Arbitrary symbolism is a linguistic doctrine that predicts an orthogonal relationship between word forms and their corresponding meanings. Recent corpora analyses have demonstrated violations of arbitrary symbolism with respect to concreteness, a variable characterizing the sensorimotor salience of a word. In addition to qualitative semantic differences, abstract and concrete words are also marked by distinct morphophonological structures such as length and morphological complexity. Native English speakers show sensitivity to these markers in tasks such as auditory word recognition and (...) naming. One unanswered question is whether this violation of arbitrariness reflects an idiosyncratic property of the English lexicon or whether word concreteness is a marked phenomenon across other natural languages. We isolated concrete and abstract English nouns, and translated each into Russian, Arabic, Dutch, Mandarin, Hindi, Korean, Hebrew, and American Sign Language. We conducted offline acoustic analyses of abstract and concrete word length discrepancies across languages. In a separate experiment, native English speakers with no prior knowledge of these foreign languages judged concreteness of these nouns. Each naïve participant heard pre-recorded words presented in randomized blocks of three foreign languages following a brief listening exposure to a narrative sample from each respective language. Concrete and abstract words differed by length across five of eight languages, and prediction accuracy exceeded chance for four of eight languages. These results suggest that word concreteness is a marked phenomenon across several of the world's most widely spoken languages. We interpret these findings as supportive of an adaptive cognitive heuristic that allows listeners to exploit non-arbitrary mappings of word form to word meaning. (shrink)

Arbitrariness is a distinctive feature of human language, and a growing body of comparative work is investigating its presence in animal communication. But what is arbitrariness, exactly? We propose to distinguish four notions of semiotic arbitrariness: a notion of opaque association between sign forms and semiotic functions, one of sign-function mapping optionality, one of acquisition-dependent sign-function coupling, and one of lack of motivatedness. We characterize these notions, illustrate the benefits of keeping them apart, and describe two reactions to our proposal: (...) abandoning arbitrariness-talk in favor of the newly introduced conceptual vocabulary, or feeding the distinctions back into the parent concept. (shrink)

Arbitrariness is a distinctive feature of human language, and a growing body of comparative work is investigating its presence in animal communication. But what is arbitrariness, exactly? We propose to distinguish four notions of semiotic arbitrariness: a notion of opaque association between sign forms and semiotic functions, one of sign‐function mapping optionality, one of acquisition‐dependent sign‐function coupling, and one of lack of motivatedness. We characterize these notions, illustrate the benefits of keeping them apart, and describe two reactions to our proposal: (...) abandoning arbitrariness‐talk in favor of the newly introduced conceptual vocabulary, or feeding the distinctions back into the parent concept. (shrink)

To make the case for non-conceptualism, Heck draws on an apparent dichotomy between linguistic and iconic representations. According to Heck, whereas linguistic representations have conceptual content, the content of iconic representations is non-conceptual. Based on the case of cartographic systems, the authors criticize Heck’s dichotomous distinction. They argue that maps are composed of semantically arbitrary elements that play different syntactic roles. Based on this, they claim that maps have a predicative structure and convey conceptual content. Finally, the authors argue (...) that, despite their differences, maps and sentences can logically interact with each other through heterogeneous inferences. These considerations not only challenge the view that conceptual content and inferential processes necessarily involve linguistic representations; furthermore, they provide a new perspective for thinking about maps, their semantics and syntax, and their interaction with linguistic systems. (shrink)

Arbitrariness and systematicity are two of language’s most fascinating properties. Although both are characterizations of the mappings between signals and meanings, their emergence and evolution in communication systems has generally been explored independently. We present an experiment in which both arbitrariness and systematicity are probed. Participants invent signs from scratch to refer to a set of items that share salient semantic features. Through interaction, the systematic re-use of arbitrary signal elements emerges.

Mental mapping is a method of interpreting with conceptual metaphors. This method is applied to the admiration song in Song of Songs 7:2–7. The song is interpreted in the context of a dance. For the purpose of interpretation, ancient Egyptian dance paintings and love poems are taken into account. The interpretation presents a methodological study that unmasks arbitrary exegesis and implausible interpretations. It discovers its subtle conceptual metaphors and shows a strategy for a comprehensible exegesis. As a side effect, (...) the male chauvinism present in this song is deconstructed. (shrink)

Sound symbolism refers to non‐arbitrary mappings between the sounds of words and their meanings and is often studied by pairing auditory pseudowords such as “maluma” and “takete” with rounded and pointed visual shapes, respectively. However, it is unclear what auditory properties of pseudowords contribute to their perception as rounded or pointed. Here, we compared perceptual ratings of the roundedness/pointedness of large sets of pseudowords and shapes to their acoustic and visual properties using a novel application of representational similarity (...) analysis (RSA). Representational dissimilarity matrices (RDMs) of the auditory and visual ratings of roundedness/pointedness were significantly correlated crossmodally. The auditory perceptual RDM correlated significantly with RDMs of spectral tilt, the temporal fast Fourier transform (FFT), and the speech envelope. Conventional correlational analyses showed that ratings of pseudowords transitioned from rounded to pointed as vocal roughness (as measured by the harmonics‐to‐noise ratio, pulse number, fraction of unvoiced frames, mean autocorrelation, shimmer, and jitter) increased. The visual perceptual RDM correlated significantly with RDMs of global indices of visual shape (the simple matching coefficient, image silhouette, image outlines, and Jaccard distance). Crossmodally, the RDMs of the auditory spectral parameters correlated weakly but significantly with those of the global indices of visual shape. Our work establishes the utility of RSA for analysis of large stimulus sets and offers novel insights into the stimulus parameters underlying sound symbolism, showing that sound‐to‐shape mapping is driven by acoustic properties of pseudowords and suggesting audiovisual cross‐modal correspondence as a basis for language users' sensitivity to this type of sound symbolism. (shrink)

Time–space synesthetes report that they experience the months of the year as having a spatial layout. In Study 1, we characterize the phenomenology of calendar sequences produced by synesthetes and non-synesthetes, and show a conservative estimate of time–space synesthesia at 2.2% of the population. We demonstrate that synesthetes most commonly experience the months in a circular path, while non-synesthetes default to linear rows or rectangles. Study 2 compared synesthetes’ and non-synesthetes’ ability to memorize a novel spatial calendar, and revealed better (...) performance in synesthetes. The capacity to learn mappings between arbitrary spatial forms and temporal sequences is present in all individuals, and time–space synesthetes’ enhanced visuo-spatial memory abilities may underlie their creation of idiosyncratic spatial calendar forms. (shrink)

In Between the Absolute and the Arbitrary, Catherine Z. Elgin maps a constructivist alternative to the standard Anglo-American conception of philosophy's ...

This article turns towards the spatial life of ‘digital infrastructures’, i.e. code, protocols, standards, and data formats that are hidden from view in everyday applications of computational technologies. It does so by drawing on the version control system Git as a case study, and telling the story of its initial development in order to reconstruct the circumstances and technical considerations surrounding its conception. This account engages with computational infrastructures on their own terms by adopting the figure of the ‘stack’ to (...) frame a technically informed analysis, and exploring its implications for a different kind of geographic inquiry. Drawing on topology as employed by Law and Mol, attention is given to the multiplicity of spatialities and temporalities enrolled in digital infrastructures in general, and Git specifically. Along the lines of the case study and by reading it against other literatures, this notion of topology is expanded to include the material performation of fundamentally arbitrary, more-than-human topologies, as well as their nested articulation, translation and negotiation within digital infrastructures. (shrink)

The significance of the concept of a mathematical transformation is explained. In particular, it is explained how to construct true statements concerning n-dimensional spaces, for arbitrary n, on the basis of true statements concerning two-dimensional spaces.

In this paper we study the algebraic structure ofω-stable bilinear maps, arbitrary rings, and nilpotent groups. We will also provide rather complete structure theorems for the above structures in the finite Morley rank case.

Walter Map was a twelfth-century courtier and royal servant. He was a prolific writer, but De Nugis Curialium is the only surviving work confidently attributed to him. The book is a collection of short stories and anecdotes about the court, religion and history. Map's references demonstrate that he read widely, not only biblical and theological works, but also classical authors such as Horace, Virgil, Ovid and Juvenal. The only surviving manuscript of the work is a fourteenth-century copy once belonging to (...) the monk John Wells of Ramsey Abbey. The Cambridge bibliographer M. R. James would have been attracted to the breadth of Map's referencing, and the author's light-hearted writing style which was intended to entertain. James' 1914 Oxford publication corrected the earlier work of Thomas Wright who published an edition for the Camden Society in 1850. (shrink)

Millikan’s theory of content purports to rely heavily on the existence of isomorphisms between a system of representations and the things in the world which they represent — “the mapping requirement for being intentional signs” (Millikan 2004, p. 106). This paper asks whether those isomorphisms are doing any substantive explanatory work. Millikan’s isomorphism requirement is deployed for two main purposes. First, she claims that the existence of an isomorphism is the basic representing relation, with teleology playing a subsidiary role — (...) to account for misrepresentation (the possibility of error). Second, Millikan relies on an isomorphism requirement in order to guarantee that a system of representations displays a kind of productivity. This seemingly strong reliance on isomorphism has prompted the objection that isomorphism is too liberal to be the basic representing relation: there are isomorphisms between any system of putative representations and any set, of the same cardinality, of items putatively represented. This paper argues that all the work in fixing content is in fact done by the teleology. Deploying Millikan’s teleology-based conditions to ascribe contents will ensure that there is an isomorphism between representations and the things they represent, but the isomorphism ‘requirement’ is playing no substantive explanatory role in Millikan’s account of content determination. So an objection to her theory based on the liberality of isomorphism is misplaced. The second role for isomorphism is to account for productivity. If some kind of productivity is indeed necessary for representation, then functional isomorphism will again be too liberal a constraint to account for that feature. The paper suggests an alternative way of specifying the relation between a system of representations and that which they represent which is capable of playing an explanatory role in accounting for Millikan’s type of productivity. In short, the liberality of isomorphism is no objection to Millikan’s teleosemantics, since the isomorphism ‘requirement’ need play no independent substantive role in Millikan’s account of representation. (shrink)

According to the age-of-acquisition hypothesis, words acquired early in life are processed faster and more accurately than words acquired later. Connectionist models have begun to explore the influence of the age/order of acquisition of items (and also their frequency of encounter). This study attempts to reconcile two different methodological and theoretical approaches (proposed by Lambon Ralph & Ehsan, 2006 and Zevin & Seidenberg, 2002) to age-limited learning effects. The current simulations extend the findings reported by Zevin and Seidenberg (2002) that (...) have shown that frequency trajectories (FTs) have limited and specific effects on word-reading tasks. Using the methodological framework proposed by Lambon Ralph and Ehsan (2006), which makes it possible to compare word-reading and picture-naming tasks in connectionist networks, we were able to show that FT has a considerable influence on age-limited learning effects in a picture naming task. The findings show that when the input–output mappings are arbitrary (simulating picture naming tasks), the links formed by the network become entrenched as a result of early experience and that subsequent variations in frequency of exposure of the items have only a minor impact. In contrast, when the mappings between input-output are quasi-systematic or systematic (simulating word-reading tasks), the training of new items was generalized and resulted in the suppression of age-limited learning effects. At a theoretical level, we suggest that FT, which simultaneously takes account of time and the level of exposure across time, represents a more precise and modulated measure compared with the order of introduction of the items and may lead to innovative hypotheses in the field of age-limited learning effects. (shrink)

Psychologists have used experimental methods to study language for more than a century. However, only with the recent availability of large-scale linguistic databases has a more complete picture begun to emerge of how language is actually used, and what information is available as input to language acquisition. Analyses of such “big data” have resulted in reappraisals of key assumptions about the nature of language. As an example, we focus on corpus-based research that has shed new light on the arbitrariness of (...) the sign: the longstanding assumption that the relationship between the sound of a word and its meaning is arbitrary. The results reveal a systematic relationship between the sound of a word and its meaning, which is stronger for early acquired words. Moreover, the analyses further uncover a systematic relationship between words and their lexical categories—nouns and verbs sound differently from each other—affecting how we learn new words and use them in sentences. Together, these results point to a division of labor between arbitrariness and systematicity in sound-meaning mappings. We conclude by arguing in favor of including “big data” analyses into the language scientist's methodological toolbox. (shrink)

Although the mapping between form and meaning is often regarded as arbitrary, there are in fact well-known constraints on words which are the result of functional pressures associated with language use and its acquisition. In particular, languages have been shown to encode meaning distinctions in their sound properties, which may be important for language learning. Here, we investigate the relationship between semantic distance and phonological distance in the large-scale structure of the lexicon. We show evidence in 100 languages from (...) a diverse array of language families that more semantically similar word pairs are also more phonologically similar. This suggests that there is an important statistical trend for lexicons to have semantically similar words be phonologically similar as well, possibly for functional reasons associated with language learning. (shrink)

When thought overwhelms the mind, the mind uses the body and the world. Several studies reveal ways that people alone or together use gesture and marks on paper to structure and augment their thought for comprehension, inference, and discovery. The studies show that the mapping of thought to gesture or the page is more direct than the arbitrary mapping to language and suggest that these forms of visual/spatial/action representation are used to “translate” language into mental representations. It is argued (...) that actions in space create patterns in the world that reflect abstractions, that the actions are incorporated into gestures and the patterns into diagrams, a network that integrates gesture, action, the designed world, and abstraction dubbed spraction. (shrink)

When thought overwhelms the mind, the mind uses the body and the world. Several studies reveal ways that people alone or together use gesture and marks on paper to structure and augment their thought for comprehension, inference, and discovery. The studies show that the mapping of thought to gesture or the page is more direct than the arbitrary mapping to language and suggest that these forms of visual/spatial/action representation are used to “translate” language into mental representations. It is argued (...) that actions in space create patterns in the world that reflect abstractions, that the actions are incorporated into gestures and the patterns into diagrams, a network that integrates gesture, action, the designed world, and abstraction dubbed spraction. (shrink)

Although language has long been regarded as a primarily arbitrary system, sound symbolism, or non-arbitrary correspondences between the sound of a word and its meaning, also exists in natural language. Previous research suggests that listeners are sensitive to sound symbolism. However, little is known about the specificity of these mappings. This study investigated whether sound symbolic properties correspond to specific meanings, or whether these properties generalize across semantic dimensions. In three experiments, native English-speaking adults heard sound symbolic (...) foreign words for dimensional adjective pairs and for each foreign word, selected a translation among English antonyms that either matched or mismatched with the correct meaning dimension. Listeners agreed more reliably on the English translation for matched relative to mismatched dimensions, though reliable cross-dimensional mappings did occur. These findings suggest that although sound symbolic properties generalize to meanings that may share overlapping semantic features, sound symbolic mappings offer semantic specificity. (shrink)

We investigate how nonstandard reals can be established constructively as arbitrary infinite sequences of rationals, following the classical approach due to Schmieden and Laugwitz. In particular, a total standard part map into Richman's generalised Dedekind reals is constructed without countable choice.

Sometimes form-meaning mappings in language are not arbitrary, but iconic: they depict what they represent. Incorporating iconic elements of language into a compositional semantics faces a number of challenges in formal frameworks as evidenced by the lengthy literature in linguistics and philosophy on quotation/direct speech, which iconically portrays the words of another in the form that they were used. This paper compares the well-studied type of iconicity found with verbs of quotation with another form of iconicity common in (...) sign languages: classifier predicates. I argue that these two types of verbal iconicity can, and should, incorporate their iconic elements in the same way using event modification via the notion of a context dependent demonstration. This unified formal account of quotation and classifier predicates predicts that a language might use the same strategy for conveying both, and I argue that this is the case with role shift in American Sign Language. Role shift is used to report others’ language and thoughts as well as their actions, and recently has been argued to provide evidence in favor of Kaplanian “monstrous” indexical expressions. By reimagining role shift as involving either quotation for language demonstrations or “body classifier” predicates for action demonstrations, the proposed account eliminates one major argument for these monsters coming from sign languages. Throughout this paper, sign languages provide a fruitful perspective for studying quotation and other forms of iconicity in natural language due to their lack of a commonly used writing system which is otherwise often mistaken as primary data instead of speech, the rich existing literature on iconicity within sign language linguistics, and the ability of role shift to overtly mark the scope of a language report. In this view, written language is merely a special case of a more general phenomenon of sign and speech demonstration, which accounts more accurately for natural language data by permitting more strict or loose verbatim interpretations of demonstrations through the context dependent pragmatics. (shrink)

In an evolutionary perspective Louwerse elaborates the Symbol Interdependency Hypothesis (Louwerse, 2011), arguing that language has evolved such that it maps onto the perceptual system, allowing to bootstrap meaning also when grounding is limited. The author concludes that in principle the processing of abstract and concrete words is the same and that in both cases language users tend to rely anyway on indexical relationships that words entertain with other words.

This argument map represents an argumentation from Heyns, C. . Report of the Special Rapporteur on extrajudicial, summary or arbitrary executions, Christof Heyns . S.l.: United Nations. Human Rights Council. The argument map is open for debate in AGORA-net, search for map ID 9206.

Two central assumptions of current models of language acquisition were addressed in this study: (1) knowledge of linguistic structure is "mapped onto" earlier forms of non-linguistic knowledge; and (2) acquiring a language involves a continuous learning sequence from early gestural communication to linguistic expression. The acquisition of the first and second person pronouns ME and YOU was investigated in a longitudinal study of two deaf children of deaf parents learning American Sign Language (ASL) as a first language. Personal pronouns in (...) ASL are formed by pointing directly to the addressee (YOU) or self (I or ME), rather than by arbitrary symbols. Thus, personal pronouns in ASL resemble paralinguistic gestures that commonly accompany speech and are used prelinguistically by both hearing and deaf children beginning around 9 months. This provides a means for investigating the transition from prelinguistic gestural to linguistic expression when both gesture and language reside in the same modality.\nThe results indicate that deaf children acquired knowledge of personal pronouns over a period of time, displaying errors similar to those of hearing children despite the transparency of the pointing gestures. The children initially (ages 10 and 12 months) pointed to persons, objects, and locations. Both children then exhibited a long avoidance period, during which one function of the pointing gesture (pointing to self and others) dropped out completely. During this period their language and cognitive development were otherwise entirely normal, and they continued to use other types of pointing (e.g., to objects). When pointing to self and others returned, it was marked with errors typical of hearing children; one child exhibited consistent pronoun reversal errors, thinking the YOU point referred to herself, while the other child exhibited reversal errors inconsistently. Evidence from experimental tasks conducted with the first child revealed that pronoun errors occurred in comprehension as well. Full control of the ME and YOU pronouns was not achieved until 25-27 months, around the same time when hearing children master these forms. Thus, the study provides evidence for a discontinuity in the child's transition from prelinguistic to linguistic communication. It is argued that aspects of linguistic structure and its acquisition appear to involve distinct, language-specific knowledge. (shrink)

By examining an exemplar sample of mental health nursing educational policies and related legislation, in this article, we trace the discursive production of madness as an “othered” identity category. We engage in a critical discourse analysis of mental health nursing education in Canada, drawing on provincial and federal policies and legislation as the main sources of data. Theoretically framed by critical posthumanism and mad studies, this article outlines how the mad subjectivity becomes decontextualized out of its identity‐based understanding and recontextualized (...) as an inferior category of “the human,” circulating within discourses of pedagogy, economics, law, and psychiatry. The article maps the intertextual nexus of the discourse of mental health nursing education, making visible the complex, the arbitrary, and the sometimes‐contradictory nature of the discipline's grappling with identity‐based mental health concepts. We close with several implications for nursing policy, education, and practice. (shrink)

The question of where, between theory and experiment, computer simulations (CSs) locate on the methodological map is one of the central questions in the epistemology of simulation (cf. Saam Journal for General Philosophy of Science, 48, 293–309, 2017). The two extremes on the map have them either be a kind of experiment in their own right (e.g. Barberousse et al. Synthese, 169, 557–574, 2009; Morgan 2002, 2003, Journal of Economic Methodology, 12(2), 317–329, 2005; Morrison Philosophical Studies, 143, 33–57, 2009; Morrison (...) 2015; Massimi and Bhimji Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 51, 71–81, 2015; Parker Synthese, 169, 483–496, 2009) or just an argument executed with the aid of a computer (e.g. Beisbart European Journal for Philosophy of Science, 2, 395–434, 2012; Beisbart and Norton International Studies in the Philosophy of Science, 26, 403–422, 2012). There exist multiple versions of the first kind of position, whereas the latter is rather unified. I will argue that, while many claims about the ‘experimental’ status of CSs seem unjustified, there is a variant of the first position that seems preferable. In particular I will argue that while CSs respect the logic of (deductively valid) arguments, they neither agree with their pragmatics nor their epistemology. I will then lay out in what sense CSs can fruitfully be seen as experiments, and what features set them apart from traditional experiments nonetheless. I conclude that they should be seen as surrogate experiments, i.e. experiments executed consciously on the wrong kind of system, but with an exploitable connection to the system of interest. Finally, I contrast my view with that of Beisbart (European Journal for Philosophy of Science, 8, 171–204, 2018), according to which CSs are surrogates for experiments, arguing that this introduces an arbitrary split between CSs and other kinds of simulations. (shrink)

Because humans cannot know one another’s minds directly, every form of communication is a solution to the same basic problem: how can privately held information be made publicly accessible through manipulations of the physical environment? Language is by far the best studied response to this challenge. But there are a diversity of non-linguistic strategies for representation with external signs as well, from facial expressions and fog horns to chronological graphs and architectural renderings. The general thesis of this dissertation is that (...) there is an impressively wide spectrum of conventional systems of representation, corresponding to the many ways that the problem of communication can be solved, and that these systems can be described and explained using the tools of contemporary mathematical semantics. As a partial corrective to the countervailing norm, this work concentrates on the class of systems arguably most different from language— those governing the interpretation of pictorial images. Such representations dominate practical communication: witness the proliferation of maps, road signs, newspaper photographs, scientific illustrations, television shows, engineering drawings, and even the fleeting imagery of manual gesture. I argue that systems of depiction and languages embody a parallel technologies of communication. Both are based on semantics: systematic and conventional mappings from signs to representational content. But I also provide evidence that these semantics are profoundly divergent. Whereas the semantics of languages are based on arbitrary associations of signs and denotations, the semantics of systems of depiction are based on rules of geometrical transformation. Drawing on recent research in computer graphics and computational vision, I go on to develop a precise theory of pictorial semantics. This in turn facilitates a detailed comparison of iconic, image-based representation, and symbolic, language-based representation. A consequence of these conclusions is that the traditional, language-centric conception of semantics must be overhauled to allow for a more general semantic theory, one which countenances the wide variety of interpretive mechanisms actually at work in human communication. (shrink)

In the present paper, we start studying epistemic updates using the standard toolkit of duality theory. We focus on public announcements, which are the simplest epistemic actions, and hence on Public Announcement Logic without the common knowledge operator. As is well known, the epistemic action of publicly announcing a given proposition is semantically represented as a transformation of the model encoding the current epistemic setup of the given agents; the given current model being replaced with its submodel relativized to the (...) announced proposition. We dually characterize the associated submodel-injection map as a certain pseudo-quotient map between the complex algebras respectively associated with the given model and with its relativized submodel. As is well known, these complex algebras are complete atomic BAOs . The dual characterization we provide naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras . Thanks to this construction, the benefits and the wider scope of applications given by a point-free, intuitionistic theory of epistemic updates are made available. As an application of this dual characterization, we axiomatize the intuitionistic analogue of PAL, which we refer to as IPAL, prove soundness and completeness of IPAL w.r.t. both algebraic and relational models, and show that the well known Muddy Children Puzzle can be formalized in IPAL. (shrink)

I introduce a mathematical account of expectation based on a qualitative criterion of coherence for qualitative comparisons between gambles (or random quantities). The qualitative comparisons may be interpreted as an agent’s comparative preference judgments over options or more directly as an agent’s comparative expectation judgments over random quantities. The criterion of coherence is reminiscent of de Finetti’s quantitative criterion of coherence for betting, yet it does not impose an Archimedean condition on an agent’s comparative judgments, it does not require the (...) binary relation reflecting an agent’s comparative judgments to be reflexive, complete or even transitive, and it applies to an absolutely arbitrary collection of gambles, free of structural conditions (e.g., closure, measurability, etc.). Moreover, unlike de Finetti’s criterion of coherence, the qualitative criterion respects the principle of weak dominance, a standard of rational decision making that obliges an agent to reject a gamble that is possibly worse and certainly no better than another gamble available for choice. Despite these weak assumptions, I establish a qualitative analogue of de Finetti’s Fundamental Theorem of Prevision, from which it follows that any coherent system of comparative expectations can be extended to a weakly ordered coherent system of comparative expectations over any collection of gambles containing the initial set of gambles of interest. The extended weakly ordered coherent system of comparative expectations satisfies familiar additivity and scale invariance postulates (i.e., independence) when the extended collection forms a linear space. In the course of these developments, I recast de Finetti’s quantitative account of coherent prevision in the qualitative framework adopted in this article. I show that comparative previsions satisfy qualitative analogues of de Finetti’s famous bookmaking theorem and his Fundamental Theorem of Prevision.The results of this article complement those of another article (Pedersen, Strictly coherent preferences, no holds barred, Manuscript, 2013). I explain how those results entail that any coherent weakly ordered system of comparative expectations over a unital linear space can be represented by an expectation function taking values in a (possibly non-Archimedean) totally ordered field extension of the system of real numbers. The ordered field extension consists of formal power series in a single infinitesimal, a natural and economical representation that provides a relief map tracing numerical non-Archimedean features to qualitative non-Archimedean features. (shrink)

I present a notion of invariance under arbitrary surjective mappings for operators on a relational finite type hierarchy generalizing the so-called Tarski-Sher criterion for logicality and I characterize the invariant operators as definable in a fragment of the first-order language. These results are compared with those obtained by Feferman and it is argued that further clarification of the notion of invariance is needed if one wants to use it to characterize logicality.

The standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean (...) algebra. We prove without choice principles that any Boolean algebra arises from a special spectral space X via the compact regular open sets of X; these sets may also be described as those that are both compact open in X and regular open in the upset topology of the specialization order of X, allowing one to apply to an arbitrary Boolean algebra simple reasoning about regular opens of a separative poset. Our representation is therefore a mix of Stone and Tarski, with the two connected by Vietoris: the relevant spectral spaces also arise as the hyperspace of nonempty closed sets of a Stone space endowed with the upper Vietoris topology. This connection makes clear the relation between our point-set topological approach to choice-free Stone duality, which may be called the hyperspace approach, and a point-free approach to choice-free Stone duality using Stone locales. Unlike Stone’s representation of Boolean algebras via Stone spaces, our choice-free topological representation of Boolean algebras does not show that every Boolean algebra can be represented as a field of sets; but like Stone’s representation, it provides the benefit of a topological perspective on Boolean algebras, only now without choice. In addition to representation, we establish a choice-free dual equivalence between the category of Boolean algebras with Boolean homomorphisms and a subcategory of the category of spectral spaces with spectral maps. We show how this duality can be used to prove some basic facts about Boolean algebras. (shrink)

I present a notion of invariance under arbitrary surjective mappings for operators on a relational finite type hierarchy generalizing the so-called Tarski-Sher criterion for logicality and I characterize the invariant operators as definable in a fragment of the first-order language. These results are compared with those obtained by Feferman and it is argued that further clarification of the notion of invariance is needed if one wants to use it to characterize logicality.

Charles S. Peirce’s semiotics uniquely divides signs into: i) symbols, which pick out their objects by arbitrary convention or habit, ii) indices, which pick out their objects by unmediated ‘pointing’, and iii) icons, which pick out their objects by resembling them (as Peirce put it: an icon’s parts are related in the same way that the objects represented by those parts are themselves related). Thus representing structure is one of the icon’s greatest strengths. It is argued that the implications (...) of scaffolding education iconically are profound: for providing learners with a navigable road-map of a subject matter, for enabling them to see further connections of their own in what is taught, and for supporting meaningful active learning. Potential objections that iconic teaching is excessively entertaining and overly susceptible to misleading rhetorical manipulation are addressed. (shrink)

Neural correlates exist for a basic component of logical formulae, PREDICATE(x). Vision and audition research in primates and humans shows two independent neural pathways; one locates objects in body-centered space, the other attributes properties, such as colour, to objects. In vision these are the dorsal and ventral pathways. In audition, similarly separable “where” and “what” pathways exist. PREDICATE(x) is a schematic representation of the brain's integration of the two processes of delivery by the senses of the location of an (...) class='Hi'>arbitrary referent object, mapped in parietal cortex, and analysis of the properties of the referent by perceptual subsystems. The brain computes actions using a few “deictic” variables pointing to objects. Parallels exist between such nonlinguistic variables and linguistic deictic devices. Indexicality and reference have linguistic and nonlinguistic (e.g., visual) versions, sharing the concept of attention. The individual variables of logical formulae are interpreted as corresponding to these mental variables. In computing action, the deictic variables are linked with “semantic” information about the objects, corresponding to logical predicates. Mental scene descriptions are necessary for practical tasks of primates, and preexist language phylogenetically. The type of scene descriptions used by nonhuman primates would be reused for more complex cognitive, ultimately linguistic, purposes. The provision by the brain's sensory/perceptual systems of about four variables for temporary assignment to objects, and the separate processes of perceptual categorization of the objects so identified, constitute a pre-adaptive platform on which an early system for the linguistic description of scenes developed. Key Words: argument; attention; deictic; dorsal; logic; neural; object; predicate; reference; ventral. (shrink)

For more than a century now, researchers have acknowledged the existence of seemingly arbitrary crossmodal congruency effects between dimensions of sensory stimuli in the general population. Such phenomena, known by a variety of terms including 'crossmodal correspondences', involve individual stimulus properties, rely on a crossmodal mapping of unisensory features, and appear to be shared by the majority of individuals. In other words, members of the general population share underlying preferences for specific pairings across the senses. Crossmodal correspondences between complementary (...) sensory cues have often been referred to as synesthetic correspondences but, we would argue, differ from full-blown synesthetic experiences in a number of important ways, including the fact that there are no idiosyncratic concurrent sensations. Recent psychophysical evidence suggests that such crossmodal correspondences can modulate multisensory integration by helping to resolve the crossmodal binding problem. Here, we propose a model to account for the effects of crossmodal correspondences between complementary auditory and visual cues and critically review their relation to full-blown synesthesia. (shrink)

This paper establishes model-theoretic properties of \, a variation of monadic first-order logic that features the generalised quantifier \. We will also prove analogous versions of these results in the simpler setting of monadic first-order logic with and without equality and \, respectively). For each logic \ we will show the following. We provide syntactically defined fragments of \ characterising four different semantic properties of \-sentences: being monotone and continuous in a given set of monadic predicates; having truth preserved under (...) taking submodels or being truth invariant under taking quotients. In each case, we produce an effectively defined map that translates an arbitrary sentence \ to a sentence \ belonging to the corresponding syntactic fragment, with the property that \ is equivalent to \ precisely when it has the associated semantic property. As a corollary of our developments, we obtain that the four semantic properties above are decidable for \-sentences. (shrink)

A survey of just war theory literature reveals the existence of quite different lists of principles. This apparent arbitrariness raises a number of questions: What is the relation between ad bellum and in bello principles? Why are there so many of the former and so few of the latter? What order is there among the various principles? To answer these questions, I first draw on some recent work by Jeff McMahan to show that ad bellum and in bello principles are (...) not, as often portrayed, independent—the justice of conduct in war largely presupposes the justice of the recourse to war. Undermining this independence claim is one important step toward revealing the unified logical structure of just war theory. I then argue that we can see the dependence of the jus in bello upon the jus ad bellum , not just in the content of certain principles, but also in the structure of the two sets of principles: I construct a one-to-one mapping between ad bellum and in bello principles. In doing so, I argue also that the shared structure successfully finds place for the questions central to the evaluation of the morality of war: what is a sufficient provocation to use force, what objectives may be sought by force, why or for what ends, who has authority to decide to use force, and when or in what circumstances? Despite variations in expression, the theory allows for a coherent and comprehensive evaluation of morality in warfare. (shrink)

One cue that may facilitate children's word learning is iconicity, or the correspondence between a word's form and meaning. Some have even proposed that iconicity in the early lexicon may serve to help children learn how to learn words, supporting the acquisition of even noniconic, or arbitrary, word–referent associations. However, this proposal remains untested. Here, we investigate the iconicity of caregivers’ speech to young children during a naturalistic free‐play session with novel stimuli and ask whether the iconicity of caregivers’ (...) speech facilitates children's learning of the noniconic novel names of those stimuli. Thirty‐four 1.5‐2‐year‐olds (19 girls; half monolingual English learners and half bilingual English‐Spanish learners) participated in a naturalistic free‐play task with their caregivers followed by a test of word‐referent retention. We found that caregivers’ use of iconicity, particularly in utterances in which they named the novel stimuli, was associated with the likelihood that children learned that novel name. This result held even when controlling for other factors associated with word learning, such as the concreteness and frequency of words in caregiver speech. Together, the results demonstrate that iconicity not only can serve to help children identify the referent of novel words (as in previous research) but can also support their ability to retain even noniconic word‐referent mappings. (shrink)

It is a well-known fact that although the poset of open sets of a topological space is a Heyting algebra, its Heyting implication is not necessarily stable under the inverse image of continuous functions and hence is not a geometric concept. This leaves us wondering if there is any stable family of implications that can be safely called geometric. In this paper, we will first recall the abstract notion of implication as a binary modality introduced in Akbar Tabatabai (Implication via (...) spacetime. In: Mathematics, logic, and their philosophies: essays in honour of Mohammad Ardeshir, pp 161–216, 2021). Then, we will use a weaker version of categorical fibrations to define the geometricity of a category of pairs of spaces and implications over a given category of spaces. We will identify the greatest geometric category over the subcategories of open-irreducible (closed-irreducible) maps as a generalization of the usual injective open (closed) maps. Using this identification, we will then characterize all geometric categories over a given category $${\mathcal {S}}$$ S, provided that $${\mathcal {S}}$$ S has some basic closure properties. Specially, we will show that there is no non-trivial geometric category over the full category of spaces. Finally, as the implications we identified are also interesting in their own right, we will spend some time to investigate their algebraic properties. We will first use a Yoneda-type argument to provide a representation theorem, making the implications a part of an adjunction-style pair. Then, we will use this result to provide a Kripke-style representation for any arbitrary implication. (shrink)

"The Natural System" is the abstract notion of the order in living diversity. The richness and complexity of this notion is revealed by the diversity of representations of the Natural System drawn by ornithologists in the Nineteenth Century. These representations varied in overall form from stars, to circles, to maps, to evolutionary trees and cross-sections through trees. They differed in their depiction of affinity, analogy, continuity, directionality, symmetry, reticulation and branching, evolution, and morphological convergence and divergence. Some representations were two-dimensional, (...) and some were three-dimensional; n-dimensional representations were discussed but never illustrated. The study of diagrammatic representations of the Natural System is made difficult by the frequent failure of authors to discuss them in their texts, and by the consequent problem of distinguishing features which carried meaning from arbitrary features and printing conventions which did not. Many of the systematics controversies of the last thirty years have their roots in the conceptual problems which surrounded the Natural System in the late 1800s, problems which were left unresolved when interest in higher-level systematics declined at the turn of this century. (shrink)

Because rate of force development is an emerging outcome measure for the assessment of neuromuscular function in unfatigued conditions, and it represents a valid alternative/complement to the classical evaluation of pure maximal strength, this scoping review aimed to map the available evidence regarding RFD as an indicator of neuromuscular fatigue. Thus, following a general overview of the main studies published on this topic, we arbitrarily compared the amount of neuromuscular fatigue between the “gold standard” measure and peak, early and late (...) RFD. Seventy full-text articles were included in the review. The most-common fatiguing exercises were resistance exercises, endurance exercises/locomotor activities, isokinetic contractions, and simulated/real sport situations. The most widely tested tasks were knee extension and plantar flexion. The reason for evaluating RFD was lacking in 36% of the studies. On average, the amount of fatigue for MVF was comparable to late RFD but lower compared to both peak RFD and early RFD. Even if the rationale for evaluating RFD in the fatigued state was often lacking and the specificity between test task and fatiguing exercise characteristics was not always respected in the included studies, RFD seems to be a valid indicator of neuromuscular fatigue. Based on our arbitrary analyses, peak RFD and early phase RFD appear even to be more sensitive to quantify neuromuscular fatigue than MVF and late phase RFD. (shrink)

Capital punishment—the legally authorized killing of a criminal offender by an agent of the state for the commission of a crime—stands in special need of moral justification. This is because execution is a particularly severe punishment. Execution is different in kind from monetary and custodial penalties in an obvious way: execution causes the death of an offender. While fines and incarceration set back some of one’s interests, death eliminates the possibility of setting and pursuing ends. While fines and incarceration narrow (...) one’s routes to happiness, death eliminates its possibility. Not surprisingly, there is much debate about the moral permissibility of capital punishment. This entry maps the terrain of this debate. The first section discusses justifications of the death penalty as they appear in major theories of punishment. The second section surveys moral objections to execution that apply to most justifications. The third addresses procedural criticisms, which do not target the morality of execution so much as the justice of its implementation. (shrink)

The standard argument against ordered tuples as propositions is that it is arbitrary what truth-conditions they should have. In this paper we generalize that argument. Firstly, we require that propositions have truth-conditions intrinsically. Secondly, we require strongly equivalent truth-conditions to be identical. Thirdly, we provide a formal framework, taken from Graph Theory, to characterize structure and structured objects in general. The argument in a nutshell is this: structured objects are too fine-grained to be identical to truth-conditions. Without identity, there (...) is no privileged mapping from structured objects to truth-conditions, and hence structured objects do not have truth-conditions intrinsically. Therefore, propositions are not structured objects. (shrink)

We show that every sufficiently iterable countable mouse has a unique iteration strategy whose associated iteration maps are lexicographically minimal. This enables us to extend the results of [3] on the good behavior of the standard parameter from tame mice to arbitrary mice.

‘The Natural System’ is the abstract notion of the order in living diversity. The richness and complexity of this notion is revealed by the diversity of representations of the Natural System drawn by ornithologists in the Nineteenth Century. These representations varied in overall form from stars, to circles, to maps, to evolutionary trees and cross-sections through trees. They differed in their depiction of affinity, analogy, continuity, directionality, symmetry, reticulation and branching, evolution, and morphological convergence and divergence. Some representations were two-dimensional, (...) and some were three-dimensional; n-dimensional representations were discussed but never illustrated. The study of diagrammatic representations of the Natural System is made difficult by the frequent failure of authors to discuss them in their texts, and by the consequent problem of distinguishing features which carried meaning from arbitrary features and printing conventions which did not. Many of the systematics controversies of the last thirty years have their roots in the conceptual problems which surrounded the Natural System in the late 1800s, problems which were left unresolved when interest in higher-level systematics declined at the turn of this century. (shrink)