An adequate semantics for generic sentences must stake out positions across a range of contested territory in philosophy and linguistics. For this reason the study of generic sentences is a venue for investigating different frameworks for understanding human rationality as manifested in linguistic phenomena such as quantification, classification of individuals under kinds, defeasible reasoning, and intensionality. Despite the wide variety of semantic theories developed for generic sentences, to date these theories have been almost universally model-theoretic and representational. This essay outlines (...) a range of proof-theoretic analyses for characterizing generics. Particular attention is given to an expressivist proof-theory that can be traced to 1) work on logical syntax that Carnap undertook prior to his turn toward truth-conditional model theory in the late 1930s, and 2) research on sequent calculi and natural deduction systems that originate in work from Gentzen and Prawitz.1. (shrink)

A generic computation of a subsetAof ℕ is a computation which correctly computes most of the bits ofA, but which potentially does not halt on all inputs. The motivation for this concept is derived from complexity theory, where it has been noticed that frequently, it is more important to know how difficult a type of problem is in the general case than how difficult it is in the worst case. When we study this concept from a recursion theoretic point of (...) view, to create a transitive relationship, we are forced to consider oracles that sometimes fail to give answers when asked questions. Unfortunately, this makes working in the generic degrees quite difficult. Indeed, we show that generic reduction is$\Pi _1^1$―complete. To help avoid this difficulty, we work with the generic degrees of density-1 reals. We demonstrate how an understanding of these degrees leads to a greater understanding of the overall structure of the generic degrees, and we also use these density-1 sets to provide a new a characterization of the hyperartithmetical Turing degrees. (shrink)

Virtuosity in music performance is often associated with fast, precise, and efficient sound-producing movements. The generation of such highly skilled movements involves complex joint and muscle control by the central nervous system, and depends on the ability to anticipate, segment, and coarticulate motor elements, all within the biomechanical constraints of the human body. When successful, such motor skill should lead to what we characterize as fluency in musical performance. Detecting typical features of fluency could be very useful for technology-enhanced learning (...) systems, assisting and supporting students during their individual practice sessions by giving feedback and helping them to adopt sustainable movement patterns. In this study, we propose to assess fluency in musical performance as the ability to smoothly and efficiently coordinate while accurately performing slow, transitionary, and rapid movements. To this end, the movements of three cello players and three drummers at different levels of skill were recorded with an optical motion capture system, while a wireless electromyogrphy (EMG) system recorded the corresponding muscle activity from relevant landmarks. We analyze the kinematic and coarticulation characteristics of these recordings separately and then propose a combined model of fluency in musical performance predicting music sophistication. Results suggest movements from expert performers' are characterized by consistently smooth strokes and scaling of muscle phasic coactivation. The explored model of fluency as function of movement smoothness and coarticulation patterns was shown to be limited by the sample size but serves as a proof of concept. Results from this study show the potential of a technology-enhanced objective measure of fluency in musical performance, which could lead to improved practices for aspiring musicians, instructors, and researchers. (shrink)

When thinking about the notion of essence or of an essential feature, philosophers typically focus on what I will call the notion of objectual essence. The main aim of this paper is to argue that beside this familiar notion stands another one, the notion of generic essence, which contrary to appearance cannot be understood in terms of the familiar notion, and which also fails to be correctly characterized by certain other accounts which naturally come to mind as well. Some of (...) my objections to these accounts are similar to some of Kit Fine’s compelling objections to the standard modal account of (objectual) essence (Fine 1994). In the light of these objections, Fine advances the view that it is metaphysical necessity which has to be understood in terms of essence, rather than the other way around, and takes essence to be unanalyzable. When formulatinghis view, Fine had only objectual essence in mind (or had both concepts in mind, but assumed that the generic is a special case of the objectual), and for that reason, I will argue, his account fails. I will suggest that Fineans should modify their view, and take it that metaphysical necessity is to be understood in terms of the two notions of essence—a view I myself find appealing. Finally, I will end by suggesting a further move which reduces the objectual to the generic, making metaphysical necessity reducible to generic essence alone—a move with which I myself have some sympathy. (shrink)

Our knowledge about the world is often expressed by generic sentences, yet their meanings are far from clear. This book provides answers to central problems concerning generics: what do they mean? Which factors affect their interpretation? How can one reason with generics? Cohen proposes that the meanings of generics are probability judgments, and shows how this view accounts for many of their puzzling properties, including lawlikeness. Generics are evaluated with respect to alternatives. Cohen argues that alternatives (...) are induced by the kind as well as by the predicated property, and thus provides a uniform account of the varied interpretations of generics. He studies the formal properties of alternatives and provides a compositional account of their derivation by focus and presupposition. Cohen uses his semantics of generics to provide a formal characterization of adequate default reasoning, and proves some desirable results of this formalism. (shrink)

Generic sentences (e.g., bare plural sentences such as “dogs have four legs” and “mosquitoes carry malaria”) are used to talk about kinds of things. Three experiments investigated the conceptual foundations of generics as well as claims within the formal semantic approaches to generics concerning the roles of prevalence, cue validity and normalcy in licensing generics. Two classes of generic sentences that pose challenges to both the conceptually based and formal semantic approaches to generics were investigated. Striking (...) property generics (e.g. “sharks bite swimmers”) are true even though only a tiny minority of instances have the property and thus pose obvious problems for quantificational approaches, and they also do not seem to characterize kinds in terms of the principled or statistical connections investigated in previous research ( Prasada and Dillingham, 2006 ; Prasada and Dillingham, 2009). The second class — minority characteristic generics (e.g. “ducks lay eggs”) — also poses serious problems for quantificational accounts, and appears to involve principled connections even though fewer than half of its instances have the relevant property. The experiments revealed three principal discoveries: first, striking generics involve neither principled nor statistical connections. Instead, they involve a causal connection between a kind and a property. Second, minority characteristic generics exhibit the characteristics of principled connections, which suggests that principled connections license the expectation that most instances will have the property, but do not require it. Finally, the experiments also provided evidence that prevalence and the acceptability of generics may be dissociated and provided data that are problematic for normalcy approaches to generics, and for the idea that cue validity licenses low prevalence generics. As such, the studies provided evidence in favor of a conceptually based approach to the semantics of generics ( Leslie, 2007 ; Leslie, 2008; see also Carlson, 2009). (shrink)

This paper is concerned with the semantics of bare plural I-generics such as ‘Tigers are striped’, ‘Chickens lay eggs’, and ‘Kangaroos live in Australia’. In a series of recent papers, Bernhard Nickel has developed a comprehensive view of a certain class of bare plural I-generics, which he calls characterizing sentences :629–648, 2009. doi:10.1007/s10988-008-9049-7; Linguist Philos 33:479–512, 2010a. doi:10.1007/s10988-011-9087-4; Philos Impr 10:1–25, 2010b). Nickel’s ambitious proposal includes a detailed account of their truth-conditions, an account of certain pragmatic phenomena (...) that they give rise to, a metaphysical picture of their truth-makers in terms of mechanisms, and an epistemological story connecting characterizing sentences to such concepts as induction and explanation. This paper offers an extended critique of the central truth-conditional component of Nickel’s proposal. In a nutshell, his account has it that ‘Tigers are striped’ is true iff, for tigers, there is a way of being normal with respect to fur-pattern such that all tigers that are normal that way are striped. I begin by explaining what characterizing sentences are and distinguish several readings that are available for sentences with bare plurals in subject position. I then introduce Nickel’s account and discuss some of its predictions which, in my view, seem highly problematic. Moreover, I argue that Nickel’s principle of Homogeneity does not go together well with his proposed truth-conditions, and that his truth-conditional account violates a plausible principle about the logic of generics, a principle I call generic non-contradiction. (shrink)

It is natural to wish to study miniaturisations of Cohen forcing suitable to sets of low arithmetic complexity. We consider extensions of the work of Schaeffer [9] and Jockusch and Posner [6] by looking at genericity notions within the Δ2 sets. Different equivalent characterisations of 1-genericity suggest different ways in which the definition might be generalised. There are two natural ways of casting the notion of 1-genericity: in terms of sets of strings and in terms of density functions, as we (...) will see here. While these definitions coincide at the first level of the difference hierarchy, they turn out to differ at other levels. Furthermore, these differences remain when the remainder of the Δ02 sets are considered. While the string characterization of 1-genericity collapses at the second level of the difference hierarchy to 2-genericity, the density function definition gives a very interesting hierarchy at level w and above. Both of these results point towards the deep similarities exhibited by the n-c.e. degrees for n ≥ 2. (shrink)

The goal of this paper is to facilitate ongoing dialogue between open and non-open theists. First, I try to make precise what open theism is by distinguishing the core commitments of the position from other secondary and optional commitments. The result is a characterization of ‘generic open theism’, the minimal set of commitments that any open theist, qua open theist, must affirm. Second, within the framework of generic open theism, I distinguish three important variants and discuss challenges distinctive to each. (...) The significance of this approach is that it helps avoid conflating arguments bearing on specific versions of open theism with arguments pertaining to open theism simpliciter. (shrink)

This article1 investigates a particular use of generic sentences (or “characterizing” sentences, in the terminology of Krifka e.a. 1995), which is most prevalent with indefinite singular subjects. Such subjects cannot always be interchanged with bare plural NPs, as has been famously pointed out by Lawler (1973).

For a supersimple SU-rank 1 theory T we introduce the notion of a generic elementary pair of models of T . We show that the theory T* of all generic T-pairs is complete and supersimple. In the strongly minimal case, T* coincides with the theory of infinite dimensional pairs, which was used in 1184–1194) to study the geometric properties of T. In our SU-rank 1 setting, we use T* for the same purpose. In particular, we obtain a characterization of linearity (...) for SU-rank 1 structures by giving several equivalent conditions on T*, find a “weak” version of local modularity which is equivalent to linearity, show that linearity coincides with 1-basedness, and use the generic pairs to “recover” projective geometries over division rings from non-trivial linear SU-rank 1 structures. (shrink)

Beginning with analyses of English generic sentences and English plural indefinite noun phrases (e.g.dogs), we proceed to apply mechanisms there motivated to a characterization of atemporalwhen, a sense ofwhen which does not appear to involve time. Dealt with are such examples as Dogs are intelligent when they have blue eyes, and their relationships to examples like Dogs that have blue eyes are intelligent. The proposed treatment of atemporalwhen helps motivate the existence of a generic verb phrase operator in English, as (...) well as the treatment of indefinite plural noun phrases as disguised definite descriptions. (shrink)

LetMbe a countably infinite ω-categorical structure. Consider Aut(M) as a complete metric space by definingd(g, h) = Ω{2−n:g(xn) ≠h(xn) org−1(xn) ≠h−1(xn)} where {xn:n∈ ω} is an enumeration ofMAn automorphism α ∈ Aut(M) is generic if its conjugacy class is comeagre. J. Truss has shown in [11] that if the set P of all finite partial isomorphisms contains a co-final subset P1closed under conjugacy and having the amalgamation property and the joint embedding property then there is a generic automorphism. In the (...) present paper we give a weaker condition of this kind which is equivalent to the existence of generic automorphisms. Really we give more: a characterization of the existence of generic expansions (defined in an appropriate way) of an ω-categorical structure. We also show that Truss' condition guarantees the existence of a countable structure consisting of automorphisms ofMwhich can be considered as an atomic model of some theory naturally associated toM. We do it in a general context of weak models for second-order quantifiers.The author thanks Ludomir Newelski for pointing out a mistake in the first version of Theorem 1.2 and for interesting discussions. Also, the author is grateful to the referee for very helpful remarks. (shrink)

In the early nineties of the previous century, leaf languages were introduced as a means for the uniform characterization of many complexity classes, mainly in the range between P and PSPACE . It was shown that the separability of two complexity classes can be reduced to a combinatorial property of the corresponding defining leaf languages. In the present paper, it is shown that every separation obtained in this way holds for every generic oracle in the sense of Blum and Impagliazzo. (...) We obtain several consequences of this result, regarding, e. g., universal oracles, simultaneous separations and type-2 complexity. (shrink)

Thomas Crisp has attempted to revive something akin to Alvin Plantinga’s Principle of Dwindling Probabilities to argue that the historical case for the resurrection of Jesus does not make the posterior probability of the resurrection very high. I argue that Crisp’s argument fails because he is attempting to evaluate a concrete argument in an a priori manner. I show that the same moves he uses would be absurd in other contexts, as applied both to our acquaintance with human beings and (...) to evidence for divine intervention. Crisp’s attempt to relate the evidence for a specific act of God such as the resurrection to generic theism, thereby creating skepticism about the power of the evidence, is symptomatic of a larger problem in the philosophy of religion which I dub “separationism” and which has characterized the work of both advocates of classical apologetics and philosophers of science. (shrink)

Let I be an F σ -ideal on natural numbers. We characterize the ultrafilters which are generic over the model L for the poset of I -positive sets of natural numbers ordered by inclusion.

This paper deals with the exceptions-tolerance property of generic sentences with indefinite singular and bare plural subjects (IS and BP generics, respectively) and with the way this property is connected to some well-known observations about felicity differences between the two types of generics (e.g. Lawler's 1973, Madrigals are popular vs. #A madrigal is popular). I show that whereas both IS and BP generics tolerate exceptional and contextually irrelevant individuals and situations in a strikingly similar way, which indicates (...) the existence of a basically equivalent tolerance mechanism, there is also a difference between them, unnoticed so far, which concerns the degree to which the properties of the legitimate exceptions can be characterized in advance. Following claims in Greenberg (2003), I argue that both this newly observed difference as well as the traditional felicity differences result from an underlying contrast in the type of ‘non-accidentalness’ expressed by the two types of generic sentences, and more formally, in the accessibility relations that their generic quantifier (Gen) is compatible with. To capture the new difference in tolerance of exceptions, I develop an improved version of the exceptions-tolerance mechanism for generic sentences suggested in Kadmon & Landman (1993), namely, a restriction on the set of individuals and situations quantified by Gen, which is partially vague to two different degrees using supervaluationist methods. The different degrees of vagueness in this restriction are shown to be systematically dependent on the two types of accessibility relations that IS and BP generics are compatible with, which are redefined as precise and vague restrictions on the generic quantification over worlds. (shrink)

We use model theoretic forcing to study and generalize the construction of ()-generic models introduced by Kueker and Laskowski. We characterize the ()-generic models in terms of forcing and introduce a more general class of models, called essential forcing generics, which have many of the same properties.

This article addresses the question which structures occur as fixed structures of stable structures with a generic automorphism. In particular we give a Galois theoretic characterization. Furthermore, we prove that any pseudofinite field is the fixed field of some model ofACFA, any one-free pseudo-differentially closed field of characteristic zero is the fixed field of some model ofDCFA, and that any one-free PAC field of finite degree of imperfection is the fixed field of some model ofSCFA.

In NIP theories, generically stable Keisler measures can be characterized in several ways. We analyze these various forms of “generic stability” in arbitrary theories. Among other things, we show that the standard definition of generic stability for types coincides with the notion of a frequency interpretation measure. We also give combinatorial examples of types in NSOP theories that are finitely approximated but not generically stable, as well as ϕ-types in simple theories that are definable and finitely satisfiable in a small (...) model, but not finitely approximated. Our proofs demonstrate interesting connections to classical results from Ramsey theory for finite graphs and hypergraphs. (shrink)

Numerous results about capturing complexity classes of queries by means of logical languages work for ordered structures only, and deal with non-generic, or order-dependent, queries. Recent attempts to improve the situation by characterizing wide classes of finite models where linear order is definable by certain simple means have not been very promising, as certain commonly believed conjectures were recently refuted (Dawar's Conjecture). We take on another approach that has to do with normalization of a given order (rather than with (...) defining a linear order from scratch). To this end, we show that normalizability of linear order is a strictly weaker condition than definability (say, in the least fixpoint logic), and still allows for extending Immerman-Vardi-style results to generic queries. It seems to be the weakest such condition. We then conjecture that linear order is normalizable in the least fixpoint logic for any finitely axiomatizable class of rigid structures. Truth of this conjecture, which is a strengthened version of Stolboushkin's conjecture, would have the same practical implications as Dawar's Conjecture. Finally, we suggest a series of reductions of the two conjectures to specialized classes of graphs, which we believe should simplify further work. (shrink)

We discuss a notion of forcing that characterizes enumeration 1-genericity, and we investigate the immunity, lowness, and quasiminimality properties of enumeration 1-generic sets and their degrees. We construct an enumeration operator Δ such that, for any A, the set ΔA is enumeration 1-generic and has the same jump complexity as A. We deduce from this and other recent results from the literature that not only does every degree a bound an enumeration 1-generic degree b such that a'=b', but also that, (...) if a is nonzero, then we can find such b satisfying 0eshrink)

When dealing with a certain class of physical systems, the mathematical characterization of a generic system aims to describe the phase portrait of all its possible states. Because they are defined only up to isomorphism, the mathematical objects involved are “schematic structures”. If one imposes the condition that these mathematical definitions completely capture the physical information of a given system, one is led to a strong requirement of individuation for physical states. However, we show there are not enough qualitatively distinct (...) properties in an abstract Hilbert space to fulfill such a requirement. It thus appears there is a fundamental tension between the physicist’s purpose in providing a mathematical definition of a mechanical system and a feature of the basic formalism used in the theory. We will show how group theory provides tools to overcome this tension and to define physical properties. (shrink)

A generalization of Příkrý's forcing is analyzed which adjoins to a model of ZFC a set of order type at most ω below each member of a discrete set of measurable cardinals. A characterization of generalized Příkrý generic sequences reminiscent of Mathias' criterion for Příkrý genericity is provided, together with a maximality theorem which states that a generalized Příkrý sequence almost contains every other one lying in the same extension.This forcing can be used to falsify the covering lemma for a (...) higher core model if there is an inner model with infinitely many measurable cardinals – changing neither cardinalities nor cofinalities. Another application is an alternative proof of a theorem of Mitchell stating that if the core model contains a regular limit θ of measurable cardinals, then there is a model in which every set of measurable cardinals of K bounded in θ has an indiscernible sequence but there is no such sequence for the entire set of measurables of K below θ. (shrink)

The current literature on indeterminacy centers around two projects. One concerns the logic of indeterminacy; the other concerns its nature or source. The aim of this paper is to introduce, motivate and go some way toward addressing a new, third project: that of providing what I call a minimal characterization of indeterminacy. An MC, to a first approximation, is a relatively pre-theoretical characterization of indeterminacy that is neutral between the various substantive theories of the nature and logic of indeterminacy. An (...) MC thus captures a generic sense of indeterminacy that, at least in principle, is recognized by all parties to the debate over the phenomenon’s underlying nature and logic. I begin by introducing the concept of an MC and outlining some of the main theoretical virtues of providing an MC. I then establish some desiderata on a suitable MC, and use these desiderata to rule out various initially attractive proposals. In the final part of the paper I sketch the beginnings of my own MC and defend it against objections. (shrink)

We show that if N and M are transitive models of ZFA such that N M, N and M have the same kernel and same set of atoms, and M AC, then N is a Fraenkel-Mostowski-Specker (FMS) submodel of M if and only if M is a generic extension of N by some almost homogeneous notion of forcing. We also develop a slightly modified notion of FMS submodels to characterize the case where M is a generic extension of N not (...) necessarily by an almost homogeneous notion of forcing. (shrink)

The paper presents semantics for a subset of generics, so-called “characterizing sentences”. It is argued that claims about the relationship between the truth of characterizing sentences and claims about the distribution of properties among individuals can be viewed independently of considerations about logical form. Some extant approaches are presented and criticized, and a positive analysis of characterizing sentences in terms of normality is introduced and defended. The main innovation is that a notion of normality enters into (...) the analysis in two separate but connected places, not just one as competing accounts suggest. (shrink)

In this paper we address our efforts to extend the well-known connection in equational logic between equational theories and fully invariant congruences to other–possibly infinitary–logics. In the special case of algebras, this problem has been formerly treated by H. J. Hoehnke [10] and R. W. Quackenbush [14]. Here we show that the connection extends at least up to the universal fragment of logic. Namely, we establish that the concept of universal theory matches the abstract notion of fully invariant system. We (...) also prove that, inside this wide group of theories, the ones which are strict universal Horn correspond to fully invariant closure systems, whereas those which are universal atomic can be characterized as principal fully invariant systems. (shrink)

In this paper, we focus on contexts where the primary activity is to expound knowledge about general classes of phenomena, either by categorizing and characterizing them or by explaining them based on some theory, ranging from a commonsense folk theory to an uncommonsense scientific theory. Texts produced in such contexts include science lectures, research articles, and entries in encyclopedias. We focus on explanations, considering them across strata in terms of context, semantics, and lexicogrammar, and summarizing contributions from different research (...) strands. Against this background, we report on a study of the registers used in secondary school chemistry textbooks in Hong Kong. We begin by summarizing a framework for classifying the contexts in which texts operate – a framework designed to allow us to differentiate different kinds of text according to the contexts they operate in. Then, we focus on one type of context – that of expounding knowledge about general classes of phenomena. Next, we identify different strategies of expounding knowledge, contrasting explanations and categorizations, and then discuss explanations in more detail. Finally, we move to the question of how these contextual types are realized semantically as texts organized as rhetorical complexes, drawing on secondary school textbooks in chemistry in particular. (shrink)

This dissertation is intended to provide a formalism for those generics that trigger nonmonotonic inferences. The formalism is to reflect intentionality and exception-tolerating features of generics, and has an emphasis on the axiomatization of generic reasoning that encodes nonmonotonicity. ;A modal conditional approach is taken to formalize the nonmonotonic reasoning in general at the level of object language. A serial of logic systems---MN, NID, NCUM, N STCUM---are constructed in an increasing strength of the characterized nonmonotonic inference relation. In (...) these systems, two binary modal operators ⩾ and > are introduced in their syntax, and a ⊛ function lifted from the traditional * function is deployed in their semantics. These systems are shown to be sound and complete with respect to certain classes of frames defined in the semantics. They are decidable as well. The nonmonotonic inference is argued to be a ternary relation "[phi], Gamma |∼ alpha", and is defined in the system NSTCUM. Many widely discussed nonmonotonic inference patterns such as Defeasible Modus Ponens, Defeasible Transitivity, the Penguin Principle etc. are justified. The specificity rule is proved to be a theorem of the system N STCUM. The impact of negated defaults on an inference is also investigated and accounted for. ;A canonical form to read off generics is proposed: All generic sentences with subject-predicate structure can be re-written into their canonical form S . If S is a plural noun phrase, it can be further refined to be . Normal objects are selected based on the "meaning" of the subject and predicate terms. The second parameter provides an aspect with respect to which certain objects of a kind are considered normal. Due to such a way to select normal objects, the drowning problem is solved. ;The inference behaviors of generics are axiomatized in the system G, which is a quantificational extension of the system NSTCUM. It is proved to be sound and complete with respect to the class of L⩾,G -frames. Those benchmark examples of generic inferences are examined in the system G. (shrink)

Probabilistic theories are a natural framework to investigate the foundations of quantum theory and possible alternative or deeper theories. In a generic probabilistic theory, states of a physical system are represented as vectors of outcomes probabilities and state spaces are convex cones. In this picture the physics of a given theory is related to the geometric shape of the cone of states. In quantum theory, for instance, the shape of the cone of states corresponds to a projective space over complex (...) numbers. In this paper we investigate geometric constraints on the state space of a generic theory imposed by the following information theoretic requirements: every non completely mixed state of a system is perfectly distinguishable from some other state in a single shot measurement; information capacity of physical systems is conserved under making mixtures of states. These assumptions guarantee that a generic physical system satisfies a natural principle asserting that the more a state of the system is mixed the less information can be stored in the system using that state as logical value. We show that all theories satisfying the above assumptions are such that the shape of their cones of states is that of a projective space over a generic field of numbers. Remarkably, these theories constitute generalizations of quantum theory where superposition principle holds with coefficients pertaining to a generic field of numbers in place of complex numbers. If the field of numbers is trivial and contains only one element we obtain classical theory. This result tells that superposition principle is quite common among probabilistic theories while its absence gives evidence of either classical theory or an implausible theory. (shrink)

Let be a countable first order structure and endow the universe of with the discrete topology. Then the automorphism group of becomes a topological group. A tuple of automorphisms is defined to be weakly generic iff its diagonal conjugacy class (in the algebraic sense) is dense (in the topological sense) and the ‐orbit of each is finite. Existence of tuples of weakly generic automorphisms are interesting from the point of view of model theory as well as from the point of (...) view of finite combinatorics.The main results of the present work are as follows. In Theorem 2.6 we characterize the existence of tuples of weakly generic automorphisms with the aid of the profinite topology of free groups. In Corollary 2.12 we will show that if has finite topological rank r (and satisfies a further, mild technical condition) then the existence of a weakly generic tuple in implies the existence of weakly generic tuples in for all natural number. Finally, in Theorem 3.2 we show that if is a countable model of an ℵ0‐categorical, simple theory in which all types over the empty set are stationary and has a pair of weakly generic automorphisms then it has tuples of weakly generic automorphisms of arbitrary finite length.At the technical level we will combine elementary investigations about the profinite topology of free groups with the results of [11] about topological ranks of the automorphism groups of some structures. (shrink)

Adjoin, to a countable standard model M of Zermelo-Fraenkel set theory (ZF), a countable set A of independent Cohen generic reals. If one attempts to construct the model generated over M by these reals (not necessarily containing A as an element) as the intersection of all standard models that include M ∪ A, the resulting model fails to satisfy the power set axiom, although it does satisfy all the other ZF axioms. Thus, there is no smallest ZF model including M (...) ∪ A, but there are minimal such models. These are classified by their sets of reals, and there is one minimal model whose set of reals is the smallest possible. We give several characterizations of this model, we determine which weak axioms of choice it satisfies, and we show that some better known models are forcing extensions of it. (shrink)

We consider sets of reals that are “adequate” in various senses, for example dominating or unbounded or splitting or non-meager. Call a real x “needed” if every adequate set contains a real in which x is recursive. We characterize the needed reals for numerous senses of “adequate.” We also consider, for various notions of forcing that add reals, the problem of characterizing the ground-model reals that are recursive in generic reals.

Literally speaking, "Philosophy of biology" is a rather old expression. William Whewell coined it in 1840, at the very time he introduced the expression "philosophy of science". Whewell was fond of creating neologisms, like Auguste Comte, his French counterpart in the field of the philosophical reflection about science. Historians of science know that a few years earlier, in 1834, Whewell had generated a small scandal when he proposed the word "scientist" as a general term by which "the students of the (...) knowledge of the material world" could describe themselves, and distinguish themselves from artists. The term "philosopher", Whewell argued, was too wide. A new generic term, more or less equivalent to the French term "savant", was needed in order to prevent the disintegration of science that seemed to flow from its specialization in modern times.1 When Whewell first introduced the terms "philosophy of science" and "philosophy of biology" in his 1840 Philosophy of the inductive sciences, the latter term was merely a special branch of "philosophy of science". The expression "philosophy of science" itself had two justifications: firstly, this phrase expressed the idea that "science" remained cognitively coherent enough to justify a critical enquiry into its methodological unity and its foundation; secondly, the phrase "philosophy of science" was required in order to distinguish a properly "philosophical" enquiry from a "historical" approach to science. Although Whewell's 1840 Philosophy of the inductive sciences 2 had approximately the same chapter structure as his 1837 History of the Inductive Sciences 3 (that is, a series of chapters successively devoted to the concept of science in general, and although there was considerable overlap between the contents of the two books, then to particular sciences), its theoretical purpose was different. Clearly, Whewell was not willing to confuse the genres of history and philosophy as Auguste Comte had done in his 1830 Cours de philosophie positive.4 Note also that the word "biology" was still extremely rare in English when Whewell used it in 1840. In fact, Whewell's 1837 History of the Inductive Sciences does not make use of the word "biology": Whewell successively examines "botany", "zoology", "physiology" and "comparative antomy" as special branches of "analytico-classificatory science", then discusses palaeontology as a special case of the "palaeo-etiological sciences". Three years later, in his Philosophy of the Inductive Sciences, Whewell does use "biology" as a generic term for all the sciences dealing with life. The various sciences which were separately examined in the previous book are now collectively considered. Furthermore, the main philosophical problem raised by biology is its dual nature: biology is both nomological and a historical science. Modern philosophers of biology are generally unaware of the story of the origins of the expression "philosophy of biology", but Whewell's dual theoretical nature of biology is still a major concern for modern "philosophy of biology". (shrink)

In this paper we show that focus structure determines the interpretation of bare plurals in English: topic bare plurals are interpreted generically, focused bare plurals are interpreted existentially. When bare plurals are topics they must be specific, i.e. they refer to kinds. After type-shifting they introduce variables which can be bound by the generic quantifier, yielding characterizing generics. Existentially interpreted bare plurals are not variables, but denote properties that are incorporated into the predicate.The type of predicate determines the (...) interpretation of its bare plural subject. The individual/stage-level distinction, though important, is not sufficient: since only arguments can be topics, only those stage-level predicates which have locative arguments can have existential bare plural subjects.Certain verbs (e.g., hate) fail to incorporate their bare plural objects; therefore no existential reading of the object is available. We provide a novel solution to this puzzle based on the following two claims: (i) incorporated bare plurals do not introduce discourse referents; (ii) nonincorporating verbs are presuppositional. (shrink)

Due to the variation, contingency and complexity of living systems, biology is often taken to be a science without fundamental theories, laws or general principles. I revisit this question in light of the quest for design principles in systems biology and show that different views can be reconciled if we distinguish between different types of generality. The philosophical literature has primarily focused on generality of specific models or explanations, or on the heuristic role of abstraction. This paper takes a different (...) approach in emphasizing a theory-constituting role of general principles. Design principles signify general dependency-relations between structures and functions, given a set of formally defined constraints. I contend that design principles increase our understanding of living systems by relating specific models to general types. The categorization of types is based on a delineation of the scope of biological possibilities, which serves to identify and define the generic features of classes of systems. To characterize the basis for general principles through generic abstraction and reasoning about possibility spaces, I coin the term constraint-based generality. I show that constraint-based generality is distinct from other types of generality in biology, and argue that general principles play a unifying role that does not entail theory reduction. (shrink)

Based on the presentation of a research framework (the shared work of teachers), this text uses an empirical approach to examine the hypothesis of a co-elaboration of the professional situation. To do so, the empirical investigation, based on the Goffman framework, analyzes the process of reconstructing a teaching session (reference situation) over the course of a pedagogical counselling session (support situation) characterized by interaction between a beginning teacher and a trainer. The invalidation of the hypothesis leads to a suggested conceptualization (...) of the professional situation combining definitional approaches (emphasizing the duality between its singularity and its genericity) and methodological approaches. -/- A partir de la présentation d’un cadre de recherche (le travail partagé des enseignants), ce texte soumet à l’empirie l’hypothèse de la co-élaboration de la situation professionnelle. Pour ce faire, en s’appuyant sur le cadre de Goffman, l’enquête empirique analyse le processus de reconstruction d’une séance d’enseignement (situation de référence) au cours d’une séance de conseil pédagogique (situation support) caractérisée par l’interaction entre une enseignante débutante et un formateur. L’invalidation de l’hypothèse débouche sur une proposition de conceptualisation de la situation professionnelle qui combine des approches définitoires (insistant sur la dualité entre sa singularité et sa généricité) et méthodologiques. (shrink)

This paper introduces a new theory of constant regions, which generalizes that of interstices, in nonstandard models of arithmetic. In particular, we show that two homogeneity notions introduced by Richard Kaye and the author, namely, constantness and pregenericity, are equivalent. This led to some new characterizations of generic cuts in terms of existential closedness.

Based on the presentation of a research framework (the shared work of teachers), this text uses an empirical approach to examine the hypothesis of a co-elaboration of the professional situation. To do so, the empirical investigation, based on the Goffman framework, analyzes the process of reconstructing a teaching session (reference situation) over the course of a pedagogical counselling session (support situation) characterized by interaction between a beginning teacher and a trainer. The invalidation of the hypothesis leads to a suggested conceptualization (...) of the professional situation combining definitional approaches (emphasizing the duality between its singularity and its genericity) and methodological approaches. A partir de la présentation d’un cadre de recherche (le travail partagé des enseignants), ce texte soumet à l’empirie l’hypothèse de la co-élaboration de la situation professionnelle. Pour ce faire, en s’appuyant sur le cadre de Goffman, l’enquête empirique analyse le processus de reconstruction d’une séance d’enseignement (situation de référence) au cours d’une séance de conseil pédagogique (situation support) caractérisée par l’interaction entre une enseignante débutante et un formateur. L’invalidation de l’hypothèse débouche sur une proposition de conceptualisation de la situation professionnelle qui combine des approches définitoires (insistant sur la dualité entre sa singularité et sa généricité) et méthodologiques. (shrink)

We refine results of Gannon [6, Theorem 4.7] and Simon [22, Lemma 2.8] on convergence of Morley sequences. We then introduce the notion of eventual $NIP$, as a property of a model, and prove a variant of [15, Corollary 2.2]. Finally, we give new characterizations of generically stable types (for countable theories) and reinforce the main result of Pillay [17] on the model-theoretic meaning of Grothendieck’s double limit theorem.

We characterize complete Boolean algebras with dense subtrees. The main results show that a complete Boolean algebra contains a dense tree if its generic filter collapses the algebra's density to its distributivity number and the reverse holds for homogeneous algebras.

Based on the presentation of a research framework (the shared work of teachers), this text uses an empirical approach to examine the hypothesis of a co-elaboration of the professional situation. To do so, the empirical investigation, based on the Goffman framework, analyzes the process of reconstructing a teaching session (reference situation) over the course of a pedagogical counselling session (support situation) characterized by interaction between a beginning teacher and a trainer. The invalidation of the hypothesis leads to a suggested conceptualization (...) of the professional situation combining definitional approaches (emphasizing the duality between its singularity and its genericity) and methodological approaches. (shrink)

We investigate a variety of cut and choose games, their relationship with (generic) large cardinals, and show that they can be used to characterize a number of properties of ideals and of partial orders: certain notions of distributivity, strategic closure, and precipitousness.

I argue that Harry Frankfurt’s doctrine of sufficiency, properly understood, presents a plausible alternative to egalitarianism. My position may be more general than Frankfurt’s, insofar as he limits himself to economic sufficiency; on my view, insufficiency is a generic reason for the rejection of principles governing permissible behavior. By situating sufficiency within a contractualist framework of moral permissibility, I provide an alternative to common (and, I think, mistaken) characterizations of the doctrine of sufficiency as either subordinate to equality or primarily (...) concerned with maximizing cases of sufficiency. (shrink)

In this article we characterize all those sequences of cardinals of length ω1 which are cardinal sequences of some compact scattered space . This extends the similar results from [R. La Grange, Concerning the cardinal sequence of a Boolean algebra, Algebra Universalis, 7 307–313] for such sequences of countable length. For ordinals between ω1 and ω2 we can only give a sufficient condition for a sequence of that length to be a cardinal sequence of a compact scattered space. This condition (...) is, arguably, the most one can expect in ZFC. In any case, ours is a significant extension of the sufficient conditions given in [J.C. Martinez, A consistency result on thin-tall superatomic Boolean algebras, Proc. Amer. Math. Soc. 115 473–477] and [J. Bagaria, Locally generic Boolean algebras and cardinal sequences, Algebra Universalis 47 283–302]. (shrink)

In this paper I consider respects of dependence, namely, the fact that some entities depend on other entities in some respect or another. In the first section, I provide a characterization of contemporary debates on dependence based on respects of dependence. I also single out seven desiderata a good theory of dependence should satisfy and three ways of interpreting respects of dependence. In the second section, I criticize two such ways and, in the third section, I defend the remaining option, (...) namely, that respects of dependence correspond to different dependence-relations between entities. In the fourth section, I develop my theory of Respect-of-Dependence Relations in order to distinguish between partial and full dependence and between specific and generic dependence, and to qualify RD -relations in temporal and modal terms. Finally, in the last section, I anticipate and reply to three objections against dependence pluralism. (shrink)

The agent portrayed in much philosophy of action is, let's face it, a square. He does nothing intentionally unless he regards it or its consequences as desirable. The reason is that he acts intentionally only when he acts out of a desire for some anticipated outcome; and in desiring that outcome, he must regard it as having some value. All of his intentional actions are therefore directed at outcomes regarded sub specie boni: under the guise of the good. This agent (...) is conceived as being capable of intentional action—and hence as being an agent—only by virtue of being a pursuer of value. I want to question whether this conception of agency can be correct. Surely, so general a capacity as agency cannot entail so narrow a cast of mind. Our moral psychology has characterized, not the generic agent, but a particular species of agent, and a particularly bland species of agent, at that. It has characterized the earnest agent while ignoring those agents who are disaffected, refractory, silly, satanic, or punk. I hope for a moral psychology that has room for the whole motley crew. I shall begin by examining why some philosophers have thought that the attitudes motivating intentional actions involve judgments of value. I shall then argue that their conception of these attitudes is incorrect. Finally, I shall argue that practical reason should not be conceived as a faculty for pursuing value. (shrink)

Across the European research area and beyond, efforts are being mobilized to align research and innovation processes and products with societal values and needs, and to create mechanisms for inclusive priority setting and knowledge production. A central concern is how to foster a culture of “Responsible Research and Innovation” (RRI) among scientists and engineers. This paper focuses on RRI teaching at higher education institutions. On the basis of interviews and reviews of academic and policy documents, it highlights the generic aspects (...) of teaching aimed at invoking a sense of care and societal obligation, and provides a set of exemplary cases of RRI-related teaching. It argues that the Aristotelian concept of phronesis can capture core properties of the objectives of RRI-related teaching activities. Teaching should nurture the students’ capacity in terms of practical wisdom, practical ethics, or administrative ability in order to enable them to act virtuously and responsibly in contexts which are often characterized by uncertainty, contention, and controversy. (shrink)

The paper begins with a generic discussion of modelling, focusing on some of its practices and problems. I then move on to a philosophical discussion about emergence and multi-scale modelling; more specifically, the reasons why what looks like a promising strategy for dealing with emergence is sometimes incapable of delivering interesting results. This becomes especially evident when we look more closely at turbulence and what I take to be the main ontological feature of emergent behavior—universality. Finally, I conclude by showing (...) why, despite displaying multi-scale behaviour and some of the characteristics we identify with emergence, turbulence fails to fit neatly into the latter category and is not successfully captured using multi-scale modelling. The complex nature of turbulence illustrates the difficulties in characterizing emergence and why specific criteria are needed in order to prevent every complex behaviour we don’t understand being classified as emergent. (shrink)