We study the theories I∇n, L∇n and overspill principles for ∇n formulas. We show that IEn ⇒ L∇n ⇒ I∇n, but we do not know if I∇n L∇n. We introduce a new scheme, the growth scheme Crγ, and we prove that L∇n ⇒ Cr∇n⇒ I∇n. Also, we analyse the utility of bounded collection axioms for the study of the above theories.

Yet this is precisely what I intend to do. As a way of conferring some initial legitimacy Perhaps the most fundamental axiom of upon this enterprise, I would like to start out modern economic science is that there simply by appealing to the “no free lunch” is no such thing as a free lunch. It is principle. To adopt productivity growth as a this axiom that gives us the concept of opporsocial priority is to set aside other objectives tunity (...) cost, an idea that has led to enormous that we might like to pursue. Therefore, one gains in the clarity of our understanding of cannot maintain rational adherence to a proindividual and societal choice. But while congram of increased productivity without a clear tinuing to endorse this fundamental axiom, sense of what the benefits of such a program many economists have also been extremely are likely to be, compared to the other things attracted by the appeal of increased economic that we might choose to do. The bulk of this efficiency. Efficiency gains are often treated, paper consists of an attempt to evaluate the if not exactly as a free lunch, certainly about size and scope of these benefits. More controas close to a free lunch as one can get in this versially, I will try to show that these benesublunar realm. As a result, economists often fits are often exaggerated. react with a certain incredulity when some- The conclusion that I draw on the basis one questions the need for such gains. It is of this survey will strike many as complacent. tempting to suppose that the critic simply But it is a principled complacency. I argue misunderstands the relevant concepts, or else that we have good reason, as a society, to strive fails to grasp the full set of constraints under for productivity gains, but that there is nothwhich economic activity occurs. ing urgent about this objective. Furthermore, Productivity growth is widely regarded we should not strive to maximize productivity as a subset of the efficiency gains that can be gains, nor should we be overly concerned realized in our economy. (shrink)

Dieser Artikel konzentriert sich auf zwei der frühesten Schriften aus Leibniz' Pariser Zeit, die „Accessio ad Arithmeticam Infinitorum“ und die „De Minimo et Maximo. De corporibus et mentibus“ , und er beurteilt die Beziehung zwischen den in der AAI angegebenen mathematischen Ergebnissen und dem Wandel in Leibniz' Metaphysik, der in MM und in den damit in Verbindung stehenden Schriften und Briefen zum Ausdruck gebracht wird. Sowohl Leibniz' mathematische Ergebnisse als auch der Wandel seiner Haltung in der Metaphysik können als Resultat (...) einer stärkeren Verpflichtung gegenüber dem Euklidischen Axiom betrachtet werden, daß das Ganze größer ist als der Teil. Indem das Euklidische Axiom eine bedeutendere Rolle in Leibniz' Metaphysik und mathematischer Arbeit einnimmt, bewegt sich Leibniz von der Vorstellung der Zusammensetzung des Kontinuums aus unteilbaren Punkten zu einer Aufgliederung des Kontinuums in unvergleichbar kleine Teile, die in sich selbst kontinuierlich sind. Dieser Wandel führt Leibniz dazu, die Rolle der Identität und eines Kalküls von Teil und Ganzem zu betonen und sich in Richtung einer Vorstellung vom Unbestimmten als eines Unendlichen zu bewegen. (shrink)

The axiom of extensionality of set theory states that any two classes that have identical members are identical. Yet the class of persons age i at time t and the class of persons age i + 1 at t + l, both including same persons, possess different demographic attributes, and thus appear to be two different classes. The contradiction could be resolved by making a clear distinction between age groups and cohorts. Cohort is a multitude of individuals, which is constituted (...) within a time interval, and endures throughout part of the time continuum. Age group, on the other hand, is only a reference term to which empirical measurement relates, as in birth or death rates. Accordingly, the two concepts, age group i at t, and age group i + 1 at t + 1, are different. The standard population growth model of Leslie and Lotka, however, does not support such a distinction in age groups. An alternative model, proposed recently, implies precisely such a distinction. (shrink)

A twenty‐person working group convened to discuss the ethical and policy considerations of the controversial intervention called “growth attenuation,” and if possible to develop practical guidance for health professionals. A consensus proved elusive, but most of the members did reach a compromise.

We explain how the field of logarithmic-exponential series constructed in 20 and 21 embeds as an exponential field in any field of exponential-logarithmic series constructed in 9, 6, and 13. On the other hand, we explain why no field of exponential-logarithmic series embeds in the field of logarithmic-exponential series. This clarifies why the two constructions are intrinsically different, in the sense that they produce non-isomorphic models of Thequation image; the elementary theory of the ordered field of real numbers, with the (...) exponential function and restricted analytic functions. (shrink)

The article examines the concept of “revolving ownership” as a metamodel of property, whose structure allows for the interchange (rotation) of diverse components included in it, each capable of achieving different objectives through varied means. It is noted that the metamodel of revolving ownership can be utilized in the creation and structuring of property models over specific entities, necessitating consideration of specific social and environmental factors. In this context, a distinction is made between yang-ownership (“classic” private ownership used as an (...) instrument for growth through extraction and accumulation, analogous to so-called “extractive” ownership) and yin-ownership (engaged possession involving a healthful balance between rights and obligations, i.e., flexible distribution of various components aimed at achieving sustainable equilibrium, analogous to the so-called “generative” ownership). The thesis is presented that the sooner the “proprietary” nature of yang-ownership is overcome, yielding to its dominance through the integration of balancing yin-components, the more easily and effectively legal professionals can propose novel and diverse ownership models. The recognition and acknowledgment of the complexity of nature imply greater intricacy in contemporary property law. It is time for property law to reconsider its unquestionable axioms and seek an appropriate solution to the challenges humanity faces today. (shrink)

Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, (...) the seeds of the theory of rates of growth of functions as developed by Paul du Bois-Reymond. One sees, with E. G. Björling, an infinitesimal definition of the criterion of uniform convergence. Cauchy’s foundational stance is hereby reconsidered. (shrink)

Are the employees working in different countries and enjoying healthy compensation truly loyal to their organization? Our study attempts to answer this question by examining the role of perception of politics on the affective commitment of expatriates in the Sultanate of Oman. Following the axiom of equity theory, the relationships between the perception of politics (POP) to affective commitment (AC) and Islamic work ethics (IWE) to affective commitment (AC) was tested. The moderating role of Islamic work ethics was also examined (...) in the POP-AC relationship. Responses from 146 employees were collected following a simple random sampling technique. Employees working in different organizations at various managerial levels were approached for data collection. Descriptive statistics, correlation, and regression tests were applied to test hypotheses using SPSS-22.0 and SmartPLS-4. Results confirmed the positive relationship between Islamic work ethics to affective commitment and the negative relationship between perception of politics to affective commitment. Moreover, the negative relationship between the perception of politics with affective commitment was weaker when Islamic work ethics were high. Practical implications of the study are presented based on the results. (shrink)

We show that Matijasevič's Theorem on the diophantine representation of r.e. predicates is provable in the subsystem I ∃ - 1 of Peano Arithmetic formed by restricting the induction scheme to diophantine formulas with no parameters. More specifically, I ∃ - 1 ⊢ IE - 1 + E ⊢ Matijasevič's Theorem where IE - 1 is the scheme of parameter-free bounded existential induction and E is an ∀∃ axiom expressing the existence of a function of exponential growth. We conclude (...) by examining the consequences of these results to the structure of countable nonstandard models of IE - 1. (shrink)

This article pursues the question whether and inasmuch theories of corporate responsibility are dependent on conceptions of managerial freedom. I argue that neglect of the idea of freedom in economic theory has led to an inadequate conceptualization of the ethical responsibilities of corporations within management theory. In a critical review of the history of economic ideas, I investigate why and how the idea of freedom was gradually removed from the canon of economics. This reconstruction aims at a deconstruction of certain (...) axioms of neoclassical economics that hamper contemporary efforts in integrating ethics firmly into management education. I intend to show by these deconstructive endeavors that a constructive use of the idea of responsible freedom could correct and complement the current quantitative focus in business theory through qualitative orientations. I argue that with the help of qualitative success criteria, the strategic integration of the tenets of both business ethics and Corporate Social Responsibility into business practice can be advanced by further research. (shrink)

Gödel’s first incompleteness result from 1931 states that there are true assertions about the natural numbers which do not follow from the Peano axioms. Since 1931 many researchers have been looking for natural examples of such assertions and breakthroughs were obtained in the seventies by Jeff Paris [Some independence results for Peano arithmetic. J. Symbolic Logic 43 725–731] , Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977] and Laurie Kirby [L. Kirby, Jeff Paris, Accessible independence results for Peano Arithmetic, Bull. (...) of the LMS 14 285–293]) and Harvey Friedman [S.G. Simpson, Non-provability of certain combinatorial properties of finite trees, in: Harvey Friedman’s Research on the Foundations of Mathematics, North-Holland, Amsterdam, 1985, pp. 87–117; R. Smith, The consistency strength of some finite forms of the Higman and Kruskal theorems, in: Harvey Friedman’s Research on the Foundations of Mathematics, North-Holland, Amsterdam, 1985, pp. 119–136] who produced the first mathematically interesting independence results in Ramsey theory and well-order and well-quasi-order theory .In this article we investigate Friedman-style principles of combinatorial well-foundedness for the ordinals below ε0. These principles state that there is a uniform bound on the length of decreasing sequences of ordinals which satisfy an elementary recursive growth rate condition with respect to their Gödel numbers.For these independence principles we classify their phase transitions, i.e. we classify exactly the bounding conditions which lead from provability to unprovability in the induced combinatorial well-foundedness principles.As Gödel numbering for ordinals we choose the one which is induced naturally from Gödel’s coding of finite sequences from his classical 1931 paper on his incompleteness results.This choice makes the investigation highly non-trivial but rewarding and we succeed in our objectives by using an intricate and surprising interplay between analytic combinatorics and the theory of descent recursive functions. For obtaining the required bounds on count functions for ordinals we use a classical 1961 Tauberian theorem of Parameswaran which apparently is far remote from Gödel’s theorem. (shrink)

Modern science developed in the interflow of culture between west and east. Combing of pratice technology with philosophic thoughts formed experimental method. Holistic views contacting atomism produced system theory. System thoughts are applicated in the science and engineering of biosystems, and the cencepts of system biomedicine (Kamada T.1992), systems biology (Zieglgansberger W, Tolle TR.1993), system bioengineering and system genetics (Zeng BJ. 1994) were established. From positive to synthetic thoughts, philosophy have been developed ontology, cosmology, organism theories. Structurity is structure logic (...) system founded on entity, develop, exist axioms, tolerance, adaptation, fluctuate, interweave, transform theorems and integrate, adaptation, construct laws. Structurity be discussed on the cosmos, life, culture system, creation, hologram theories of structure ontology, construct mutation, simi-structure organism and entity emergence, symbol implication. From the relation of structure, function and development, the structurity put forward the cycle, spiral, triangle structure stability patterns of self-organization in structure complement each other and stratification, functional couple and interflow bounds growth, coordinativetransformation and holographic symmetry. (shrink)

One cannot really speak of a school of personalistic economists. Moreover, there is a wide gulf between the economic philosophy of the personalists and the mathematical context of economic science. Since the thirties, philosophers such as Alexandre Marc, Jacques Maritain, Emmanuel Mounier and many others have been searching, on the basis of a personalistic view of man, for a `third way' between individualistic capitalism and statist socialism , but there was seldom interest from the side of the scientific economists.Fortunately, there (...) are some notable exceptions. François Perroux, Kenneth Boulding, Ernst Schumacher, Serge Christophe Kolm, and Amartya Sen are economists who, in various ways, have attempted to bridge the gulf between the personalistic view of man and economic rationality. By carrying out an immanent critique of some of the standard economic assumptions, they opened a path for a normative economics that was clearly distinct from a purely positive economics as well as from Pareto's welfare economics. One can affix various labels to these attempts: humanistic economics , socio-economics , moral economics . In what follows, I shall interpret these attempts as initiatives in the direction of a personalistic economics. I would also situate the current research in `economics and ethics', which is becoming part of the mainstream of economic thought, and which has received official recognition with the recent Nobel prize award to Sen, within this tendency towards a more personalistic economics.Attention to moral feelings, human rights, altruistic motives, justice and solidarity, non-profit organizations, etc., contribute to situating the economic problem in a field where economics, politics and ethics no longer function as three distinct domains but where their interaction is central.Yet does this interactive economics fit into a personalistic way of thinking? Is a generalized system theory not more attractive? System theory has a different focus than personalistic economics. System theory considers the axioms of system equilibrium and sustainable growth as the ultimate horizon, whereas a personalist sees them as merely important conditions for a good society and economy. However refined it may be, system theory views the person from an external point of view, while the personalist refers to the internal experience of human freedom and meaning as something that transcends and regulates the system's functionality.One could object that neo-classical economists do not use system theory as their point of departure. In their eyes, system equilibrium is the result of the utility-maximizing behaviour of individuals. These individuals subjectively determine what their preferences are and then act accordingly. Is this openness for a free, utility-maximizing actor — where there is room for both material and immaterial, egoistic and altruistic preferences — not sufficient to speak of a personalistic economics ? If this were true, then the discourse of personalism would be more or less superfluous.I take the term `personalistic economics' to refer to a normative economics that does not simply reconstruct the problem of efficient allocation as an individual or social problem of utility, but in the first instance as a problem of human dignity and social justice. To reduce the problem of human choice to a problem of subjective utility is in itself a far-reaching normative standpoint. As soon as one realizes this, there is no reason to exclude other normative assumptions, such as personalistic ones. (shrink)

Social cognition can be based on two contrary axioms that answer the question of whether the society can provide for the universal survival of all of its members. Negative answer (relativist model of society) is more productive methodologically. The key notion here is the technosocial formula of society, the physical meaning of which is that the society as an aggregate of people needs bigger vital space than it can create. The growth of man in nature was the result (...) not only of the supplanting of other species but also of the intraspecific struggle which became the main factor of the development process. The criterion of social progress is reduced in the end to only one index – the ability of society’s survival and it doesn’t have any absolute value in space and time. (shrink)

I consider the general question of whether a study of the life of a philosopher can help us to understand his/her philosophical principles. This topic is narrowed to the consideration of principles of moral and political philosophy, especially in instances in which the philosopher deliberately uses the experiences of his/her own life in formulating his/her views. Such use raises the problem of justification of the self as sampIe. As part of my general defense of the merits of studying a life (...) to grasp a philosophy, I argue that the meaning of a principle in the philosophy of X can be illuminated by trying to recognize what that principIe meant to X. All of these general issues are deployed in my study of the philosophy of John Stuart Mill. In particular I focus on five points, the understanding of which I feel is deepened by studying how they involved his own life. These five are: a change in tone in ch. III of On Liberty, his conviction about free will, his commitment to a principle of vigorous action, his principle of balanced growth, and his fundamental axiom of Individualism. (shrink)

I consider the general question of whether a study of the life of a philosopher can help us to understand his/her philosophical principles. This topic is narrowed to the consideration of principles of moral and political philosophy, especially in instances in which the philosopher deliberately uses the experiences of his/her own life in formulating his/her views. Such use raises the problem of justification of the self as sampIe. As part of my general defense of the merits of studying a life (...) to grasp a philosophy, I argue that the meaning of a principle in the philosophy of X can be illuminated by trying to recognize what that principIe meant to X. All of these general issues are deployed in my study of the philosophy of John Stuart Mill. In particular I focus on five points, the understanding of which I feel is deepened by studying how they involved his own life. These five are: a change in tone in ch. III of On Liberty, his conviction about free will, his commitment to a principle of vigorous action, his principle of balanced growth, and his fundamental axiom of Individualism. (shrink)

Welfare biology is the study of living things and their environment with respect to their welfare. Despite difficulties of ascertaining and measuring welfare and relevancy to normative issues, welfare biology is a positive science. Evolutionary economics and population dynamics are used to help answer basic questions in welfare biology : Which species are affective sentients capable of welfare? Do they enjoy positive or negative welfare? Can their welfare be dramatically increased? Under plausible axioms, all conscious species are plastic and (...) all plastic species are conscious. More complex niches favour the evolution of more rational species. Evolutionary economics also supports the common-sense view that individual sentients failing to survive to mate suffer negative welfare. A kind of God-made fairness between species is also unexpectedly found. The contrast between growth maximization, average welfare, and total welfare maximization is discussed. It is shown that welfare could be increased without even sacrificing numbers. Since the long-term reduction in animal suffering depends on scientific advances, strict restrictions on animal experimentation may be counter-productive to animal welfare. (shrink)

We study the extension of public announcement logic PAL by public assignments, which we call PALA. Just as in the case of PAL, the standard procedure for deciding PALA validity, i.e. the use of so-called reduction axioms to translate PALA formulae into formulae in epistemic logic EL, may lead to exponential growth. In this paper, we show that such a price is not mandatory, for we provide a polynomial translation of PALA into EL. This is based on abbreviations (...) of subformulae by new propositional letters. Such optimal translation also enables us to show the computational complexity of the problem of deciding PALA validity, which turns out to be coNP-complete in the single-agent case and PSPACE-complete in the multiagent case. (shrink)

The notion of a function from ℕ to ℕ defined by recursion on ordinal notations is fundamental in proof theory. Here this notion is generalized to functions on the universe of sets, using notations for well orderings longer than the class of ordinals. The generalization is used to bound the rate of growth of any function on the universe of sets that is Σ1-definable in Kripke–Platek admissible set theory with an axiom of infinity. Formalizing the argument provides an ordinal (...) analysis. (shrink)

The youth of Bentham (1776-1789).--The evolution of the utilitarian doctrine from 1789 to 1815.--Philosophic radicalism.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Explores the development of the ideas of evolutionary biology, particularly as affected by the increasing understanding of genetics and of the chemical basis of inheritance.

We prove rigidity results for large classes of corona algebras, assuming the Proper Forcing Axiom. In particular, we prove that a conjecture of Coskey and Farah holds for all separable [Formula: see text]-algebras with the metric approximation property and an increasing approximate identity of projections.

We prove rigidity results for large classes of corona algebras, assuming the Proper Forcing Axiom. In particular, we prove that a conjecture of Coskey and Farah holds for all separable [Formula: see text]-algebras with the metric approximation property and an increasing approximate identity of projections.

Richard Bradley and others endorse Reverse Bayesianism as the way to model awareness growth. I raise a problem for Reverse Bayesianism—at least for the general version that Bradley endorses—and argue that there is no plausible way to restrict the principle that will give us the right results. To get the right results, we need to pay attention to the attitudes that agents have towards propositions of which they are unaware. This raises more general questions about how awareness growth (...) should be modelled. (shrink)

This essay applies a plausible model for moral growth to examples of secular and religious children’s literature. The point is that moral maturation, given this model, requires imaginary worlds on both secular and religious presuppositions. Trying to guide a child’s reading toward either religious or secular books rather than toward good literature is shown therefore to miss the mark of good parenting.

We construct peculiar Hilbert spaces from counterexamples to the axiom of choice. We identify the intrinsically effective Hamiltonians with those observables of quantum theory which may coexist with such spaces. Here a self adjoint operator is intrinsically effective if and only if the Schrödinger equation of its generated semigroup is soluble by means of eigenfunction series expansions.

There seems to be a view that intuitionists not only take the Axiom of Choice (AC) to be true, but also believe it a consequence of their fundamental posits. Widespread or not, this view is largely mistaken. This article offers a brief, yet comprehensive, overview of the status of AC in various intuitionistic and constructivist systems. The survey makes it clear that the Axiom of Choice fails to be a theorem in most contexts and is even outright false in some (...) important contexts. Of the systems surveyed, only intensional type theory renders AC a theorem, but the extent of AC in that theory does not include, for instance, real analysis. Only a small amount of extensionality is required in order for the obvious proof an intuitionist might offer for AC to break down. (shrink)

In this paper we give axiom systems for classical and intuitionistic hybrid logic. Our axiom systems can be extended with additional rules corresponding to conditions on the accessibility relation expressed by so-called geometric theories. In the classical case other axiomatisations than ours can be found in the literature but in the intuitionistic case no axiomatisations have been published. We consider plain intuitionistic hybrid logic as well as a hybridized version of the constructive and paraconsistent logic N4.

We introduce the resurrection axioms, a new class of forcing axioms, and the uplifting cardinals, a new large cardinal notion, and prove that various instances of the resurrection axioms are equiconsistent over ZFC with the existence of an uplifting cardinal.

It seems that whenever there is a struggle between cultures, the culture of the victorious people becomes the culture of the people as a whole in the beginning, but later on the culture of the subjugated people asserts itself and many of its essential elements have to be integrated in the elite culture. We can see this process at work in the making of the Indian civilization. In the beginning the culture of the newly triumphant Aryan hordes naturally became the (...) dominant culture of the Indian sub-continent. But later on the culture of the subjugated non-Aryans asserted itself, and during the second Brahmanical revival it found full-blooded expression in the Mahabharata, the Rāmāyana and the Puranas. As we shall see in this paper, even though the Aryans were conscious of the non-Aryan influence and resisted it, their attempts could not prevent copious inflow of non-Aryan culture. (shrink)

On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. (...) The distinctions introduced aim at clarifying discussions in philosophy of mathematics and contributing towards a more refined view of mathematical practice. (shrink)

Algebraic quantum field theory (AQFT) puts forward three ``causal axioms'' that aim to characterize the theory as one that implements relativistic causation: the spectrum condition, microcausality, and primitive causality. In this paper, I aim to show, in a minimally technical way, that none of them fully explains the notion of causation appropriate for AQFT because they only capture some of the desiderata for relativistic causation I state or because it is often unclear how each axiom implements its respective desideratum. (...) After this diagnostic, I will show that a fourth condition, local primitive causality (LPC), fully characterizes relativistic causation in the sense of fulfilling all the relevant desiderata. However, it only encompasses the virtues of the other axioms because it is implied by them, as I will show from a construction by Haag and Schroer (1962). Since the conjunction of the three causal axioms implies LPC and other important results in QFT that LPC does not imply, and since LPC helps clarify some of the shortcomings of the three axioms, I advocate for a holistic interpretation of how the axioms characterize the causal structure of AQFT against the strategy in the literature to rivalize the axioms and privilege one among them. (shrink)

There is a crisis of valuation practices in the current academic life sciences, triggered by unsustainable growth and “hyper-competition.” Quantitative metrics in evaluating researchers are seen as replacing deeper considerations of the quality and novelty of work, as well as substantive care for the societal implications of research. Junior researchers are frequently mentioned as those most strongly affected by these dynamics. However, their own perceptions of these issues are much less frequently considered. This paper aims at contributing to a (...) better understanding of the interplay between how research is valued and how young researchers learn to live, work and produce knowledge within academia. We thus analyze how PhD students and postdocs in the Austrian life sciences ascribe worth to people, objects and practices as they talk about their own present and future lives in research. We draw on literature from the field of valuation studies and its interest in how actors refer to different forms of valuation to account for their actions. We explore how young researchers are socialized into different valuation practices in different stages of their growing into science. Introducing the concept of “regimes of valuation” we show that PhD students relate to a wider evaluative repertoire while postdocs base their decisions on one dominant regime of valuing research. In conclusion, we discuss the implications of these findings for the epistemic and social development of the life sciences, and for other scientific fields. (shrink)

We present a new axiomatization of classical mereology in which the three components of the theory—ordering, composition, and decomposition prin-ciples—are neatly separated. The equivalence of our axiom system with other, more familiar systems is established by purely deductive methods, along with additional results on the relative strengths of the composition and decomposition axioms of each theory.

Current dynamic epistemic logics often become cumbersome and opaque when common knowledge is added. In this paper we propose new versions that extend the underlying static epistemic language in such a way that dynamic completeness proofs can be obtained by perspicuous reduction axioms.

We analyze axioms and postulates as speech acts. After a brief historical appraisal of the concept of axiom in Euclid, Frege, and Hilbert, we evaluate contemporary axiomatics from a linguistic perspective. Our reading is inspired by Hilbert and is meant to account for the assertive, directive, and declarative components of modern axiomatics. We will do this by describing the constitutive and regulative roles that axioms possess with respect to the linguistic practice of mathematics.

Elementary geometry can be axiomatized constructively by taking as primitive the concepts of the apartness of a point from a line and the convergence of two lines, instead of incidence and parallelism as in the classical axiomatizations. I first give the axioms of a general plane geometry of apartness and convergence. Constructive projective geometry is obtained by adding the principle that any two distinct lines converge, and affine geometry by adding a parallel line construction, etc. Constructive axiomatization allows solutions (...) to geometric problems to be effected as computer programs. I present a formalization of the axiomatization in type theory. This formalization works directly as a computer implementation of geometry. (shrink)

Incremental implicit theories are associated with a belief regarding it is possible to improve one’s intelligence or ability through efforts. Previous studies have demonstrated that incremental implicit theories contributed to better academic achievement and positive youth development. Our study aimed to examine whether incremental implicit theories of morality significantly influenced change in students’ engagement in voluntary service activities. In our study, 54 Korean college students for Study 1 and 180 Korean 8th graders for Study 2 were recruited to conduct two (...) two-wave studies. We surveyed participants’ implicit theories of morality and participation in voluntary service activities. The effect of implicit theories of morality on change in service engagement was analyzed through regression analysis. In Study 1, the moral growth mindset significantly moderated longitudinal change in service engagement. In Study 2, the moral growth mindset significantly influenced engagement in art-related activities, while it significantly moderated change in engagement in youth-related activities. (shrink)

A weak form of intuitionistic set theory WST lacking the axiom of extensionality is introduced. While WST is too weak to support the derivation of the law of excluded middle from the axiom of choice, we show that bee.ng up WST with moderate extensionality principles or quotient sets enables the derivation to go through.

We will give a simple philosophical "proof" of the negation of Cantor's continuum hypothesis (CH). (A formal proof for or against CH from the axioms of ZFC is impossible; see Cohen [1].) We will assume the axioms of ZFC together with intuitively clear axioms which are based on some intuition of Stuart Davidson and an old theorem of Sierpinski and are justified by the symmetry in a thought experiment throwing darts at the real number line. We will (...) in fact show why there must be an infinity of cardinalities between the integers and the reals. We will also show why Martin's Axiom must be false, and we will prove the extension of Fubini's Theorem for Lebesgue measure where joint measurability is not assumed. Following the philosophy--if you reject CH you are only two steps away from rejecting the axiom of choice (AC)--we will point out along the way some extensions of our intuition which contradict AC. (shrink)

This paper analyses the hidden use of new axioms in set-theoretic practice with a focus on large cardinal axioms and presents a general overview of set-theoretic practices using large cardinal axioms. The hidden use of a new axiom provides extrinsic reasons in support of this axiom via the idea of verifiable consequences, which is especially relevant for set-theoretic practitioners with an absolutist view. Besides that, the hidden use has pragmatic significance for further important sub-groups of the set-theoretic (...) community---set-theoretic practitioners with a pluralist view and set-theoretic practitioners who aim for ZFC-proofs. By describing this, the paper gives a more complete picture of new axioms in set-theoretic practice. These observations, for instance, show that set-theoretic practitioners interested in ZFC-proofs use tools that go beyond ZFC. The analysis is based on empirical data that was collected in an extensive interview study with set-theoretic practitioners. (shrink)

The axiom of reducibility plays an important role in the logic of Principia Mathematica, but has generally been condemned as an ad hoc non-logical axiom which was added simply because the ramified type theory without it would not yield all the required theorems. In this paper I examine the status of the axiom of reducibility. Whether the axiom can plausibly be included as a logical axiom will depend in no small part on the understanding of propositional functions. If we understand (...) propositional functions as constructions of the mind, it is clear that the axiom is clearly not a logical axiom and in fact makes an implausible claim. I look at two other ways of understanding propositional functions, a nominalist interpretation along the lines of Landini and a realist interpretation along the lines of Linsky and Mares. I argue that while on either of these interpretations it is not easy to see the axiom as a non-logical claim about the world, there are also appear to be difficulties in accepting it as a purely logical axiom. (shrink)