How can we explain our capacity to think about particulars in our external environment? Many philosophers have answered this question in terms of a sophisticated conception of space and time and the movement of objects therein. A more recent reaction against this view sought to explain this capacity solely in terms of perceptual mechanisms of object individuation. Neither explanation remains fully satisfactory. This book argues for a more desirable middle ground in terms of a pragmatist approach to demonstrative thought, where (...) this capacity is explained through graded practical knowledge of objects. This view allows us to do justice to important insights put forward by both positions criticized in the book, while avoiding their potential shortcomings. It also paves the way to a more pragmatist approach to the theory of mental representation, where the notion of practical knowledge is allowed to play a central role in our cognitive life. Finally, it shows how practical knowledge may be firmly rooted in neurobiological processes and mechanisms that conform to what the empirical sciences tell us about the mind. (shrink)

Can unattended objects by seen? Ned Block has claimed they can on the basis of “identity-crowding.” This paper summarizes the ensuing debate with particular emphasis on the role of unconscious perception. Although unconscious perception plays an important role, it cannot support conscious object-seeing in identity-crowding. Nevertheless, unconscious perception assists in making successful judgments about unseen objects. Further, compelling conceptual evidence against seeing unattended objects places the burden of proof on Block. I argue that countability is necessary for seeing objects and (...) sufficient for attention to them; thus, no unattended objects are seen. (shrink)

Eric Schwitzgebel (2011) argues that phenomenal judgments are in general less reliable than perceptual judgments. This paper distinguishes two versions of this unreliability thesis. The process unreliability thesis says that unreliability in phenomenal judgments is due to faulty domain-specific mechanisms involved in producing these judgments, whereas the statistical unreliability thesis says that it is simply a matter of higher numbers of errors. Against the process unreliability thesis, I argue that the main errors and limitations in making phenomenal judgments can be (...) accounted for by domain-general factors: attention, working memory limits and conceptualization. As these factors are shared with the production of perceptual judgments, errors in phenomenal judgments are not due to faulty domain-specific processes. Furthermore, this account defends phenomenal judgments against general scepticism by providing criteria for distinguishing between reliable and unreliable phenomenal judgments. (shrink)

The paper presents a formal model of the system of number representations as a multiplicity of mental number axes with a hierarchical structure. The hierarchy is determined by the mind as it acquires successive types of mental number axes generated by virtue of some algebraic mechanisms. Three types of algebraic structures, responsible for functioning these mechanisms, are distinguished: BASAN-structures, CASAN-structures and CAPPAN-structures. A foundational order holds between these structures. CAPPAN-structures are derivative from CASAN-structures which are extensions of BASAN-structures. The constructed (...) formal model unifies two competitive conceptions of cognitive arithmetic: namely, the conception of the mental number line and the conception of parallel individuation. The paper is the continuation of a paper entitled Representational structures of arithmetical thinking, in which rich empirical evidence supporting the model is presented. The main result achieved in the present paper may be philosophically interpreted as an attempt to formalize the Kantian conception of the pure idea of time, understood as the a priori form of human arithmetical thinking. In this way, our theory may be comprehended as a result of applying the hard method of logical reconstruction of fundamental epistemological categories. (shrink)

What could someone represent that would enable her to track, at least within limits, others' perceptions, knowledge states and beliefs including false beliefs? An obvious possibility is that she might represent these very attitudes as such. It is sometimes tacitly or explicitly assumed that this is the only possible answer. However, we argue that several recent discoveries in developmental, cognitive, and comparative psychology indicate the need for other, less obvious possibilities. Our aim is to meet this need by describing the (...) construction of a minimal theory of mind. Minimal theory of mind is rich enough to explain systematic success on tasks held to be acid tests for theory of mind cognition including many false belief tasks. Yet minimal theory of mind does not require representing propositional attitudes, or any other kind of representation, as such. Minimal theory of mind may be what enables those with limited cognitive resources or little conceptual sophistication, such as infants, chimpanzees, scrub‐jays and human adults under load, to track others' perceptions, knowledge states and beliefs. (shrink)

Using a novel enumeration task, we examined the encoding of spatial information during subitizing. Observers were shown masked presentations of randomly-placed discs on a screen and were required to mark the perceived locations of these discs on a subsequent blank screen. This provided a measure of recall for object locations and an indirect measure of display numerosity. Observers were tested on three stimulus durations and eight numerosities. Enumeration performance was high for displays containing up to six discs—a higher subitizing range (...) than reported in previous studies. Error in the location data was measured as the distance between corresponding stimulus and response discs. Overall, location errors increased in magnitude with larger numerosities and shorter display durations. When errors were computed as disc distance from display centroid, results suggest a compressed representation by observers. Additionally, enumeration and localization accuracy increased with display regularity. (shrink)

Adult number representations can belong to either of two types. One is discrete, language-specific, and culturally-derived; the other is analog and language-independent. Quantitative evidence is presented to demonstrate that analog number representations are adult-like in young children. Five- to 7-year-olds accurately estimated rapidly presented groups of 5--11 items. Groups were presented in random order and random arrangements controlling for overall area. Children's data were qualitatively, and to some degree quantitatively, similar to adult data with one exception: the ratio of the (...) standard deviation of estimates to mean estimates decreased with age. (shrink)

Six-month-old infants discriminate between large sets of objects on the basis of numerosity when other extraneous variables are controlled, provided that the sets to be discriminated differ by a large ratio (8 vs. 16 but not 8 vs. 12). The capacities to represent approximate numerosity found in adult animals and humans evidently develop in human infants prior to language and symbolic counting.

In this paper, I claim that extant empirical data do not support a radically embodied understanding of the mind but, instead, suggest (along with a variety of other results) a massively representational view. According to this massively representational view, the brain is rife with representations that possess overlapping and redundant content, and many of these represent other mental representations or derive their content from them. Moreover, many behavioral phenomena associated with attention and consciousness are best explained by the coordinated activity (...) of units with redundant content. I finish by arguing that this massively representational picture challenges the reliability of a priori theorizing about consciousness. (shrink)

People’s awareness of tactile stimuli has been investigated in far less detail than their awareness of stimuli in other sensory modalities. In an attempt to fill this gap, we provide an overview of studies that are pertinent to the topic of tactile consciousness. We discuss the results of research that has investigated phenomena such as “change blindness”, phantom limb sensations, and numerosity judgments in tactile perception, together with the results obtained from the study of patients affected by deficits that can (...) adversely affect tactile perception such as neglect, extinction, and numbsense. The similarities as well as some of the important differences that have emerged when visual and tactile conscious information processing have been compared using similar experimental procedures are highlighted. We suggest that conscious information processing in the tactile modality cannot be separated completely from the more general processing of spatial information in the brain. Finally, the importance of considering tactile consciousness within the larger framework of multisensory information processing is also discussed. (shrink)

The lack of consensus on how to characterize humans’ capacity for belief reasoning has been brought into sharp focus by recent research. Children fail critical tests of belief reasoning before 3 to 4 years (Wellman, Cross, & Watson, 2001; Wimmer & Perner, 1983), yet infants apparently pass false belief tasks at 13 or 15 months (Onishi & Baillargeon, 2005; Surian, Caldi, & Sperber, 2007). Non-human animals also fail critical tests of belief reasoning but can show very complex social behaviour (e.g., (...) Call & Tomasello, 2005). Fluent social interaction in adult humans implies efficient processing of beliefs, yet direct tests suggest that belief reasoning is cognitively demanding, even for adults (e.g., Apperly, Samson & Humphreys, 2005). We interpret these findings by drawing an analogy with the domain of number cognition, where similarly contrasting results have been observed. We propose that the success of infants and non-human animals on some belief reasoning tasks may be best explained by a cognitively efficient but inflexible capacity for tracking belief-like states. In humans this capacity persists in parallel with later-developing, more flexible but more cognitively demanding theory of mind abilities. (shrink)

We consider connections between number sense—the ability to judge number—and the interpretation of natural language quantifiers. In particular, we present empirical evidence concerning the neuroanatomical underpinnings of number sense and quantifier interpretation. We show, further, that impairment of number sense in patients can result in the impairment of the ability to interpret sentences containing quantifiers. This result demonstrates that number sense supports some aspects of the language faculty.

While endorsing Gopnik's proposal that studies of the emergence and modification of scientific theories and studies of cognitive development in children are mutually illuminating, we offer a different picture of the beginning points of cognitive development from Gopnik's picture of "theories all the way down." Human infants are endowed with several distinct core systems of knowledge which are theory-like in some, but not all, important ways. The existence of these core systems of knowledge has implications for the joint research program (...) between philosophers and psychologists that Gopnik advocates and we endorse. A few lessons already gained from this program of research are sketched. (shrink)

In this paper, I study the kind of questions we can ask about the existence of numbers. In addition to asking whether numbers exist, and how, I argue that there is also a third relevant question: why numbers exist. In platonist and nominalist accounts this question may not make sense, but in the psychologist account I develop, it is as well-placed as the other two questions. In fact, there are two such why-questions: the causal why-question asks what causes numbers to (...) exist and the teleological why-question asks for what purpose numbers exist. I argue that in a psychologist constructivist account, in which numbers are understood to exist as referents of a particular type of culturally shared concepts, both why-questions can get plausible answers. (shrink)

The common view of the transition between subitizing and numerosity estimation regimes is that there is a hard bound on the subitizing range, and beyond this range, people estimate. However, this view does not adequately address the behavioral signatures of enumeration under conditions of attentional load or in the immediate post-subitizing range. The possibility that there might exist a numerosity range where both processes of subitizing and estimation operate in conjunction has so far been ignored. Here, we investigate this new (...) proposal, that people strategically combine the processes of subitizing and estimation to maximize accuracy and precision, given time or attentional constraints. We present a process-level account of how subitizing and estimation can be combined through strategic deployment of attention to maximize the precision of perceived numerosity given time constraints. We then describe a computational model of this account and apply it in two experimental simulations to demonstrate how it can explain key findings in prior enumeration research. While recent modeling work has argued that the behavioral signatures of enumeration can best be explained through a single numerosity system with a single form of representation, we argue that our model demonstrates how the traditional two-systems view of numerical representation accounts for behavioral data through coordination with a unified attentional mechanism, rather than a unified representation. (shrink)

One main challenge of non-platonist philosophy of mathematics is to account for the apparent objectivity of mathematical knowledge. Cole and Feferman have proposed accounts that aim to explain objectivity through the intersubjectivity of mathematical knowledge. In this paper, focusing on arithmetic, I will argue that these accounts as such cannot explain the apparent objectivity of mathematical knowledge. However, with support from recent progress in the empirical study of the development of arithmetical cognition, a stronger argument can be provided. I will (...) show that since the development of arithmetic is (partly) determined by biologically evolved proto-arithmetical abilities, arithmetical knowledge can be understood as maximally intersubjective. This maximal intersubjectivity, I argue, can lead to the experience of objectivity, thus providing a solution to the problem of reconciling non-platonist philosophy of mathematics with the (apparent) objectivity of mathematical knowledge. (shrink)

El presente artículo intenta ofrecer un marco documental para la discusión sobre la estructura cosmológica de Ferecides de Siros. Partiendo de la polémica entre quienes le adjudican un cosmograma quinario y aquellos que lo interpretan septenario, proponemos un recorrido por las antiguas doctrinas cosmológicas quinarias, tanto griegas como orientales, a fin de explorar su recurrencia y variedad. Se constata que la disputa religiosa entre los apologetas del cinco y los del siete existía ya en la antigüedad, pudiendo haber afectado a (...) la lectura que los doxógrafos hicieron entonces de la obra de Ferecides. Se expone la teoría de Nick Allen sobre la existencia de una «ideología pentádica» indoeuropea y se critica su sesgo idealista (pitagórico en la línea de Dumézil). Finalmente, se suscribe la hipótesis del origen «protogeométrico» de muchos de estos mapas ontológicos quinarios y se recapitulan las posibles referencias que manejaba el maestro de Pitágoras cuando ideó su teogonía. (shrink)

Less salient, lower contrast disks appear to be more numerous than more salient, higher contrast disks when intermingled in equal numbers into the same display, but they are equal in perceived numerosity when segregated into different displays. Comparative judgements indicate that the apparent numerosity of the lower contrast disks is unaffected by being intermingled with high contrast disks, whereas the high contrast disks are reduced in numerosity by being intermingled with the low contrast ones. Here, we report that this illusion (...) also occurs for absolute judgements of the numerosities of displays of from 20 to 80 disks. A model based on luminance-difference contrast normalization explains the illusory loss of high-contrast items along with veridical perception of the low-contrast ones. The model correctly predicts that perceived numerosity is linearly related to the square-root of the number of disks, with the extent of the illusion depending on an attentionally-weighted function of contrast and assimilation. (shrink)

The number of elements in a small set of items is appraised in a fast and exact manner, a phenomenon called subitizing. In contrast, humans provide imprecise responses when comparing larger numerosities, with decreasing precision as the number of elements increases. Estimation is thought to rely on a dedicated system for the approximate representation of numerosity. While previous behavioral and neuroimaging studies associate subitizing to a domain-general system related to object tracking and identification, the nature of small numerosity processing is (...) still debated. We investigated the neural processing of numerosity across subitizing and estimation ranges by examining electrophysiological activity during the memory retention period in a delayed numerical match-to-sample task. We also assessed potential differences in the neural signature of numerical magnitude in a fully non-symbolic or cross-format comparison. In line with behavioral performance, we observed modulation of parietal-occipital neural activity as a function of numerosity that differed in two ranges, with distinctive neural signatures of small numerosities showing clear similarities with those observed in visuospatial working memory tasks. We also found differences in neural activity related to numerical information in anticipation of single vs. cross-format comparison, suggesting a top-down modulation of numerical processing. Finally, behavioral results revealed enhanced performance in the mixed-format conditions and a significant correlation between task performance and symbolic mathematical skills. Overall, we provide evidence for distinct mechanisms related to small and large numerosity and differences in numerical encoding based on task demands. (shrink)

Beck presents an outline of the procedure of bootstrapping of integer concepts, with the purpose of explicating the account of Carey. According to that theory, integer concepts are acquired through a process of inductive and analogous reasoning based on the object tracking system, which allows individuating objects in a parallel fashion. Discussing the bootstrapping theory, Beck dismisses what he calls the "deviant-interpretation challenge"—the possibility that the bootstrapped integer sequence does not follow a linear progression after some point—as being general to (...) any account of inductive learning. While the account of Carey and Beck focuses on the OTS, in this paper I want to reconsider the importance of another empirically well-established cognitive core system for treating numerosities, namely the approximate number system. Since the ANS-based account offers a potential alternative for integer concept acquisition, I show that it provides a good reason to revisit the deviant-interpretation challenge. Finally, I will present a hybrid OTS-ANS model as the foundation of integer concept acquisition and the framework of enculturation as a solution to the challenge. (shrink)

Research on the capacity to understand others' minds has tended to focus on representations ofbeliefs,which are widely taken to be among the most central and basic theory of mind representations. Representations ofknowledge, by contrast, have received comparatively little attention and have often been understood as depending on prior representations of belief. After all, how could one represent someone as knowing something if one does not even represent them as believing it? Drawing on a wide range of methods across cognitive science, (...) we ask whether belief or knowledge is the more basic kind of representation. The evidence indicates that nonhuman primates attribute knowledge but not belief, that knowledge representations arise earlier in human development than belief representations, that the capacity to represent knowledge may remain intact in patient populations even when belief representation is disrupted, that knowledge (but not belief) attributions are likely automatic, and that explicit knowledge attributions are made more quickly than equivalent belief attributions. Critically, the theory of mind representations uncovered by these various methods exhibits a set of signature features clearly indicative of knowledge: they are not modality-specific, they are factive, they are not just true belief, and they allow for representations of egocentric ignorance. We argue that these signature features elucidate the primary function of knowledge representation: facilitating learning from others about the external world. This suggests a new way of understanding theory of mind – one that is focused on understanding others' minds in relation to the actual world, rather than independent from it. (shrink)

Some epistemologists and philosophers of mind hold that the non-epistemic perceptual relation of which feature-seeing and object-seeing are special cases is the foundation of perceptual knowledge. This paper argues that such relations are best understood as having only a technological role in explaining perceptual knowledge. After introducing the opposing view in §1, §2 considers why its defenders deny that some cases in which one has perceptual knowledge without the relevant acquaintance relations are counterexamples, detailing their case for lurking inferential epistemology. (...) §§3-4 suggest that this strategy fails in many other cases. While there is a computational tale that might be deemed ‘inferential’ in these cases, there is no corresponding tale in epistemic structure, not even if one rejects what Siegel (2017) calls the ‘Reckoning Model’ of inference. §5 offers a more fundamental dilemma. §6 concludes that there is only a technological role for non-epistemic perception in grounding perceptual knowledge, but allows that it might play a more-than-technological role elsewhere. (shrink)

Neural network models of memory are notorious for catastrophic interference: Old items are forgotten as new items are memorized (French, 1999; McCloskey & Cohen, 1989). While working memory (WM) in human adults shows severe capacity limitations, these capacity limitations do not reflect neural network style catastrophic interference. However, our ability to quickly apprehend the numerosity of small sets of objects (i.e., subitizing) does show catastrophic capacity limitations, and this subitizing capacity and WM might reflect a common capacity. Accordingly, computational investigations (...) (Knops, Piazza, Sengupta, Eger & Melcher, 2014; Sengupta, Surampudi & Melcher, 2014) suggest that mutual inhibition among neurons can explain both kinds of capacity limitations as well as why our ability to estimate the numerosity of larger sets is limited according to a Weber ratio signature. Based on simulations with a saliency map‐like network and mathematical proofs, we provide three results. First, mutual inhibition among neurons leads to catastrophic interference when items are presented simultaneously. The network can remember a limited number of items, but when more items are presented, the network forgets all of them. Second, if memory items are presented sequentially rather than simultaneously, the network remembers the most recent items rather than forgetting all of them. Hence, the tendency in WM tasks to sequentially attend even to simultaneously presented items might not only reflect attentional limitations, but also an adaptive strategy to avoid catastrophic interference. Third, the mean activation level in the network can be used to estimate the number of items in small sets, but it does not accurately reflect the number of items in larger sets. Rather, we suggest that the Weber ratio signature of large number discrimination emerges naturally from the interaction between the limited precision of a numeric estimation system and a multiplicative gain control mechanism. (shrink)

The model presented by the authors can explain an inherent contradiction in people's naïve theory of time. In this commentary I suggest a way in which another paradox of our phenomenal temporality may be addressed along these lines. In the final section, I also discuss some concerns that may arise about the clear-cut distinction between humans and non-human animals.

In this article we review the discussion over the thesis that language serves as an integrator of contents coming from different cognitive modules. After presenting the theoretical considerations, we examine two strands of empirical research that tested the hypothesis — spatial cognition and mathematical cognition. The idea shared by both of them is that each is composed of two separate modules processing information of a specific kind. For spatial thinking these are geometric information about the location of the object and (...) the information about the object’s properties such as color or size. For mathematical thinking, they are the absolute representation of small numbers and the approximate representation of numerosities. Language is said to integrate the two kinds of information within each of these domains, which the reviewed data demonstrates. In the final part of the paper, we offer some comments on the theoretical side of the discussion. (shrink)

Number morphology (e.g., singular vs. plural) is a part of the grammar that captures numerical information. Some languages have morphological Number values, which express few (paucal), two (dual), three (trial) and sometimes (possibly) four (quadral). Interestingly, the limit of the attested morphological Number values matches the limit of non‐verbal numerical cognition. The latter is based on two systems, one estimating approximate numerosities and the other computing exact numerosities up to three or four. We compared the literature on non‐verbal number systems (...) with data on Number morphology from 218 languages. Our observations suggest that non‐verbal numerical cognition is reflected as a core part of language. (shrink)

This dissertation defends the reliability of first-person methods for studying consciousness, and applies first-person experiments to two philosophical problems: the experience of size and of the self. In chapter 1, I discuss the motivations for taking a first-person approach to consciousness, the background assumptions of the dissertation and some methodological preliminaries. In chapter 2, I address the claim that phenomenal judgements are far less reliable than perceptual judgements (Schwitzgebel, 2011). I argue that the main errors and limitations in making phenomenal (...) judgements are due to domain-general factors, which are shared in the formation of perceptual judgements. Phenomenal judgements may still be statistically less reliable than perceptual judgements, though I provide reasons for thinking that Schwitzgebel (2011) overstates the case for statistical unreliability. I also provide criteria for distinguishing between reliable and unreliable phenomenal judgements, hence defending phenomenal judgements against general introspective scepticism. Having identified the main errors in making phenomenal judgements, in chapter 3, I discuss how first-person experiments can be used to control for these errors. I provide examples, and discuss how they overcome attentional and conceptual errors, minimise biases, and exhibit high intersubjective reliability. In chapter 4, I investigate size experience. I use first-person experiments and empirical findings to argue that distant things looking smaller cannot be explained as an awareness of instantiated objective properties (visual angle or retinal image size). I also discuss how an awareness of uninstantiated objective properties cannot adequately account for the phenomenal character of size experience. This provides support for a subjectivist account of variance in size experience. In chapter 5, I investigate the sense of self. I distinguish between a weak sense of self (for-me-ness) and a strong sense of self in which there is a polarity between subject and object. I use first-person experiments from Douglas Harding to demonstrate an explicit strong sense of self, specifically when I point at where others see my face. I also argue that this sense of self is not explained by inference, thoughts, feelings, imagination nor the viewpoint. Rather, it is part of the structure of experience that I seem to be looking from here. Even if there is a sense of self, there may be no self. The question of chapter 6 is whether there can be a direct experience of the self. I argue that to function as a bearer of experience the subject must be single and lack sensory qualities in itself. I use Harding’s first-person experiments to investigate the visual gap where I cannot see my head. I argue that it conforms to the above criteria, and hence is a candidate for being the subject. This finding, in conjunction with the fact that I seem to be looking from the same location, provides prima facie evidence for the reality of the subject. I hold then that contrary to Hume and most philosophers since, that there can be a direct self-experience, if one knows which direction to attend. (shrink)

Determining the nature of binding in grapheme-color synaesthesia has consequences for understanding the neural basis of synaesthesia and visual awareness in general. We evaluated type- and token-based letter-color binding using a synaesthetic version of the object-reviewing paradigm. Although mean response times failed to reveal any significant differences between synaesthetes and control participants, RT analyses with ex-Gaussian distributions revealed that the response facilitation in the synaesthesia group reflected type representations exclusively, while response facilitation in the control group, who learned letter-color associations, (...) was dominated by token representations. Thus, letter-color associations in associator synaesthetes are type-based, and do not involve binding to object tokens, consistent with their subjective reports. Contrary to recent studies that failed to find differences between synaesthetes and non-synaesthetes with behavioral measures, response time distribution analyses indicate that color sensations in synaesthetes are not simply the extreme form of normal letter-color associations, and cannot be attributed to demand characteristics. (shrink)