The first of these claims says that there are mereological atoms, i.e. minimal elements in the mereological structure of reality. The second says that there are fundamental truths, i.e. minimal elements in the grounding structure of reality. A philosopher who defended both of these claims was Bernard Bolzano; the present paper is an exploration of his views on the matter.

Given a d.c.e. degree d, consider the d.c.e. sets in d and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree d > 0, the class of its c.e. predecessors in which d is c.e., denoted as R[d], can consist of either just one element, or an interval of c.e. degrees. After this, Ishmukhametov asked whether there exists a d.c.e. degree d for which the class (...) R[d] has no minimal element. We give a positive answer to this question. (shrink)

The foundation scheme in set theory asserts that every nonempty class has an ∈\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\in $$\end{document}-minimal element. In this paper, we investigate the logical strength of the foundation principle in basic set theory and α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-recursion theory. We take KP set theory without foundation as the base theory. We show that KP-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} (...) \setlength{\oddsidemargin}{-69pt} \begin{document}$$^-$$\end{document} + Π1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Pi _1$$\end{document}-Foundation + V=L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V=L$$\end{document} is enough to carry out finite injury arguments in α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-recursion theory, proving both the Friedberg-Muchnik theorem and the Sacks splitting theorem in this theory. In addition, we compare the strengths of some fragments of KP. (shrink)

Minimally, metaphysical realists hold that there exist some mind-independent entities. Metaphysical realists also hold that we can speak meaningfully or truthfully about mind-independent entities. Those who reject metaphysical realism deny one or more of these commitments. This Element aims to introduce the reader to the core commitments of metaphysical realism and to illustrate how these commitments have changed over time by surveying some of the main families of views that realism has been contrasted with: such as scepticism, idealism, and (...) anti-realism. (shrink)

Minimally, myth means “story,” and religion means “that which binds” a community into a coherent unity. Myth and religion are closely associated because a shared myth is the most efficient and effective means for achieving social coherence. Ancient myths were initially formulated in terms of the science of their day, Thus, an integration of science, myth, and religion is essential to a healthy culture. As these elements become disintegrated there arises a need to generate new mythic visions. The question of (...) our day is whether science offers resources relevant to the expression of a new myth. (shrink)