Philosophy and Phenomenological Research, EarlyView.

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)

I will sustain in this article that Peirce can be seen as the last great representative of that inconspicuous but persistent tradition that, from the thirteenth to the seventeenth century, spent its energies on discovering a universal language. His project of Existential Graphs is in fact grounded on the isomorphism among a Sheet of Assertion, in which Graphs-signs are drawn, a Mind, with its thoughts-signs, and the Universe, with its facts-signs. In the same sense, Leibniz worked on his Characteristica (...) Universalis, seen as a general Encyclopedia or alphabet of human thoughts, and a pictum mundi amphitheatrum. (shrink)

Peirce's career as a logician spanned almost half a century, during which time he produced several increasingly complex sign systems. The best-known, from 1903, defined amongst other things a signifying process involving sign, object and interpretant, the universally-known icon-index-symbol division and a set of 10 distinct classes of signs. Peirce subsequently expanded this process to include 2 objects, the sign and 3 interpretants. Uncoincidentally, in the 5 years between 1903 and the final system of 1908, he introduced a number of (...) highly innovative semiotic concepts which he never developed. One such concept is hypoiconicity, which comprises 3 levels of isomorphism holding between sign and object and, in spite of the mutations these varieties of icon subsequently underwent, offers qualitative analysis as a complement to the traditional literal-figurative binarism in the discussion of verbal and nonverbal signs. Another is semiosis, which Peirce introduced and defined in 1907 but only rarely illustrated. Involving a complex combination of object, perception, interpretation and a medium, this is shown to be a far more complex signifying process than the one implicit in the three-correlate definition of the sign of 1903. Exploring the evolving theoretical background to the emergence of these new concepts and showing how they differ from certain contemporary conceptions of sign, mind and signification, the book proposes an introduction to, and explanations and illustrations of, these important developments. (shrink)

The isomorphism invariance criterion of logical nature has much to commend it. It can be philosophically motivated by the thought that logic is distinctively general or topic neutral. It is capable of precise set-theoretic formulation. And it delivers an extension of ‘logical constant’ which respects the intuitively clear cases. Despite its attractions, the criterion has recently come under attack. Critics such as Feferman, MacFarlane and Bonnay argue that the criterion overgenerates by incorrectly judging mathematical notions as logical. We consider (...) five possible precisifications of the overgeneration argument and find them all unconvincing. (shrink)

For the information theorist, the lawful generalizations that subsume instantiations of properties in the environment and instantiations of properties of perceptual representations determine the latter's content. Perceptual representations are also commonly thought to be isomorphic to what they represent, which presents the information theorist with a puzzle. What role could isomorphism play in perceptual representation when lawful generalizations determine content? I show that in order for the information that they carry to be available to cognition, perceptual representations must be (...) isomorphic with respect to the constituent structure of the properties that they represent. Isomorphism therefore plays an important role in the information theorist's account of perceptual representation, even though it plays no role in determining content. (shrink)

This paper discusses some engineering considerations that should be taken into account when building a knowledge based system, and recommends isomorphism, the well defined correspondence of the knowledge base to the source texts, as a basic principle of system construction in the legal domain. Isomorphism, as it has been used in the field of legal knowledge based systems, is characterised and the benefits which stem from its use are described. Some objections to and limitations of the approach are (...) discussed. The paper concludes with a case study giving a detailed example of the use of the isomorphic approach in a particular application. (shrink)

This study aims to find out whether speakers of different language backgrounds (English, French, Spanish, and Macedonian) are sensitive to semantic associations (‘fluid’ and ‘forcible contact’) attached respectively to two purported phonaesthemes (/fl-/ and /tr-/). Participants completed the task in oral and written conditions. They had to match phonaestheme-related definitions with either of two non-words (one phonaestheme-bearing and the other containing a distractor). The results obtained indicate that participants significantly chose non-words beginning with /tr-/ when the definition activated a meaning (...) related to forcible contact, and non-words starting with /fl-/ when the definitions made reference to fluids in the four languages. The results point to the existence of non-arbitrary sound-meaning relations. A corpus-driven study of frequencies of lemmas and word tokens starting with the purported phonaesthemes also sheds light on the possible origin of the phonaesthemic associations, suggesting that both iconicity and systematicity motivate such associations. The results obtained are interpreted in the context of a functional, usage-based model of language, which can accommodate the existence of iconic tendencies, the role of learning and linguistic experience in language, and arbitrariness. (shrink)

An icon is part of the visible world, moreover, of things that are visible in a second degree. It is not only a sensitive thing, but a sensitive image of a sensitive entity. As an eikon, it is located in a platonic sense among the lowest degree of the doxa, and within the lowest degree of the scale of being. However it is not a simple sensitive and illusory representation of God, such as one criticized from a Kantian point of (...) view. The profound sense of an icon lies in its opening towards the invisible. An icon tries to capture the invisible. How is this meeting point of the visible and the invisible entangled? Can an icon really allow us to “see” the invisible or is it only a profanation of the invisible? It is my aim to analyze those questions in the following article. (shrink)

Iconicity refers to a resemblance between word form and meaning. Previous work has shown that iconic words are learned earlier and processed faster. Here, we examined whether iconic words are recognized better on a recognition memory task. We also manipulated the level at which items were encoded—with a focus on either their meaning or their form—in order to gain insight into the mechanism by which iconicity would affect memory. In comparison with non‐iconic words, iconic words were (...) associated with a higher false alarm rate, a lower d’ score, and a lower response criterion in Experiment 1. We did not observe any interaction between iconicity and encoding condition. To test the generalizability of these findings, we examined effects of iconicity in a recognition memory megastudy across 3880 items. After controlling for a variety of lexical and semantic variables, iconicity was predictive of more hits and false alarms, and a lower response criterion in this dataset. In Experiment 2, we examined whether these effects were due to increased feelings of familiarity for iconic items by including a familiar versus recollect decision. This experiment replicated the overall results of Experiment 1 and found that participants were more likely to categorize words that they had seen before as familiar (vs. recollected) if they were iconic. Together, these results demonstrate that iconicity has an effect on memory. We discuss implications for theories of iconicity. (shrink)

Iconicity, the resemblance between the form of a word and its meaning, has effects on behavior in both communicative symbol development and language learning experiments. These results have invited speculation about iconicity being a key feature of the origins of language, yet the presence of iconicity in natural languages seems limited. In a diachronic study of language change, we investigated the extent to which iconicity is a stable property of vocabulary, alongside previously investigated psycholinguistic predictors of change. Analyzing 784 English (...) words with data on their historical forms, we found that stable words are higher in iconicity, longer in length, and earlier acquired during development, but that the role of frequency and grammatical category may be less important than previously suggested. Iconicity is revealed as a feature of ultra-conserved words and potentially also as a property of vocabulary early in the history of language origins. (shrink)

Mathematical notation includes a vast array of signs. Most mathematical signs appear to be symbolic, in the sense that their meaning is arbitrarily related to their visual appearance. We explored the hypothesis that mathematical signs with iconic aspects—those which visually resemble in some way the concepts they represent—offer a cognitive advantage over those which are purely symbolic. An early formulation of this hypothesis was made by Christine Ladd in 1883 who suggested that symmetrical signs should be used to convey (...) commutative relations, because they visually resemble the mathematical concept they represent. Two controlled experiments provide the first empirical test of, and evidence for, Ladd's hypothesis. In Experiment 1 we find that participants are more likely to attribute commutativity to operations denoted by symmetric signs. In Experiment 2 we further show that using symmetric signs as notation for commutative operations can increase mathematical performance. (shrink)

Based on neo-institutional literature, this article aims to show the influence of organizational isomorphism on corruption. The focus is institutional explanations of corruption. Our model is based on empirical research in Russia at the end of the 1990s. A face-to-face questionnaire was conducted with 552 top executives in private firms across various economic sectors. We used the structural equation model Partial Least Squares, PLS, technique to test our hypotheses. The developed model provides an integrated approach to the study of (...) the relationship between corruption and organizational isomorphism. Our empirical data from firms in Russia allowed us to test various theoretical hypotheses concerning the influence of organizational isomorphism on corruption. Our emphasis is on the influence of competitive and institutional isomorphism on corruption. (shrink)

We examine how degrees of computably enumerable equivalence relations under computable reduction break down into isomorphism classes. Two ceers are isomorphic if there is a computable permutation of ω which reduces one to the other. As a method of focusing on nontrivial differences in isomorphism classes, we give special attention to weakly precomplete ceers. For any degree, we consider the number of isomorphism types contained in the degree and the number of isomorphism types of weakly precomplete (...) ceers contained in the degree. We show that the number of isomorphism types must be 1 or ω, and it is 1 if and only if the ceer is self-full and has no computable classes. On the other hand, we show that the number of isomorphism types of weakly precomplete ceers contained in the degree can be any member of $[0,\omega ]$. In fact, for any $n \in [0,\omega ]$, there is a degree d and weakly precomplete ceers ${E_1}, \ldots,{E_n}$ in d so that any ceer R in d is isomorphic to ${E_i} \oplus D$ for some $i \le n$ and D a ceer with domain either finite or ω comprised of finitely many computable classes. Thus, up to a trivial equivalence, the degree d splits into exactly n classes.We conclude by answering some lingering open questions from the literature: Gao and Gerdes [11] define the collection of essentially FC ceers to be those which are reducible to a ceer all of whose classes are finite. They show that the index set of essentially FC ceers is ${\rm{\Pi }}_3^0$-hard, though the definition is ${\rm{\Sigma }}_4^0$. We close the gap by showing that the index set is ${\rm{\Sigma }}_4^0$-complete. They also use index sets to show that there is a ceer all of whose classes are computable, but which is not essentially FC, and they ask for an explicit construction, which we provide.Andrews and Sorbi [4] examined strong minimal covers of downwards-closed sets of degrees of ceers. We show that if $\left$ is a uniform c.e. sequence of non universal ceers, then $\left\{ {{ \oplus _{i \le j}}{E_i}|j \in \omega } \right\}$ has infinitely many incomparable strong minimal covers, which we use to answer some open questions from [4].Lastly, we show that there exists an infinite antichain of weakly precomplete ceers. (shrink)

We consider the complexity of the isomorphism relation on countable first-order structures with transitive automorphism groups. We use the theory of Borel reducibility of equivalence relations to show that the isomorphism problem for vertex-transitive graphs is as complicated as the isomorphism problem for arbitrary graphs and determine for which first-order languages the isomorphism problem for transitive countable structures is as complicated as it is for arbitrary countable structures. We then use these results to characterize the complexity (...) of the isometry relation for certain classes of homogeneous and ultrahomogeneous metric spaces. (shrink)

A cofinitary group is a subgroup of Sym(ℕ) where all nonidentity elements have finitely many fixed points. A maximal cofinitary group is a cofinitary group, maximal with respect to inclusion. We show that a maximal cofinitary group cannot have infinitely many orbits. We also show, using Martin's Axiom, that no further restrictions on the number of orbits can be obtained. We show that Martin's Axiom implies there exist locally finite maximal cofinitary groups. Finally we show that there exists a uniformly (...) computable sequence of permutations generating a cofinitary group whose isomorphism type is not computable. (shrink)

This paper presents and defends a novel meta‐epistemological thesis, epistemic isomorphism, according to which our relations to others and to ourselves have the same pattern of relevance to our rationality. This means that correct epistemological theorizing will give formal parity to interpersonal and intrapersonal epistemic norms, such that what holds interpersonally also holds, mutatis mutandis, intrapersonally. In addition to arguing for epistemic isomorphism, the paper presents some epistemological case studies in which it is shown that the methodological and (...) argumentative strategies used by epistemologists in these case studies give expression to the idea of epistemic isomorphism as well as the argument presented here for its truth. Finally, the paper considers a possible counterexample to epistemic isomorphism based on an agent‐centered theory of justification, but it shows how to reconcile this theory with epistemic isomorphism. (shrink)

Iconicity is a relationship of resemblance between the form and meaning of a sign. Compelling evidence from diverse areas of the cognitive sciences suggests that iconicity plays a pivotal role in the processing, memory, learning, and evolution of both spoken and signed language, indicating that iconicity is a general property of language. However, the language‐specific aspect of iconicity, illustrated by the fact that the meanings of ideophones in an unfamiliar language are hard to guess (e.g., shigeshige ‘staring at something’ in (...) Japanese), remains to be fully investigated. In the present study, native speakers of Japanese and English rated the iconicity and familiarity of Japanese ideophones (e.g., gatagata ‘rattling’, butsubutsu ‘murmuring’) and their English equivalents (e.g., rattle, murmur). Two main findings emerged: (1) individuals generally perceived their native language as more iconic than their non‐native language, replicating the previous findings in signed language, and (2) the familiarity of words in their native language boosted their perceived iconicity. These findings shed a light on the language‐specific, subjective, and acquired nature of iconicity. (shrink)

The suggestion that analytic isomorphism should be rejected applies especially to the domain of speech perception because (1) the guiding assumption that solving the lack of invariance problem is the key to explaining speech perception is a form of analytic isomorphism, and (2) after nearly half a century of research there is virtually no empirical evidence of isomorphism between perceptual experience and lower-level processing units.

Emotions can be insensitive to certain attributes of a situation: Fear of flying is not always reduced by remembering air crash probabilities. A large body of evidence shows that information on probabilities, large numerical counts, and intentions is frequently disregarded in the elicitation and regulation of emotions. To date, no existing theory comprehensively accounts for the features that tend to be overlooked by emotion. In this paper, I call attention to the common denominator of such features: they do not contribute (...) to the iconic representation of events. For instance, the exceedingly low probability of a plane crash does not affect its imagistic representation (i.e., the iconic representation of the event is silent about the event’s probability). This paper introduces the Iconic Prioritization Hypothesis, positing that the prioritization of input in the iconic format by emotions can explain the neglect of information that is representationally silent in this format. Delving into the causes of this format prioritization, I argue that emotion might favour iconicity as it is the format of immediate information about our surroundings (perception) and of stored first-hand evidence (episodic memory). Lastly, the hypothesis's compatibility with philosophical theories of emotion causation and its implications for experimental research are examined. (shrink)

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out several examples. One motivation is to see whether some classes whose set of countable members is very complex become classifiable when we consider only computable members. We follow recent work (...) by Goncharov and Knight in using the degree of the isomorphism problem for a class to distinguish classifiable classes from non-classifiable. For real closed fields we show that the isomorphism problem is Δ1 1 complete (the maximum possible), and for others we show that it is of relatively low complexity. We show that the isomorphism problem for algebraically closed fields, Archimedean real closed fields, or vector spaces is Π0 3 complete. (shrink)

This article studies the cognitive and communicative effects of typographical iconicity in poetry from the perspective of relevance theory. It argues that the visual aspect pertaining to an instance of typographical iconicity conveys a sensory impression, which perceptually resembles elements of the semantic material represented via the typographical iconicity’s lexical aspect. It is suggested that the non-propositional information relating to this impression can trigger the derivation of a wide array of weak implicatures which can combine to form an impressionistic and (...) indeterminate cognitive state described within relevance theory as a poetic effect. Furthermore, since the added effort, which the typographical iconicity requires to be perceived and processed, is offset by the derived implicatures, the use of typographical iconicity may be said to produce an optimally relevant level of processing. (shrink)

Global policy transfer has become increasingly popular in recent years, and one recent example of such policy transfer is the England–China Teacher Exchange, which was initiated in 2014 with the explicit aim of raising attainment in maths in English primary schools by trialling concepts used in Shanghai schools, Shanghai rising to the top of the PISA rankings in 2009. However, as this paper will argue this is an overly simplistic attempt to transfer a policy between two wholly different contexts, the (...) lack of success of the policy seen in the very limited impact on student attainment in the participating schools. Whilst such policy transfer has increasingly taken place in the context of isomorphism and global pressures to adopt policy from high performing education systems, it is argued that policy needs to be explicitly reconsidered in terms of the local context it is being imported into if it is to be embedded in an effective manner, as well as rooted firmly in research. It is also argued that the England–China Teacher Exchange reflects a broader ideological focus in coalition government policy on the marketisation of education alongside the PISA rankings, rather any wider consideration of how this particular policy would drive up standards. (shrink)

At the beginning of the 20th century, Gestalt psychologists put forward the concept of psychoneural isomorphism, which was meant to replace Fechner’s obscure notion of psychophysical parallelism and provide a heuristics that may facilitate the search for the neural correlates of the mind. However, the concept has generated much confusion in the debate, and today its role is still unclear. In this contribution, I will attempt a little conceptual spadework in clarifying the concept of psychoneural isomorphism, focusing exclusively (...) on conscious visual perceptual experience and its neural correlates. Firstly, I will outline the history of our concept, and its alleged metaphysical and epistemic roles. Then, I will clarify the nature of isomorphism and rule out its metaphysical role. Finally, I will review some epistemic roles of our concept, zooming in on the work of Jean Petitot, and suggest that it does not play a relevant heuristic role. I conclude suggesting that psychoneural isomorphism might be an indicator of robustness for certain mathematical descriptions of perceptual content. (shrink)

Short‐term memory in vision is typically thought to divide into at least two memory stores: a short, fragile, high‐capacity store known as iconic memory, and a longer, durable, capacity‐limited store known as visual working memory (VWM). This paper argues that iconic memory stores icons, i.e., image‐like perceptual representations. The iconicity of iconic memory has significant consequences for understanding consciousness, nonconceptual content, and the perception–cognition border. Steven Gross and Jonathan Flombaum have recently challenged the division between iconic (...) memory and VWM by arguing against the idea of capacity limits in favor of a flexible resource‐based model of short‐term memory. I argue that, while VWM capacity is probably governed by flexible resources rather than a sharp limit, the two memory stores should still be distinguished by their representational formats. Iconic memory stores icons, while VWM stores discursive (i.e., language‐like) representations. I conclude by arguing that this format‐based distinction between memory stores entails that prominent views about consciousness and the perception–cognition border will likely have to be revised. (shrink)

The ultraproduct construction is generalized to p‐ultramean constructions () by replacing ultrafilters with finitely additive measures. These constructions correspond to the linear fragments of continuous logic and are very close to the constructions in real analysis. A powermean variant of the Keisler‐Shelah isomorphism theorem is proved for. It is then proved that ‐sentences (and their approximations) are exactly those sentences of continuous logic which are preserved by such constructions. Some other applications are also given.

This review covers experimental approaches to sound-symbolism—from infants to adults, and from Sapir’s foundational studies to twenty-first century product naming. It synthesizes recent behavioral, developmental, and neuroimaging work into a systematic overview of the cross-modal correspondences that underpin iconic links between form and meaning. It also identifies open questions and opportunities, showing how the future course of experimental iconicity research can benefit from an integrated interdisciplinary perspective. Combining insights from psychology and neuroscience with evidence from natural languages provides us (...) with opportunities for the experimental investigation of the role of sound-symbolism in language learning, language processing, and communication. The review finishes by describing how hypothesis-testing and model-building will help contribute to a cumulative science of sound-symbolism in human language. (shrink)

This article explores the theoretical and substantive connections between iconicity and consumerism in the field of contemporary iconic architecture within the framework of a critical theory of globalization. Iconicity in architecture is defined in terms of fame and special symbolic/aesthetic significance as applied to buildings, spaces and in some cases architects themselves. Iconic architecture is conceptualized as a hegemonic project of the transnational capitalist class. In the global era, I argue, iconic architecture strives to turn more or (...) less all public space into consumerist space, not only in the obvious case of shopping malls but more generally in all cultural spaces, notably museums and sports complexes. The inspiration that iconic architecture has provided historically generally coexisted with repressive political and economic systems, and for change to happen an alternative form of non-capitalist globalization is necessary. Under such conditions truly inspiring iconic architecture, including existing architectural icons, may create genuinely democratic public spaces in which the culture-ideology of consumerism fades away. In this way, a built environment in which the full array of human talents can flourish may begin to emerge. (shrink)

We study the complexity of the isomorphism relation on classes of computable structures. We use the notion of FF-reducibility introduced in [9] to show completeness of the isomorphism relation on many familiar classes in the context of all ${\mathrm{\Sigma }}_{1}^{1}$ equivalence relations on hyperarithmetical subsets of ω.

Palast der Republik, by the photographer Christoph Rokitta, is an independent photobook published in 2013 in Berlin. In the photobook different semiotic resources are coupled in order to iconically model the demolition of the homonymous building in Berlin. In opposition to the trivial notion of icon as sign that stands for its object in a relation of similarity, we analyze the photobook as an icon whose main feature is the possibility of discovering information about its object through its manipulation. This (...) specific feature is called operational criterion for iconicity, and it stresses the inherent quality of icons of revealing information available through their manipulation and observation. Our aim is to describe and analyze the relations between semiotic resources in this photobook by exploring the operational criterion of iconicity, and models as epistemic artifacts. We are interested in how couplings between semiotic resources in the photobook can iconically model a spatio-temporal process. (shrink)

This paper answers some questions of D. Ross in [R]. In § 1, we show that some consequences of the ℵ0- or ℵ1-special model axiom in [R] cannot be proved by the κ-isomorphism property for any cardinal κ. In § 2, we show that with one exception, the ℵ0-isomorphism property does imply the remaining consequences of the special model axiom in [R]. In § 3, we improve a result in [R] by showing that the κ-special model axiom is (...) equivalent to the ℵ0-special model axiom plus κ-saturation. (shrink)

We argue that some sign language loci (i.e. positions in signing space that realize discourse referents) are both formal variables and simplified representations of what they denote; in other words, they are simultaneously logical symbols and pictorial representations. We develop a 'formal semantics with iconicity' that accounts for their dual life; the key idea ('formal iconicity') is that some geometric properties of signs must be preserved by the interpretation function. We analyze in these terms three kinds of iconic effects (...) in American and French Sign Language (ASL and LSF): (i) structural iconicity, where relations of inclusion and complementation among loci are directly reflected in their denotations; (ii) locus-external iconicity, where the high or low position of a locus in signing space has a direct semantic reflex, akin to the semantic contribution of gender features of pronouns; and (iii) locus-internal iconicity, where different parts of a structured locus are targeted by different directional verbs, as was argued by Liddell and Kegl. The resulting semantics combines insights of two traditions that have been sharply divided by recent debates. In line with the 'formalist camp' (e.g. Lillo-Martin and Klima, Neidle, and Sandler and Lillo-Martin), our theory treats loci as variables, and develops an explicit formal analysis of their behavior. But we also incorporate insights of the 'iconic camp', which emphasized the role of iconic constraints in sign language in general and in pronominals in particular (e.g. Cuxac, Taub, Liddell). However, this synthesis is only possible if formal semantics makes provisions for iconic requirements at the very core of its interpretive procedure. (An Appendix discusses relevant data from Italian Sign Language [LIS].). (shrink)

When one tries to determine what the iconic dimension of thought consists in for Peirce and what its range is, one might have the impression that his remarks on this matter are inconsistent. For instance, on the one hand he writes the following: Remember it is by icons only that we really reason, and abstract statements are valueless in reasoning except so far as they aid us to construct diagrams. The sectaries of the opinion I am combating seem, on (...) the contrary, to suppose that reasoning is performed with abstract "judgments," and that an icon is of use only as enabling me to frame abstract statements as premisses. In an apparently similar fashion, Peirce argues that the predicate of a... (shrink)

Modern microscopes create a capacity to see and act at the scale where unassisted human senses are powerless. Images of nanoscale phenomena represent a world that effectively intervenes in human life while remaining distant and ineffable. This combination of an unbridgeable distance between man and technology with a real power of the latter over the human condition is characteristic, not only of nanotechnology, but also of the theology of sacred icons that mediate in the knowledge of divine reality. We draw (...) an anthropological analogy between nanotechnological images and sacred icons, and we employ it to analyze the functioning of such images in society. The questions that we study include: a) the art of mediation in representing the ineffable and its necessity; b) the effects provoked by such images; c) primitive comprehension of nanoscale images. This work has repercussions for a wide variety of disciplinary accounts and practices, from the anthropologist and the philosopher to the laboratory scientist, the art critic, and the engineer who conceives and designs nanoscale instruments. (shrink)

This book consolidates and extends the authors’ work on the connection between iconicity and abductive inference. It emphasizes a pragmatic, experimental and fallibilist view of knowledge without sacrificing formal rigor. Within this context, the book focuses particularly on scientific knowledge and its prevalent use of mathematics. To find an answer to the question “What kind of experimental activity is the scientific employment of mathematics?” the book addresses the problems involved in formalizing abductive cognition. For this, it implements the concept and (...) method of iconicity, modeling this theoretical framework mathematically through category theory and topoi. Peirce's concept of iconic signs is treated in depth, and it is shown how Peirce's diagrammatic logical notation of Existential Graphs makes use of iconicity and how important features of this iconicity are representable within category theory. Alain Badiou’s set-theoretical model of truth procedures and his relational sheaf-based theory of phenomenology are then integrated within the Peircean logical context. Finally, the book opens the path towards a more naturalist interpretation of the abductive models developed in Peirce and Badiou through an analysis of several recent attempts to reformulate quantum mechanics with categorical methods. Overall, the book offers a comprehensive and rigorous overview of past approaches to iconic semiotics and abduction, and it encompasses new extensions of these methods towards an innovative naturalist interpretation of abductive reasoning. (shrink)

According to one important proposal, the difference between perception and cognition consists in the representational formats used in the two systems (Carey, 2009; Burge, 2010; Block, 2014). In particular, it is claimed that perceptual representations are iconic, or image-like, while cognitive representations are discursive, or language-like. Taking object perception as a test case, this paper argues on empirical grounds that it requires discursive label-like representations. These representations segment the perceptual field, continuously pick out objects despite changes in their features, (...) and abstractly represent high-level features, none of which appears possible for purely iconic representations. (shrink)

Grammatical asymmetries in possessive constructions are overtly coded in about 18% of the world’s languages according to the World Atlas of Language Structures What primarily motivates these grammatical asymmetries is controversial and has been at the crux of the “iconicity vs. frequency” debate This paper contributes to this debate by focusing on the grammatical asymmetries of Paamese possessive constructions, and looking for the primary motivating factor in their multidimensional experiential context. After a careful account of four experiential dimensions of distance, (...) the degrees of experiential distance are shown to systematically correspond to the degrees of formal distance of the possessive constructions used to refer to these experiences. Relevant anthropological and linguistic data concerning Paamese is used to explore whether this correspondence between language and experience is primarily motivated by iconicity or economy. I argue that diagrammatic iconicity is the primary motivating factor for the grammatical asymmetries in Paamese possessive constructions, and that economy can account for some, but not all cases. I also show that economy and iconicity can collaborate in motivating some cases, and thus do not necessarily need to be opposed. (shrink)

This paper concerns the role of the structural properties of representations in determining the nature of their content. I take as a starting point Fodor's (2007) and Heck's (2007) recent arguments making the iconic structure of perceptual representations essential in establishing their content as content of a different (nonconceptual) kind. I argue that the prima facie state–content error this strategy seems to display is nothing but a case of “state–content error error,” i.e., the mistake of considering that the properties (...) that characterize the type of content certain representations have are indeed independent of their structural properties. I also consider another objection to the general strategy, namely that it falls short of showing that the nonconceptual content of perceptual experiences thus established is the kind of content that figures in true explanations of intentional behavior. I concede this point in respect of Fodor's version of the strategy, while denying that it has any bearing on Heck's approach. The success of this objection in Heck's case ultimately depends, I argue, upon an unjustified commitment to a certain empirically suspect model of perception. (shrink)

The results herein form part of a larger project to characterize the classification properties of the class of submodels of a homogeneous stable diagram in terms of the solvability (in the sense of [1]) of the potential isomorphism problem for this class of submodels. We restrict ourselves to locally saturated submodels of the monster model m of some power π. We assume that in Gödel's constructible universe ������, π is a regular cardinal at least the successor of the first (...) cardinal in which ������ is stable. We show that the collection of pairs of submodels in ������ as above which are potentially isomorphic with respect to certain cardinal-preserving extensions of ������ is equiconstructible with 0 # . As 0 # is highly "transcendental" over ������, this provides a very strong statement to the effect that potential isomorphism for this class of models not only fails to be set-theoretically absolute, but is of high (indeed of the highest possible) complexity. The proof uses a novel method that does away with the need for a linear order on the skeleton. (shrink)

Lehar tries to build a computational theory that succeeds in offering the same computational model for both phenomenal experience and visual processing. However, the vision that Lehar has about isomorphism in Gestalttheorie as representational, is not adequate. The main limit of Lehar's model derives from this misunderstanding of the relation between phenomenal and physiological levels.

In language, recombination of a discrete set of meaningless building blocks forms an unlimited set of possible utterances. How such combinatorial structure emerged in the evolution of human language is increasingly being studied. It has been shown that it can emerge when languages culturally evolve and adapt to human cognitive biases. How the emergence of combinatorial structure interacts with the existence of holistic iconic form-meaning mappings in a language is still unknown. The experiment presented in this paper studies the (...) role of iconicity and human cognitive learning biases in the emergence of combinatorial structure in artificial whistled languages. Participants learned and reproduced whistled words for novel objects with the use of a slide whistle. Their reproductions were used as input for the next participant, to create transmission chains and simulate cultural transmission. Two conditions were studied: one in which the persistence of iconic form-meaning mappings was possible and one in which this was experimentally made impossible. In both conditions, cultural transmission caused the whistled languages to become more learnable and more structured, but this process was slightly delayed in the first condition. Our findings help to gain insight into when and how words may lose their iconic origins when they become part of an organized linguistic system. (shrink)

An interesting feature of some sets of representations is that their structure mirrors the structure of the items they represent. Founding an account of representational content on isomorphism, homomorphism or structural resemblance has proven elusive, however, largely because these relations are too liberal when the candidate structure over representational vehicles is unconstrained. Furthermore, in many cases where there is a clear isomorphism, it is not relied on in the way the representations are used. That points to a potential (...) resolution: that an isomorphism must be used, hence usable, if it is to be an ingredient in a theory of content. This paper argues that the class of exploitable isomorphisms can indeed play a content-constituting role. (shrink)

The essay proposes a notion of “icon” understood, according to the paradigm born of the Second Council of Nicaea, as a visible image of the invisible qua invisible. In this light, the distinctive feature of the icon-image is its ability to manifest the paradoxical identity-difference relationship that links visible and invisible, and, consequently, representable and unrepresentable, immanence and transcendence, eternity and time. By offering itself as the privileged place for the presentation of an absence and of a “withdrawal”, the icon (...) is distinguished in the first place by its apophatic and kenotic character. In this sense, the salient trait of the icon is its constitutive disquiet: it is founded on the “relational economy” of the image, which implies the need of an incessant articulation of the relation between visible and invisible. We can thus see in the icon the paradigm itself of “great art”: indeed, like the icon, great art is always primarily characterised by its disquiet, that is its ability to make transcendence appear in immanence, the Other of the visible appear in the visible. (shrink)

The main result of this paper states that the isomorphism problem for ω-automatic trees of finite height is at least has hard as second-order arithmetic and therefore not analytical. This strengthens a recent result by Hjorth, Khoussainov, Montalbán, and Nies showing that the isomorphism problem for ω-automatic structures is not in . Moreover, assuming the continuum hypothesis CH, we can show that the isomorphism problem for ω-automatic trees of finite height is recursively equivalent with second-order arithmetic. On (...) the way to our main results, we show lower and upper bounds for the isomorphism problem for ω-automatic trees of every finite height: It is decidable , for height 1 , -hard and in for height 3, and - and -hard and in for height . All proofs are elementary and do not rely on theorems from set theory. (shrink)

The originator of the notion of structural isomorphism was the philosopher Roy Wood Sellars. Many modern philosophers are unaware how this notion vitiates their attacks on the concept of an internal sensory presentation. His view that this allowed for corrective feedback undercuts Palmer's belief that there is a mapping of objects. The privacy of subjective experience is also shown not to be inviolable.

We study the isomorphism relation on Borel classes of locally compact Polish metric structures. We prove that isomorphism on such classes is always classifiable by countable structures (equivalently: Borel reducible to graph isomorphism), which implies, in particular, that isometry of locally compact Polish metric spaces is Borel reducible to graph isomorphism. We show that potentially $\boldsymbol {\Pi }^{0}_{\alpha + 1}$ isomorphism relations are Borel reducible to equality on hereditarily countable sets of rank $\alpha $, $\alpha (...) \geq 2$. We also study approximations of the Hjorth-isomorphism game, and formulate a condition ruling out classifiability by countable structures. (shrink)

Sign languages are known to display the same general grammatical properties as spoken languages, but also to make greater use of iconic mechanisms. In Schlenker et al.’s ‘Iconic Variables’ :91–149, 2013), it was argued that loci can have an iconic semantics, in the sense that certain geometric relations among loci are preserved by the interpretation function. Here we ask whether plural and height specifications of loci display the formal behavior of phi-features in remaining uninterpreted in focus- and (...) ellipsis-constructions. Data from ASL and LSF show that plural and height specifications may indeed remain uninterpreted in these constructions; furthermore, there are cases in which a single high locus is construed iconically and left uninterpreted in the course of ellipsis resolution. We argue that our data are compatible with two theories. According to the Strong View, plural and height specifications of loci display exactly the behavior of spoken language features. According to the Weak View, our data just show that plural and height specifications share the behavior of features and other non-assertive elements in being separable from the referential terms they specify. Our LSF data are compatible with the Weak View; our ASL data might provide support for the Strong View. While our aim is merely to open the debate about the featural status of iconic specifications, the question is of some importance: if features are innate and primitive elements of grammar, and if some of them have an intrinsically geometric semantics, the signed modality might play a greater role than is usually thought at the very core of Universal Grammar. (shrink)

This paper is divided into three sections. In the first section we offer a retooling of some traditional concepts, namely icons and symbols, which allows us to describe an evolutionary continuum of communication systems. The second section consists of an argument from theoretical biology. In it we explore the advantages and disadvantages of phenotypic plasticity. We argue that a range of the conditions that selectively favor phenotypic plasticity also favor a nongenetic transmission system that would allow for the inheritance of (...) acquired characters. The first two sections are independent, the third depends on both of them. In it we offer an argument that human natural languages have just the features required of an ideal transmission mechanism under the conditions described in section 2. (shrink)