: Fodor’s view of the mind is thoroughly computational. This means that the basic kind of mental entity is a “discursive” mental representation and operations over this kind of mental representation have broad architectural scope, extending out to the edges of perception and the motor system. However, in multiple epochs of his work, Fodor attempted to define a functional role for non-discursive, imagistic representation. I describe and critique his two considered proposals. The first view says that images play a particular (...) kind of functional role in certain types of deliberative tasks. The second says that images are solely restricted to the borders of perception, and act as a sort of medium for the fixing of conceptual reference. I argue, against the first proposal, that a broad-scope computationalism such as Fodor’s renders images in principle functionally redundant. I argue, against the second proposal, that empirical evidence suggests that non-discursive representations are learned through perceptual learning, and directly inform category judgments. In each case, I point out extant debates for which the arguments are relevant. The upshot is that there is motivation for limited scope computationalism, in which some, but not all, mental processes operate on discursive mental representations. Keywords: Computational Theory of Mind; Mental Representation; Perception; Mental Image; Jerry Fodor Fodor e le rappresentazioni mentali come immagini Riassunto: La concezione della mente di Fodor è rigorosamente computazionale, ossia le entità mentali di base sono rappresentazioni mentali “discorsive”. Le operazioni su queste rappresentazioni hanno un fine architettonico ampio, che va fino ai confini della percezione e del sistema motorio. In periodi diversi del suo lavoro, Fodor ha proposto due modi per definire un ruolo funzionale per la rappresentazione non-discorsiva come immagine. Tratterò criticamente entrambi. Per il primo, le immagini giocano un particolare tipo di ruolo funzionale in certi tipi di compiti deliberativi, mentre, per il secondo, sono relegate unicamente ai confini della percezione, agendo come medium per fissare il riferimento concettuale. Contro il primo sosterrò che un computazionalismo così ampio come quello di Fodor rende le immagini in principio funzionalmente ridondanti. Contro il secondo sosterrò che l’evidenza empirica suggerisce che le rappresentazioni non-discorsive vengono apprese percettivamente, agendo direttamente sui giudizi di categorizzazione. In entrambi i casi considererò gli argomenti più rilevanti nel dibattito corrente. Si vedrà che ci sono buone ragioni in favore di un computazionalismo più limitato, in cui alcuni processi mentali operano su rappresentazioni mentali discorsive. Parole chiave: Teoria computazionale della mente; Rappresentazione mentale; Percezione; Immagine mentale; Jerry Fodor. (shrink)

Humans are standouts in their propensity to trade. More specially, the kind of trading found in humans—featuring the exchange of many different goods and services with many different others, for the mutual benefit of all the involved parties—far exceeds anything that is found in any other creature. However, a number of important questions about this propensity remain open. First, it is not clear exactly what makes this propensity so different in the human case from that of other animals. Second, it (...) is not clear why other animals did not acquire this propensity to the extent that humans did. Third, it is not clear what explains the fact that the extent to which humans engage in trade is culturally highly variable. The paper argues that at the heart of the human-animal divergence in this propensity is the particular socio-cultural environment in which humans evolved. This has led them to sometimes, but not always, acquire the cognitive technology (writing, algebra, tallying devices, money, etc.) to support a sophisticated disposition and capacity for reciprocal cooperation, and deep and wide concepts of property and exchange value. (shrink)

This article discusses the concept of mathematical metaphor as a tool for analyzing the formation of mathematical knowledge. It reflects on the work of Lakoff and Núñez as a reference point against which to rearticulate a richer notion of mathematical metaphor that can account for actual mathematical evolution. To reach its goal this article analyzes historical case studies, draws on cognitive research, and applies lessons from the history of metaphors in philosophy as analyzed by Derrida and de Man.

This paper takes an embodied and extended cognition perspective to ER integration – a cognitive process through which a learner integrates external representations in a domain, with her internal model, as she interacts with, uses, understands and transforms between those ERs. In the paper, I argue for a theoretical as well as empirical shift in future investigations of ER integration, by proposing a model of cognitive mechanisms underlying the process, based on recent advances in extended and embodied cognition. I present (...) this new model in contrast to the still dominant classical cognitivist approaches to ER integration, and the educational technology intervention designs such approaches inspire. I then exemplify this distinction between the information processing model and the new model through a case of arithmetic problem solving. Corroborative neuroscience evidence presented in relation to this case provides empirical support for the new model by showing how bodily actions are critical to ER integration and learning. Finally, as educational implications of the new model, I demonstrate the need for: re-viewing the development of ER integration and expertise as fine-tuning of the learner's action or sensorimotor system, and a shift of focus in new-media intervention design principles based on this newer understanding of ER integration in science, technology, engineering and mathematics. (shrink)

Dove and Machery both argue that recent findings about the nature of numerical representation present problems for Concept Empiricism. I shall argue that, whilst this evidence does challenge certain versions of CE, such as Prinz, it needn’t be seen as problematic to the general CE approach. Recent research can arguably be seen to support a CE account of number concepts. Neurological and behavioral evidence suggests that systems involved in the perception of numerical properties are also implicated in numerical cognition. Furthermore, (...) the discovery of associations between spatial and numerical representations also lends independent support to a CE approach. Although these findings support CE in general, certain versions of the theory may need revising in order to accommodate them. In particular, it may be necessary to either jettison Prinz's Modal Specificity Hypothesis or to revise one’s method for individuating modal representational formats. (shrink)

In this paper, we focus on the development of geometric cognition. We argue that to understand how geometric cognition has been constituted, one must appreciate not only individual cognitive factors, such as phylogenetically ancient and ontogenetically early core cognitive systems, but also the social history of the spread and use of cognitive artifacts. In particular, we show that the development of Greek mathematics, enshrined in Euclid’s Elements, was driven by the use of two tightly intertwined cognitive artifacts: the use of (...) lettered diagrams; and the creation of linguistic formulae. Together, these artifacts formed the professional language of geometry. In this respect, the case of Greek geometry clearly shows that explanations of geometric reasoning have to go beyond the confines of methodological individualism to account for how the distributed practice of artifact use has stabilized over time. This practice, as we suggest, has also contributed heavily to the understanding of what mathematical proof is; classically, it has been assumed that proofs are not merely deductively correct but also remain invariant over various individuals sharing the same cognitive practice. Cognitive artifacts in Greek geometry constrained the repertoire of admissible inferential operations, which made these proofs inter-subjectively testable and compelling. By focusing on the cognitive operations on artifacts, we also stress that mental mechanisms that contribute to these operations are still poorly understood, in contrast to those mechanisms which drive symbolic logical inference. (shrink)

In the first part of the paper, previous work about embodied mathematics and the practice of topology will be presented. According to the proposed view, in order to become experts, topologists have to learn how to use manipulative imagination: representations are cognitive tools whose functioning depends from pre-existing cognitive abilities and from specific training. In the second part of the paper, the notion of imagination as “make-believe” is discussed to give an account of cognitive tools in mathematics as props; to (...) better specify the claim, the notion of “affordance” is explored in its possible extension from concrete objects to representations. (shrink)

Embodied cognition represents one of most important theoretical developments in contemporary cognitive science. Many cognitive processes appear to be influenced by body morphology, emotions, and sensorimotor systems. This perspective is supported by an ever increasing collection of empirical studies that fall into two broad classes: one consisting of experiments that implicate action, emotion, and perception systems in seemingly abstract cognitive tasks and the other consisting of experiments that demonstrate the contribution of bodily interaction with the external environment to the performance (...) of such tasks. Now that embodied cognition is fairly well established, the time seems right for assessing its further promise and potential limitations. This research topic aimed to create an interdisciplinary forum for discussing where we go from here. Given that we have good reason to think that the body influences cognition in surprisingly robust ways, the central question is no longer whether or not some cognitive processes are embodied. Other questions have come to the forefront. To what extent are cognitive processes embodied? Are there disembodied processes? Among those that are embodied, how are they embodied? Is there more than one kind of embodiment? Is embodiment a matter of degree? Extending the Research ProgramMany of the contributions to this research topic involve experiments that extend the empirical reach of embodied cognition. For instance, Soliman, Gibson, and Gl... (shrink)

Novel computational representations, such as simulation models of complex systems and video games for scientific discovery, are dramatically changing the way discoveries emerge in science and engineering. The cognitive roles played by such computational representations in discovery are not well understood. We present a theoretical analysis of the cognitive roles such representations play, based on an ethnographic study of the building of computational models in a systems biology laboratory. Specifically, we focus on a case of model-building by an engineer that (...) led to a remarkable discovery in basic bioscience. Accounting for such discoveries requires a distributed cognition analysis, as DC focuses on the roles played by external representations in cognitive processes. However, DC analyses by and large have not examined scientific discovery, and they mostly focus on memory offloading, particularly how the use of existing external representations changes the nature of cognitive tasks. In contrast, we study discovery processes and argue that discoveries emerge from the processes of building the computational representation. The building process integrates manipulations in imagination and in the representation, creating a coupled cognitive system of model and modeler, where the model is incorporated into the modeler's imagination. This account extends DC significantly, and we present some of the theoretical and application implications of this extended account. (shrink)

This thesis studies the role of conceptual content in inference and reasoning. The first two chapters offer a theoretical and historical overview of the relation between inference and meaning in philosophy and psychology. In particular, a critical analysis of the formality thesis, i.e., the idea that rational inference is a rule-based and topic-neutral mechanism, is advanced. The origins of this idea in logic and its influence in philosophy and cognitive psychology are discussed. Chapter 3 consists of an analysis of the (...) relationship between inference and representation. It is argued that inference has to be studied from a pluralistic per- spective due to its dependence on different formats of representing information. The following four chapters apply conceptual spaces, a formal theory of concepts within cognitive semantics, to three concept-based inference-types. First, an explication of Sellars notion of material inference is advanced. Later, the model is extended to account for nonmonotonic inference by studying the role expectations in reasoning. Finally, a conceptual space-model of category-based induction is presented. This model predicts most of the empirical properties of this psychological phenomenon and subsumes some of the previous theories in psychology. It is stated that the explanatory fruitfulness of this new approach is evidence for the failure of the formality thesis and calls for a unified model of rational inference that puts semantics at center stage. The last chapter of the thesis discusses how inference and concepts interact in scientific reasoning, which makes constant use of hybrid symbolic structures for representing conceptual information. Stephen Toulmin’s notions of method of representation and inferential technique are developed and applied in a case study about the emergence of the notion of instantaneous speed during the passage from geometrical physics to analytical mechanics. It is claimed that this analysis provides support to the pluralistic perspective for theorizing about reasoning. (shrink)

A growing body of evidence suggests that cognition is embodied and grounded. Abstract concepts, though, remain a significant theoretical chal- lenge. A number of researchers have proposed that language makes an important contribution to our capacity to acquire and employ concepts, particularly abstract ones. In this essay, I critically examine this suggestion and ultimately defend a version of it. I argue that a successful account of how language augments cognition should emphasize its symbolic properties and incorporate a view of embodiment (...) that recognizes the flexible, multi- modal and task-related nature of action, emotion and perception systems. On this view, language is an ontogenetically disruptive cognitive technology that expands our conceptual reach. (shrink)