Abstract
Human body sense is surprisingly flexible — in the Rubber Hand Illusion (RHI), precisely administered visuo-tactile stimulation elicits a sense of ownership over a fake hand. The general consensus is that there are certain semantic top-down constraints on which objects may be incorporated in this way: in particular, to-be-embodied objects should be structurally similar to a visual representation stored in an internal body model. However, empirical evidence shows that the sense of ownership may extend to objects strikingly distinct in morphology and structure (e.g., robotic arms) and the hypothesis about the relevance of appearance lacks direct empirical support. Probabilistic multisensory integration approaches constitute a promising alternative. However, the recent Bayesian models of RHI limit too strictly the possible factors influencing likelihood and prior probability distributions. In this paper, I analyse how Bayesian models of RHI could be extended. The introduction of skin-based spatial information can account for the cross-compensation of sensory signals giving rise to RHI. Furthermore, addition of Bayesian Coupling Priors, depending on (1) internal learned models of relatedness (coupling strength) of sensory cues, (2) scope of temporal binding windows, and (3) extension of peripersonal space, would allow quantification of individual tendencies to integrate divergent visual and somatosensory signals. The extension of Bayesian models would yield an empirically testable proposition accounting comprehensively for a wide spectrum of RHI-related phenomena and rendering appearance-oriented internal body models explanatorily redundant.
In this paper, I argue that embodied cognition, like many other research traditions in cognitive science, offers mostly fallible research heuristics rather than
grand principles true of all cognitive processing. To illustrate this claim, I discuss
Aizawa’s rebuttal of embodied and enactive accounts of vision. While Aizawa’s argument is sound against a strong reading of the enactive account, it does not
undermine the way embodied cognition proceeds, because the claim he attacks
is one of fallible heuristics. These heuristics may be helpful in developing models
of cognition in an interdisciplinary fashion. I briefly discuss the issue of whether
this fallibility actually makes embodied cognition vulnerable to charges of being untestable or non-scientific. I also stress that the historical approach to this
research tradition suggests that embodied cognition is not poised to become
a grand unified theory of cognition.
In this article, I show the role that the philosopher of cognitive science can currently play in cognitive science research. I argue for the important, and not yet considered, role of the philosophy of cognitive science in cognitive science, that
is, the importance of cooperation between philosophers of science with cognitive scientists in investigating the research methods and theoretical assumptions of cognitive science. At the beginning of the paper I point out, how the
philosopher of science, here, the philosopher of cognitive science, can participate
in interdisciplinary research. I am opting of the cooperation in investigating the
so-called reflective problems. Then, I discuss four examples of issues important
for the cognitive science, in which the competences possessed by the philosopher
are useful. At the ending I point out wider landscape of possible cooperation
of philosophers with cognitive scientists.
Our paper, written together by myself and Marcin Miłkowski, entitled Cognitive artifacts for geometric reasoning was published in Foundations of Sciencea few days ago (online first, open access). In our joint paper, we claim that explanations of geometric cognition should go beyond methodological individualism and take into account the role of distributed cognitive factors in the shaping of Euclidean geometry. In other words, we argue that abstract geometry that raised in ancient Greece cannot be satisfactorily explained only as a product of individual minds, or skull-bound cognitive processes. Instead, we propose that cognitive artifacts, i.e., diagrams and well-structured language, scaffolded visuospatial capacities of our brains, and contributed to building a unique cognitive niche within Euclidean geometry, originated as a result of collective thinking and problem-solving. In addition to this, we emphasize that in contrast to mental mechanisms of symbolic logical inference, mechanisms of diagrammatic inference are still weakly understood in cognitive science.
In the first part of the paper, we note that contemporary cognitive science of mathematics is focused on numbers and calculations much more than on the mental processing of geometry, which is reflected at least in bibliometric evidence. This does not, however, mean that cognitive scientists completely ignore geometry. The theory of cognitive systems of core geometric knowledge by Elizabeth Spelke is a creditable example that we discuss in the paper. In a nutshell, relying on developmental, neuroscientific, comparative, and evolutionarily data, Spelke claims that cognitive base of geometry consists of two phylogenetically ancient and ontogenetically early systems hardwired in the brain. We call these core systems, respectively, the system of layout geometry and the system of object geometry. The former is implemented in the hippocampus and surrounding structures of the vertebrate brain, and its primary function is supporting navigation in large-scale spatial layouts. The latter is localized in the lateral occipital complex and supports recognition of 2D shapes and 3D manipulable objects. According to Spelke, none of these systems, however, provide representations of geometric objects characterized by properties such as angle, sense, and length. Therefore, Euclidean representations involving all these geometric properties require a flexible combination of the core systems during ontogeny. Although Spelke agrees that the developmental shift toward a full-blooded representational system of geometry is mediated by cognitive artifacts, i.e., acquiring the language involving spatial expressions and using map-like scale objects, her account remains silent about shaping of geometric cognition in the historical time-scale.
Therefore, in the second part of our article, we explore the role of cognitive artifacts in the emergence of the Greek geometry, summarized in Euclid’s masterpiece, Elements. Drawing from the Reviel Netz’s approach called cognitive history, we look at properties and mutual relationships of two specific artifacts developed by Greek geometers. The first one is a lettered diagram, and the second one is the technical language composed of fixed strings of words, called–in line of a tradition of Homeric philological studies–formulae. Despite the fact that Babylonian, Egyptian, and Chinese geometers used diagrams before the Greeks, marking them with letters is a uniquely Greek invention. Letters associated with the points make diagrams something more than just auxiliary drawings that facilitate the initial recognition of the problem. On the one hand, thanks to letters Euclidean diagrams are strictly embedded in the discursive (textual) components of mathematical discourse that disambiguate theirs understanding. On the other hand, diagrams allow us to understand the text, because they determine geometric points. One of the crucial discoveries about Greek geometry is that diagrams are full-blooded deductive components of proofs, and without them many statements would lose their truth-value. Furthermore, according to Netz, a fine-grained logical network established by diagrams and linguistic formulae is sufficient to make geometric reasoning compelling and it’s results universally valid. Last but not least, as the researcher claims, lettered diagrams serve as a substitute for mathematical ontology, which means that the geometer does not have to participate in ontological discussions about the semantics of diagrams.
Although we fully agree with Netz about the role of the cognitive artifacts in the shaping of the deductive practices in Greek mathematics, we simultaneously point out two problems. The first one is associated with a thesis that the diagram serves as a substitute for the ontology of geometry. In our opinion, the use of the geometric cognitive artifacts should be investigated from both an epistemological and an ontological point of view. We claim that while using diagrams (and formulae as well) epistemologically non-neutral (in Netz’s line), but ontologically neutral (contrary to Netz). Diagrams constrain the permitted steps in the proof (and thus they indeed contribute to establishing deductive practices), but at the same time do not constrain ontological commitments of geometry. In other words, a mathematician is capable of proving proofs characterized by the necessity of subsequent inferences and the generality of the outputs, however, he or she has still the free choice of mathematical ontology. We ground this thesis in the historical setting, showing that debates about the ontology of geometry existed in ancient times. For instance, the constructive school of Menaechemus accepted the literal interpretation of Euclidean constructions, while Speusippus claimed that constructions should be considered only as heuristic devices, that allow mathematicians to grasp Platonic geometric ideas. To sum up, we claim that deductive practices of Greeks were ontologically neutral.
The second problem with Netz’s cognitive history is that although it elucidates the emergence of two hallmark epistemic properties of Euclidean geometry, namely, necessity and generality of proof, it, however, lacks a substantial account of geometric operations that are performed using these cognitive artifacts. Looking at Proposition 1 of the Book 1 of Euclid’s Elements we show that linguistic formulae supplemented by the diagram indeed reflects inference steps leading to a universal result in a necessity-preserving way, but all the internal, or cognitive, work remains hidden beneath these external representations. By referring to Peirce’s and Magnani’s works we claim that investigation of cognitive foundations of geometric reasoning should go beyond the deductive product that is easy to observe in the final proof and elucidate abductive operations (or manipulative abductions in Magnani’s terms) performed on the diagram. In our opinion, further studies on geometric cognition should look not only at the context of justification but explain the context of discovery, in an empirically grounded way.
Even though our investigation is far from complete, especially regarding cognitive operations involved in geometric reasoning, we stress that cognitive artifacts play a non-negligible role in the emergence of full-blooded geometric cognition not only in the developmental time-scale but also in the historical one. Therefore, our message is that the studies on geometric cognition should take into account not only individual cognitive factors but also distributed cognitive practices facilitated, or even constituted, by external devices.
The above and related problems are further elucidated in my forthcoming book entitled Foundations of Geometric Cognition, which will be published in autumn 2019 by Routledge.
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 (namely non-compositional fixed strings of words used repetitively within authors and between them). 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.
It could be argued that computationalism presupposes multiple realizability of computation, while embodiment of cognitive agents is incompatible, or difficult to reconcile with multiple realizability. Thus, some proponents of embodied cognition could reject computationalism for this reason. This paper offers a reply: It is argued that computational systems are not fruitfully described as multiply realizable, and that the notion of organizational invariance captures the underlying intuitions better. But that notion also applies to embodied cognitive agents. Thus, the argument fails, but for a different reason than the one usually presupposed in the debate.
Abstract. Is the mathematical function being computed by a given physical system determined by the system’s dynamics? This question is at the heart of the inde
Our joint paper (written by myself, Mateusz Hohol, and Witold Hensel) on reproducibility of computational neuroscience has just been assigned to the December issue of the Journal of Computational Neuroscience (open access). In this paper, we argue that assuring replication of scientific results does not yield to a single solution. And this is still a problem, with few reproductions being published and low code availability in major journals of computational neuroscience, as our preliminary study shows:
Most importantly, repeating the model, or rerunning the same model by the same researchers, and replicating the model, or rerunning it by others, requires different set of best practices. They actually would benefit from minute documentation of the whole modelling process, including noting random seeds, versioning all the scripts, recording all intermediate results, etc. (a proposal of ensuring repeatability and replicability of computer science this way was recently defended by Sandve et al. 2013).
But for theoretical purposes of understanding and explanation, these could be detrimental. If one wishes to actually reproduce the results by building another model by following its theoretical description, all the minute details could be actually detrimental and distracting. As we argue in the paper, publications regarding models in computational neuroscience should therefore contain all and only information relevant to reproducing a model and evaluating its value. Alas, many papers currently publish fail in both respects: sometimes they include redundant introductions of the theoretical framework, for example, instead of describing how a particular model was produced, and sometimes they simply fail to make clear how theoretical understanding was operationalized in a model.
Our proposal is, as it turned out, similar in spirit to what Guest and Cooper proposed in their paper. They argue that what they call ‘specification of a model’ is not to be conflated with its implementation. Thus, a theory behind a model should be included in its specification, and implementation details, which sometimes include ad hoc assumptions required to make the model actually run, should not be confused with the theory. A good example of such a confusion is how Pinker and Prince (1988) criticize the influential model of past-tense learning by Rumelhart and McClelland (1986): they take the implementation detail to be theoretically important, while later connectionist work shows that the theoretical account is much more general than a particular choice of problem representation (such as the particular phonological representation in the first model).
Our approach is similar to what Guest and Cooper defend. Nonetheless, we stress that one should distinguish two practices – and ensure not only replication and repetition but also reproduction. The first is served better by open repositories, public code review and such, while the second is best ensured by good theoretical publication and subsequent attempted reproduction.
