The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...) and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (shrink)

Participants in the cognitive phenomenology debate have proceeded by (a) proposing a bifurcation of theoretical options into inflationary and non-inflationary theories, and then (b) providing arguments for/against one of these theories. I suggest that this method has failed to illuminate the commonalities and differences among conscious intentional states of different types, in the absence of a theory of the structure of these states. I propose such a theory. In perception, phenomenal-intentional properties combine with somatosensory properties to form P-I property clusters (...) that serve as phenomenal modes of presentations of particulars. In imagination, somatosensory properties are replaced with phenomenal-intentional properties whose intentional objects are somatosensory properties, thus resulting in imaginative facsimiles of perceptual P-I property clusters. Such structures can then be used as phenomenal prototypes that pick out individuals and kinds. Sets of such prototypes constitute a subject’s conception of individuals and kinds. Combined with a few additional elements, these imaginative P-I property clusters serve as the building-blocks of conscious cognitive states. Different ways of carving up theoretical space classify my theory either as inflationary or as non-inflationary. I conclude that the theory is anti-inflationary in letter but inflationary in spirit. (shrink)

It is well-documented that children do not begin school as blank slates but that they bring with them extensive knowledge about how the world around them works. This conceptual knowledge, embedded within rich theoretical structures, is not always accurate and requires change through learning and instruction. Yet some ideas – such as object motion – appear to be particularly resistant to such change. So how can conceptual change be achieved or facilitated? Collaboration, for one, has long been recognised as a (...) beneficial learning and teaching approach, including early science education. However, for deep-rooted ideas collaborating with others may not always have the desired impact. Instead, the notion of self-collaboration is considered in this review. The current state of research in the field of predictive and underlying knowledge in childhood is outlined and different models of how the knowledge systems relate to each other are discussed. While further work is still needed to establish a clearer picture of how self-collaboration might effect conceptual change, research to-date clearly identifies significant differences between predictive and underlying knowledge structures throughout childhood, how these structures can be related to traditional conceptual change theories, and how they may play a role in future learning and instructional approaches. (shrink)

The paper undertakes three interdisciplinary tasks. The first one consists in constructing a formal model of the basic arithmetic competence, that is, the competence sufficient for solving simple arithmetic story-tasks which do not require any mathematical mastery knowledge about laws, definitions and theorems. The second task is to present a generalized arithmetic theory, called the arithmetic of indexed numbers (INA). All models of the development of counting abilities presuppose the common assumption that our simple, folk arithmetic encoded linguistically in the (...) mind is based on the linear number representation. This classical conception is rejected and a competitive hypothesis is formulated according to which the basic mature representational system of cognitive arithmetic is a structure composed of many numerical axes which possess a common constituent, namely, the numeral zero. Arithmetic of indexed numbers is just a formal tool for modelling the basic mature arithmetic competence. The third task is to develop a standpoint called temporal pluralism, which is motivated by neo-Kantian philosophy of arithmetic. (shrink)

For the past two decades, it has widely been assumed by linguists that there is a single computational operation, Merge, which is unique to language, distinguishing it from other cognitive domains. The intention of this paper is to progress the discussion of language evolution in two ways: (i) survey what the ethological record reveals about the uniqueness of the human computational system, and (ii) explore how syntactic theories account for what ethology may determine to be human-specific. It is shown that (...) the operation Label, not Merge, constitutes the evolutionary novelty which distinguishes human language from non-human computational systems; a proposal lending weight to a Weak Continuity Hypothesis and leading to the formation of what is termed Computational Ethology. Some directions for future ethological research are suggested. (shrink)

This paper will discuss the origin of the human mind, and the qualitative discontinuity between human and animal cognition. We locate the source of this discontinuity within the language faculty, and thus take the origin of the mind to depend on the origin of the language faculty. We will look at one such proposal put forward by Hauser et al. (Science 298:1569-1579, 2002), which takes the evolution of a Merge trait (recursion) to solely explain the differences between human and animal (...) cognition. We argue that the Merge-only hypothesis fails to account for various aspects of the human mind. Instead we propose that the process of lexicalisation is also unique to humans, and that this process is key to explaining the vast qualitative differences. We will argue that lexicalisation is a process through which concepts are reformatted to be able to take on semantic features and to take part in grammatical relations. These are both necessary conditions for a grammatical mind and the increased ability to express conceptual content. We therefore propose a possible explanans for the discontinuity between humans and animals, namely that merge with lexicalisation (and consequently semantic features and grammatical relations) is a minimal requirement for the human mind. (shrink)

According to a posteriori physicalism, phenomenal properties are physical properties, despite the unbridgeable cognitive gap that holds between phenomenal concepts and physical concepts. Current debates about a posteriori physicalism turn on what I call “the perspicuity principle”: it is impossible for a suitably astute cognizer to possess concepts of a certain sort—viz., narrow concepts—without being able to tell whether the referents of those concepts are the same or different. The perspicuity principle tends to strike a posteriori physicalists as implausibly rationalistic; (...) further, a posteriori physicalists maintain that even if the principle is applicable to many narrow concepts, phenomenal concepts have unique features that render them inferentially isolated from other narrow concepts ). I argue, on the contrary, that the case for the perspicuity principle is quite strong. Moreover, not only have versions of the PCS repeatedly failed, likely, all versions will, given the strange combination of lucidity and opacity that the PCS has to juggle. I conclude that a posteriori physicalists currently lack a principled objection to classic anti-physicalist arguments. (shrink)

Philosophers of information, according to Luciano Floridi (The philosophy of information. Oxford University Press, Oxford, 2010, p 32), study how information should be “adequately created, processed, managed, and used.” A small number of epistemologists have employed the concept of information as a cornerstone of their theoretical framework. How this concept can be used to make sense of seemingly intractable epistemological problems, however, has not been widely explored. This paper examines Fred Dretske’s information-based epistemology, in particular his response to radical epistemological (...) skepticism. We discuss the relationship between information, evidence and knowledge in relation to the problem of skepticism and the options available to an information-based epistemology for dealing with it. (shrink)

In this article, we analyze and reject two versions of the content‐argument against animal beliefs, namely, the ontological argument from Davidson and the epistemological argument from Stich. One of the main defects of the strongest version of the argument is that it over‐intellectualizes belief ascriptions in humans and thus sets the comparative bar for belief ascriptions in animals too high. In the second part of the article, we develop a gradualist notion of belief which captures basic beliefs as well as (...) Davidsonian linguistic beliefs, and we specify the conditions under which belief ascriptions to nonlinguistic animals are justified. (shrink)

How can we solve the paradox of false-belief understanding: if infants pass the implicit false belief task by nonverbal behavioural responses why do they nonetheless typically fail the explicit FBT till they are 4 years old? Starting with the divide between situational and cognitive accounts of the development of false-belief understanding, we argue that we need to consider both situational and internal cognitive factors together and describe their interaction to adequately explain the development of children’s Theory of Mind ability. We (...) then argue that a further challenge is raised for existing accounts by helping behaviour versions of the FBT. We argue that the common two-stage accounts are inadequate: we need to allow for three central stages in a continuous development. Furthermore, drawing on Perner et al.’s and Perner and Leahy’s : 491–508, 2016) recent mental files account, we provide a new account of the development of these three stages of ToM ability by describing the changes of the structure and organisation of mental files including the systematic triggering role of types of situations. Thereby we aim to establish a situational mental file account as a new and adequate solution to the paradox of false-belief understanding. (shrink)

In the debate about the nature of social cognition we see a shift towards theories that explain social understanding through interaction. This paper discusses autopoietic enactivism and the we-mode approach in the light of such developments. We argue that a problem seems to arise for these theories: an interactionist account of social cognition makes the capacity of shared intentionality a presupposition of social understanding, while the capacity of engaging in scenes of shared intentionality in turn presupposes exactly the kind of (...) social understanding that it is intended to explain. The social capacity in question that is presupposed by these accounts is then analyzed in the second section via a discussion and further development of Searle’s ‘sense of us’ and ‘sense of the other’ as a precondition for social cognition and joint action. After a critical discussion of Schmid’s recent proposal to analyze this in terms of plural pre-reflective selfawareness, we develop an alternative account. Starting from the idea that infants distinguish in perception between physical objects and other agents we distinguish between affordances and social affordances and cash out the notion of a social affordance in terms of “interaction-oriented representations”, parallel to the analysis of object affordances in terms of “action-oriented representations”. By characterizing their respective features we demonstrate how this approach can solve the problem formulated in the first part. (shrink)

The generality problem is commonly considered to be a critical difficulty for reliabilism. In this paper, we present a dynamical perspective on the problem in the spirit of naturalized epistemology. According to this outlook, it is worth investigating how token belief-forming processes instantiate specific types in the biological agent’s cognitive architecture and background experience, consisting in the process of attractor-guided neural activation. While our discussion of the generality problem assigns “scientific types” to token processes, it represents a unified account in (...) the sense that it incorporates contextual and common sense features emphasized by other authors. (shrink)

The present study investigated 3-year-old children’s learning processes about object functions. We built on children’s tendency to commit scale errors with tools to explore whether they would selectively endorse object functions from a linguistic in-group over an out-group model. Participants ( n = 37) were presented with different object sets, and a model speaking either in their native or a foreign language demonstrated how to use the presented tools. In the test phase, children received the object sets with two modifications: (...) the original tool was replaced by one that was too big to achieve the goal but was otherwise identical, and another tool was added to the set that looked different but was appropriately scaled for goal attainment. Children in the Native language condition were significantly more likely to commit scale errors – that is, choose the over-sized tool – than children in the Foreign language condition (48 vs. 30%). We propose that these results provide insight into the characteristics of human-specific learning processes by showing that children are more likely to generalize object functions to a category of artifacts following a demonstration from an in-group member. (shrink)