Attempts to account for the significance of materiality for cognition should pay special attention to the vehicle in which meaning and information are embedded. Distributed cognition pays surprisingly little attention to conceptualizing the distinction between transitory and durable representations. I use the example of David Kirsh’s research to argue that the bias toward defining cognitive extensions in terms of stable objects existing in space leads to their reification. The aim of this paper is to indicate the sources of reification and (...) argue that implicit ambiguity emerges toward external representations due to an over-reified view of cognitive extensions. (shrink)

We argue that existing learning algorithms are often poorly equipped to solve problems involving a certain type of important and widespread regularity that we call “type-2 regularity.” The solution in these cases is to trade achieved representation against computational search. We investigate several ways in which such a trade-off may be pursued including simple incremental learning, modular connectionism, and the developmental hypothesis of “representational redescription.”.

This paper reviews 30 years of progress in U.S. cognitive science research related to education and training, as seen from the perspective of a research manager who was personally involved in many of these developments.

In order to effectively communicate information, the choice of representation is important. Ideally, a chosen representation will aid readers in making desired inferences. In this paper, we develop the theory of observation: what it means for one statement to be observable from another. Using observability, we give a formal characterization of the observational advantages of one representation of information over another. By considering observational advantages, people will be able to make better informed choices of representations of information. To demonstrate the (...) benefit of observation and observational advantages, we apply these concepts to set theory and Euler diagrams. In particular, we can show that Euler diagrams have significant observational advantages over set theory. This formally justifies Larkin and Simon’s claim that “a diagram is worth ten thousand words”. (shrink)

En este artículo recuperamos la lógica diagramática lineal de Leibniz para la silogística y descubrimos sus propiedades lógicas y computacionales a través de una aproximación formal en términos metalógicos, lo cual es algo que, hasta donde sabemos, aún falta por hacerse. Así, en esta contribución buscamos, respectivamente, dos metas, una histórica y una lógica: i) prestar más atención a los aspectos algorítmicos del sistema diagramático lineal de Leibniz para la silogística, de los cuales creemos que han sido desdeñados por un (...) prejuicio general en contra del razonamiento diagramático; y ii) probar propiedades metalógicas del sistema para argumentar que es un sistema lógico bona fide. (shrink)

Constraints and dependencies among the elements of embodied cognition form patterns or microstrategies of interactive behavior. Hard constraints determine which microstrategies are possible. Soft constraints determine which of the possible microstrategies are most likely to be selected. When selection is non‐deliberate or automatic the least effort microstrategy is chosen. In calculating the effort required to execute a microstrategy each of the three types of operations, memory retrieval, perception, and action, are given equal weight; that is, perceptual‐motor activity does not have (...) a privileged status with respect to memory. Soft constraints can work contrary to the designer's intentions by making the access of perfect knowledge in‐the‐world more effortful than the access of imperfect knowledge in‐the‐head. These implications of soft constraints are tested in two experiments. In experiment 1 we varied the perceptual‐motor effort of accessing knowledge in‐the‐world as well as the effort of retrieving items from memory. In experiment 2 we replicated one of the experiment 1 conditions to collect eye movement data. The results suggest that milliseconds matter. Soft constraints lead to a reliance on knowledge in‐the‐head even when the absolute difference in perceptual‐motor versus memory retrieval effort is small, and even when relying on memory leads to a higher error rate and lower performance. We discuss the implications of soft constraints for routine interactive behavior, accounts of embodied cognition, and tool and interface design. (shrink)

The terms nested sets, partitive frequencies, inside-outside view, and dual processes add little but confusion to our original analysis (Gigerenzer & Hoffrage 1995; 1999). The idea of nested set was introduced because of an oversight; it simply rephrases two of our equations. Representation in terms of chances, in contrast, is a novel contribution yet consistent with our computational analysis System 1.dual process theory” is: Unless the two processes are defined, this distinction can account post hoc for almost everything. In contrast, (...) an ecological view of cognition helps to explain how insight is elicited from the outside (the external representation of information) and, more generally, how cognitive strategies match with environmental structures. (shrink)

The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one (...) of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of ‘diagram chases’. In order to draw inferences, experts move algebraic elements around the diagrams. It will be argued that these diagrams are dynamic. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture formation. (shrink)

Diagrams are a form of spatial representation that supports reasoning and problem solving. Even when diagrams are external, not to mention when there are no external representations, problem solving often calls for internal representations, that is, representations in cognition, of diagrammatic elements and internal perceptions on them. General cognitive architectures—Soar and ACT-R, to name the most prominent—do not have representations and operations to support diagrammatic reasoning. In this article, we examine some requirements for such internal representations and processes in cognitive (...) architectures. We discuss the degree to which DRS, our earlier proposal for such an internal representation for diagrams, meets these requirements. In DRS, the diagrams are not raw images, but a composition of objects that can be individuated and thus symbolized, while, unlike traditional symbols, the referent of the symbol is an object that retains its perceptual essence, namely, its spatiality. This duality provides a way to resolve what anti-imagists thought was a contradiction in mental imagery: the compositionality of mental images that seemed to be unique to symbol systems, and their support of a perceptual experience of images and some types of perception on them. We briefly review the use of DRS to augment Soar and ACT-R with a diagrammatic representation component. We identify issues for further research. (shrink)

The phenomenon of base-rate neglect has elicited much debate. One arena of debate concerns how people make judgments under conditions of uncertainty. Another more controversial arena concerns human rationality. In this target article, we attempt to unpack the perspectives in the literature on both kinds of issues and evaluate their ability to explain existing data and their conceptual coherence. From this evaluation we conclude that the best account of the data should be framed in terms of a dual-process model of (...) judgment, which attributes base-rate neglect to associative judgment strategies that fail to adequately represent the set structure of the problem. Base-rate neglect is reduced when problems are presented in a format that affords accurate representation in terms of nested sets of individuals. (shrink)

Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of (...) the latter. This essay describes some of the ways that mathematical practice makes it possible to reliably and robustly meet the formal standard, preserving the standard normative account while doing justice to epistemically important features of informal mathematical justification. (shrink)

In this paper I aim to defend a twofold thesis. On one hand, I will sup-port, against Perini [7], the indispensability of diagrams when structurally complex biomolecules are concerned, since it is not possible to satisfactorily use linguistic-sentential representations at that domain. On the other hand, even when diagrams are dispensable I will defend than they will generally be more effective than other representations in encoding biomolecular knowledge, relying on Kulvicki-Shimojima’s diagrammatic effectiveness thesis. Finally, I will ground many epistemic virtues (...) of biomolecular diagrams (understandability, explanatory power, prediction and hypothesis evaluation) on their cognitive-computational indispensability and their semantic-epistemic effectiveness. (shrink)

This paper is intended to sketch the definition of a methodological tool -- the notion of a format of representation -- for the study of scientific theorising. One of its main assumption is that a philosophical study of theorising needs to pay attention to other types of units of analysis than the traditional ones, namely, theories and models approached in a logical and structural way, since scientific reasoning is always led on concrete representational devices and depends upon their specific properties. (...) The notion of a format is intended to characterise the differences between various types of representational devices, in terms of the inferences they enable cognitive agents to draw. (shrink)