We give an example of a structure equation image on the real line, and a manifold M definable in equation image, such that M is definably connected but is not connected.

The concept of constructive negation we refer to in this paper is (minimally) intuitionistic in character (see [1]). The idea is to understand the negation of a proposition A as equivalent to A implying a falsity constant of some sort. Then, negation is introduced either by means of this falsity constant or, as in this paper, by means of a propositional connective defined with the constant. But, unlike intuitionisitc logic, the type of negation we develop here is, of course, devoid (...) of paradoxes of relevance. (shrink)

Aphantasia is a condition characterised by a deficit of mental imagery. Since several psychopathologies are partially maintained by mental imagery, it may be illuminating to consider the condition against the background of psychological disorder. After outlining current findings and hypotheses regarding aphantasia and psychopathology, this paper suggests that some support for defining aphantasia as a lack of voluntary imagery may be found here. The paper then outlines potentially fruitful directions for future research into aphantasia in general and its relation to (...) psychopathology in particular, including rethinking use of the SUIS to measure involuntary imagery, whether aphantasia offers protection against addiction, and whether hyperphantasia is a potential risk factor for maladaptive daydreaming, among others. (shrink)

The Converse Ackermann Property is the unprovability of formulas of the form (A -> B) -> C when C does contain neither -> nor ¬. Intuitively, the CAP amounts to rule out the derivability of pure non-necessitive propositions from non-necessitive ones. A constructive negation of the sort historically defined by, e.g., Johansson is added to positive logics with the CAP in the spectrum delimited by Ticket Entailment and Dummett’s logic LC.

Conceptual analysis, like any exclusively theoretical activity, is far from overrated in current psychology. Such a situation can be related both to the contingent influences of contextual and historical character and to the more essential metatheoretical reasons. After a short discussion of the latter it is argued that even within a strictly empirical psychology there are non-trivial tasks that can be attached to well-defined and methodologically reliable, conceptual work. This kind of method, inspired by the ideas of Ludwig Wittgenstein, Peter (...) Strawson (conceptual grammar), and Gilbert Ryle (conceptual geography), is proposed and formally depicted as being holistic, descriptive, and connective. Finally, the newly presented framework of connective conceptual analysis is defended against the “Charge from Psychology,” in a version developed by William Ramsey, claiming that conceptual analysis is based on psychological assumptions that have already been refuted by empirical psychology. (shrink)

The variably strict analysis of conditionals does not only largely dominate the philosophical literature, since its invention by Stalnaker and Lewis, it also found its way into linguistics and psychology. Yet, the shortcomings of Lewis–Stalnaker’s account initiated a plethora of modifications, such as non-vacuist conditionals, presuppositional indicatives, perfect conditionals, or other conditional constructions, for example: reason relations, difference-making conditionals, counterfactual dependency, or probabilistic relevance. Many of these new connectives can be treated as strengthened or weakened conditionals. They are definable conditionals. (...) This article develops a technique to infer the logic for such definable conditionals from the known logic of the underlying defining conditional. The technique is applied to central examples. The results show that a large part of the zoo of conditionals arises from a basic conditional—a constant nucleus of the different contextual and conceptual variations of variably strict conditionals. (shrink)

Let M be an o-minimal expansion of a real closed field. Let G be a definably compact definably connected abelian n-dimensional group definable in M. We show the following: the o-minimal fundamental group of G is isomorphic to ℤn; for each k>0, the k-torsion subgroup of G is isomorphic to n, and the o-minimal cohomology algebra over ℚ of G is isomorphic to the exterior algebra over ℚ with n generators of degree one.

We study randomizations of definable groups. Whenever the underlying theory is stable or NIP and the group is definably amenable, we show its randomization is definably connected.

Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a 'definable quotient group' U/L, for some convex V-definable subgroup U of 〈Mⁿ, +〉 and a lattice L of rank n. As two consequences, (...) we derive Pillay's conjecture for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L. (shrink)

Let [Formula: see text] be an expansion of either an ordered field [Formula: see text], or a valued field [Formula: see text]. Given a definable set [Formula: see text] let [Formula: see text] be the ring of continuous definable functions from [Formula: see text] to [Formula: see text]. Under very mild assumptions on the geometry of [Formula: see text] and on the structure [Formula: see text], in particular when [Formula: see text] is [Formula: see text]-minimal or [Formula: see text]-minimal, or (...) an expansion of a local field, we prove that the ring of integers [Formula: see text] is interpretable in [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] is definably connected of pure dimension [Formula: see text], then [Formula: see text] defines the subring [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] has no isolated points, then there is a discrete ring [Formula: see text] contained in [Formula: see text] and naturally isomorphic to [Formula: see text], such that the ring of functions [Formula: see text] which take values in [Formula: see text] is definable in [Formula: see text]. (shrink)

We study definable groups in dense/codense expansions of geometric theories with a new predicate P such as lovely pairs and expansions of fields by groups with the Mann property. We show that in such expansions, large definable subgroups of groups definable in the original language \ are also \-definable, and definably amenable \-definable groups remain amenable in the expansion. We also show that if the underlying geometric theory is NIP, and G is a group definable in a model of (...) T, then the connected component \ of G in the expansion agrees with the connected component \ in the original language. We prove similar preservation results for \^n\), the P-part of G in a lovely pair, and for subgroups of G in pairs where R is a real closed field and G is a subgroup of \ or the unit circle \\) with the Mann property. (shrink)

We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. 18 885–903]. Let [Formula: see text] be an abelian semialgebraic group over a real closed field [Formula: see text] and let [Formula: see text] be a semialgebraic subset of [Formula: see text]. Then the group generated by [Formula: see text] contains a generic set and, if connected, it is divisible. More generally, the same result holds (...) when [Formula: see text] is definable in any o-minimal expansion of [Formula: see text] which is elementarily equivalent to [Formula: see text]. We observe that the above statement is equivalent to saying: there exists an [Formula: see text] such that [Formula: see text] is an approximate subgroup of [Formula: see text]. (shrink)

An argument of A. Borel [Bor—61, Proposition 3.1] shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an o-minimal expansion of a real closed field. As opposed to the Lie case, however, we provide an example showing that the derived subgroup may not have a definable semidirect complement.

An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all (...) connectives defined implicitly by axiomatic extensions of the logic are explicitly definable. (shrink)

We explore the notion of a measure in a mereological structure and we deal with the difficulties arising. We show that measure theory on connection spaces is closely related to measure theory on the class of ortholattices and we present an approach akin to Dempster’s and Shafer’s. Finally, the paper contains some suggestions for further research.

We prove that there exists no sentence F of the language of rings with an extra binary predicat I2 satisfying the following property: for every definable set X ⊆ ℂ2, X is connected if and only if ⊧ F, where I2 is interpreted by X. We conjecture that the same result holds for closed subset of ℂ2. We prove some results motivated by this conjecture.

Political extremism remains relatively insufficiently explored due to the fact that the phenomenon is controversial and hard to define. Its ambiguity and variability depending on time and spatial point of view further complicates its definition. Its structure is amorphous and eclectic as it often includes elements from different ideologies and connects incompatible ideas. A multidimensional conceptualization and an interdisciplinary approach - sociological, social, psychological and historical, are the Author’s tools in explaining the phenomenon of political extremism in Serbia, hopefully contributing (...) to its clarification and laying a foundation for its further explanatory theoretical studies. (shrink)

We are currently witnessing the emergence of new forms of collective identities and a redefinition of the old ones through networked digital interactions, and these can be explicitly measured and analyzed. We distinguish between three major trends on the development of the concept of identity in the social realm: (1) an essentialist sense (based on conditions and properties shared by members of a group), (2) a representational or ideational sense (based on the application of categories by oneself or others), and (...) (3) a relational and interactional sense (based on interaction processes between actors and their environments). The interactional approach aligns with current empirical and methodological progress in social network analysis. Moreover, it has been argued that, within the network society, the notion of collective identity (Melucci, 1995) in the political field must be rethought as technologically mediated and interactive. We suggest that collective identities should be understood as recurrent, cohesive, and coordinated communicative interaction networks. We here propose that such identities can be depicted by: (a) mapping and filtering a relevant interaction network, (b) delimiting a set of communities, (c) determining the strongly connected component(s) of such communities (the core identity) in a directed graph, and (d) defining the identity audiences and sources within the community. This technical graph–theoretical characterization is explained and justified in... (shrink)

To support healthcare professionals in dealing with ethically difficult situations, Clinical Ethics Support (CES) services like Moral Case Deliberation (MCD) are increasingly implemented. To assess the impact of CES, it is important to evaluate outcomes. Despite general claims about outcomes from MCD experts and some qualitative research, there exists no conceptual analysis of outcomes yet. Therefore, the aim of this study was to systematically define and categorize MCD outcomes. An additional aim was to compare these outcomes with the outcomes in (...) the Euro-MCD Instrument from 2014, to further validate this Instrument. The concept mapping method was used and involves qualitative and quantitative steps including brainstorming, individual structuring, computation of concept maps (by principal component analysis and cluster analysis), group interpretation and utilization. In total, 12 experienced MCD participants from a variety of professional backgrounds participated in two sessions. The focus group brainstorm resulted in a list of 85 possible MCD outcomes, of which a point map and concept maps were constructed. After a thorough discussion of each cluster, final consensus was reached on the names and position of 8 clusters of MCD outcomes: 1) Organisation and Policy; 2) Team development; 3) Personal development focused on the Other Person; 4) Personal development as Professional, focused on Skills; 5) Personal development as Professional, focused on Knowledge; 6) Personal development as an Individual; 7) Perception and Connection; and 8) Concrete action. This study explored and categorized MCD outcomes in a concept mapping focus group. When comparing the results with the Euro-MCD Instrument, our study confirms that outcomes of MCD can be categorized in clusters referring to the organisational level, team development, personal development (both as an individual and a professional) and the concrete case-level. In developing CES evaluation tools, it is important to be explicit if an outcome refers to the individual or the team, to knowledge or skills, to the organisation or the specific case. The findings will be used in the further validation of the Euro-MCD Instrument. The current study further contributes to the field of evaluating CES in general and defining outcomes of MCD in particular. (shrink)

This paper outlines the process of verbal communication of emotion as this occurs through the phases of the referential process, including arousal of an emotion schema; detailed and specific descriptions of images and episodes that are exemplars of emotion schemas; and reflection and reorganization, which may include emotion labels and other types of categorical terms. The concepts of emotion schemas and the referential process are defined in the theoretical framework of multiple code theory which includes subsymbolic sensory, visceral and motoric (...) processes, symbolic images and words. Emotion schemas are defined as clusters of representations of events incorporating similar bodily, sensory and motoric processes activated in relation to different people in different contexts. Through the referential process subsymbolic components of a schema that have been activated in a speaker or writer and that may be connected only partially to words may be evoked in a listener or reader. The concept of the emotion schemas is examined in relation to current work in emotion theory and neuroscience. The unique effects of detailed descriptions of episodes in conveying complex aspects of emotional experience are discussed, as recognized by writers, and as demonstrated in empirical research. Computerized measures of the phases of the referential process are presented, focusing particularly on the central measure, the Weighted Referential Activity Dictionary which identifies points of narrative and imagery. The operation of the function words that dominate the WRAD are examined in relation to the structure of narrative expression underlying the verbal representation of emotion schemas. (shrink)

This paper aims to connect philosophy of chemistry, green chemistry, and moral philosophy. We first characterize chemistry by underlining how chemists: co-define chemical bodies, operations, and transformations; always refer to active and context-sensitive bodies to explain the reactions under study; and develop strategies that require and intertwine with a molecular whole, its parts, and the surroundings at the same time within an explanation. We will then point out how green chemists are transforming their current activities in order to act upon (...) the world without jeopardizing life. This part will allow us to highlight that green chemistry follows the three aforementioned characteristics while including the world as a partner, as well as biodegradability and sustainability concerns, into chemical practices. In the third part of this paper, we will show how moral philosophy can help green chemists: identify the consequentialist assumptions that ground their reasoning; and widen the scope of their ethical considerations by integrating the notion of care and that of vulnerability into their arguments. In the fourth part of the paper, we will emphasize how, in return, this investigation could help philosophers querying consequentialism as soon as the consequences of chemical activities over the world are taken into account. Furthermore, we will point out how the philosophy of chemistry provides philosophers with new arguments concerning the key debate about the ‘intrinsic value’ of life, ecosystems and the Earth, in environmental ethics. To conclude, we will highlight how mesology, that is to say the study of ‘milieux’, and the concept of ‘ecumeme’ proposed by the philosopher and geographer Augustin Berque, could become important both for green chemists and moral philosophers in order to investigate our relationships with the Earth. (shrink)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor (−1)2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. (...) This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required. (shrink)

Let $\scr{M}=\langle M,+,<,0,S\rangle $ be a linear o-minimal expansion of an ordered group, and $G=\langle G,\oplus ,e_{G}\rangle $ an n-dimensional group definable in $\scr{M}$ . We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L, for some convex ${\ssf V}\text{-definable}$ subgroup U of $\langle M^{n},+\rangle $ and a lattice L of rank equal to the dimension of the 'compact part' of G.

We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space \ \) is definably homeomorphic to an affine definable space with the induced subspace topology). One of the main results says that it is sufficient for X to be regular and decompose into finitely many definably connected components.

We study connections between asymptotic structure in a Banach space and model theoretic properties of the space. We show that, in an asymptotic sense, a sequence $$ in a Banach space X generates copies of one of the classical sequence spaces $\ell_p$ or $c_0$ inside X if and only if the quantifier-free types approximated by $$ inside X are quantifier-free definable. More precisely, if $$ is a bounded sequence X such that no normalized sequence of blocks of $$ converges, then (...) the following two conditions are equivalent. There exists a sequence $$ of blocks of $$ such that for every finite dimensional subspace E of X, every quantifier-free type over $E +\overline{\rm span}\{y_n\mid n\in \mathbb{N}\}$ is quantifier-free definable. One of the following two conditions holds: there exists $1\le p 0$ and every finite dimensional subspace E of X there exists a sequence of blocks of $$ which is $$-equivalent over E to the standard unit basis of $\ell_p$; for every $\epsilon>0$ and every finite dimensional subspace E of X there exists a sequence of blocks of $$ which is $$-equivalent over E to the standard unit basis of $c_0$. Several byproducts of the proof are analyzed. (shrink)

The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spin-quantization axis, is exchanged along with the other parameters. The spin factor 2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. (...) This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required. (shrink)

An extensions by new axioms and rules of an algebraizable logic in the sense of Blok and Pigozzi is not necessarily algebraizable if it involves new connective symbols, or it may be algebraizable in an essentially different way than the original logic. However, extension whose axioms and rules define implicitly the new connectives are algebraizable, via the same equivalence formulas and defining equations of the original logic, by enriched algebras of its equivalente quasivariety semantics. For certain strongly algebraizable logics, all (...) connectives defined implicitly by axiomatic extensions of the logic are explicitly definable. (shrink)

The article puts forward a branching-style framework for the analysis of determinism and indeterminism of scientific theories, starting from the core idea that an indeterministic system is one whose present allows for more than one alternative possible future. We describe how a definition of determinism stated in terms of branching models supplements and improves current treatments of determinism of theories of physics. In these treatments, we identify three main approaches: one based on the study of equations, one based on mappings (...) between temporal realizations, and one based on branching models. We first give an overview of these approaches and show that current orthodoxy advocates a combination of the mapping- and the equations-based approaches. After giving a detailed formal explication of a branching-based definition of determinism, we consider three concrete applications and end with a formal comparison of the branching- and the mapping-based approach. We conclude that the branching-based definition of determinism most usefully combines formal clarity, connection with an underlying philosophical notion of determinism, and relevance for the practical assessment of theories. 1 Introduction2 Determinism in Philosophy of Science: Three Approaches2.1 Determinism: The core idea and how to spell it out2.2 The three approaches in more detail2.3 Representing indeterminism3 Orthodoxy: DMAP, with Invocations of DEQN4 Branching-Style Determinism 4.1 Models and realizations4.2 Faithfulness4.3 Two types of branching topologies 5 Comparing the Approaches5.1 Case studies5.2 Formal comparison of the DMAP and DBRN frameworks6 Conclusions. (shrink)

A new set of conversions for derivations in the system of sequents for intuitionistic predicate logic will be defined. These conversions will be some modifications of Zucker's conversions from the system of sequents from [11], which will have the following characteristics: (1) these conversions will be sufficient for transforming a derivation into a cut-free one, and (2) in the natural deduction the image of each of these conversions will be either in the set of conversions for normalization procedure, or an (...) identity of derivations. This will be used to give a new proof of the normalization theorem for natural deduction, as a consequence of the cut-elimination theorem for the system of sequents. (shrink)

A connected graph is called Hamilton-connected if there exists a Hamiltonian path between any pair of its vertices. Determining whether a graph is Hamilton-connected is an NP-complete problem. Hamiltonian and Hamilton-connected graphs have diverse applications in computer science and electrical engineering. The detour index of a graph is defined to be the sum of lengths of detours between all the unordered pairs of vertices. The detour index has diverse applications in chemistry. Computing the detour index for (...) a graph is also an NP-complete problem. In this paper, we study the Hamilton-connectivity of convex polytopes. We construct three infinite families of convex polytopes and show that they are Hamilton-connected. An infinite family of non-Hamilton-connected convex polytopes is also constructed, which, in turn, shows that not all convex polytopes are Hamilton-connected. By using Hamilton connectivity of these families of graphs, we compute exact analytical formulas of their detour index. (shrink)

There has recently been a good deal of controversy about Landauer's Principle, which is often stated as follows: The erasure of one bit of information in a computational device is necessarily accompanied by a generation of kTln2 heat. This is often generalised to the claim that any logically irreversible operation cannot be implemented in a thermodynamically reversible way. John Norton (2005) and Owen Maroney (2005) both argue that Landauer's Principle has not been shown to hold in general, and Maroney offers (...) a method that he claims instantiates the operation Reset in a thermodynamically reversible way. In this paper we defend the qualitative form of Landauer's Principle, and clarify its quantitative consequences (assuming the second law of thermodynamics). We analyse in detail what it means for a physical system to implement a logical transformation L, and we make this precise by defining the notion of an L-machine. Then we show that logical irreversibility of L implies thermodynamic irreversibility of every corresponding L-machine. We do this in two ways. First, by assuming the phenomenological validity of the Kelvin statement of the second law, and second, by using information-theoretic reasoning. We illustrate our results with the example of the logical transformation 'Reset', and thereby recover the quantitative form of Landauer's Principle. (shrink)

Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution to the (...) problem of many-valued truth-tables for classical sentential logic. I close by outlining the technicalities surrounding nasty connectives on many-valued truth-tables. (shrink)

In this paper we are concerned with definably, with or without parameters, complete expansions of ordered fields, i. e. those with no definable gaps. We present several axiomatizations, like being definably connected, in each of the two cases. As a corollary, when parameters are allowed, expansions of ordered fields are o-minimal if and only if all their definable subsets are finite disjoint unions of definably connected subsets. We pay attention to how simply a definable gap (...) in an expansion is so. Next we prove that over parametrically definably complete expansions of ordered fields, all one-to-one definable continuous functions are monotone and open. Moreover, in both parameter and parameter-free cases again, definably complete expansions of ordered fields satisfy definable versions of the Heine-Borel and Extreme Value theorems and also Bounded Intersection Property for definable families of closed bounded subsets. (shrink)

This paper offers a definition of social holism that makes the doctrine non-trivial but possibly true. According to that definition, the social holist maintains that people depend non-causally on interaction with one another for possession of the capacity to think; the thesis is meant to be a contingent truth but one, like physicalism, that is plausible in the light of some a priori argument and some plausible empirical assumptions. The paper also sketches an argument in support of social holism, which (...) connects with themes in a number of traditions, philosophical and sociological. The key idea is that people depend on socially shared dispositions and responses for the ability to identify - identify fallibly - the properties and other entities that they consider in each individual has to the course of thinking. (shrink)

There has recently been a good deal of controversy about Landauer's Principle, which is often stated as follows: The erasure of one bit of information in a computational device is necessarily accompanied by a generation of kTln2 heat. This is often generalised to the claim that any logically irreversible operation cannot be implemented in a thermodynamically reversible way. John Norton and Owen Maroney both argue that Landauer's Principle has not been shown to hold in general, and Maroney offers a method (...) that he claims instantiates the operation Reset in a thermodynamically reversible way. In this paper we defend the qualitative form of Landauer's Principle, and clarify its quantitative consequences. We analyse in detail what it means for a physical system to implement a logical transformation L, and we make this precise by defining the notion of an L-machine. Then we show that logical irreversibility of L implies thermodynamic irreversibility of every corresponding L-machine. We do this in two ways. First, by assuming the phenomenological validity of the Kelvin statement of the second law, and second, by using information-theoretic reasoning. We illustrate our results with the example of the logical transformation 'Reset', and thereby recover the quantitative form of Landauer's Principle. (shrink)

Connections between partially ordered connectives and Henkin quantifiers are considered. It is proved that the logic with all partially ordered connectives and the logic with all Henkin quantifiers coincide. This implies that the hierarchy of partially ordered connectives is strongly hierarchical and gives several nondefinability results between some of them. It is also deduced that each Henkin quantifier can be defined by a quantifier of the form equation imagewhat is a strengthening of the Walkoe result. MSC: 03C80.

The aim of this paper is to develop the theory of groups definable in the p-adic field ${{\mathbb {Q}}_p}$, with “definable f-generics” in the sense of an ambient saturated elementary extension of ${{\mathbb {Q}}_p}$. We call such groups definable f-generic groups.So, by a “definable f-generic” or $dfg$ group we mean a definable group in a saturated model with a global f-generic type which is definable over a small model. In the present context the group is definable over ${{\mathbb {Q}}_p}$, and (...) the small model will be ${{\mathbb {Q}}_p}$ itself. The notion of a $\mathrm {dfg}$ group is dual, or rather opposite to that of an $\operatorname {\mathrm {fsg}}$ group (group with “finitely satisfiable generics”) and is a useful tool to describe the analogue of torsion-free o-minimal groups in the p-adic context.In the current paper our group will be definable over ${{\mathbb {Q}}_p}$ in an ambient saturated elementary extension $\mathbb {K}$ of ${{\mathbb {Q}}_p}$, so as to make sense of the notions of f-generic type, etc. In this paper we will show that every definable f-generic group definable in ${{\mathbb {Q}}_p}$ is virtually isomorphic to a finite index subgroup of a trigonalizable algebraic group over ${{\mathbb {Q}}_p}$. This is analogous to the o-minimal context, where every connected torsion-free group definable in $\mathbb {R}$ is isomorphic to a trigonalizable algebraic group [5, Lemma 3.4]. We will also show that every open definable f-generic subgroup of a definable f-generic group has finite index, and every f-generic type of a definable f-generic group is almost periodic, which gives a positive answer to the problem raised in [28] of whether f-generic types coincide with almost periodic types in the p-adic case. (shrink)

Although the theory of definability had many important antecedents—such as the descriptive set theory initiated by the French semi-intuitionists in the early 1900s—the main ideas were first laid out in precise mathematical terms by Alfred Tarski beginning in 1929. We review here the basic notions of languages, explicit definability, and grammatical complexity, and emphasize common themes in the theories of definability for four important languages underlying, respectively, descriptive set theory, recursive function theory, classical pure logic, and finite-universe logic. We review (...) the history of previous studies of the similarities and differences in the theories of definability of the first three of these four languages. A seminal role leading toward unification of the theories has been played by the separation principles introduced by Nikolai Luzin in 1927. Emphasizing analogies and driving toward further unification embracing finite-universe logic we concentrate on a simple example—the first and second separation principles for existential-universal first-order sentences . Using this as a test case for the fundamental problem of how to “finitize” arguments in classical pure logic to the finite-universe case, we are led to the analogous negative solution by using the theory of certain special graphs: a graph is - special for any positive integers m , n , p , q iff it is bipartite with m red points and n blue points and for every p -tuple of red points there is a blue point to which they are all connected . As an aside we introduce for further study a natural “Ramseyesque” increasing sequence A of positive integers, where A is the least positive integer n for which an -special graph exists. (shrink)

Heather M. Farley and Zachary A. Smith, Sustainability: If It’s Everything, Is It Nothing? xiv + 176 pp., index. New York: Routledge, 2014. $39.95 Leslie Paul Thiele, Sustainability. viii + 234 p., bibl., index. New York: Polity Press, 2013. $22.95 The authors of both of these books offer new definitions of sustainability. They do so in order to battle “faux interpretations” or “hypocritical” or “unsupported endorsements” of sustainability. While I think many people, including I expect many readers of this journal, (...) would agree that sustainability is a rather imprecise concept that sometimes gets misused, I am not convinced the definitions in these books offer a way forward. Partly this is due to the specific ways the authors develop their discussions, and partly it is due to issues connected to their shared methodological approach, viz. the search for a new, univocal, strong definition. After discussing each book, I examine briefly that shared .. (shrink)

This article discusses female office workers' own definitions of information technology, based on a study with a group of Finnish office workers, in which they studied and evaluated information systems and analysed their work as well as making proposals for their IT systems. IT is considered as a textuality that is connected with the office workers' subjectivities and their organizational activities. For office workers, defining information systems means a struggle for their own subjectivities. Starting from the concrete practices and (...) interviews with the office workers, the article examines how their 'own' definitions of IT were constructed; how office workers' situated interpretations and textualities interacted; how organizational relations and textualities intervened in the definitions; and how women's mutual support made it possible to approach something that could be considered women's 'own' definitions. (shrink)

If the contemporaneity of difference seems the most striking characteristic of contemporary life today, its conceptual structure continues to elude definition. The same lack of clarity attends a frequently evoked parameter for the most desired resolution of such volatile differences: a cohesive, consensual world picturing, sometimes named “planetarity.” My overall project is a close examination of these two concepts, aimed at finding productive connections between them. Previous attempts to think them, from the confessions of St Augustine to the New York (...) Times columns of Thomas Friedman, reveal a plethora of illuminating insights, but the overall record reveals that both concepts remain inadequately imagined for current circumstances. Temporality and world-being seems to constellate around these concepts: contemporaneity, history, decoloniality, connectivity, artworlds, and planetarity. How might the contemporaneity of difference and the embattled yet emergent planetary commons be imagined in terms appropriate to present need – that is, as contemporaneous, differential and convergent? While this question is obviously of the broadest relevance, my specific goal within the history and theory of art and architecture is to articulate the conceptual structure underlying my recent accounts of the relationships between contemporary art and architecture and contemporary life. (shrink)

The word _meṇḍaka_, a derivative of _meṇḍa_ (“ram”), is generally translated as “made of the ram” or “about the ram” or “horned.” However, in the Pāli _Milindapañha_ (_Questions of Milinda_), the word _meṇḍakapañha_, literally, a question about the ram, is also rendered as a logical conclusion that refutes an imaginary dilemma. Hence, in this treatise, the word _meṇḍaka_ is a special logical term which means an imaginary dilemma that can be logically refuted. This raises the question as to why the (...) word _meṇḍaka_ has come to be associated with this logical technique. To answer this question, this paper examines various aspects of the word and its possible connections to a dilemma and its refutation. The discussion ranges from the meaning of this word in a tale in the _Jātaka_ (Birth Stories), within the contextual usage in a _meṇḍaka_ question, to a relatively recent commentarial text (_aṭṭhakathā_) which gives a different perspective on the etymology of the word. The _Milindapañha_ is explicit in defining a _meṇḍaka_ question as knotty, hard to penetrate, and difficult to resolve, some of which an opponent puts forth to undermine certain aspects of the Buddhist system. However, the way certain _meṇḍaka_ questions are framed, though not directly stated, seem to utilize the principles of logic in a dilemmatic form of argument. With that, a _meṇḍaka_ question, at least in the _Milindapañha_, could also mean “a dilemmatic expression put forth by a challenger to undermine an opponent, but which can be logically refuted.”. (shrink)