Online research in philosophy

§ i. After deserting for a time the old Euclidean standards of rigour, mathematics is now returning to them, and even making efforts to go beyond them. ...

What is central to the progression of a sequence is the idea of succession, which is fundamentally a temporal notion. In Kant's ontology numbers are not objects but rules (schemata) for representing the magnitude of a quantum. The magnitude of a discrete quantum 11...11 is determined by a counting procedure, an operation which can be understood as a mapping from the ordinals to the cardinals. All empirical models for numbers isomorphic to 11...11 must conform to the transcendental determination of time-order. (...) Kant's transcendental model for number entails a procedural semantics in which the semantic value of the number-concept is defined in terms of temporal procedures. A number is constructible if and only if it can be schematized in a procedural form. This representability condition explains how an arbitrarily large number is representable and why Kant thinks that arithmetical statements are synthetic and not analytic. (shrink)

We describe recent developments in research on mathematical practice and cognition and outline the nine contributions in this special issue of topiCS. We divide these contributions into those that address (a) mathematical reasoning: patterns, levels, and evaluation; (b) mathematical concepts: evolution and meaning; and (c) the number concept: representation and processing.

This exploration of how people came to appreciate numbers traces the ways in which early humans gradually evolved methods for recording numerical data and ...

"With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics."--Carl B. Boyer, Brooklyn College. This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition. Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; and the rigorous construction of elementary arithmetic. (...) Advanced topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers. 1959 ed. 27 Figures. Index. (shrink)

The paper examines the roots of Husserlian phenomenology in Weierstrass's approach to analysis. After elaborating on Weierstrass's programme of arithmetization of analysis, the paper examines Husserl's Philosophy of Arithmetic as an attempt to provide foundations to analysis. The Philosophy of Arithmetic consists of two parts; the first discusses authentic arithmetic and the second symbolic arithmetic. Husserl's novelty is to use Brentanian descriptive analysis to clarify the fundamental concepts of arithmetic in the first part. In the second part, he founds the (...) symbolic extension of the authentically given arithmetic with stepwise symbolic operations. In the process of doing so, Husserl comes close to defining the modern concept of computability. The paper concludes with a brief comparison between Husserl and Frege. While Frege chose to subject arithmetic to logical analysis, Husserl wants to clarify arithmetic as it is given to us. Both engage in a kind of analysis, but while Frege analyses within Begriffsschrift, Husserl analyses our experiences. The difference in their methods of analysis is what ultimately grows into two separate schools in philosophy in the 20th century. (shrink)

A new edition of the classic introduction to mathematics, first published in 1930 and revised in the 1950s, explains the history and tenets of mathematics, ...

There can be no doubt about the value of Frege's contributions to the philosophy of mathematics. First, he invented quantification theory and this was the first step toward making precise the notion of a purely logical deduction. Secondly, he was the first to publish a logical analysis of the ancestral R* of a relation R, which yields a definition of R* in second-order logic.1 Only a narrow and arid conception of philosophy would exclude these two achievements. Thirdly and very importantly, (...) the discussion in §§58-60 of the G r u n d l a g e n defends a conception of mathematical existence, to be found in Cantor (1883) and later in the writings of Dedekind and Hilbert, by basing it upon considerations about meaning which have general application, outside mathematics.2.. (shrink)

Christopher Peacocke, in A Study of Concepts, motivates his account of possession conditions for concepts by means of an alleged parallel with the conditions under which numbers are abstracted to give the numerosity of a predicate. There are, however, logical mistakes in Peacocke.

In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51–B60.] argue that such an inductive inference is consistent with a representational system (...) that clearly does not express the natural numbers and that possession of the natural numbers requires further principles that make the inductive inference superfluous. We argue that their critique is unsuccessful. Provided that children have access to a suitable initial system of representation, the sort of inductive inference that Rips et al. call into question can in fact facilitate the acquisition of larger integer concepts without the addition of any further principles. Ó 2007 Elsevier B.V. All rights reserved. (shrink)

The mole and Avogadro’s number are two important concepts of science that provide a link between the properties of individual atoms or molecules and the properties of bulk matter. It is clear that an early theorist of the idea of these two concepts was Avogadro. However, the research literature shows that there is a controversy about the subjects of when and by whom the mole concept was first introduced into science and when and by whom Avogadro’s number (...) was first calculated. Based on this point, the following five matters are taken into consideration in this paper. First, in order to base the subject matter on a strong ground, the historical development of understanding the particulate nature of matter is presented. Second, in 1811, Amedeo Avogadro built the theoretical foundations of the mole concept and the number 6.022 × 1023 mol−1. Third, in 1865, Johann Josef Loschmidt first estimated the number of molecules in a cubic centimetre of a gas under normal conditions as 1.83 × 1018. Fourth, in 1881, August Horstmann first introduced the concept of gram-molecular weight in the sense of today’s mole concept into chemistry and, in 1900, Wilhelm Ostwald first used the term mole instead of the term ‘gram-molecular weight’. Lastly, in 1889, Károly Than first determined the gram-molecular volume of gases under normal conditions as 22,330 cm3. Accordingly, the first value for Avogadro’s number in science history should be 4.09 × 1022 molecules/gram-molecular weight, which is calculated by multiplying Loschmidt’s 1.83 × 1018 molecules/cm3 by Than’s 22,330 cm3/gram-molecular weight. Hence, Avogadro is the originator of the ideas of the mole and the number 6.022 × 1023 mol−1, Horstmann first introduced the mole concept into science/chemistry, and Loschmidt and Than are the scientists who first calculated Avogadro’s number. However, in the science research literature, it is widely expressed that the mole concept was first introduced into chemistry by Ostwald in 1900 and that Avogadro’s number was first calculated by Jean Baptiste Perrin in 1908. As a result, in this study, it is particularly emphasised that Horstmann first introduced the mole concept into science/chemistry and the first value of Avogadro’s number in the history of science was 4.09 × 1022 molecules/gram-molecular weight and Loschmidt and Than together first calculated this number. (shrink)

Understanding what numbers are means knowing several things. It means knowing how counting relates to numbers (called the cardinal principle or cardinality); it means knowing that each number is generated by adding one to the previous number (called the successor function or succession), and it means knowing that all and only sets whose members can be placed in one-to-one correspondence have the same number of items (called exact equality or equinumerosity). A previous study (Sarnecka & Carey, 2008) (...) linked children's understanding of cardinality to their understanding of succession for the numbers five and six. This study investigates the link between cardinality and equinumerosity for these numbers, finding that children either understand both cardinality and equinumerosity or they understand neither. This suggests that cardinality and equinumerosity (along with succession) are interrelated facets of the concepts five and six, the acquisition of which is an important conceptual achievement of early childhood. (shrink)

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and (...) logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)

Mathematics often seems incomprehensible, a melee of strange symbols thrown down on a page. But while formulae, theorems, and proofs can involve highly complex concepts, the math becomes transparent when viewed as part of a bigger picture. What Is a Number? provides that picture. Robert Tubbs examines how mathematical concepts like number, geometric truth, infinity, and proof have been employed by artists, theologians, philosophers, writers, and cosmologists from ancient times to the modern era. Looking at a broad range (...) of topics -- from Pythagoras's exploration of the connection between harmonious sounds and mathematical ratios to the understanding of time in both Western and pre-Columbian thought -- Tubbs ties together seemingly disparate ideas to demonstrate the relationship between the sometimes elusive thought of artists and philosophers and the concrete logic of mathematicians. He complements his textual arguments with diagrams and illustrations. This historic and thematic study refutes the received wisdom that mathematical concepts are esoteric and divorced from other intellectual pursuits -- revealing them instead as dynamic and intrinsic to almost every human endeavor. (shrink)

Bloom's book underscores the importance of specifying the role of words and grammar in cognition. We propose that the cognitive power of language lies in the lexicon rather than grammar. We suggest ways in which studies involving children and patients with aphasia can provide insights into the basis of abstract cognition in the domain of number and mathematics.

By examining Klein’s discussion of the difference between Plato and Aristotle regarding the ontology of number, this article aims to spells out the significanceof that debate both in itself and for the development of the later mathematical sciences. This is accomplished by explicating and expanding Klein’s account of the differences that exist in the understanding of number presented by these two thinkers. It is ultimately argued that Klein’s analysis can be used to show that the transition from the (...) ancient to the modern number concept has some roots in this disagreement between Plato and Aristotle regarding number. This, in turn, sets up that dispute as an essential part of the background to the more general break between ancient and modern conceptuality, the uncovering of whichis Klein’s main concern. (shrink)

Ancient Greek Philosophy routinely relied upon concepts of number to explain the tangible order of the universe. Plotinus' contribution to this tradition, however, has been often omitted, if not ignored. The main reason for this, at first glance, is the Plotinus does not treat the subject of number in the Enneads as pervasively as the Neopythagoreans or even his own successors Lamblichus, Syrianus, and Proclus. Nevertheless, a close examination of the Enneads reveals that Plotinus systematically discusses number (...) in relation to each of his underlying principles of existence--the One, Intellect, and Soul. Plotinus on Number offers the first comprehensive analysis of Plotinus' concept of number, beginning with its origins in Plato and the Neopythagoreans and ending with its influence on Porphyry's arrangement of the Enneads. It's main argument is that Plotinus adapts Plato's and the Neopythagoreans' cosmology to place number in the foundation of the intelligible realm and in the construction of the universe. Through Plotinus' defense of Plato's Ideal Numbers from Aristotle's criticism, Svetla Slaveva-Griffin reveals the founder of Neoplatonism as the first post-Platonic philosopher who purposefully and systematically develops what we may call a theory of number, distinguishing between number in the intelligible realm and number in the quantitative, mathematical realm. Finally, the book draws attention to Plotinus' concept as a necesscary and fundamental linke between Platonic and late Neoplatonic schools of philosophy. (shrink)

It is nowadays a dominant opinion in a number of disciplines (anthropology, genetics, psychology, philosophy of science) that the taxonomy of human races does not make much biological sense. My aim is to challenge the arguments that are usually thought to invalidate the biological concept of race. I will try to show that the way “race” was defined by biologists several decades ago (by Dobzhansky and others) is in no way discredited by conceptual criticisms that are now fashionable (...) and widely regarded as cogent. These criticisms often arbitrarily burden the biological category of race with some implausible connotations, which then opens the path for a quick eliminative move. However, when properly understood, the biological notion of race proves remarkably resistant to these deconstructive attempts. Moreover, by analyzing statements of some leading contemporary scholars who support social constructivism about race, I hope to demonstrate that their eliminativist views are actually in conflict with what the best contemporary science tells us about human genetic variation. (shrink)

Frank Jackson’s famous Knowledge Argument moves from the premise that complete physical knowledge is not complete knowledge about experiences to the falsity of physicalism. In recent years, a consensus has emerged that the credibility of this and other well-known anti-physicalist arguments can be undermined by allowing that we possess a special category of concepts of experiences, phenomenal concepts, which are conceptually independent from physical/functional concepts. It is held by a large number of philosophers that since the conceptual independence of (...) phenomenal concepts does not imply the metaphysical independence of phenomenal properties, physicalism is safe. This paper distinguishes between two versions of this novel physicalist strategy –Phenomenal Concept Strategy (PCS) – depending on how it cashes out “conceptual independence,” and argues that neither helps the physicalist cause. A dilemma for PCS arises: cashing out “conceptual independence” in a way compatible with physicalism requires abandoning some manifest phenomenological intuitions, and cashing it out in a way compatible with those intuitions requires dropping physicalism. The upshot is that contra Brian Loar and others, one cannot “have it both ways.”. (shrink)

The biological species (biospecies) concept applies only to sexually reproducing species, which means that until sexual reproduction evolved, there were no biospecies. On the universal tree of life, biospecies concepts therefore apply only to a relatively small number of clades, notably plants andanimals. I argue that it is useful to treat the various ways of being a species (species modes) as traits of clades. By extension from biospecies to the other concepts intended to capture the natural realities of (...) what keeps taxa distinct, we can treat other modes as traits also, and so come to understand that theplurality of species concepts reflects the biological realities of monophyletic groups.We should expect that specialists in different organisms will tend to favour those concepts that best represent the intrinsic mechanisms that keep taxa distinct in their clades. I will address the question whether modes ofreproduction such as asexual and sexual reproduction are natural classes, given that they are paraphyletic in most clades. (shrink)

not analytic. This seems to be the point of Kant's claim that the concept of the sum of seven and five does not include its equality to the number twelve ...

Radical concept nativism is the thesis that virtually all lexical concepts are innate. Notoriously endorsed by Jerry Fodor (1975, 1981), radical concept nativism has had few supporters. However, it has proven difficult to say exactly what’s wrong with Fodor’s argument. We show that previous responses are inadequate on a number of grounds. Chief among these is that they typically do not achieve sufficient distance from Fodor’s dialectic, and, as a result, they do not illuminate the central question (...) of how new primitive concepts are acquired. To achieve a fully satisfactory response to Fodor’s argument, one has to juxtapose questions about conceptual content with questions about cognitive development. To this end, we formulate a general schema for thinking about how concepts are acquired and then present a detailed illustration. (shrink)

Sometimes your concept and mine have exactly the same content. When this is so, it is comparatively easy for me to understand what you say when you deploy your concept, for us to disagree, agree, and so on. But what if your concept and mine do not have exactly the same content? This question has occupied a number of philosophers, including Paul Churchland, Jerry Fodor, and Ernie Lepore. This paper develops a novel and rigorous measure of (...) concept similarity, Proportion, such that concepts with different contents but sufficiently high Proportion scores will also conduce to understanding, agreement, and disagreement. (shrink)

In this short paper I begin by underlining the sense in which my intentional-historical theory of art, first proposed in 1979, attributes to art a certain irreducible historicality. I next defend the theory, in broad outline, against a number of objections that have been raised against it in the past ten years. I conclude with some remarks on the similarities and differences between ordinary artefact concepts and the concept of an artwork.

In [Laurence, Margolis 2003] the authors try - within their polemics against F.Jackson’s views in [Jackson 1998] - to decide the question whether concepts are a priori (in their formulation “to be defined a priori”). Their discussion suffers - as a number of similar articles - from a typical drawback: some problem whose solution requires an exact notion of concept is handled as if the latter were quite clear. The consequence of this ‘conceptual laxity’ is that a) the (...) topic of the discussion is not very clear (what does the phrase ‘concepts must be defined a priori’ mean?); b) the relevance of the Quinean criticism of the “second dogma of empiricism”, i.e., of Quine’s claim that “science sometimes overturns our most cherished beliefs” and therefore there is no sharp boundary between analytic and synthetic is uncritically accepted; c) no distinction is made between the question whether the relation between an expression and its meaning is a priori and the question whether the relation between a concept and the object identified by the concept is a priori. The present article intends to elucidate and then to answer the questions that can be asked when we say something like “concepts are a priori ”. (shrink)

Theodor Adorno's concept of 'natural history' [Naturgeschichte] was central for a number of Adorno's theoretical projects, but remains elusive. In this essay, I analyse different dimensions of the concept of natural history, distinguishing amongst (a) a reflection on the normative and methodological bases of philosophical anthropology and critical social science; (b) a conception of critical memory oriented toward the preservation of the memory of historical suffering; and (c) the notion of 'mindfulness of nature in the subject' provocatively (...) asserted in Max Horkheimer and Adorno's Dialectic of Enlightenment. These strands are united by the notion of transience and goal of developing a critical theory sensitive to the transient in history. The essay concludes by suggesting some implications of an expanded concept of natural history for issues in the discourse theory of Jürgen Habermas. (shrink)

The concept of voluntary motor control(VMC) frequently appears in the neuroscientific literature, specifically in the context of cortically-mediated, intentional motor actions. For cognitive scientists, this concept of VMC raises a number of interesting questions:(i) Are there dedicated, modular-like structures within the motor system associated with VMC? Or (ii) is it the case that VMC is distributed over multiple cortical as well as subcortical structures?(iii) Is there any one place within the so-calledhierarchy of motor control where voluntary movements (...) could be said to originate? And (iv) in the current neurological literature how is the adjective voluntary in VMC being used? These questions are here considered in the context of how higher- and lower-levels of motor control, plan, initiate, coordinate, sequence, and modulate goal-directed motor outputs in response to changing internal and external inputs. Particularly relevant are the conceptual implications of current neurological modeling of VMC concerning causal agency. (shrink)

This dissertation reconsiders some traditional issues in the foundations of quantum mechanics in the context of relativistic quantum field theory (RQFT); and it considers some novel foundational issues that arise first in the context of RQFT. The first part of the dissertation considers quantum nonlocality in RQFT. Here I show that the generic state of RQFT displays Bell correlations relative to measurements performed in any pair of spacelike separated regions, no matter how distant. I also show that local systems in (...) RQFT are "open" to influence from their environment, in the sense that it is generally impossible to perform local operations that would remove the entanglement between a local system and any other spacelike separated system. The second part of the dissertation argues that RQFT does not support a particle ontology -- at least if particles are understood to be localizable objects. In particular, while RQFT permits us to describe situations in which a determinate number of particles are present, it does not permit us to speak of the location of any individual particle, nor of the number of particles in any particular region of space. Nonetheless, the absence of localizable particles in RQFT does not threaten the integrity of our commonsense concept of a localized object. Indeed, RQFT itself predicts that descriptions in terms of localized objects can be quite accurate on the macroscopic level. The third part of the dissertation examines the so-called observer-dependence of the particle concept in RQFT -- that is, whether there are any particles present must be relativized to an observer's state of motion. Now, it is not uncommon for modern physical theories to subsume observer-dependent descriptions under a more general observer-independent description of some underlying state of affairs. However, I show that the conflicting accounts concerning the particle content of the field cannot be reconciled in this way. In fact, I argue that these conflicting accounts should be thought of as "complementary" in the same sense that position and momentum descriptions are complementary in elementary quantum mechanics. (shrink)

One of the most important abilities we have as humans is the ability to think about number. In this chapter, we examine the question of whether there is an essential connection between language and number. We provide a careful examination of two prominent theories according to which concepts of the positive integers are dependent on language. The first of these claims that language creates the positive integers on the basis of an innate capacity to represent real numbers. The (...) second claims that language’s function is to integrate contents from modules that humans share with other animals. We argue that neither model is successful. (shrink)

The theoretical work of European and American structuralism has produced a number of important elements which have resulted in (especially with respect to certain new, fundamental approaches in semantics, philosophy and methodology) essential shifts in the modes of thinking in the humanities, and in the cultural and social sciences. Despite these shifts, Western discourses have still not produced any integral, coherent structural model of epistemology. The present article intends to show that such a model can be found in the (...) pan-structural epistemology of the modern Chinese philosopher Zhang Dongsun (1886?1973), and that the crucial, theoretical underpinnings of such models were developed much earlier in the history of Chinese thought, given that the bases of a structural approach to comprehension had already been established in ancient Chinese philosophy. This paradigmatic foundation (the concept li) was further developed and elaborated by various Chinese philosophers in later centuries as a crucial feature of the classical Chinese logic of binary analogies. The article also points out that the central binary concept of the Neo-Confucian tradition (i.e. the concept of structure and creativity; li and qi) has generally been interpreted as a dualism of idea and matter by Euro-American sinologists. However, such interpretations have overlooked an important feature of traditional, structurally determined Chinese onto-epistemology. (shrink)

In recent years, an increasing number of medical books and papers attempting to analyse the concepts of health and disease from the perspective of evolutionary biology have been published (Eaton etal., 1993; Ewald, 1993; Harrison, 1993; Nesse and Williams, 1995; Profet, 1991; Rose, 1991; Temple and Burkitt, 1994). This paper introduces the evolutionary approach to health and disease in an attempt to illuminate the premisses and the framework of Darwinian medicine. My primary aim is to analyse to what extent (...) evolutionary theory provides for a biological definition of the concept of disease. This analysis reveals some important differences between functional explanations in the field of evolutionary biology and functional explanations in the field of medicine. Moreover, I shall argue that the biological functions relevant to the health of an organism cannot be determined on the basis of evolutionary theory. Accordingly, it seems that Darwinian medicine does not provide for the definition of a biological concept of disease. Still,Darwinian medicine may suggest why we are susceptible to certain diseases; it might also prove a suggestive heuristic on the basis of which new hypotheses concerning relevant treatments of various diseases might be advanced. (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)

In his Grundgesetze, Frege hints that prior to his theory that cardinal numbers are objects (courses-of-values) he had an “almost completed” manuscript on cardinals. Taking this early theory to have been an account of cardinals as second-level functions, this paper works out the significance of the fact that Frege’s cardinal numbers (as objects) is a theory of concept-correlates. Frege held that, where n>2, there is a one–one correlation between each n-level function and an n−1 level function, and a one–one (...) correlation between each first-level function and an object (a course-of-values of the function). Applied to cardinals, the correlation offers new answers to some perplexing features of Frege’s philosophy. It is shown that within Frege’s concept-script, a generalized form of Hume’s Principle is equivalent to Russell’s Principle of Abstraction – a principle Russell employed to demonstrate the inadequacy of definition by abstraction. Accordingly, Frege’s rejection of definition of cardinal number by Hume’s Principle parallels Russell’s objection to definition by abstraction. Frege’s correlation thesis reveals that he has a way of meeting the structuralist challenge (later revived by Benacerraf, 1965) that it is arithmetic, and not a privileged progression of objects, that matters to the finite cardinals. (shrink)

Abstract Scientists and philosophers generally agree that the replication of experiments is a key ingredient of good and successful scientific practice. “One-offs“ are not significant; experiments must be replicable to be considered valid and important. But the term “replication“ has been used in a number of ways, and it is therefore quite difficult to appraise the meaning and significance of replications. I consider how history may help - and has helped - with this task. I propose that: 1) Studies (...) of past scientific episodes in historical context and of recent philosophical contributions to the discussion are heuristic tools for exploring and clarifying the meaning of that concept. 2) The analysis of the development of the methodological imperative of replication sheds light on the significance scientists have attached to it, thereby contributing further to the clarification of the concept. 3) The analysis of the history of philosophical thought about methods and scientific methodology helps understand why philosophers have not paid much attention to the analysis of the concept of replication. (shrink)

We discuss the concept of a cardinal number and its history, focussing on Cantor's work and its reception. J'ay fait icy peu pres comme Euclide, qui ne pouvant pas bien >faire< entendre absolument ce que c'est que raison prise dans le sens des Geometres, definit bien ce que c'est que memes raisons. (Leibniz) 1.

This paper explores Simon Stevin’s l’Arithmétique of 1585, where we find a novel understanding of the concept of number. I will discuss the dynamics between his practice and philosophy of mathematics, and put it in the context of his general epistemological attitude. Subsequently, I will take a close look at his justificational concerns, and at how these are reflected in his inductive, a postiori and structuralist approach to investigating the numerical field. I will argue that Stevin’s renewed (...) conceptualisation of the notion of number is a sort of “existential closure” of the numerical domain, founded upon the practice of his predecessors and contemporaries. Accordingly, I want to make clear that l’Aritmetique have to be read not as an ontological analysis or exploration of the numerical field, but as an explication of a mathematical ethos. In this sense, this article also intends to make a specific contribution to the broader issue of the “ethics of geometry.”. (shrink)

Community remains a potent symbol and aspiration in political and intellectual life. However, it has largely passed out of sociological analysis. The paper shows why this has occurred, and it develops a new typology that can make the concept useful again in sociology. The new typology is based on identifying structurally distinct subtypes of community using a small number of partitioning variables. The first partition is defined by the ultimate context of interaction; the second by the primary motivation (...) for interaction; the third by rates of interaction and location of members; and the fourth by the amount of face-to-face as opposed to computer-mediated interaction. This small number of partitioning variables yields eight major subtypes of community. The paper shows how and why these major subtypes are related to important variations in the behavioral and organizational outcomes of community. The paper also seeks to resolve some disagreements between classical liberalism and communitarians. It shows that only a few of the major subtypes of community are likely to be as illiberal and intolerant as the selective imagery of classical liberals asserts, while at the same time only a few are prone to generate as much fraternalism and equity as the selective imagery of communitarians suggests. The paper concludes by discussing the forms of community that are best suited to the modern world. (shrink)

This article presents a discussion of how postmodernist, poststructuralist and critical educational thinking relate to different theories of power. I argue that both Critical Theory and some poststructuralist ideas base themselves on a concept of power borrowed from a modernist tradition. I argue as well that we are better off combining a postmodern idea of education with a postmodern idea of power. To this end the concept of power presented by the works of Ernesto Laclau and Chantal Mouffe (...) is introduced. This concept controverts a number of major educational concepts, i.e. concepts such as causality, autonomy, subjectivity and originality. In other words, it allows us to take a fresh look at old concepts. Finally, I relate the discussion to a number of recent theories of learning. (shrink)

How-many numbers, such as 2 and 1000, relate or are capable of expressing the size of a group or set. Both Cantor and Frege analyzed how-many number in terms of one-to-one correspondence between two sets. That is to say, one arrived at numbers by either abstracting from the concept of correspondence, in the case of Cantor, or by using it to provide an out-and-out definition, in the case of Frege.

The aim of this paper is to present the Nyya concept of number in the light of contemporary philosophy and to show that the Frege-Russell concept of number does not contradict the Nyya concept of number but rather supplements it.

Species are the basis of the taxonomic scheme. They are the lowest taxonomic category that are used as units for describing biodiversity and evolution. In this contribution we discuss the current species concept for prokaryotes. Such organisms are considered to represent the widest diversity among living organisms. Species is currently circumscribed as follows: A prokaryotic species is a category that circumscribes a (preferably) genomically coherent group of individual isolates/strains sharing a high degree of similarity in (many) independent features, comparatively (...) tested under highly standardized conditions. Although the number of described prokaryotic species is underrepresented in the living world, this phylo-phenetic or polythetic species concept currently in use is considered to be pragmatic, operational and universally applicable and successfully used for identification processes. (shrink)

Nonclarity around the understandingof the concept of chaos has caused someconfusion in the contemporary natural science.For instance, not making a clear distinctionbetween the deterministic and quantum chaos hasmade it impossible to evaluate the approach ofIlya Prigogine in an appropriate way. It isshown that Jean Bricmont has missed the targetin his critique of I. Prigogine's ideas, as thelatter has concentrated his interest on systemsconsisting of infinite (arbitrarily large)number of particles in incessant mutualimpact, the former on systems that have afinite (...) (not necessarily large, althoughsometimes very large) number of particles,which move freely of any mutual impact orparticipate only in transient interaction. Thedifference may sometimes be quite crucial. Itis also suggested that if we consider theirreversibility as the basic element ofdescription of physical world, the world oftrajectories and wave functions cannot beresearched apart from this real irreversibility. (shrink)

This paper investigates the role of the concept of group heritability in group selection theory, in relation to the well-known distinction between type 1 and type 2 group selection (GS1 and GS2). I argue that group heritability is required for the operation of GS1 but not GS2, despite what a number of authors have claimed. I offer a numerical example of the evolution of altruism in a multi-group population which demonstrates that a group heritability coefficient of zero is (...) perfectly compatible with the successful operation of group selection in the GS2 sense. A diagnosis of why group heritability has wrongly been regarded as necessary for GS2 is suggested. (shrink)

Species are the basis of the taxonomic scheme. They are the lowest taxonomic category that are used as units for describing biodiversity and evolution. In this contribution we discuss the current species concept for prokaryotes. Such organisms are considered to represent the widest diversity among living organisms. Species is currently circumscribed as follows: A prokaryotic species is a category that circumscribes a (preferably) genomically coherent group of individual isolates/strains sharing a high degree of similarity in (many) independent features, comparatively (...) tested under highly standardized conditions. Although the number of described prokaryotic species is underrepresented in the living world, this phylo-phenetic or polythetic species concept currently in use is considered to be pragmatic, operational and universally applicable and successfully used for identification processes. (shrink)

Developments in biotechnology and genomics have moved the issue of patenting scientific and technological inventions toward the center of interest. In particular, the patentability of genes of plants, animals, or humans and of genetically modified (parts of) living organisms has been discussed, and questioned, from various normative perspectives. This paper aims to contribute to this debate. For this purpose, it first explains a number of relevant aspects of the theory and practice of patenting. The focus is on a special (...) and increasingly significant type of patents, namely product patents. The paper provides three general arguments against the concept and practice of product patenting. The first argument briefly considers the claim that patents are legitimate because they promote socially useful innovation. Against this claim, it is argued that product patents may hamper rather than promote such innovation. The second and main argument concludes that product patents are not adequately based on actual technological inventions, as they should be according to the usual criteria of patentability. The principal moral issue is that product patents tend to reward patentees for inventions they have not really made available. The final argument proposes a method for patenting the heat of the sun. Assuming that granting this patent will be generally considered absurd, the argument exposes a further, fundamental problem of the concept and practice of product patenting. (shrink)

. Current debates concerning the concept of mental disorder involve many different philosophical issues. However, it is not always clear from these discussions how, or whether, these issues relate to one another, or in exactly what way they are important for the definition of disorder. This article aims to sort through some of the philosophical issues that arise in the current literature and provide a clarification of how these issues are related to one another and whether they are necessary (...) for defining disorder. I argue that the main concern in defining disorder, namely demarcation, is obscured by a number of these other philosophical issues and that a focus on demarcation gives us a means of placing these other issues in a clarifying context. (shrink)

Given a set of objects characterized by a number of attributes, hidden patterns can be discovered in them for the grouping of similar objects into clusters. If each of these clusters can be considered as exemplifying a certain concept, then the problem concerned can be referred to as a concept discovery problem. This concept discovery problem can be solved to some extent by existing data clustering techniques. However, they may not be applicable when the concept (...) involved is vague in nature or when the attributes characterizing the objects can be qualitative, quantitative, and fuzzy at the same time. To discover such concepts from objects with such characteristics, we propose a Genetic-Algorithm-based technique. By encoding a specific object grouping in a chromosome and a fitness measure to evaluate the cluster quality, the proposed technique is able to discover meaningful fuzzy clusters and assign membership degrees to objects that do not fully exemplify a certain concept. For evaluation, we tested the proposed technique with simulated and real data and the results are found to be very promising. (shrink)

A cellular automaton that is related to the "mosaic cycle concept" is considered. We explain why such automata sustain very often, but not always, n-periodic trajectories (n being the number of states of the automaton). Our work is a first step in the direction of a theory of these type of automata which might be useful in modeling mosaic successions.

The paper aims to put certain basic mathematical elements and operations into an empirical perspective, evaluate the empirical status of various analytic operations widely used within psychology and suggest alternatives to procedures criticized as inadequate. Experimentation shows the "manyness" of items to be a perceptual quality for both young children and animals and that natural operations are performed by naive children analogous to those performed by persons tutored in arithmetic. Number, counting, arithmetic operations therefore can make distinctions that are (...) not inevitably arbitrary, and conceptual operations can obviously have a status as natural events with psychology. If the elements and conceptual operations involved in mathematical systems were not inherent in physiological process, various primitive discriminations could not be possible. Also, since some calculi have a natural status in a given empirical circumstance, the axioms of others can not be satisfied. Therefore the psychologist when acting as an empirical scientist seeks a calculus having a structure whose elements are isomorphic with natural units of stimulus and response and whose operations are isomorphic with whatever natural processes are involved. Measurement poses a special problem for the empirical scientist. It concerns but a single class of natural qualities and this only in a limited way. The concept of quantity has a natural counterpart but quantity and measurement are not wholly analogous. Measurement is defined, as H. S. Leonard suggests, as a theoretical activity. Measurement theory has a formal structure but empirical end. Measurement hypothesizes about the position of a particular quality within a definite range of qualities. It therefore is beholden to definite empirical restrictions. Some hypotheses-making systems use terms and relations per se as the context and starting point for dealing with discriminable events. Such procedures are 'transcendent." In empirical science, questions are part of problem-solving activity and their reference is naturally restricted. In providing description and explanation, psychological researchers frequently use calculi in a transcendent way. This results in theories that are only quasi-empirical and "half" true. The roles measurement plays in psychology are discussed. Of particular concern are those cases in which the results of measuring or a theory of measurement are used to define the "real" units, or the "real" relations involved in problematic psychological events, and thence to describe and explain behaviors of interest. Metaphysical or ontological usages of measurement sometimes occur. The implication of these arguments with regard to a view of empirical science is discussed. (shrink)

A concept language with role intersection and number restriction is defined and its modal equivalent is provided. The main reasoning tasks of satisfiability and subsumption checking are formulated in terms of modal logic and an algorithm for their solution is provided. An axiomatization for a restricted graded modal language with intersection of modalities (the modal counterpart of the concept language we examine)is given and used in the proposed algorithm.

Biologists studying short-lived organisms have become aware of the need to recognize an explicit temporal extend of a population over a considerable time. In this article we outline the concept and the realm of populations with explicit spatial and temporary boundaries. We call such populations “temporally bounded populations”. In the concept, time is of the same importance as space in terms of a dimension to which a population is restricted. Two parameters not available for populations that are only (...) spatially defined characterise temporally bounded populations: total population size, which is the total number of individuals present within the temporal borders, and total residence time, which is the sum of the residence times of all individuals. We briefly review methods to estimate these parameters. We illustrate the concept for the large blue butterfly (Maculinea nausithous) and outline insights into ecological and conservation-relevant processes that cannot be gained without the use of the concept. (shrink)

The paper examines Dummett's argument for the indefinite extensibility of the concepts set, ordinal, real number, set of natural numbers, and natural number. In particular it investigates how the indefinite extensibility of the concept set affects our understanding of the notion of real number and whether the argument to the indefinite extensibility of the reals is cogent. It claims that Dummett is right to think of the universe of sets as an indefinitely extensible domain but questions (...) the cogency of the further claim that this fact raises an issue as to what sets or real numbers there are. (shrink)

Let κ and λ be infinite cardinals such that κ ≤ λ (we have new information for the case when $\kappa ). Let T be a theory in L κ +, ω of cardinality at most κ, let φ(x̄, ȳ) ∈ L λ +, ω . Now define $\mu^\ast_\varphi (\lambda, T) = \operatorname{Min} \{\mu^\ast:$ If T satisfies $(\forall\mu \kappa)(\exists M_\chi \models T)(\exists \{a_i: i Our main concept in this paper is $\mu^\ast_\varphi (\lambda, \kappa) = \operatorname{Sup}\{\mu^\ast(\lambda, T): T$ is a (...) theory in L κ +, ω of cardinality κ at most, and φ (x, y) ∈ L λ +, ω }. This concept is interesting because of THEOREM 1. Let $T \subseteq L_{\kappa^+,\omega}$ of cardinality ≤ κ, and φ (x̄, ȳ) ∈ L λ +, ω . If $(\forall\mu then $(\forall_\chi > \kappa) I(\chi, T) = 2^\chi$ (where I(χ, T) stands for the number of isomorphism types of models of T of cardinality χ). Many years ago the second author proved that $\mu^\ast (\lambda, \kappa) \leq \beth_{(2^\lambda)^+}$ . Here we continue that work by proving. THEOREM 2. $\mu^\ast (\lambda, \aleph_0) = \beth_{\lambda^+}$ . THEOREM 3. For every κ ≤ λ we have $\mu^\ast (\lambda, \kappa) \leq \beth)_{(\lambda^\kappa)}^+$ . For some κ or λ we have better bounds than in Theorem 3, and this is proved via a new two cardinal theorem. THEOREM 4. For every $\kappa \leq \lambda, T \subseteq L_{\kappa^+,\omega}$ , and any set of formulas $\Lambda \subseteq L_{\lambda^+,\omega}$ such that $\Lambda \subseteq L_{\kappa^+,\omega}$ , if T is (Λ,μ)-unstable for μ satisfying μ μ * (λ, κ) = μ then T is Λ-unstable (i.e. for every χ ≥ λ, T is (Λ, χ)-unstable). Moreover, T is L κ +, ω -unstable. In the second part of the paper, we show that always in the applications it is possible to replace the function I(χ, T) by the function IE(χ, T), and we give an application of the theorems to Boolean powers. (shrink)

The number of studies related to natural and artificial mechanisms of learning rapidly increases. However, there is no general theory of learning that could provide a unifying basis for exploring different directions in this growing field. For a long time the development of such a theory has been hindered by nativists' belief that the development of a biological organism during ontogeny should be viewed as parameterization of an innate, encoded in the genome structure by an innate algorithm, and nothing (...) essentially new is created during this process. Noam Chomsky has claimed, therefore, that the creation of a non-trivial general mathematical theory of learning is not feasible, since any algorithm cannot produce a more complex algorithm. This study refutes the above argumentation by developing a counter-example based on the mathematical theory of algorithms and computable functions. It introduces a novel concept of a Universal Learning System (ULS) capable of learning to control in an optimal way any given constructive system from a certain class. The necessary conditions for the existence of a ULS and its main functional properties are investigated. The impossibility of building an algorithmic ULS for a sufficiently complex class of controlled objects is shown, and a proof of the existence of a non-algorithmic ULS based on the axioms of classical mathematics is presented. It is argued that a non-algorithmic ULS is a legitimate object of not only mathematics, but also the world of nature. These results indicate that an algorithmic description of the organization and adaptive development of biological systems in general is not sufficient. At the same time, it is possible to create a rigorous non-algorithmic general theory of learning as a theory of ULS. The utilization of this framework for integrating learning-related studies is discussed. (shrink)

This paper discusses the widespread use of heritability calculations in recent behaviour research including behaviour genetics. In the sequel, a radical criticism concerning the basic axioms of the underlying, more general concept itself is presented. The starting point for testing the proclaimed universal validity of this concept stems from a fictitious yet realistic example taken from learning research. The theoretical result, based on the application of the conventional reasoning in this field, states that developmental processes — and learning (...) is only one specific case out of an immense number of similar behavioural mechanisms — can neither be adequately described nor causally explained with sufficient reliability within the context of the heredity paradigm. On the contrary, an inherent inconsistency of the concept itself when applied to behaviour processes is demonstrated. Finally, a conceptual alternative involving a systems-theoretical approach to the problem is presented: In such a perspective it is the concept of cognition which represents the adequate explanatory theorem - a theorem in which quantitative processing of information from the environment is clearly revealed to belong to a subordinate level of living organization. (shrink)

The rise of “dignity talk” has led to the concept of human dignity being criticized in recent years. Some critics argue that human dignity must either be something we have or something we acquire. Others argue that there is no such thing as human dignity and people really mean something else when they appeal to it. Both “dignity talk” and the criticisms arise from a problematic conception of medical ethics as a legalistic, procedural techne. A retrieval of hermeneutical ethics, (...) by contrast, offers a way to overcome both the legalism of contemporary ethics and the abuses and criticisms of the concept of human dignity. Such an ethics affirms both the inherent dignity of a human being as a multi-dimensional, meaning-seeking, historically-situated, relational individual, who desires to live a good life, and the realized sense of his/her own dignity toward which s/he works. As such, human dignity cannot be reduced to one feature of the human, and instead functions as both a descriptive category that avoids moralism, and as a normative category that allows relativity whilst avoiding relativism . Content Type Journal Article Category Article Pages 141-154 DOI 10.1558/hrge.v17i2.141 Authors David G. Kirchhoffer, School of Theology, Australian Catholic University, PO Box 456, Virgina QLD, 4014 Australia Journal Human Reproduction & Genetic Ethics Online ISSN 2043-0469 Print ISSN 1028-7825 Journal Volume Volume 17 Journal Issue Volume 17, Number 2 / 2011. (shrink)

Abstract A principle aim of this paper is to convince friends and critics of deconstruction that they have overlooked two crucial aspects of Derrida's work, namely, his rearticulation of the concept of experience and his account of the experience of undecidability as an ordeal. This is important because sensitivity to Derrida's emphasis on the ordeal of undecidability and his rearticulation of the concept of experience-a rearticulation that is already under way in his early engagement with Husserl and continued (...) in later work-necessitates a rethinking of what the `experience of undecidability' entails. Rather than signaling a withdrawal from politics or a normatively impotent ethics of `mere openness to the other,' Derrida's account of the experience of undecidability not only points to a fundamental aspect of our basic ethical experience but also leads to a number of ethico-political demands, which I summarize as the demand to maintain an ethos of interruption. (shrink)

The least common subsumer (lcs) of a set of concept descriptions is the most specific concept description that subsumes all of the concept descriptions in the given set. By computing the lcs, commonalities between concept descriptions can be made explicit. This is an important inference task useful in several applications, including, for instance, the bottom-up construction of description logic knowledge bases. Previous work on the lcs has concentrated on description logics that either allow for number (...) restrictions or for existential restrictions. Many applications, however, require to combine these constructors. In this work, we present an algorithm for computing the lcs in the description logic ALEN which comprises both constructors—number and existential restrictions—as well as concept conjunction, primitive negation, and value restrictions. To prove correctness of our lcs algorithm, we develop a structural characterization of subsumption in ALEN. (shrink)

Exploratory analysis is an area of increasing interest in the computational linguistics arena. Pragmatically speaking, exploratory analysis may be paraphrased as natural language processing by means of analyzing large corpora of text. Concerning the analysis, appropriate means are statistics, on the one hand, and artificial neural networks, on the other hand. As a challenging application area for exploratory analysis of text corpora we may certainly identify text databases, be it information retrieval or information filtering systems. With this paper we present (...) recent findings of exploratory analysis based on both statistical and neural models applied to legal text corpora. Concerning the artificial neural networks, we rely on a model adhering to the unsupervised learning paradigm. This choice appears naturally when taking into account the specific properties of large text corpora where one is faced with the fact that input-output-mappings as required by supervised learning models cannot be provided beforehand to a satisfying extent. This is due to the fact of the highly changing contents of text archives. In a nutshell, artificial neural networks count for their highly robust behavior regarding the parameters for model optimization. In particular, we found statistical classification techniques much more susceptible to minor parameter variations than unsupervised artificial neural networks. In this paper we describe two different lines of research in exploratory analysis. First, we use the classification methods for concept analysis. The general goal is to uncover different meanings of one and the same natural language concept. A task that, obviously, is of specific importance during the creation of thesauri. As a convenient environment to present the results we selected the legal term of neutrality, which is a perfect representative of a concept having a number of highly divergent meanings. Second, we describe the classification methods in the setting of document classification. The ultimate goal in such an application is to uncover semantic similarities of various text documents in order to increase the efficiency of an information retrieval system. In this sense, document classification has its fixed position in information retrieval research from the very beginning. Nowadays renewed massive interest in document classification may be witnessed due to the appearance of large-scale digital libraries. (shrink)

During the last two decades, several different anti-physicalist arguments based on an epistemic or conceptual gap between the phenomenal and the physical have been proposed. The most promising physicalist line of defense in the face of these arguments – the Phenomenal Concept Strategy – is based on the idea that these epistemic and conceptual gaps can be explained by appeal to the nature of phenomenal concepts rather than the nature of non-physical phenomenal properties. Phenomenal concepts, on this proposal, involve (...) unique cognitive mechanisms, but none that could not be fully physically implemented. David Chalmers has recently presented a Master Argument to show that the Phenomenal Concept Strategy – not just this or that version of it, but any version of it – fails. Chalmers argues that the phenomenal concepts posited by such theories are either not physicalistically explicable, or they cannot explain our epistemic situation with regard to qualia. I argue that it is his Master Argument that fails. My claim is his argument does not provide any new reasons to reject the Phenomenal Concept Strategy. I also argue that, although the Phenomenal Concept Strategy is successful in showing that the physicalist is not rationally compelled to give up physicalism in the light of the anti-physicalist arguments, the anti-physicalist is not rationally compelled to give up the anti-physicalist argument in the light of the Phenomenal Concept Strategy either. (shrink)

In this paper I argue that Plato's Apology is the principal text on which Kierkegaard relies in arguing for the idea that Socrates is fundamentally an ironist. After providing an overview of the structure of this argument, I then consider Kierkegaard's more general discussion of irony, unpacking the distinction he draws between irony as a figure of speech and irony as a standpoint. I conclude by examining Kierkegaard's claim that the Apology itself is “splendidly suited for obtaining a clear (...) class='Hi'>concept of Socrates' ironic activity,” considering in particular Kierkegaard's discussion of Socrates' remarks about death and his use of Friedrich Ast's commentary to help his readers to discover the irony that he contends runs throughout Socrates' defense speech. (shrink)

I argue that Frege's so-called "concept 'horse' problem" is not one problem but many. When these separate sub-problems are distinguished, some are revealed to be more tractable than others. I further argue that there is, contrary to a widespread scholarly assumption originating with Peter Geach, little evidence that Frege was concerned with the general problem of the inexpressibility of logical category distinctions in writings available to Wittgenstein. In consequence, Geach is mistaken in thinking that in the Tractatus Wittgenstein simply (...) accepts from Frege certain lessons about the inexpressibility of logical category distinctions and the say-show distinction. In truth, Wittgenstein drew his own morals about these matters, quite possibly as the result of reflecting on how the general problem of the inexpressibility of logical category distinctions arises in Frege's writings (whether Frege was aware of it or not), but also, quite possibly, by seeing certain glimmerings of these doctrines in the writings of Russell. (shrink)

A phenomenon “emerges” when a concept is instantiated for the first time: hence emergence is relative to a set of concepts. Propositional thought and language emerge together. It is proposed that the degree of complexity of an object language relative to a given metalanguage can be gauged by the number of ways it can be translated into that metalanguage: in analogy with other forms of measurement, the more ways the object language can be translated into the metalanguage, the (...) less powerful the conceptual resources of the object language. (shrink)

The aim of this paper is to assess the relationship between anti-physicalist arguments in the philosophy of mind and anti-naturalist arguments in metaethics, and to show how the literature on the mind-body problem can inform metaethics. Among the questions we will consider are: (1) whether a moral parallel of the knowledge argument can be constructed to create trouble for naturalists, (2) the relationship between such a "Moral Knowledge Argument" and the familiar Open Question Argument, and (3) how naturalists can respond (...) to the Moral Twin Earth argument. We will give particular attention to recent arguments in the philosophy of mind that aim to show that anti-physicalist arguments can be defused by acknowledging a distinctive kind of conceptual dualism between the phenomenal and the physical. This tactic for evading anti-physicalist arguments has come to be known as the Phenomenal Concept Strategy. We will propose a metaethical version of this strategy, which we shall call the `Moral Concept Strategy'. We suggest that the Moral Concept Strategy offers the most promising way out of these anti-naturalist arguments,though signi cant challenges remain. (shrink)

This paper explores how the diagnosis of mental disorder may affect the diagnosed subject’s self-concept by supplying an account that emphasizes the influence of autobiographical and social narratives on self-understanding. It focuses primarily on the diagnoses made according to the criteria provided by the Diagnostic Statistical Manual of Mental Disorders (DSM), and suggests that the DSM diagnosis may function as a source of narrative that affects the subject’s self-concept. Engaging in this analysis by appealing to autobiographies and memoirs (...) written by people diagnosed with mental disorder, the paper concludes that a DSM diagnosis is a double-edged sword for self- concept. On the one hand, it sets the subject’s experience in an established classificatory system which can facilitate self-understanding by providing insight into subject’s condition and guiding her personal growth, as well as treatment and recovery. In this sense, the DSM diagnosis may have positive repercussions on self-development. On the other hand, however, given the DSM’s symptom-based approach and its adoption of the Biomedical Disease model, a diagnosis may force the subject to make sense of her condition divorced from other elements in her life that may be affecting her mental- health. It may lead her frame her experience only as an irreversible imbalance. This form of self-understanding may set limits on the subject’s hopes of recovery and may create impediments to her flourishing. (shrink)

In this paper I argue that the most prominent and familiar features of Wittgenstein’s rule following considerations generate a powerful argument for the thesis that most of our concepts are innate, an argument that echoes a Chomskyan poverty of the stimulus argument. This argument has a significance over and above what it tells us about Wittgenstein’s implicit commitments. For, it puts considerable pressure on widely held contemporary views of concept learning, such as the view that we learn concepts by (...) constructing prototypes. This should lead us to abandon our general default hostility to concept nativism and be much more sceptical of claims made on behalf of learning theories. (shrink)

In this paper, I develop a novel account of concept acquisition for an atomistic theory of concepts. Conceptual atomism is rarely explored in cognitive science because of the feeling that atomistic treatments of concepts are inherently nativistic. My model illustrates, on the contrary, that atomism does not preclude the learning of a concept.

Abstract: There is a long tradition of trying to analyze art either by providing a definition (essentialism) or by tracing its contours as an indefinable, open concept (anti-essentialism). Both art essentialists and art anti-essentialists share an implicit assumption of art concept monism. This article argues that this assumption is a mistake. Species concept pluralism—a well-explored position in philosophy of biology—provides a model for art concept pluralism. The article explores the conditions under which concept pluralism is (...) appropriate, and argues that they obtain for art. Art concept pluralism allows us to recognize that different art concepts are useful for different purposes, and what has been feuding definitions can be seen as characterizations of specific art concepts. (shrink)

Several scholars have argued that Wittgenstein held the view that the notion of number is presupposed by the notion of one-one correlation, and that therefore Hume's principle is not a sound basis for a definition of number. I offer a new interpretation of the relevant fragments on philosophy of mathematics from Wittgenstein's Nachlass, showing that if different uses of ‘presupposition’ are understood in terms of de re and de dicto knowledge, Wittgenstein's argument against the Frege-Russell definition of (...) class='Hi'>number turns out to be valid on its own terms, even though it depends on two epistemological principles logicist philosophers of mathematics may find too ‘constructivist’. (shrink)

The concept of the self is a highly contested topic. Traditionally it belonged to speculative metaphysics. Almost every philosopher, whether Western or Indian, has tried to explore the nature of self. Generally, the self is taken as a substance which has permanent existence, which is eternal and non-specio-temporal. In some traditions, like the Hindu tradition, it is believed to take rebirth as the body perishes. Many Western philosophers also think that it is immortal. The nature of the self also (...) has then ethical implications. The views of David Hume and Gautama Buddha on the self, which I have chosen to discuss here, are similar. Though both belong to different traditions, both are skeptical of any permanent existence of self. This is not to say that one has borrowed from the other. For the nature and purpose of denial of the self in both the philosophers is different. So a comprehensive and comparative study of their views is very interesting. It is the intention of this article to analyze and compare the philosophical positions of Gautama and Hume on the self—a problem which was of central concern to both and which has since exercised a continuing fascination for philosophers, both of the East and the West. (shrink)

The relationship between language and conceptual thought is an unresolved problem in both philosophy and psychology. It remains unclear whether linguistic structure plays a role in our cognitive processes. This special issue brings together cognitive scientists and philosophers to focus on the role of language in numerical cognition: because of their universality and variability across languages, number words can serve as a fruitful test case to investigate claims of linguistic relativism.

This paper addresses a number of closely related questions concerning Kant's model of intentionality, and his conceptions of unity and of magnitude [Gröβe]. These questions are important because they shed light on three issues which are central to the Critical system, and which connect directly to the recent analytic literature on perception: the issues are conceptualism, the status of the imagination, and perceptual atomism. In Section 1, I provide a sketch of the exegetical and philosophical problems raised by Kant's (...) views on these issues. I then develop, in Section 2, a detailed analysis of Kant's theory of perception as elaborated in both the Critique of Pure Reason and the Critique of Judgment; I show how this analysis provides a preliminary framework for resolving the difficulties raised in Section 1. In Section 3, I extend my analysis of Kant's position by considering a specific test case: the Axioms of Intuition. I contend that one way to make sense of Kant's argument is by juxtaposing it with Russell's response to Bradley's regress; I focus in particular on the concept of ‘unity’. Finally, I offer, in Section 4, a philosophical assessment of the position attributed to Kant in Sections 2 and 3. I argue that, while Kant's account has significant strengths, a number of key areas remain underdeveloped; I suggest that the phenomenological tradition may be read as attempting to fill precisely those gaps. (shrink)

The acquisition of concepts has proven especially difficult for philosophers and psychologists to explain. In this paper, I examine Jerry Fodor’s most recent attempt to explain the acquisition of concepts relative to experiences of their referents. In reevaluating his earlier position, Fodor attempts to co-opt informational semantics into an account of concept acquisition that avoids the radical nativism of his earlier views. I argue that Fodor’s attempts ultimately fail to be persuasive. He must either accept his earlier nativism or (...) adopt a rational causal model of concept acquisition. His animus towards the latter dictates, in my view, a return to the nativism with which he began. (shrink)

To have a propositional attitude, a thinker must possess the concepts included in its content. Surprisingly, this rather trivial principle refl ects badly on many theories of concept possession because, in its light, they seem to require too much. To solve this problem, I point out an ambiguity in attributions of the form 'S possesses the concept of Fs'. There is an undemanding sense which is involved in the given principle, whereas the theoretical claims concern a stronger sense (...) which can be brought out by formulations such as 'S has an adequate conception of Fs' or 'S knows what Fs are'. (shrink)

This essay adjudicates between theoretical models of psychological concept acquisition. I provide new reasons to be skeptical about both simulationist and modularist models. I then defend the scientific-theory-theory account against familiar objections. I conclude by arguing that the scientific-theory-theory account must be supplemented by an account of hypothesis discovery.

Conceptual structures are commonly likened to scientific theories, yet the content and motivation of the theory analogy are rarely discussed. Gregory Murphy and Douglas Medin's The Role of Theories in Conceptual Coherence is a notable exception and has become an authoritative exposition of the utility of the theory analogy. For Murphy and Medin, the theory analogy solves what they call the problem of conceptual coherence or the problem of conceptual glue. I argue that they conflate a number of issues (...) under these rubrics and that in each case either the problem to be solved isn't subject to a general solution or the theory analogy is of little use. The issues I consider are: (1) what makes a concept efficient, useful, and informative, (2) what makes a concept refer to what it does, (3) what makes a set of objects form a single category, and (4) what makes concepts combine in one way rather than another. (shrink)

It's a sort of moebus strip argument. Rather than circularly assuming what it should prove, it assumes one of the things Fodor says he has disproved. It assumes that the extensions of those concepts thought by some to be recognitional are in fact controlled by stereotypes. Why do I say that? Because Fodor assumes that what makes an instance of a concept a "good instance" is that it is an average instance, that it sports the properties statistically most commonly (...) found among instances of that concept. But that the "good instances" are always the common instances is remotely plausible only if we take concepts to be organized by stereotypes. True, a goldfish is not an average or stereotypical fish (SSis that true?) and the nursing profession is not average for a male and maleness is not average for a nurse. But there is surely is nothing borderline about the fishiness of a goldfish nor, typically, about the maleness of a male nurse or the petness of a pet fish. Notice also that good examples of some kinds of things are very hard to find, for example, good examples of the fallacy of accent, and good examples of wild children, and (nowadays) good examples of scurvy are hard to find. If good instances had to be instances that were average, including in respects having nothing to do with the point of the category being defined, and if recognitional concepts had to recognize by attending to average properties, then I suppose the recognitional ability defining the concept "sphere" would have to include the ability to tell whether a thing bounces! (shrink)

Pierre Jacob's book, What Minds Can Do , is mainly concerned with intentionality. Jacob's primary goal is to explain both how it is possible for a physical system to have intentional mental states and how the intentional content of such mental states can play a role in the causal explanation of behaviour. Yet, he also tackles the issue of the nature of conscious experience. I shall focus here on a claim he makes in connection with this latter topic. The claim (...) (made at the very end of Chapter 2, p. 77) is that in order to undergo states of consciousness a creature must have concept-forming abilities. At first sight, this contention seems implausibly strong. Although our intuitions in such matters may not be very reliable, I think many people would be willing to attribute to members of certain animal species a capacity to enjoy conscious experiences, while being reluctant to grant them concept forming abilities. The plausibility or implausibility of Jacob's claim depends in a large part on how one construes the notion of a conscious experience, as well as on what one considers concept-forming abilities to be. Since the topic of consciousness is rather peripheral in Jacob's book, the rejection of this claim would not directly affect his more central theses. Yet, examining it gives us an opportunity to scrutinize a distinction that plays a central role in Dretske's work and that Jacob endorses, namely, the distinction between analogical and digital coding of information. Since this distinction underlies in turn the distinction between sensory content and conceptual content and since the latter distinction is at the core of informational semantics, this discussion may have at least indirect implications for some other problems discussed by Jacob in his book. (shrink)

A realist view of numbers often rests on the following thesis: statements like ‘The number of moons of Jupiter is four’ are identity statements in which the copula is flanked by singular terms whose semantic function consists in referring to a number (henceforth: Identity). On the basis of Identity the realists argue that the assertive use of such statements commits us to numbers. Recently, some anti-realists have disputed this argument. According to them, Identity is false, and, thus, we (...) may deny that the relevant statements commit us to numbers. The present paper argues that the correct linguistic analysis of the relevant number statements supports the anti-realist view that Identity is false. However, as will further be shown, pace the anti-realist, this analysis does not establish that such statements do not commit us to numbers after all. (shrink)

The performance of the Mundurucu on the number-space task may exemplify a general competence for drawing analogies between space and other linear dimensions, but Mundurucu participants spontaneously chose number when other dimensions were available. Response placement may not reflect the subjective scale for numbers, but Cantlon et al.'s proposal of a linear scale with scalar variability requires additional hypotheses that are problematic.

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics (...) education. By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)

This paper introduces current acoustic theories relating to the phenomenology of sound as a framework for interrogating concepts relating to the ecologies of acoustic and landscape phenomena in a Japanese stroll garden. By applying the technique of Formal Concept Analysis, a partially ordered lattice of garden objects and attributes is visualized as a means to investigate the relationship between elements of the taxonomy.

Recent findings indicate that the constituting digits of multi-digit numbers are processed, decomposed into units, tens, and so on, rather than integrated into one entity. This is suggested by interfering effects of unit digit processing on two-digit number comparison. In the present study, we extended the computational model for two-digit number magnitude comparison of Moeller, Huber, Nuerk, and Willmes (2011a) to the case of three-digit number comparison (e.g., 371_826). In a second step, we evaluated how hundred-decade and (...) hundred-unit compatibility effects were moderated by varying the percentage of within-hundred (e.g., 539_582) and within-hundred-and-decade filler items (e.g., 483_489). From the results we predict that numerical distance as well as compatibility effects should indeed be modulated by the relevance of tens and units in three-digit number magnitude comparison: While in particular the hundred distance effect should decrease, we predict hundred-decade and hundred-unit compatibility effects to increase with the relevance of tens and units. (shrink)

In a recent paper, Dennis Plaisted examines an important argument that Leibniz gives for the existence of primitive concepts. After sketching a natural reading of this argument, Plaisted observes that the argument appears to imply something clearly inconsistent with Leibniz’s other views. To save Leibniz from contradiction, Plaisted offers a revision. However, his account faces a number of serious difficulties and therefore does not successfully eliminate the inconsistency. We explain these difficulties and defend a more plausible alternative. In the (...) process, we call attention to the neglected topic of Leibniz’s views on the nature of conceiving, and reveal his commitment to the somewhat surprising thesis that one can conceive something through a concept even if one has no conscious grasp of that concept. (shrink)

I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning (...) of Russell's paradox, this position is a natural position for him to have retreated to, when properly understood. (shrink)