In recent years, neologicists have demonstrated that Hume's principle, based on the one-to-one correspondence relation, suffices to construct the natural numbers. This formal work is shown to be relevant for empirical research on mathematical cognition. I give a hypothetical account of how nonnumerate societies may acquire arithmetical knowledge on the basis of the one-to-one correspondence relation only, whereby the acquisition of number concepts need not rely on enumeration (the stable-order principle). The existing empirical data on the role of the one-to-one (...) correspondence relation for numerical abilities is assessed and additional empirical tests are proposed. In the final part, it is argued that the fact that the successor relation and the one-to-one correspondence relation can play independent roles in number concept acquisition may be a complication for testing the Whorfian hypothesis. (shrink)

Rips et al. argue that the construction of math schemas roughly similar to the Dedekind/Peano axioms may be necessary for arriving at arithmetical skills. However, they neglect the neo-Fregean alternative axiomatization of arithmetic, based on Hume's principle. Frege arithmetic is arguably a more plausible start for a top-down approach in the psychological study of mathematical cognition than Peano arithmetic.

In the present article two possible meanings of the term mathematical structure are discussed: a formal and a nonformal one. It is claimed that contemporary mathematics is structural only in the nonformal sense of the term. Bourbaki's definition of structure is presented as one among several attempts to elucidate the meaning of that nonformal idea by developing a formal theory which allegedly accounts for it. It is shown that Bourbaki's concept of structure was, from a mathematical point of view, a (...) superfluous undertaking. This is done by analyzing the role played by the concept, in the first place, within Bourbaki's own mathematical output. Likewise, the interaction between Bourbaki's work and the first stages of category theory is analyzed, on the basis of both published texts and personal documents. (shrink)

Within the context of structural theories this paper examines what health professionals say about their clinical service structures. We firstly trace various conceptual perspectives on clinical service structures, discussing multiple theoretical axes. These theories question whether clinical service structures represent either superficial or more profound changes in hospitals. We secondly explore which view is supported though a content analysis of the free text responses of 111 health professionals (44 doctors, 45 nurses and 22 allied health practitioners) about their clinical service (...) structures in a questionnaire survey in two large hospitals that had implemented clinical service structures three years previously. Commentaries unfavourable toward clinical service structures were made by 47.7% of staff, favourable by 24.3%, mixed (both favourable and unfavourable) by 17.1% and non-evaluative statements were made by 10.8%. The most frequent criticisms were inefficient organisation of change (27%), poor management (24.3%), lack of cooperation between staff (15.9%) and failure to empower health practitioners (13.5%). All professions made more negative than positive evaluations of their clinical service structures but the ratio was highest for doctors and lowest for allied health. Ranking of nurses' and allied health staffs' specific evaluations were similar but both differed significantly from doctors.' Unfavourable or negative comments predominated, and change appears more superficial and less profound than advocates of structural contributions hope. Four types of belief systems about clinical service structures are apparent. Some study participants are disposed toward the status quo; others toward restructuring; yet others are team oriented; and a final group is tribally oriented. The implication of this paper for managers is that more work is needed if clinical service structures are to realise the promise of more multi-disciplinarity and less fragmentation across professional groups. For scholars, the implication is that marrying different theoretical frames with empirical data can serve to produce fresh perspectives and perhaps new insights. (shrink)

The holism-reductionism debate, one of the classic subjects of study in the philosopy of science, is currently at the heart of epistemological concerns in ecology. Yet the division between holism and reductionism does not always stand out clearly in this field. In particular, almost all work in ecosystem ecology and landscape ecology presents itself as holistic and emergentist. Nonetheless, the operational approaches used rely on conventional reductionist methodology.From an emergentist epistemological perspective, a set of general 'transactional' principles inspired by the (...) work of J. Dewey and J.K. Feibleman are proposed in an effort to develop a coherent ontological and methodological semantics. (shrink)

The subject of this paper is the philosophical problem of accounting for the relationship between mathematics and non-mathematical reality. The first section, devoted to the importance of the problem, suggests that many of the reasons for engaging in philosophy at all make an account of the relationship between mathematics and reality a priority, not only in philosophy of mathematics and philosophy of science, but also in general epistemology/metaphysics. This is followed by a (rather brief) survey of the major, traditional philosophies (...) of mathematics indicating how each is prepared to deal with the present problem. It is shown that (the standard formulations of) some views seem to deny outright that there is a relationship between mathematics and any non-mathematical reality; such philosophies are clearly unacceptable. Other views leave the relationship rather mysterious and, thus, are incomplete at best. The final, more speculative section provides the direction of a positive account. A structuralist philosophy of mathematics is outlined and it is proposed that mathematics applies to reality though the discovery of mathematical structures underlying the non-mathematical universe. (shrink)

That Piagetian epistemology has the dynamics of knowledge growth as its core consideration predetermines a need to consider it as potentially applicable to teaching. This paper addresses that need by first outlining the Piagetian theory of equilibration and then applying it to the construction of methods of teaching science.

This paper addresses the question whether we can conceive of music cognition in ecosemiotic terms. It claims that music knowledge must be generated as a tool for adaptation to the sonic world and calls forth a shift from a structural description of music as an artifact to a process-like approach to dealing with music. As listeners, we are observers who construct and organize our knowledge and bring with us our observational tools. What matters is not merely the sonic world in (...) its objective qualities, but the world as perceived. In order to make these claims operational we can rely on the ecological concept of coping with the sonic world and the cybernetic concepts of artificial and adaptive devices. Listeners, on this view, are able to change their semantic relations with the sonic world through functional adaptations at the level of sensing, acting and coordinating between action and perception. This allows us to understand music in functional terms of what it affords to us and not merely in terms of its acoustic qualities. There are, however, degrees of freedom and constraints which shape the semiotization of the sonic world. As such we must consider the role of event perception and cognitive economy: listeners do not perceive the acoustical environment in terms of phenomenological descriptions but as ecological events. (shrink)

Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic (both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”, “permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s “logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a (...) “deontic hexagon” as being the geometrical representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie 73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter, Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic has appeared, that is “ n -opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m ” ( m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper, by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”, “deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra), whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional very regular solid). (shrink)

Depuis que le structuralisme a franchi le seuil de Ia mode et que l'on parle maintenant volontiers d’ une ère post-structuraliste, le moment se prête davantage à une réflexion philosophique et critique sur ce type d'épistémè qui a pratiquement envahi tout le champ des sciences humaines. Quoique le structuralisme ait été une mode, et une mode qui a réussi, selon l'expression de Raymond Boudon,1 il reste toutefois encore difficile d'apprécier ses succès dans des travaux comme ceux de Foucault, d'Aithusser, de (...) Barthes ou de Lacan. Là où cependant le succès est le plus évident c'est du côté des sciences sociales, en particulier du côté de Ia linguistique et de l'anthropologie. (shrink)

Retracing the primary common aspects between anthropological and psychoanalytic thought, in this article, we will further discuss the main common points between the notions of the unconscious according to Carl Gustav Jung and Claude Lévi-Strauss, taking into account the thought of Erich Neumann. On the basis of very simple elementary logic considerations centered around the basic notion of the separation of opposites, our observations might be useful for speculations on the possible origins of rational thought and hence on the origins (...) of consciousness. (shrink)

This paper reviews and extends ideas of eukaryotization by endosymbiosis. These ideas are put within an historical context of processes that may have led up to eukaryotization and those that seem to have resulted from this process. Our starting point for considering the emergence and development of life as an organized system of chemical reactions should in the first place be in accordance with thermodynamic principles and hence should, as far as possible, be derived from these principles. One trend to (...) be observed is the ever-increasing complexity resulting in several layers of compartmentalization of the reaction system, either spatial (of which the eukaryotic cell is an example), or functional (as in the gradually deepening distinction between metabolic, enzymatic and information-storing functions within the cell). One of the causes of this complexification of living systems will have been the changes in environmental conditions, particularly the geochemical impoverishment of the biosphere during geological history, partly brought about by living systems themselves, and partly by the trend towards increasing efficiency and specificity of the reactions that occur. (shrink)

In a paper which examined the ‘simultaneous emergence of evolutionary theories in biology and sociology in the nineteenth century’, J. C. Greene said of Comte that ‘it was not from biology that his inspiration [the inspiration of his evolutionary view] was drawn; his writings and letters in the formative period sing the praises of Bichat and Gall but not of Lamarck. His intellectual debt in social theory lay in a different direction—to Condorcet'sSketch of an historical picture of the progress of (...) the human mind, to the historical writings of Hume and Robertson, and to the ideas of Saint-Simon’. This statement from a paper published almost twenty years ago as an exploratory reconnaissance of virgin territory is representative of the kind of confused judgements which still surround a discussion of the inter-relations between social, biological and medical thought in the century 1750 to 1850. It makes some valid points which a critical examination should not be allowed to overwhelm, the most significant being that Comte is unequivocally identified with the Enlightenment tradition represented here by Condorcet, Robertson and Hume. But since it is a very condensed statement about a complex set of relationships, it invites interpretations which the author did not necessarily intend. (shrink)

The contextual mind is found attested in various usages of the term complement, in the background of Kant. The difficulties of Kant's intuitionism are taken up through Quine, but referential opacity is resolved as semantic presence in lived context. A further critique of rationalist linguistics is developed from Jakobson, showing generic functions in thought supporting abstraction, binding and thereby semantic categories. Thus Bolzano's influential philosophy of mathematics and science gives way to a critical view of the ancient heritage acknowledged by (...) Plato. (shrink)

In continuation of what has been said in the first part of this two-part paper, herein we present further considerations on symbolism, reconsider some related psychodynamic case reports with some possible variants about their interpretations, and will apply what is said to some further speculations on mathematical symbolism and thought. In this second part, we continue with the numeration of the first part Σύμβολου, 1.