A permutation group G on a set A is ${\kappa }$ -homogeneous iff for all $X,Y\in \bigl [ {A} \bigr ]^ {\kappa } $ with $|A\setminus X|=|A\setminus Y|=|A|$ there is a $g\in G$ with $g[X]=Y$. G is ${\kappa }$ -transitive iff for any injective function f with $\operatorname {dom}(f)\cup \operatorname {ran}(f)\in \bigl [ {A} \bigr ]^ {\le {\kappa }} $ and $|A\setminus \operatorname {dom}(f)|=|A\setminus \operatorname {ran}(f)|=|A|$ there is a $g\in G$ with $f\subset g$.Giving a partial answer to a question of (...) P. M. Neumann [6] we show that there is an ${\omega }$ -homogeneous but not ${\omega }$ -transitive permutation group on a cardinal ${\lambda }$ provided (i) ${\lambda } {\omega }$ we give a method to construct large ${\kappa }$ -homogeneous, but not ${\kappa }$ -transitive permutation groups. Using this method we show that there exist ${\kappa }^+$ -homogeneous, but not ${\kappa }^+$ -transitive permutation groups on ${\kappa }^{+n}$ for each infinite cardinal ${\kappa }$ and natural number $n\ge 1$ provided $V=L$. (shrink)

The first classification of general types of transition between phases of matter, introduced by Paul Ehrenfest in 1933, lies at a crossroads in the thermodynamical study of critical phenomena. It arose following the discovery in 1932 of a suprising new phase transition in liquid helium, the “lambda transition,” when W. H. Keesom and coworkers in Leiden, Holland observed a λhaped “jump” discontinuity in the curve giving the temperature dependence of the specific heat of helium at a (...) critical value. This apparent jump led Ehrenfest to introduce a classification of phase transitions on the basis of jumps in derivatives of the free energy function. This classification was immediately applied by A.J. Rutgers to the study of the transition from the normal to superconducting state in metals. Eduard Justi and Max von Laue soon questioned the possibility of its class of “second-order phase transitions” -- of which the “lambda transition was believed to be the arche type -- but C.J. Gorter and H.B.G. Casimir used an “order parameter to demonstrate their existence in superconductors. As a crossroads of study, the Ehrenfest classification was forced to undergo a slow, adaptive evolution during subsequent decades. During the 1940s the classification was increasingly used in discussions of liquid-gas, order-disorder, paramagnetic-ferromagnetic and normal-super-conducting phase transitions. Already in 1944 however, Lars Onsagers solution of the Ising model for two-dimensional magnets was seen to possess a derivative with a logarithmic divergence rather than a jump as the critical point was approached. In the 1950s, experiments further revealed the lambda transition in helium to exhibit similar behavior. Rather than being a prime example of an Ehrenfest phase transition, the lambda transition was seen to lie outside the Ehrenfest classification. The Ehrenfest scheme was then extended to include such singularities, most notably by A. Brain Pippard in 1957, with widespread acceptance. During the 1960s these logarithmic infinities were the focus of the investigation of “scaling” by Leo Kadanoff, B. Widom and others. By the 1970s, a radically simplified binary classification of phase transitions into “first-order” and “continuous” transitions was increasingly adopted. (shrink)

We introduce new proof systems G[β] and G ext[β], which are equivalent to the standard equational calculi of λβ- and λβη- conversion, and which may be qualified as ‘analytic’ because it is possible to establish, by purely proof-theoretical methods, that in both of them the transitivity rule admits effective elimination. This key feature, besides its intrinsic conceptual significance, turns out to provide a common logical background to new and comparatively simple demonstrations—rooted in nice proof-theoretical properties of transitivity-free derivations—of a number (...) of well-known and central results concerning β- and βη-reduction. The latter include the Church–Rosser theorem for both reductions, the Standardization theorem for β- reduction, as well as the Normalization (Leftmost reduction) theorem and the Postponement of η-reduction theorem for βη-reduction. (shrink)

Modern microscopic theory is employed to construct a powerful analytical algorithm that permits a clear description of characteristic features of strongly correlated quantum fluids in thermodynamic equilibrium. Using recently developed formal results we uncover an intricate relationship between strongly correlated systems and free quantum gases of appropriately defined constituents. The latter entities are precisely defined renormalized bosons or fermions. They carry all the information contained in the statistical correlations of the strongly interacting many-particle system by virtue of their effective masses. (...) The mass of such a renormalized boson or fermion depends in a specific form on temperature, bulk particle number density of the many-body system, and eventually on momentum. Due to these properties the renormalized bosons and fermions determine in particular the location and nature of the transition to non-normal phases. (shrink)

One can add the machinery of relation symbols and terms to a propositional modal logic without adding quantifiers. Ordinarily this is no extension beyond the propositional. But if terms are allowed to be non-rigid, a scoping mechanism (usually written using lambda abstraction) must also be introduced to avoid ambiguity. Since quantifiers are not present, this is not really a first-order logic, but it is not exactly propositional either. For propositional logics such as K, T and D, adding such machinery (...) produces a decidable logic, but adding it to S5 produces an undecidable one. Further, if an equality symbol is in the language, and interpreted by the equality relation, logics from K4 to S5 yield undecidable versions. (Thus transitivity is the villain here.) The proof of undecidability consists in showing that classical first-order logic can be embedded. (shrink)

This volume presents the proceedings of the Computer Science Logic Workshop CSL '92, held in Pisa, Italy, in September/October 1992. CSL '92 was the sixth of the series and the first one held as Annual Conference of the European Association for Computer Science Logic (EACSL). Full versions of the workshop contributions were collected after their presentation and reviewed. On the basis of 58 reviews, 26 papers were selected for publication, and appear here in revised final form. Topics covered in the (...) volume include: Turing machines, linear logic, logic of proofs, optimization problems, lambda calculus, fixpoint logic, NP-completeness, resolution, transition system semantics, higher order partial functions, evolving algebras, functional logic programming, inductive definability, semantics of C, classes for a functional language, NP-optimization problems, theory of types and names, sconing and relators, 3-satisfiability, Kleene's slash, negation-complete logic programs, polynomial-time oracle machines, and monadic second-order properties. (shrink)

In this paper, the following are proved:Theorem A. The quotient algebra ${\cal P} (\kappa )/I$ is complete if and only if the only non-trivial I -closed ideals extending I are of the form $I\lceil A$ for some $A\in I^+$ .Theorem B. If $\kappa$ is a stationary cardinal, then the quotient algebra ${\cal P} (\kappa )/ NS_\kappa$ is not complete.Corollary. (1) If $\kappa$ is a weak compact cardinal, then the quotient algebra ${\cal P} (\kappa )/NS_\kappa$ is not complete.(2) If $\kappa$ bears (...) $\kappa$ -saturated ideal, then the quotient algebra ${\cal P} (\kappa )/NS_\kappa$ is not complete.Theorem C. Assume that $\kappa$ is a strongly compact cardinal, I is a non-trivial normal $\kappa$ -complete ideal on $\kappa$ and B is an I -regular complete Boolean algebra. Then if ${\cal P} (\kappa )/I$ is complete, it is B -valid that for some $A\subseteq\check\kappa$ , ${\cal P} (\kappa )/({\bf J}\lceil A)$ is complete, where J is the ideal generated by $\check I$ in $V^B$ .Corollary. Let M be a transitive model of ZFC and in M , let $\kappa$ be a strongly compact cardinal and $\lambda$ a regular uncountable cardinal less than $\kappa$ . Then there exists a generic extension M [ G ] in which $\kappa =\lambda^+$ and $\kappa$ carries a non-trivial $\kappa$ -complete ideal I which is completive but not $\kappa^+$ -saturated. (shrink)

The Theme. Strong forcing axioms like Martin’s Maximum give a reasonably satisfactory structural analysis of $H(\omega _2)$. A broad program in modern Set Theory is searching for strong forcing axioms beyond $\omega _1$. In other words, one would like to figure out the structural properties of taller initial segments of the universe. However, the classical techniques of forcing iterations seem unable to bypass the obstacles, as the resulting forcings axioms beyond $\omega _1$ have not thus far been strong enough! However, (...) with his celebrated work on generalised side conditions, I. Neeman introduced us to a novel paradigm to iterate forcings. In particular, he could, among other things, reprove the consistency of the Proper Forcing Axiom using an iterated forcing with finite supports. In 2015, using his technology of virtual models, Veličković built up an iteration of semi-proper forcings with finite supports, hence reproving the consistency of Martin’s Maximum, an achievement leading to the notion of a virtual model.In this thesis, we are interested in constructing forcing notions with finitely many virtual models as side conditions to preserve three uncountable cardinals. The thesis constitutes six chapters and three appendices that amount to 118 pages, where Section 1 is devoted to preliminaries, and Section 2 is a warm-up about the scaffolding poset of a proper forcing. In Section 3, we present the general theory of virtual models in the context of forcing with sets of models of two types, where we, e.g., define the “meet” between two virtual models and prove its properties.The main results are joint with Boban Veličković, and partly appeared in Guessing models and the approachability ideal, J. Math. Log. 21 (2021).Pure Side Conditions. In Section 4, we use two types of virtual models (countable and large non-transitive ones induced by a supercompact cardinal, which we call Magidor models) to construct our forcing with pure side conditions. The forcing covertly uses a third type of models that are transitive. We also add decorations to the conditions to add many clubs in the generic $\omega _2$. In contrast to Neeman’s method, we do not have a single chain, but $\alpha $ -chains, for an ordinal $\alpha $ with $V_\alpha \prec V_\lambda $. Thus, starting from suitable large cardinals $\kappa <\lambda $, we construct a forcing notion whose conditions are finite sets of virtual models described earlier. The forcing is strongly proper, preserves $\kappa $, and has the $\lambda $ -Knaster property. The relevant quotients of the forcing are strongly proper, which helps us prove strong guessing model principles. The construction is generalisable to a ${<}\mu $ -closed forcing, for any given cardinal $\mu $ with $\mu ^{<\mu }=\mu <\kappa $.The Iteration Theorem. In Section 5, we use the forcing with pure side conditions to iterate a subclass of proper and $\aleph _2$ -c.c. forcings and obtain a forcing axiom at the level of $\aleph _2$. The iterable class is closely related to Asperó–Mota’s forcing axiom for finitely proper forcings.Guessing Model Principles. Section 6 encompasses the main parts of the thesis. We prove the consistency of the guessing principle $\mathrm {GMP}^+(\omega _3,\omega _1)$ that states for any cardinal ${\theta \geq \omega _3}$, the set of $\aleph _2$ -sized elementary submodels M of $H(\theta )$, which are the union of an $\omega _1$ -continuous $\in $ -chain of $\omega _1$ -guessing, I.C. models is stationary in $\mathcal P_{\omega _3}(H(\theta ))$. The consistency and consequences of this principle are demonstrated in the following diagram. We also prove that one can obtain the above guessing models in a way that the $\omega _1$ -sized $\omega _1$ -guessing models remain $\omega _1$ -guessing model in any outer transitive model with the same $\omega _1$, and we denote this principle by $\rm{SGMP}^+(\omega_3,\omega_1)$.In the following diagram, $\mathrm{TP}$ stands for the tree property; $w\mathrm{KH}$ stands for the weak Kurepa Hypothesis; $\mathrm{MP}$ stands for Mitchell property, i.e., the approachability ideal is trivial modulo the nonstationary ideal; $\mathrm{AP}$ stands for the approachability property; $\mathrm {AMTP}(\kappa ^+)$ states that if $2^\kappa <\aleph _{\kappa ^+}$, then every forcing which adds a new subset of $\kappa ^+$ whose initial segments are in the ground model, collapses some cardinal $\leq 2^{\kappa }$. The dotted arrow denotes the relative consistency, while others are logical implications.Appendices. Appendix A includes merely the above diagram. Appendix B presents a proof of the Mapping Reflection Principle with finite conditions under $\mathrm {PFA}$. Appendix C contains open problems. Finally, the thesis’s bibliography consists of 42 items.Abstract prepared by Rahman MohammadpourE-mail: [email protected]: https://theses.hal.science/tel-03209264. (shrink)

The connection between sense, verification, and mode of verification never entirely disappeared from Wittgenstein’s philosophy. However, there was a time – the years 1929– 1932 – when Wittgenstein upheld explicitly verificationist views: he identified a proposition’s meaning with the mode or method of its verification, and he said that to understand a proposition is to know how the proposition is verified. This has been regarded as puzzling, in view of the fact that the Tractatus is usually considered not to be (...) committed to verificationism; indeed, it is usually regarded as incompatible with verificationism. Several people have proposed to revise such a received view: Michael Wrigley (1989) has claimed that verificationism must be implicit in the Tractatus; and P. M.S. Hacker (1986) has argued that the Tractatus, though not verificationist, is not as distant from verificationism as it has been taken to be. In another paper (Marconi, forthcoming) I discuss their views. Here I will just notice that, even if one regards the Tractatus as implicitly verificationist, the problem remains of explaining why and how did Wittgenstein reach the explicitly – indeed, blatantly – verificationist outlook of the early Thirties. This is the first question I would like to try to answer in this paper. The second question is, why was such rampant verificationism short-lived? Or in other words, why was verificationism de-emphasized so that, although verificationist themes are undoubtedly present in the later Wittgenstein’s writings, the extreme formulations of the early Thirties tend to disappear after 1933? (shrink)

The ideas of continental philosopher Martin Heidegger have been influential in cognitive science and artificial intelligence, despite the fact that there has been no effort to analyze these ideas empirically. The experiments reported here are designed to lend empirical support to Heidegger’s phenomenology and more specifically his description of the transition between ready-to-hand and unready-to-hand modes in interactions with tools. In experiment 1, we found that a smoothly coping cognitive system exhibits 1/fβ type positively correlated noise and that its (...) correlated character is reduced when the system is perturbed. This indicates that the participant and tool constitute a self-assembled, extended device during smooth coping and this device is disrupted by the perturbation. In experiment 2, we examine the re-organization of awareness that occurs when a smoothly coping, self-assembled, extended cognitive system is perturbed. We found that the disruption is accompanied by a change in attention which interferes with participants’ performance on a simultaneous cognitive task. Together these experiments show that a smoothly coping participant-tool system can be temporarily disrupted and that this disruption causes a change in the participant’s awareness. Since these two events follow as predictions from Heidegger’s work, our study offers evidence for the hypothesized transition from readiness-to-hand to unreadiness-to-hand. (shrink)

In this paper we describe an approach to practical reasoning, reasoning about what it is best for a particular agent to do in a given situation, based on presumptive justifications of action through the instantiation of an argument scheme, which is then subject to examination through a series of critical questions. We identify three particular aspects of practical reasoning which distinguish it from theoretical reasoning. We next provide an argument scheme and an associated set of critical questions which is able (...) to capture these features. In order that both the argument scheme and the critical questions can be given precise interpretations we use the semantic structure of an Action-Based Alternating Transition System as the basis for their definition. We then work through a detailed example to show how this approach to practical reasoning can be applied to a problem solving situation, and briefly describe some other previous applications of the general approach. In a second example we relate our account to the social laws paradigm for co-ordinating multi-agent systems. The contribution of the paper is to provide firm foundations for an approach to practical reasoning based on presumptive argument in terms of a well-known model for representing the effects of actions of a group of agents. (shrink)

: Two major philosophers of the twentieth century, the German existential phenomenologist Martin Heidegger and the seminal Japanese Kyoto School philosopher Nishida Kitarō are examined here in an attempt to discern to what extent their ideas may converge. Both are viewed as expressing, each through the lens of his own tradition, a world in transition with the rise of modernity in the West and its subsequent globalization. The popularity of Heidegger's thought among Japanese philosophers, despite its own admitted limitation (...) to the Western "history of being," is connected to Nishida's opening of a uniquely Japanese path in its confrontation with Western philosophy. The focus is primarily on their later works (the post-Kehre Heidegger and the works of Nishida that have been designated "Nishida philosophy"), in which each in his own way attempts to overcome the subject-object dichotomy inherited from the tradition of Western metaphysics by looking to a deeper structure from out of which both subjectivity and objectivity are derived and which embraces both. For Heidegger, the answer lies in being as the opening of unconcealment, from out of which beings emerge, and for Nishida, it is the place of nothingness within which beings are co-determined in their oppositions and relations. Concepts such as Nishida's "discontinuous continuity," "absolutely self-contradictory identity" (between one and many, whole and part, world and things), the mutual interdependence of individuals, and the self-determination of the world through the co-relative self-determination of individuals, and Heidegger's "simultaneity" (zugleich) and "within one another" (ineinander) (of unconcealment and concealment, presencing and absencing), and their "between" (Zwischen) and "jointure" (Fuge) are examined. Through a discussion of these ideas, the suggestion is made of a possible "transition" (Übergang) of both Western and Eastern thinking, in their mutual encounter, both in relation to each other and each in relation to its own past history, leading to both a self-discovery in the other and to a simultaneous self-reconstitution. (shrink)

In this paper I articulate a minimal conception of the idea of doing philosophy that informs a curriculum and pedagogy for producing students who are capable of engaging in philosophical activity and not just competent with a specific domain of knowledge. The paper then relates, by way of background, the departmental assessment practices that have played a vital role in the development of my department’s current curriculum and in particular in the design of a junior-year seminar in philosophical research required (...) of all majors. After a brief survey of the learning theory literature that has informed its design, I share the content of this junior-year seminar. In the paper’s conclusion I provide some initial data that indicates our approach to curriculum and pedagogy has had a positive impact on student achievement with respect to reaching the learning goals associated with “doing” as opposed to “merely studying” philosophy. (shrink)

This article explores the transition to integrated reporting by a customer-owned bank and identifies the drivers of this transition, thereby providing insights for other businesses seeking to engage in such reporting. Practice theory provides a theoretical lens for this study. A case study approach encompassing in-depth interviews and documents analysis enabled the data to be collected for this research. This study finds that a customer-owned business context enables innovative approaches to reporting. An understanding of reporting and recognition of (...) the potential value of integrated reporting, basic guidelines for such a practice, and organisational ethical values and goals based on a combination of economic, social and environmental considerations matched by an organisational structure that embeds economic, social and environmental responsibilities rather than treating these as separate silos, enabled Goodbank to transition to integrated reporting and differentiate itself from its competitors and other organisations. (shrink)

We study the strictness of the modal μ-calculus hierarchy over some restricted classes of transition systems. First, we prove that over transitive systems the hierarchy collapses to the alternationfree fragment. In order to do this the finite model theorem for transitive transition systems is proved. Further, we verify that if symmetry is added to transitivity the hierarchy collapses to the purely modal fragment. Finally, we show that the hierarchy is strict over reflexive frames. By proving the finite model (...) theorem for reflexive systems the same results holds for finite models. (shrink)

A successful energy transition is multifaceted and requires a list of social metrics to be met, which the fossil fuel industry was never obliged to satisfy. The comprehensive set of social metrics include addressing public acceptance, community engagement, social innovation, governance mechanisms, and social justice implications, a set which seems rather excessive for an industry that promises to heal the world from its carbon problem. This chapter argues that while seemingly broad-ranging, these social metrics are unilateral in so far (...) as they capture a neoliberal worldview defined by resource-thinking. I aim to recast some of this thinking through the philosophical treatment of place attachment beyond a GPS coordinate or as the location of emotional responsiveness. More than a social license to operate, I argue that the many social challenges expected to be met for a successful energy transition are more appropriately considered cultural. (shrink)

Offers a detailed exposition of Wittgenstein's philosophy as a continuous engagement with a single set of problems. The author argues that the key to understanding the transition in Wittgenstein's thought is his 1929 essay ""Some Remarks on Logical Form"" which is reprinted in this book.

Inside the family, all individuals define their identity in relation to previous generations, the present ones, and the future ones. This intergenerational exchange plays important educational roles: it fosters a sense of belonging and identification, promotes dialogue, and guarantees the passing down of ethical orientations. In addition to feelings of security and reliance on others, family memory creates a matrix that gives people a placement in the world, a sort of existential code through which to be located in existence. Fostering (...) the habit of memory-making becomes therefore a major educational imperative, which however is not without challenges. The present contribution will consider those phenomena which can give rise to a weakening of bonds between generations and a growing exclusion of the ethical value of family heritage. The educational perspective that will be drawn is that of building a sense of alliance.. (shrink)

The emergence of individuality during the evolutionary transition from single cells to multicellularity poses a range of problems. A key issue is how variation in lower‐level individuals generates a corporate (collective) entity with Darwinian characteristics. Of central importance to this process is the evolution of a means of collective reproduction, however, the evolution of a means of collective reproduction is not a trivial issue, requiring careful consideration of mechanistic details. Calling upon observations from experiments, we draw attention to proto‐life (...) cycles that emerge via unconventional routes and that transition, in single steps, individuality to higher levels. One such life cycle arises from conflicts among levels of selection and invokes cheats as a primitive germ line: it lays the foundation for collective reproduction, the basis of a self‐policing system, the selective environment for the emergence of development, and hints at a plausible origin for a soma/germ line distinction. (shrink)