One of the important challenges in the philosophy of mathematics is to account for the semantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can (...) be addressed by accepting a Chomskyan conception of natural languages and a matching internalist, mentalist and nativist view of semantics. A helpful perspective on the epistemic aspect of the puzzle can be gained by translating Kurt G ̈odel’s neo-Kantian conception of the nature of mathematics and its objects into modern, cognitive terms. (shrink)

The aim of this paper is to demonstrate that empirically delimited structures of mind are also differentiable by means of systematic logical analysis. In the sake of this aim, the paper first summarizes Demetriou's theory of cognitive organization and growth. This theory assumes that the mind is a multistructural entity that develops across three fronts: the processing system that constrains processing potentials, a set of specialized structural systems (SSSs) that guide processing within different reality and knowledge domains, and a hypecognitive (...) system that monitors and controls the functioning of all other systems. In the second part the paper focuses on the SSSs, which are the target of our logical analysis, and it summarizes a series of empirical studies demonstrating their autonomous operation. The third part develops the logical proof showing that each SSS involves a kernel element that cannot be reduced to standard logic or to any other SSS. The implications of this analysis for the general theory of knowledge and cognitive development are discussed in the concluding part of the paper. (shrink)

Recent findings indicate that toddlers can use geometric cues to locate an object hidden in a corner of a rectangular room after being disoriented [Cognition 61 (1996) 195]. It has been suggested that locating the object involves reestablishing one's initial heading. The present experiments examine search behavior after disorientation. We find that toddlers go directly to a particular corner, indicating that they do not have to reestablish their original heading. It also has been suggested that toddlers ability to use geometric (...) cues is limited to surrounding spaces. We find that toddlers can locate an object from outside as well as from inside a space, although the task is harder from outside. Based on these results, we argue that while toddlers do not represent their position relative to a particular portion of a space, they nevertheless may represent their position relative to the entire space (i.e., outside vs. inside). (shrink)

Space can be understood through perception and language, but are the processes that represent spatial information the same in both cases? This paper reviews psychological evidence for the functional equivalence of spatial representations based on perceptual and linguistic inputs. It is proposed that spatial information is processed by a specialised spatial representation system (SRS) that creates geometric representations of space. The SRS receives inputs from perceptual and linguistic systems and uses these basic inputs to construct mental spatial models of the (...) observed or described environment. A mental spatial model is created by determining the coordinate locations of objects in the egocentric or allocentric frame of reference. The goal of the SRS is not to represent strictly what is perceived, but to model an environment that has an inherent three‐dimensional spatial structure. (shrink)

Fundamental to spatial knowledge in all species are the representations underlying object recognition, object search, and navigation through space. But what sets humans apart from other species is our ability to express spatial experience through language. This target article explores the language ofobjectsandplaces, asking what geometric properties are preserved in the representations underlying object nouns and spatial prepositions in English. Evidence from these two aspects of language suggests there are significant differences in the geometric richness with which objects and places (...) are encoded. When an object is named (i.e., with count nouns), detailed geometric properties – principally the object's shape (axes, solid and hollow volumes, surfaces, and parts) – are represented. In contrast, when an object plays the role of either “figure” (located object) or “ground” (reference object) in a locational expression, only very coarse geometric object properties are represented, primarily the main axes. In addition, the spatial functions encoded by spatial prepositions tend to be nonmetric and relatively coarse, for example, “containment,” “contact,” “relative distance,” and “relative direction.” These properties are representative of other languages as well. The striking differences in the way language encodes objects versus places lead us to suggest two explanations: First, there is a tendency for languages to level out geometric detail from both object and place representations. Second, a nonlinguistic disparity between the representations of “what” and “where” underlies how language represents objects and places. The language of objects and places converges with and enriches our understanding of corresponding spatial representations. (shrink)

Name der Zeitschrift: Semiotica Jahrgang: 2016 Heft: 210 Seiten: 35-56.

If reason is a real causal force,operative in some, but not all ofour cognition and conation, then itought to be possible to tell anaturalistic story that distinguishes themind which is moved byreason from the mind which is movedby forces other than reason.This essay proposes some steps towardthat end. I proceed by showingthat it is possible to reconcile certainemerging psychological ideasabout the causal powers of themind/brain with a venerablephilosophical vision of reason as the facultyof norms. My accountof reason is psychologistic, social, (...) and consistent with anevolutionary approach to mind. The account preserves thenormativity by deflating it. But I argue that onlysuch deflated normativity has any chance of beingmade naturalistically respectable. (shrink)

Where does human knowledge begin? Research on human infants, children, adults, and nonhuman animals, using diverse methods from the cognitive, brain, and computational sciences, provides evidence for six early emerging, domain-specific systems of core knowledge. These automatic, unconscious systems are situated between perceptual systems and systems of explicit concepts and beliefs. They emerge early in infancy, guide children's learning, and function throughout life.

In this article, I revisit Landau and Jackendoff's () paper, “What and where in spatial language and spatial cognition,” proposing a friendly amendment and reformulation. The original paper emphasized the distinct geometries that are engaged when objects are represented as members of object kinds, versus when they are represented as figure and ground in spatial expressions. We provided empirical and theoretical arguments for the link between these distinct representations in spatial language and their accompanying nonlinguistic neural representations, emphasizing the “what” (...) and “where” systems of the visual system. In the present paper, I propose a second division of labor between two classes of spatial prepositions in English that appear to be quite distinct. One class includes prepositions such as in and on, whose core meanings engage force-dynamic, functional relationships between objects, with geometry only a marginal player. The second class includes prepositions such as above/below and right/left, whose core meanings engage geometry, with force-dynamic relationships a passing or irrelevant variable. The insight that objects’ force-dynamic relationships matter to spatial terms’ uses is not new; but thinking of these terms as a distinct set within spatial language has theoretical and empirical consequences that are new. I propose three such consequences, rooted in the fact that geometric knowledge is highly constrained and early-emerging in life, while force-dynamic knowledge of objects and their interactions is relatively unconstrained and needs to be learned piecemeal over a lengthy timeline. First, the two classes will engage different learning problems, with different developmental trajectories for both first and second language learners; second, the classes will naturally lead to different degrees of cross-linguistic variation; and third, they may be rooted in different neural representations. (shrink)