In this paper, we introduce the systems ns-ACA₀ and ns-WKL₀ of non-standard second-order arithmetic in which we can formalize non-standard arguments in ACA₀ and WKL₀, respectively. Then, we give direct transformations from non-standard proofs in ns-ACA₀ or ns-WKL₀ into proofs in ACA₀ or WKL₀.

A partial map f of a structure M is called almost total if |M — dom| = |M — ran| < ω. We study a difference between an almost total elementary map and an automorphism.

Paul Hirst’s philosophical ‘conversion’ from forms of knowledge to forms of social practices was largely prompted by his radical reappraisal of the philosophical underpinnings that had validated his classic conception of liberal education. The primary motivation for Hirst’s later works was to remedy his own neglect of practical reason, whose sharp distinction from theoretical reason he acknowledged he had failed to appreciate. There is much to commend in his ‘practical’ turn. The main challenge that remains, however, is that the social (...) practices view is something of a ‘foundationalist’ two-part picture, where overwhelming priority is given to practical reason. I appreciate the importance of the two issues Hirst puts on the table, in his debate with Wilfred Carr particularly and in his later works more generally: the issues of cultivating phronesis and of making sense of the practical character of critical-reflective activities. But I argue that addressing these issues fully requires us to recognize that neither theoretical nor practical rationality can be intelligible apart from the other. To press the point home, I review the analogous debate between Hubert Dreyfus and John McDowell over whether to accept, and how to understand, the view that rational conceptuality in a relevant sense pervades not only deliberation and propositional thinking but also perception and embodied coping skills. I conclude by briefly considering the prospect that the legacy of Hirst and recent discussions around human nature, practical rationality, and the formation of reason will interactively enrich our philosophical-educational scholarship. (shrink)

Comment comprendre la nyctophobie? Les uns pensent, comme John Locke, que la nuit n’a rien qui fasse peur, et cherchent la cause de cette angoisse ailleurs que dans l’obscurité. Les autres, à commencer par Edmund Burke, affirment que l’obscurité est la source par excellence de la peur : pour Emmanuel Levinas comme pour Maurice Merleau-Ponty, qui s’appuient tous deux sur la description de l’« espace noir » par Eugène Minkowski, la nuit noire menace de déposséder le sujet de sa souveraineté (...) pour le submerger dans une unité sans articulation. Mais, une dizaine d’années plus tôt, Roger Caillois se réfère aussi à Minkowski pour voir dans la nyctophobie l’effet de la « tentation de l’espace » : pour lui, la peur de la nuit est la peur d’être la nuit – de ne faire qu’un avec elle. (shrink)

“What is the nature of the beings that we are?” is perhaps the most difficult question. The difficulty lies in our being a natural animal in a normative environment. In harmony with John McDowell’s conception of a naturalism of second nature, this paper claims that we should not rest satisfied with the predominant scientific picture in which the seeming rift between our animality and our rationality is to be resolved by detailed studies of empirically knowable facts about our animal modes (...) of existence. Instead, appreciating the sui generis character of a distinctive mode of human engagement with the world is a necessary clearing of the ground and an essential first step toward addressing meticulously the above difficult question on human nature. The paper suggests that the human sciences in general and education studies in particular should start off not with disclosed first-natural facts but with a sensitivity to second-natural backgrounds that set the stage for the first-natural facts. (shrink)

The Schrödinger equation for quantum mechanics, which is approachable in third-person description, takes for granted tenseless time that does not distinguish between different tenses such as past, present, and future. The time-reversal symmetry grounded upon tenseless time globally may, however, be broken once measurement in the form of exchanging indivisible quantum particles between the measured and the measuring intervenes. Measurement breaks tenseless time locally and distinguishes different tenses. Since measurement is about the material process of feeding and acting upon the (...) quantum resources already available from any material bodies to be measured internally, the agency of measurement is sought within the environment in the broadest sense. Most indicative of internal measurement of the environmental origin are chemical reactions in the reaction environment. Temporality naturalized in chemical reactions proceeding as being subjected to frequent interventions of internal measurement is approachable in second-person description because of the participation of multiple agents of measurement there. The use of second-person description is found in the appraisal of the material capacity of generating, distinguishing, and integrating different tenses. An essence of the temporality to be naturalized is within the genesis of different tenses. A most conspicuous exemplar of naturalized temporality is sought in the origins of life conceivable exclusively on the material ground. (shrink)

Koichiro Kokubun focuses on Deleuze's method of 'free indirect discourse' to locate and explicate Deleuze's philosophy of transcendental empiricism and its constitutive limits. He works through Deleuze's confrontations with Hume, Kant, Bergson, Freud, Lacan, Foucault and Guattari, and the influence of structuralism and psychoanalysis.

In philosophy, it is almost a platitude to argue that fact and value intertwine. However, in empirically oriented educational research, it is not. Hence, there is some affinity between logical positivism, which is no longer tenable in philosophy, and empirically based contemporary educational research in terms of assumptions each makes about “the given.” In this essay, Koichiro Misawa casts light on how fact and value intertwine by invoking the notion of “second nature” that John McDowell has reanimated. This will in (...) turn prompt us to see the relation between nature and nurture, as well as between mind and world, quite differently and to discern two senses of “the given”: one is illusory; the other educational. Misawa concludes that the philosophy of education should and can take the lead in forming rigorous interdisciplinary studies of the human future with a certain sensitivity to the tight and complex interweaving between the empirical and the conceptual, or between the factual and the normative. (shrink)

David Bakhurst's 2011 book ‘The Formation of Reason’ explores the philosophy of John McDowell in general and the Aristotelian notion of second nature more specifically, topics to which philosophers of education have not yet given adequate attention. The book's widespread appeal led to the symposium ‘Second Nature, Bildung and McDowell: David Bakhurst's The Formation of Reason’, which appeared in the first issue of the 50th anniversary volume of the Journal of Philosophy of Education in 2016. Despite its obvious educational relevance, (...) whether and how Bakhurst's McDowellian line of philosophical argument shapes the domain of educational enquiry or discourse remains up for debate. The rich contributions of Sebastian Rödl, Paul Standish and Jan Derry help us confront this issue. Proceeding with an analysis that is partly explanatory and partly critical of the central aspects of their respective views, I try to show that the basic attraction of the McDowellian/Bakhurstian line of argument concerning educational thinking is that it enables us to address education in the proper context of the natural and the social. In other words, their depiction of a human being as a natural animal in a normative world allows us not to be perturbed either by the natural-scientific conception of the natural or by the social constructivist thinking of the social, both of which have occasionally distorted how education is addressed and therefore impoverished our understanding of education itself. I conclude with a brief word on the significance of continuing and advancing the conversation initiated by the symposium by noting two viable examples of future work. (shrink)

An infinite structure is said to be minimal if each of its definable subset is finite or cofinite. Modifying Hrushovski's method we construct minimal, non strongly minimal structures with arbitrary finite dimensions. This answers negatively to a problem posed by B. I Zilber.

ABSTRACT At the heart of our current environmental predicament lies the issue of our relationship with nature. Michael Bonnett’s educational rehabilitation of nature, which might be called a ‘metaphysical’ turn in nature-related issues, brings us back to the core question of educational-philosophical thinking: how we are to understand ourselves and our relation to the world. In this paper, by confronting his environmental philosophy of education with what John McDowell, in his debate with Hubert Dreyfus, terms the ‘pervasiveness thesis’ – that (...) conceptual rationality in a relevant sense pervades human lives – I try to offer an analytical supplement to the notion Bonnett entertains: that a phenomenological project to ‘retrieve’ nature and ‘ecologise’ education can have massive implications for the character of philosophy of education and the whole enterprise of education. I also argue a confluence of their nature-related ideas adds an educational nuance to the traditional picture of human beings as rational animals. (shrink)

A theory T is called almost [MATHEMATICAL SCRIPT CAPITAL N]0-categorical if for any pure types p1,…,pn there are only finitely many pure types which extend p1 ∪…∪pn. It is shown that if T is an almost [MATHEMATICAL SCRIPT CAPITAL N]0-categorical theory with I = 3, then a dense linear ordering is interpretable in T.

In this paper, we show that equation image is a equation image-conservative extension of BΣ1 + exp, thus it does not imply IΣ1.

Chemical affinity is by itself inclusive of the action of a sign. Naturalization of the action of a sign is latent in the material organization holding its own identity by means of the exchange of material. A concrete experimental example is the citric acid cycle running in the absence of biological enzymes. The carbon atoms to be exchanged round the cycle serve as the signs for holding the cycle as a natural system. The action of a sign operates in the (...) present progressive tense and is also descriptively approachable in the same tense, as implying that a natural system holding its own identity assumes the first-person status acting for its own sake. The action of a sign is thus addressable in first person descriptions on the level of the supporting material system that can recognize the sign as such from within. Furthermore, if the action of a sign happens to precipitate the record registered in the present perfect tense, the record itself will be approachable in third person descriptions in the present tense. When one can relate the record of an earlier event to that of a later one, what is called information will come up. Information to be externalized and objectified is about the completed outcome from the action of a sign that is accessible in third person descriptions in the present tense. Conversely, if the action of a sign is carried by a natural system holding its own identity in a manner to be registered in the present perfect tense after the event, information will appear in a proper form of bookkeeping as relating the memory to anticipation on the part of the material agency. Although information in the present has the capacity of relating the past to future in the present tense as avoiding direct confrontation with the dynamic nature of the present or now head on, the action of a sign facing the present squarely is competent enough to address and decipher the generative capacity of information itself operating in the present progressive tense. (shrink)

Let L be a finite relational language and α=(αR:R ∈ L) a tuple with 0 < αR ≤1 for each R ∈ L. Consider a dimension function $ \delta _\alpha (A) = \left| A \right| - \sum\limits_{R \in L} {\alpha {\mathop{\rm Re}\nolimits} R(A)} $ where each eR(A) is the number of realizations of R in A. Let $K_\alpha $ be the class of finite structures A such that $\delta _\alpha (X) \ge 0$ 0 for any substructure X of A. We (...) show that the theory of the generic model of $K_\alpha $ is AE-axiomatizable for any α. (shrink)

Approaches to studying the ‘social’ are prominent in educational research. Yet, because of their insufficient acknowledgement of the social nature of human beings and the reality we experience, such attempts often commit themselves to the dualism of scheme and content, which in turn is a by-product of the underlying dualism of reason and nature that has characterised modern thinking. Drawing largely on John McDowell’s argument, this paper attempts to illuminate the sense that nature, nurture and human nature are interconnected and (...) that the capacity to be responsive to reasons is a necessary prerequisite for the essential nature of human beings as social and natural animals at the same time. It ends by acknowledging the importance of philosophy in the study of education as a primary discipline that highlights distinctive features of human beings that make us the kind of beings we are, and by briefly mentioning how we could do more than draw obvious but trivial ‘educational implications’ from McDowell’s argument. (shrink)

(1993). Evolving dissipative structures viewed from the eyes of molecules. World Futures: Vol. 38, Theoretical Achievements and Practical Applications of General Evolutionary Theory, pp. 149-156.

One common denominator between biosemiotics and quantum physics is the participation of agents detecting their surroundings. In biosemiotics, any biological agents as the internal observers including the molecular and cellular ones are involved in detecting their surroundings. Likewise, the physicist as the external observer is also involved in detecting what should be all about the physical world with use of a wide variety of sophisticated measurement apparatuses. On the other hand, the difference between the two is in the nature of (...) the agents of detection involved there. One obvious difference is that although the physicist can report the results of measurement with use of the symbolic language, the biological beings take the indexical act of measurement to simply be a matter of experiencing. The internal observers are phenomenological in constructing something durable as participating in the construction of the phenomenon. In a similar vein, the external observer is also phenomenological in getting into interpreting the constructed durable class property of an object with use of the symbolic language. In particular, the potential use of phenomenology is not limited only to the phenomenologist as the external observer. A possible integration of both the internal and external observers may be sought within quantum phenomenology allowing for the external observer to descriptively make access to the durable objects the internal observers could eventually have constructed. The internal observers are ubiquitous in the environment that functions as the absorbers of whatever quantum particles available there. (shrink)

Michael Bonnett has long attempted to rehabilitate the concept of nature, thereby challenging us to reconsider its profound implications for diverse educational issues. Castigating both ‘postmodern’ and ‘scientistic’ accounts of nature for failing to appreciate that nature is at once transcendent and normative, Bonnett proposes his phenomenology-inspired view of nature as the ‘self-arising’, which is bound up with the notion of ‘our experience of nature’. Despite its enormous strengths, however, Bonnett’s argument might obscure the ways in which the real issue (...) involved in nature is addressed: the issue of our nature, which enables our experience of nature in the first place. In this paper, after reviewing Bonnett’s view of nature and considering his criticism of Richard Rorty’s assault on the reality of nature, I will try to show how the Aristotelian notion of second nature that John McDowell has reanimated can supplement Bonnett’s project and render plausible the idea that the naturalness of our sensibility is unique to human beings; through this approach, the issue of human nature can be located in discussions of nature at large and, connectedly, brought again within the scope of the philosophical study of education in the present-day intellectual climate that increasingly marginalises non-scientific, intellectual endeavours. I will also briefly reflect on the relevance of the notion of second nature to Stephen Boulter’s recently proposed idea of ‘education from a biological point of view’. (shrink)

Life distinguishes itself from non-life in taking advantage of the cohesion of temporal origin which non-life cannot afford. The temporal cohesion letting the local participants adhere to each other in a contemporaneous manner refers to an instance of the precedent product being pulled into the subsequent production. Setting the precedent is equivalent to preparing the conditions for the subsequent to follow. A concrete implementation of the cohesion of temporal origin, compared with the spatial cohesion common in physics, is found in (...) the natural construction of a reaction cycle with use of the temporal affinity exerted from the immediate local environment. That construction is a temporally local phenomenon in the experiential domain, rather than in the theoretical. The cohesion originating in the local environment is due to the local act of measurement by the environment. A major component of the local environment to each reactant in the reaction cycle is the cycle itself. The cohesion specific to the reaction cycle rests upon the fact that every reaction product from the upstream production in the cycle comes to be fed upon by the immediate downstream production. Every production constituting the reaction cycle is temporally adjacent to and contemporaneous with the similar others residing in the whole cycle, in sharp contrast to the case of the open-ended linear chain of reaction. One externalist scheme of appreciating the internalist enterprise of constructing a durable reaction cycle in a contemporaneous manner may become possible as referring to the Bayesian probability. The durable reaction cycle may be made actual with probability unity under the condition that the products from the preceding production come with the protocol for the similar production to come subsequently. (shrink)

We are concerned with two modes of describing the dynamics of natural systems. Global descriptions require simultaneous global coordination of all dynamical operations. Global dynamics, including mechanics, remain invariant in the absence of external perturbation. But, failing impossible global coordination, dynamical operations could actually become coordinated only locally. In local records, as in global ones, the law of the excluded middle would be strictly observed, but without global coordination it could only be fullfilled sequentially by passing causative factors forward onto (...) subsequent contiguous operations.The local dynamics of sequential operations would be indefinite with regard to how commitments will be made which will avoid violating the law of the excluded middle, but any resulting record will be as definite as if there had been global coordination. While maintaining an agential capacity for making contingent choices internally, local dynamics could be cumulated into a global record of seemingly simultaneous operations. Natural selection within a framework of local dynamics would have a capacity for making opportunistic commitments, but its effects in a posterior record can be reduced to the mechanistic neodarwinian version as if there had been a global dynamics. However, the resulting global description falsifies the actual material nature of the dynamics. (shrink)

This research is motivated by the program of reverse mathematics and non-standard arguments in second-order arithmetic. Within a weak subsystem of second-order arithmetic ACA0, we investigate some aspects of non-standard analysis related to sequential compactness. Then, using arguments of non-standard analysis, we show the equivalence of the Riemann mapping theorem and ACA0 over WKL0. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim).

Let L be a countable relational language. Baldwin asked whether there is an ab initio generic L-structure which is superstable but not ω-stable. We give a positive answer to his question, and prove that there is no ab initio generic L-structure which is superstable but not ω-stable, if L is finite and the generic is saturated.

We construct an ab initio generic structure for a predimension function with a positive rational coefficient less than or equal to 1 which is unsaturated and has a superstable non-ω-stable theory.

Hrushovski constructed an -categorical stable pseudoplane which refuted Lachlan's conjecture. In this note, we show that an -categorical projective plane cannot be constructed by "the Hrushovski method.".

The central thesis of this article is that the notion of second nature that John McDowell has reanimated has something of ethical and educational importance, thereby possibly extending the borders of the philosophy of education. The argument to this conclusion is the subject of serious consideration and criticism. The aim of this article is therefore to clarify the educational implications of the conception of second nature by responding to the three likely objections: (1) the charge of idealism, (2) the charge (...) of anthropocentrism, and (3) the charge of triviality. Through critical discussions of these criticisms, it is made explicit that second nature, from the outset, illuminates every sphere of the lives of human beings. A lively appreciation of this leads to the conclusion that the issue of how we develop our world of meaning with the conception of second nature should come under the scope of serious philosophical discourse on education. (shrink)