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)

We continue the study of the connection between the “geometric” properties of SU -rank 1 structures and the properties of “generic” pairs of such structures, started in [8]. In particular, we show that the SU-rank of the theory of generic pairs of models of an SU -rank 1 theory T can only take values 1 , 2 or ω, generalizing the corresponding results for a strongly minimal T in [3]. We also use pairs to derive the implication from (...) pseudolinearity to linearity for ω -categorical SU -rank 1 structures, established in [7], from the conjecture that an ω -categorical supersimple theory has finite SU -rank, and find a condition on generic pairs, equivalent to pseudolinearity in the general case. (shrink)

A generic computation of a subset $A$ of $\mathbb{N}$ consists of a computation that correctly computes most of the bits of $A$, and never incorrectly computes any bits of $A$, but which does not necessarily give an answer for every input. The motivation for this concept comes from group theory and complexity theory, but the purely recursion theoretic analysis proves to be interesting, and often counterintuitive. The primary result of this paper is that there are no minimal pairs for (...) generic computability, answering a question of Jockusch and Schupp. (shrink)

We show that there is a minimal pair in the nonuniform generic degrees, and hence also in the uniform generic degrees. This fact contrasts with Igusa’s result that there are no minimal pairs for relative generic computability and answers a basic structural question mentioned in several papers in the area.

We introduce the notion of a lovely pair of models of a simple theory T, generalizing Poizat's “belles paires” of models of a stable theory and the third author's “generic pairs” of models of an SU-rank 1 theory. We characterize when a saturated model of the theory TP of lovely pairs is a lovely pair , finding an analog of the nonfinite cover property for simple theories. We show that, under these hypotheses, TP is also simple, and (...) we study forking and canonical bases in TP. We also prove that assuming only that T is low, the existentially universal models of the universal part of a natural expansion TP+ of TP, are lovely pairs, and “simple Robinson universal domains”. (shrink)

In support of a recent conjecture by Nielsen (1999), we prove that the phenomena of ‘incomparable entanglement’— whereby, neither member of a pair of pure entangled states can be transformed into the other via local operations and classical communication (LOCC)—is a generic feature when the states at issue live in an infinite-dimensional Hilbert space.  2002 Elsevier Science B.V. All rights reserved.

In support of a recent conjecture by Nielsen (1999), we prove that the phenomena of ‘incomparable entanglement’— whereby, neither member of a pair of pure entangled states can be transformed into the other via local operations and classical communication (LOCC)—is a generic feature when the states at issue live in an infinite-dimensional Hilbert space.  2002 Elsevier Science B.V. All rights reserved.

We ask when, for a pair of structures $\mathcal {A}_1,\mathcal {A}_2$, there is a uniform effective procedure that, given copies of the two structures, unlabeled, always produces a copy of $\mathcal {A}_1$. We give some conditions guaranteeing that there is such a procedure. The conditions might suggest that for the pair of orderings $\mathcal {A}_1$ of type $\omega _1^{CK}$ and $\mathcal {A}_2$ of Harrison type, there should not be any such procedure, but, in fact, there is one. We (...) construct an example for which there is no such procedure. The construction involves forcing. On the way to constructing our example, we prove a general result on modifying Cohen generics. (shrink)

We show that every two-dimensional class of topological similarity, and hence every diagonal conjugacy class of pairs, is meager in the group of order preserving bijections of the rationale and in the group of automorphisms of the ordered rational Urysohn space.

A generic extension of the constructible universe by reals is defined, in which the union of ‐classes of x and y is a lightface set, but neither of these two ‐classes is separately ordinal‐definable.

Children and adults commonly produce more generic noun phrases (e.g., birds fly) about animals than artifacts. This may reflect differences in participants’ generic knowledge about specific animals/artifacts (e.g., dogs/chairs), or it may reflect a more general distinction. To test this, the current experiments asked adults and preschoolers to generate properties about novel animals and artifacts (Experiment 1: real animals/artifacts; Experiments 2 and 3: matched pairs of maximally similar, novel animals/artifacts). Data demonstrate that even without prior knowledge about these (...) items, the likelihood of producing a generic is significantly greater for animals than artifacts. These results leave open the question of whether this pattern is the product of experience and learned associations or instead a set of early-developing theories about animals and artifacts. (shrink)

This paper examines the way Charles Darwin applied his domestic breeding analogy to the practical workings of species evolution: that application, it is argued, centered on Darwin's distinction between methodical and unconscious selection. Methodical selection, which entailed pairing particular individuals for mating purposes, represented conditions of strict geographic isolation, obviously useful for species multiplication (speciation). By contrast, unconscious selection represented an open landmass with a large breeding population. Yet Darwin held that this latter scenario, which often would include multiple ecological (...) subdistricts and thus partial isolation, was better suited for speciation than were isolated conditions. At the same time, many passages in Darwin's writings that apparently portrayed phyletic evolution exclusively (these including references to unconscious selection), actually applied to speciation as well, for phyletic change in a single district could constitute a local manifestation of a larger common-descent pattern. This generic use of "phyletic" change was reflected in Darwin's deployment of the unconscious selection analogy in his published writings as well as in his dispute with Moritz Wagner over the necessity of geographic isolation for speciation. We can thus understand Darwin's otherwise puzzling declaration in The Origin of Species that unconscious selection was 'more important' than the methodical approach. (shrink)

In this paper, we study the power and limitations of computing effectively generic sequences using effectively random oracles. Previously, it was known that every 2-random sequence computes a 1-generic sequence and every 2-random sequence forms a minimal pair in the Turing degrees with every 2-generic sequence. We strengthen these results by showing that every Demuth random sequence computes a 1-generic sequence and that every Demuth random sequence forms a minimal pair with every pb-generic (...) sequence. Moreover, we prove that for every comeager${\cal G} \subseteq {2^\omega }$, there is some weakly 2-random sequenceXthat computes some$Y \in {\cal G}$, a result that allows us to provide a fairly complete classification as to how various notions of effective randomness interact in the Turing degrees with various notions of effective genericity. (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)

The aim of this work is an analysis of distal and non‐distal behavior in dense pairs of o‐minimal structures. A characterization of distal types is given through orthogonality to a generic type in, non‐distality is geometrically analyzed through Keisler measures, and a distal expansion for the case of pairs of ordered vector spaces is computed.

TOT states may be viewed as a temporary and reversible microamnesia. We investigated the effects of lorazepam on TOT states in response to general knowledge questions. The lorazepam participants produced more commission errors and more TOTs following commission errors than the placebo participants . The resolution of the TOTs was unimpaired by the drug. Neither feeling-of-knowing accuracy nor recognition were affected by lorazepam. The higher level of incorrect recalls produced by lorazepam participants may be due to the fact that they (...) were more frequently temporarily unable to access a known item. For some of these items, the awareness of the retrieval failure resulted in a commission TOT . The resolution of the TOT conflict is discussed in the light of the anxiolytic and anticonflict effects of lorazepam. The data are discussed in terms of contemporary theories of TOTs and the effects that benzodiazepines have on semantic memory. (shrink)

Background: Walking while performing a secondary task walking) increases cognitive workload in young adults. To date, few studies have used neurophysiological measures in combination to subjective measures to assess cognitive workload during a walking task. This combined approach can provide more insights into the amount of cognitive resources in relation with the perceived mental effort involving in a walking task.Research Question: The objective was to examine cognitive workload in young adults during walking conditions varying in complexity.Methods: Twenty-five young adults performed (...) four conditions: usual walking, simple DT walking, complex DT walking and standing while subtracting. During the walking task, mean speed, cadence, stride time, stride length, and their respective coefficient of variation were recorded. Cognitive workload will be measured through changes in oxy- and deoxy-hemoglobin during walking in the dorsolateral prefrontal cortex and perceived mental demand score from NASA-TLX questionnaire.Results: In young adults, ΔHbO2 in the DLPFC increased from usual walking to both DT walking conditions and standing while subtracting condition. ΔHbO2 did not differ between the simple and complex DT and between the complex DT and standing while subtracting condition. Perceived mental demand gradually increased with walking task complexity. As expected, all mean values of gait parameters were altered according to task complexity. CV of speed, cadence and stride time were significantly higher during DT walking conditions than during usual walking whereas CV of stride length was only higher during complex DT walking than during usual walking.Significance: Young adults had greater cognitive workload in the two DT walking conditions compared to usual walking. However, only the mental demand score from NASA-TLX questionnaire discriminated simple from complex DT walking. Subjective measure provides complementary information to objective one on changes in cognitive workload during challenging walking tasks in young adults. These results may be useful to improve our understanding of cognitive workload during walking. (shrink)

We show that the countable universal homogeneous meet-tree has a generic automorphism, but does not have a generic pair of automorphisms.

We study the class of weakly locally modular geometric theories introduced in [4], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories. We find new conditions equivalent to weak local modularity: "weak one-basedness", absence of type definable "almost quasidesigns", and "generic linearity". Among other things, we show that weak one-basedness is closed under reducts. We also show that the lovely pair expansion of a non-trivial weakly one-based ω-categorical geometric theory interprets an infinite vector (...) space over a finite field. (shrink)

In a pair of recent articles, William Hasker has attempted to defend Robert Adams’s new anti-Molinist argument. But I argue that the sense of explanatory priority operative in the argument is either equivocal or, if a univocal sense can be given to it, it is either so generic that we should have to deny its transitivity or so weak that it would not be incompatible with human freedom.

We show: There are pairs of universes V1V2 and there is a notion of forcing PV1 such that the change mentioned in the title occurs when going from V1[G] to V2[G] for a P-generic filter G over V2. We use forcing iterations with partial memories. Moreover, we implement highly transitive automorphism groups into the forcing orders.

A definable pair of disjoint non-OD sets of reals exists in the Sacks and ????0-large generic extensions of the constructible universe L. More specifically, if a∈2ω is eith...

Let A[ω]ω be a maximal almost disjoint family and assume P is a forcing notion. Say A is P-indestructible if A is still maximal in any P-generic extension. We investigate P-indestructibility for several classical forcing notions P. In particular, we provide a combinatorial characterization of P-indestructibility and, assuming a fragment of MA, we construct maximal almost disjoint families which are P-indestructible yet Q-destructible for several pairs of forcing notions . We close with a detailed investigation of iterated Sacks indestructibility.

We give a necessary and sufficient condition in order that a type-shifting automorphism be constructed on a model of the Theory of Simple Types (TST) by forcing. Namely it is proved that, if for every n ≥ 1 there is a model of TST in the ground model M of ZFC that contains an n-extendible coherent pair, then there is a generic extension M[G] of M that contains a model of TST with a type-shifting automorphism, and hence M[G] (...) contains a model of NF. The converse holds trivially. It is also proved that there exist models of TST containing l-extendible coherent pairs. (shrink)

This paper reports a literature review on the topic of ethical issues in in-depth interviews. The review returned three types of article: general discussion, issues in particular studies, and studies of interview-based research ethics. Whilst many of the issues discussed in these articles are generic to research ethics, such as confidentiality, they often had particular manifestations in this type of research. For example, privacy was a significant problem as interviews sometimes probe unexpected areas. For similar reasons, it is difficult (...) to give full information of the nature of a particular interview at the outset, hence informed consent is problematic. Where a pair is interviewed (such as carer and cared-for) there are major difficulties in maintaining confidentiality and protecting privacy. The potential for interviews to harm participants emotionally is noted in some papers, although this is often set against potential therapeutic benefit. As well as these generic issues, there are some ethical issues fairly specific to in-depth interviews. The problem of dual role is noted in many papers. It can take many forms: an interviewer might be nurse and researcher, scientist and counsellor, or reporter and evangelist. There are other specific issues such as taking sides in an interview, and protecting vulnerable groups. Little specific study of the ethics of in-depth interviews has taken place. However, that which has shows some important findings. For example, one study shows participants are not averse to discussing painful issues provided they feel the study is worthwhile. Some papers make recommendations for researchers. One such is that they should consider using a model of continuous (or process) consent rather than viewing consent as occurring once, at signature, prior to the interview. However, there is a need for further study of this area, both philosophical and empirical. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Perceiving Particulars-as-such Is Incoherent—A Reply to Mark SideritsMonima ChadhaI am honored by Mark Siderits' response to my article1 and thankful to him for the opportunity it affords me to clarify the arguments and develop the theses presented therein further. My discussion focuses primarily on a pair of epistemological theses drawing attention to what we can and cannot perceive.2 The negative thesis is that we cannot perceive particulars, and, (...) indeed, the very idea of "perceiving a particular-as-such" (which represents the position of some Buddhist philosophers, specifically Yogācāra-Sautrāntikas) is incoherent. The positive thesis, which draws its inspiration from the Navya-Naiyāyikas, is that we can perceive only universal features. Siderits focuses his response on the negative thesis. He does not explicitly complain about the positive thesis, although, being an enthusiast for the Buddhist approach, he cannot help but be suspicious about it. He complains that the argument for the negative thesis is wanting, for I seem to have "misconstrued those realist intuitions that stand behind the Yogācāra-Sautrāntika." Not only that, in section 2 of his response, he claims that my argument rests on a controversial thesis that presupposes a mistaken internalism about conscious content. I will argue that the difficulties Siderits raises for my argument are based on a misinterpretation of the central claim that underlies the argument for the negative thesis. This, in turn, will help to develop further the argument for my positive thesis.Before we turn to the arguments, I will attend to some terminological matters that Siderits draws attention to in the first section of his response. He complains that some distinctions, which are important in the context of this discussion, are conflated in my article. One of his suggestions—the distinction between particulars and individuals—is very helpful. The notion of "non-particular individuals" can be wheeled in here to clarify my theses and arguments.3 Henceforth, I will use "non-particular individuals" to refer to universal features.Siderits also underscores the differences between Nyāya universals and Kantian concepts by emphasizing the distinct metaphysical positions held by these philosophers. I am not convinced that he has shown that Nyāya universals are essentially incompatible with Kantian concepts. But, in any event, highlighting the differences [End Page 382] distracts us from the epistemological concerns raised in my earlier paper, so I will not examine those differences here.4Siderits rightly emphasizes the mind-independence of Nyāya universals: the thesis is indispensable to their metaphysics. Nyāya holds that some universals, namely those that pick out generic properties, are objectively real. Real universals are not mere mental constructions (figments of our imagination, as the Yogācāra-Sautrāntika puts it), or mere abstractions formed by putting together the common features of real particulars. Using the typical example of "cowness," the Naiyāyika explains that when we observe cows we not only grasp "that particular," we also grasp "cowness" as the common character manifested in distinct particular cows. For the Naiyāyikas, cowness is an example of a real universal: it presents a simple, indivisible property present in every cow and is directly grasped whenever we perceive a particular cow. Real universals are simple unanalyzable properties that exist "out there" and are cognized in perception. They are not complex ideas put together by the mind, and so in this sense they are mind-independent.However, to say that universals are mind-independent does not amount to saying that the mind cannot be implicated in their perception. Siderits' sympathies lie with the Buddhists, and, like them, he holds that since perception is our link with mind-independent reality, the perceptual link must be independent of any intervention by the mind. Nyāya universals are not "mind-independent" in this latter sense. The Naiyāyikas hold that the perception of universals requires abstraction in singling out one feature or property from the given. Furthermore, they would agree that a subject's perceptual grasp of universals is revealed in acquiring dispositional abilities to recognize other instances exemplifying the same property. The Naiyāyikas would readily admit a mental component for the perception... (shrink)

Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic multiverse while preserving the nonexistence of upper bounds. We obtain several improvements of his result, using what we call the blockchain construction to build generic objects with varying degrees of mutual genericity. The method accommodates certain infinite posets, and we can (...) realize these embeddings via a wide variety of forcing notions, while providing control over lower bounds as well. We also give a generalization to class forcing in the context of second-order set theory, and exhibit some further structure in the generic multiverse, such as the existence of exact pairs. (shrink)

We prove the preservation theorems for NATP; many of them extend the previously established preservation results for other model-theoretic tree properties. Using them, we also furnish proper examples of NATP theories which are simultaneously TP2 and SOP. First, we show that NATP is preserved by the parametrization and sum of the theories of Fraïssé limits of Fraïssé classes satisfying strong amalgamation property. Second, the preservation of NATP for two kinds of dense/co-dense expansions, i.e. the theories of lovely pairs and of (...) [Formula: see text]-structures for geometric theories, and dense/co-dense expansion on vector spaces is proved. Next, we prove the preservation of NATP for the generic predicate expansion and the pair of an algebraically closed field and its distinguished subfield; for the latter, not only NATP, but also the preservation of NTP1 and NTP2 is considered. Finally, we present some proper examples of NATP theories using the results proved in this paper, including the parametrization of DLO and the expansion of an algebraically closed field by adding a generic linear order. In particular, we show that the model companion of the theory of algebraically closed fields with circular orders (ACFO) is NATP. (shrink)

I postulate that the extension of a degree adjective is fixed by implicitly accepted non-analytic reference-fixing principles (“preconceptions”) that combine appeals to paradigmatic cases with generic principles designed to expand the extension of the adjective beyond the paradigmatic range. In regular occasions of use, the paradigm and generic preconceptions are jointly satisfied and determine the existence of an extension/anti-extension pair dividing the adjective’s comparison class into two mutually exclusive and jointly exhaustive subclasses. Sorites paradoxical occasions of use (...) are irregular occasions of use in which the paradigm and generic preconceptions are not jointly satisfied. In them, the relevant degree adjective lacks an extension, and utterances of sentences containing it appearing in sorites arguments do not have truth conditions. I also postulate a probable psychology of paradigm intuitions, used in a psychological explanation of the preference for solutions of the sorites paradox on which paradigm preconceptions retain their intuitive truth-values. (shrink)

Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and geometry of symmetry (...) is controlled by numerical parameters, which act in analogy with a biological organism’s DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional (2D) design parameters, affine geometry and shape symmetry for visual or tactile shape sensation and perception-based decision making in populations of experts and non-experts. It will be shown that 2D fractal symmetry, referred to herein as the “symmetry of things in a thing”, results from principles very similar to those of affine projection. Results from experiments on aesthetic and visual preference judgments in response to 2D fractal trees with varying degrees of asymmetry are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (on a scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from “symmetry of things in a thing” significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. We generically construct a model in which the [math]-separation property is true, i.e. every pair of disjoint [math]-sets can be separated by a [math]-definable set. This answers an old question from the problem list “Surrealist landscape with figures” by A. Mathias from 1968. We also construct a model in which the (lightface) [math]-separation property is true.

Posner [6] has shown, by a nonuniform proof, that every ▵ 0 2 degree has a complement below 0'. We show that a 1-generic complement for each ▵ 0 2 set of degree between 0 and 0' can be found uniformly. Moreover, the methods just as easily can be used to produce a complement whose jump has the degree of any real recursively enumerable in and above $\varnothing'$ . In the second half of the paper, we show that the (...) complementation of the degrees below 0' does not extend to all recursively enumerable degrees. Namely, there is a pair of recursively enumerable degrees a above b such that no degree strictly below a joins b above a. (This result is independently due to S. B. Cooper.) We end with some open problems. (shrink)

We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-12 particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to pairs of particles of (...) arbitrary spin. The class of correlations allowed by quantum mechanics is still represented by the elliptope; the subclass of those allowed by local hidden-variable theories by polyhedra with increasing numbers of vertices and facets that get closer and closer to the elliptope. We use these results to advocate for an interpretation of quantum mechanics like Bub's. Probabilities and expectation values are primary in this interpretation. They are determined by inner products of vectors in Hilbert space. Such vectors do not themselves represent what is real in the quantum world. They encode families of probability distributions over values of different sets of observables. As in classical theory, these values ultimately represent what is real in the quantum world. Hilbert space puts constraints on possible combinations of such values, just as Minkowski space-time puts constraints on possible spatio-temporal constellations of events. Illustrating how generic such constraints are, the equation for the elliptope derived in this paper is a general constraint on correlation coefficients that can be found in older literature on statistics and probability theory. Yule (1896) already stated the constraint. De Finetti (1937) already gave it a geometrical interpretation. (shrink)

This dissertation reconsiders some traditional issues in the foundations of quantum mechanics in the context of relativistic quantum field theory (RQFT); and it considers some novel foundational issues that arise first in the context of RQFT. The first part of the dissertation considers quantum nonlocality in RQFT. Here I show that the generic state of RQFT displays Bell correlations relative to measurements performed in any pair of spacelike separated regions, no matter how distant. I also show that local (...) systems in RQFT are "open" to influence from their environment, in the sense that it is generally impossible to perform local operations that would remove the entanglement between a local system and any other spacelike separated system. The second part of the dissertation argues that RQFT does not support a particle ontology -- at least if particles are understood to be localizable objects. In particular, while RQFT permits us to describe situations in which a determinate number of particles are present, it does not permit us to speak of the location of any individual particle, nor of the number of particles in any particular region of space. Nonetheless, the absence of localizable particles in RQFT does not threaten the integrity of our commonsense concept of a localized object. Indeed, RQFT itself predicts that descriptions in terms of localized objects can be quite accurate on the macroscopic level. The third part of the dissertation examines the so-called observer-dependence of the particle concept in RQFT -- that is, whether there are any particles present must be relativized to an observer's state of motion. Now, it is not uncommon for modern physical theories to subsume observer-dependent descriptions under a more general observer-independent description of some underlying state of affairs. However, I show that the conflicting accounts concerning the particle content of the field cannot be reconciled in this way. In fact, I argue that these conflicting accounts should be thought of as "complementary" in the same sense that position and momentum descriptions are complementary in elementary quantum mechanics. (shrink)

Let I be a countable jump ideal in $\mathscr{D} = \langle \text{The Turing degrees}, \leq\rangle$ . The central theorem of this paper is: a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a (1) computes. We may replace "the join of an I-exact pair" in the above theorem by "a weak uniform upper bound on I". We also answer two minimality questions: the class of uniform upper bounds (...) on I never has a minimal member; if ∪ I = L α [ A] ∩ ω ω for α admissible or a limit of admissibles, the same holds for nice uniform upper bounds. The central technique used in proving these theorems consists in this: by trial and error construct a generic sequence approximating the desired object; simultaneously settle definitely on finite pieces of that object; make sure that the guessing settles down to the object determined by the limit of these finite pieces. (shrink)

According to several prominent philosophers, pleasure and pain come in measurable quantities. This thesis is controversial, however, and many philosophers have presented or felt compelled to respond to arguments for the conclusion that it is false. One important class of these arguments concerns the problem of aggregation, which says that if pleasure and pain were measurable quantities, then, by definition, it would be possible to perform various mathematical and statistical operations on numbers representing amounts of them. It is sometimes argued (...) that such operations cannot be sensibly applied to pleasure and pain, and that sentences expressing such operations must be false or meaningless. The purpose of this paper is to present, explain, and rebut several versions of this argument. In the first section, I present a generic version of the argument. In the second section, I present a defense of its key premise based on a case involving comparisons of relief from pain, and explain why I think it fails. In the third section, I present and rebut another defense, based on a pair of analogies with temperature. In the final section, I present a third defense, based on an analogy with spatial distances. I then present my reasons for rejecting it. Along the way, I explain my reasons for thinking that pleasure and pain are amenable to interval measurement. (shrink)

Hunting Causes and Using Them: Approaches in Philosophy and Economics (HC&UT) is about notions of causality appropriate to the sciences, mostly generic causal claims (causal laws) and especially notions that connect causality with probability. 1 Most of the work for the book is associated with the project ‘Causality: Metaphysics and Methods’. This project argued that metaphysics – our account of what causal laws are or what general causal claims say – should march hand-in-hand with our ways of establishing them. (...) It should be apparent, given the kind of thing we think causality is, why our methods are good for finding it. If our metaphysics does not mesh with and underwrite the methods, we are willing to trust, we should be wary of both. Many philosophers nowadays look for a single informative feature that characterizes causal laws. HC&UT argues instead for causal pluralism, for a large variety of kinds of causal laws as well as purposes for which we call scientific claims causal. Correlatively different methods for testing causal claims are suited to different kinds of causal laws. No one analysis is privileged and no methods are universally applicable. Much of the argument for pluralism is provided by authors of different accounts of causality, who provide intuitively plausible counter-examples to each other. Still, most of these accounts seem adequate for the kinds of examples the authors focus on. From the point of view of HC&UT, these examples involve different kinds of causal laws or set causality to different jobs, and the concomitant characterizing feature marks out this one kind of causal law. Importantly for the argument, often we can specify what characteristics a system of laws should have in order for an account/method pair to be applicable. An example is James Woodward’s level invariance, which I see as a …. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:A Treatise on Efficacy: Between Western and Chinese ThinkingJeremy E. HenkelA Treatise on Efficacy: Between Western and Chinese Thinking. By François Jullien, translated by Janet Lloyd. Honolulu: University of Hawai'i Press, 2004. Pp. x + 202. $22.00.In A Treatise on Efficacy: Between Western and Chinese Thinking François Jullien argues that the different ways Chinese and Western thinkers have dealt with warfare and diplomacy reflect important differences in how (...) the two cultures understand human action in the world. When Chinese texts such as the Sunzi and the Guiguzi are set up as counterpoints to the Europeans Clausewitz and Machiavelli, Jullien argues that the Aristotelian inheritance of the latter pair is shown to be the cause of their inability to provide clean theories with the consistent predictive power they desired. Chinese strategists, by contrast, meet with no such limitations in the realm of human interaction. The basic difference between Western and Chinese thought that Jullien seeks to demonstrate is that "one constructs a model that is then projected onto the situation, which implies that the situation is momentarily 'frozen.' The other relies on the situation as on a disposition that is known to be constantly evolving" (p. 189; italics in original).Jullien's regular use of the generic terms "Western" and "Chinese" in constructing his comparison will likely give many comparative philosophers pause. But this [End Page 347] need not be a source of worry, as he is careful not to essentialize the two world-views. While he is pointing out patterns and tendencies in the thinking of Europe and China, he is not positing an essential incommensurable difference between them. Rather, he is pointing out that "what remains underdeveloped in the one context is more developed in the other" (p. 145). He goes on to say, "The purpose of our foray into China is not to imagine-let alone fabricate-other 'mentalities'.... It is simply to make use of other possible sources of intelligibility" (ibid.).Jullien begins by showing that Western thought regards human action as something that imposes itself on the world in order to bring about a predetermined goal. This is a natural consequence of the belief that the world is created: belief in creation implies something existing outside that creation, thus an intention behind that creation, and thus a transcendent norm toward which things within that creation aim. This two-leveled ontology of creator and creation yields a distinction between theory and practice, wherein practice always aims-and ultimately fails-at implementing an ideal that is established by theory. This worldview has led to demonstrable success in the sciences but meets with frequent frustration in the arena of human interaction. This limitation has been recognized by strategists in the West but has never been successfully resolved.Aristotle was the first to identify and try to resolve this problem. He posited phronesis as the skill that enables an individual to apply a model to the world successfully. For Aristotle such successful action consists of first identifying one's desired end and then reasoning back to one's present situation in order to establish the best means to achieve that end. Jullien's analysis shows that Clausewitz was working with the same model more than two thousand years later. Clausewitz believed that earlier attempts at creating a general theory of warfare had failed to achieve their goal-namely, to provide a model of warfare that a general could use to ensure victory-because the opponent's actions are unpredictable. The system that the military strategist is dealing with, then, is not mechanistic, and consequently plans are easily frustrated by ever-changing circumstances. But Clausewitz was unable to conceive of strategy as based on anything other than plans.For Clausewitz, warfare is composed of distinct engagements, separate moments in time where an army seeks to impose a plan on the world. Seeing warfare as composed of distinct moments means that time is an opponent, for time brings with it change and uncertainty and thus a greater chance that one's plans will be frustrated. Opportunity, then, is something unexpected-a chance happening at a specific moment that can be taken advantage of only... (shrink)

Generics are sentences such as Birds fly, which express generalizations. They are prevalent in speech, and as far as is known, no human language lacks generics. Yet, it is very far from clear what they mean. After all, not all birds fly—penguins don’t! -/- There are two general views about the meaning of generics in the literature, and each view encompasses many specific theories. According to the inductivist view, a generic states that a sufficient number of individuals satisfy a (...) certain property—in the example above, it says that sufficiently many birds fly. This view faces the complicated problem of spelling out exactly how many is “sufficiently many” in a way that correctly captures the intuitive truth conditions of generics. -/- An alternative, the rules and regulations view, despairs from this project and proposes instead that generics directly express rules in the world. Rules are taken to be abstract objects, which are not related to the properties of specific individuals. This view faces the difficult problem of explaining how people come to know of such rules when judging the truth of falsity of generics, and accounting for the strong intuition that a sentence such as Birds fly talks about birds, not abstract objects. -/- What seems to be beyond dispute is that generics, even if they do not express rules, are lawlike: they state non-accidental generalizations. Many scholars have taken this fact to indicate that generics are parametric on possible worlds: they refer to worlds other than the actual world. This, again, raises the problem of how people come to know about what happens in these other worlds. However, a rigorous application of standard tests for intensionality shows that generics are not, in fact, parametric on possible worlds, but only on time. This unusual property may explain much of the mystery surrounding generics. -/- Another mysterious property of generics is that although there is no language without them, there is no linguistic construction that is devoted to the expression of genericity. Rather, generics can be expressed in a variety of ways, each of which can also express nongenerics. Yet, each manifestation of generics differs subtly (or sometimes not so subtly) in its meaning from the others. -/- Even when these and other puzzles of genericity are solved, one mystery would remain: Why are generics, which are so easy to produce and understand in conversation, so difficult to analyze? (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)

In an attempt to address the theoretical gap between linguistics and philosophy, a group of semanticists, calling itself the Generic Group, has worked to develop a common view of genericity. Their research has resulted in this book, which consists of a substantive introduction and eleven original articles on important aspects of the interpretation of generic expressions. The introduction provides a clear overview of the issues and synthesizes the major analytical approaches to them. Taken together, the papers that follow (...) reflect the current state of the art in the semantics of generics, and afford insight into various generic phenomena. (shrink)

Some generic sentences seem to be true despite the fact that almost all the members of the relevant kind are exceptions. It’s controversial whether generics of this type express relatively weak generalizations or relatively strong ones. If the latter, then we’re systematically mistaken about their truth, but they make no trouble for our semantic theorizing. In this brief note, I present several arguments for the former: sentences of the relevant type are weak generics.

The animalist says we are animals. This thesis is commonly understood as the universal generalization that all human persons are human animals. This article proposes an alternative: the thesis is a generic that admits of exceptions. We defend the resulting view, which we call ‘generic animalism’, and show its aptitude for diagnosing the limits of eight case-based objections to animalism.

Generic statements (e.g., “Birds lay eggs”) express generalizations about categories. In this paper, we hypothesized that there is a paradoxical asymmetry at the core of generic meaning, such that these sentences have extremely strong implications but require little evidence to be judged true. Four experiments confirmed the hypothesized asymmetry: Participants interpreted novel generics such as “Lorches have purple feathers” as referring to nearly all lorches, but they judged the same novel generics to be true given a wide range (...) of prevalence levels (e.g., even when only 10% or 30% of lorches had purple feathers). A second hypothesis, also confirmed by the results, was that novel generic sentences about dangerous or distinctive properties would be more acceptable than generic sentences that were similar but did not have these connotations. In addition to clarifying important aspects of generics’ meaning, these findings are applicable to a range of real-world processes such as stereotyping and political discourse. (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)

Consensus has it that generic sentences such as “Dogs bark” and “Birds fly” contain, at the level of logical form, an unpronounced generic operator: Gen. On this view, generics have a tripartite structure similar to overtly quantified sentences such as “Most dogs bark” and “Typically, birds fly”. I argue that Gen doesn’t exist and that generics have a simple bipartite structure on par with ordinary atomic sentences such as “Homer is drinking”. On my view, the subject terms of (...) generics are kind-referring. The interesting truth conditions characteristic of generics arise from the interesting ways in which kinds inherit properties from their members. (shrink)

This paper is about an underappreciated aspect of generics: their non-specificity. Many uses of generics, utterances like ‘Seagulls swoop down to steal food’, express non-specific generalisations which do not specify their quantificational force or flavour. I consider whether this non-specificity arises as a by-product of context-sensitivity or semantic incompleteness but argue instead that generics semantically express non-specific generalisations by default as a result of quantifying existentially over more specific ones.