Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended a new pluralist thesis. Recent criticisms such as Priest 2006a and Field 2009 have suggested that there is a relationship between their type of logical pluralism and the meaning-variance thesis for logic. This is the claim, often associated with Quine 1970, that a change of logic entails a change of meaning. Here we explore the connection between logical pluralism and meaning- (...) class='Hi'>variance, both in general and for Beall and Restall's theory specifically. We argue that contrary to what Beall and Restall claim, their type of pluralism is wedded to meaning-variance. We then develop an alternative form of logical pluralism that circumvents at least some forms of meaning-variance. (shrink)

An extensive literature overlapping economics, statistical decision theory and finance, contrasts expected utility [EU] with the more recent framework of mean–variance (MV). A basic proposition is that MV follows from EU under the assumption of quadratic utility. A less recognized proposition, first raised by Markowitz, is that MV is fully justified under EU, if and only if utility is quadratic. The existing proof of this proposition relies on an assumption from EU, described here as “Buridan’s axiom” after the French (...) philosopher’s fable of the ass that starved out of indifference between two bales of hay. To satisfy this axiom, MV must represent not only “pure” strategies, but also their probability mixtures, as points in the (σ, μ) plane. Markowitz and others have argued that probability mixtures are represented sufficiently by (σ, μ) only under quadratic utility, and hence that MV, interpreted as a mathematical re-expression of EU, implies quadratic utility. We prove a stronger form of this theorem, not involving or contradicting Buridan’s axiom, nor any more fundamental axiom of utility theory. (shrink)

The paper gives an overview of key themes of twentieth century philosophical treatment of the language of science, with special emphasis on the meaning variance of scientific terms and the comparison of alternative theories. These themes are dealt with via discussion of the topics of: (a) the logical positivist principle of verifiability and the problem of the meaning of theoretical terms, (b) the postpositivist thesis of semantic incommensurability, and (c) the scientific realist response to incommensurability based on (...) the causal theory of reference. (shrink)

Quantifier variance entails that ‘there exists’ has a variety of meanings. Determining what makes all these meanings quantifier meanings is a problem associated with this view. A reasonable candidate suggested by Hirsch is the set of formal rules governing quantification. However, the collapse argument presents a notorious objection to the viability of the candidate: there cannot be more than one quantifier obeying the same rules up to logical equivalence. It is proposed that a quantifier variantist who intends to retain (...) Hirsch’s proposed solution can admit a many-sorted language in order to block the collapse argument. Within the many-sorted language, a Kaplanian thesis about the rules governing sorted quantifiers saves quantifier variance from meaning variance. (shrink)

This article offers a critical review of various ontological-relativist arguments, mostly deriving from the work of W. V. Quine and Thomas K hn. I maintain that these arguments are (1) internally contradictory, (2) incapable of accounting for our knowledge of the growth of scientific knowledge, and (3) shown up as fallacious from the standpoint of a causal-realist approach to issues of truth, meaning, and interpretation. Moreover, they have often been viewed as lending support to such programmes as the 'strong' (...) sociology of knowledge and the turn towards wholesale cultural-relativist doctrines, whether of the Wittgensteinian ('language-games') or Heideggerian (depth-hermeneutic) varieties. Thus Richard Rorty recommends that we should henceforth drop all that old-fashioned talk of 'truth', 'knowledge', or 'reality', since whatever warrants those descriptions from time to time is just the product of some currently favoured language-game or range of elective metaphors. Such ideas have little in common with Quine's general outlook of robust physicalism, nor again - though the case is less clear - with Kuhn's reconsidered approach to these issues as set forth in his 1969 Postscript to The Structure of Scientific Revolutions . However, both thinkers have left themselves open to misconstrual by adopting a sceptical-relativist fallback position in response to the well-known problems with logical empiricism. This essay therefore reviews those problems with reference to alternative, more adequate accounts of what is involved in the process of scientific discovery and theory-change. (shrink)

In the financial markets, there is a well established portfolio optimization model called generalized mean-variance model (or generalized Markowitz model). This model considers that a typical investor, while expecting returns to be high, also expects returns to be as certain as possible. In this paper we introduce a new media optimization system based on the mean-variance model, a novel approach in media planning. After presenting the model in its full generality, we discuss possible advantages of the mean-variance (...) paradigm, such as its flexibility in modeling the optimization problem, its ability of dealing with many media performance indices – satisfying most of the media plan needs – and, most important, the property of diversifying the media portfolios in a natural way, without the need to set up ad hoc constraints to enforce diversification. (shrink)

We analyze the comparative static effects of changes in the means, the standard deviations and the covariance of asset returns in a standard portfolio selection problem when investors have mean variance preferences. Simple and intuitive characterizations in terms of the elasticity of risk aversion are provided.

This paper uses duality to elaborate Slutzky equations of risks in quasi-linear decision models extended by independent background risks. Wealth, substitution and total effects are characterized in terms of mean-variance preferences. It is shown that both Pratt and Zeckhauser’s proper risk aversion and Kimball’s standard risk aversion are sufficient for negative substitution effects.

In his book, The Justification of Scientific Change, Carl Kordig claims that the radical meaning variance view of Feyerabend and others becomes ensnared in a self-referential paradox. The accusation fails because it rests upon a confusion of that view with its "counterparts" in other linguistic/theoretical contexts.

RESUMEN: En este artículo tratamos de hacer plausible la hipótesis de que las conectivas de diferentes lógicas no necesariamente difieren en significado. Utilizando el tratamiento categorista de las conectivas, argumentaremos contra la tesis quineana de que la diferencia de lógicas implica diferencia de significado entre sus conectivas, y ubicamos el cambio de tema en la diferencia de objetos más que en una tal diferencia de significado. Finalmente, intentamos mostrar que ese tratamiento categorista es una forma de minimalismo semántico, de acuerdo (...) con el cual no todos los elementos semánticos usuales son relevantes para determinar el significado de las conectivas.ABSTRACT: We argue here that the meanings of logical connectives need not differ in different logics. treatment of the logical connectives, we argue against the well-known Quinean thesis that a difference between logics implies a difference in the meanings of connectives. We thus locate this change in the difference between certain objects rather than in the difference between the meaning of connectives. Finally, we try to show that the category-theoretic treatment of logical connectives is a form of semantic minimalism, according to which not all the usual semantic components are relevant in fixing the meaning of a connective. (shrink)

Calculation of the mean of an observable in quantum mechanics is typically assumed to require that the state vector be in the domain of the corresponding self-adjoint operator or for a mixed state that the operator times the density matrix be in the trace class. We remind the reader that these assumptions are unnecessary. We state what is actually needed to calculate the mean of an observable as well as its variance.

Quantifier variance holds that different languages can have unrestricted quantifier expressions that differ in meaning, where an expression is a “quantifier” just in case it plays the right inferential role. Several critics argued that J.H. Harris’s “collapse” argument refutes variance by showing that identity of inferential role is incompatible with meaning variance. This standard, syntactic collapse argument has generated several responses. More recently, Cian Dorr proved semantic collapse theorems to generate a semantic collapse argument against (...) variance. The argument is significantly different from standard collapse, so it requires a new response. Here I clarify and analyze the semantic collapse argument, and explain how variantists can and should respond to it. The paper also includes an appendix showing the difficulties of positing identity variance without quantifier variance. The argument in the appendix has yet to appear in print, but is familiar to specialists. (shrink)

This essay clarifies quantifier variance and uses it to provide a theory of indefinite extensibility that I call the variance theory of indefinite extensibility. The indefinite extensibility response to the set-theoretic paradoxes sees each argument for paradox as a demonstration that we have come to a different and more expansive understanding of ‘all sets’. But indefinite extensibility is philosophically puzzling: extant accounts are either metasemantically suspect in requiring mysterious mechanisms of domain expansion, or metaphysically suspect in requiring nonstandard (...) assumptions about mathematical objects. Happily, the view of quantifier meanings that underwrites quantifier variance can be used to provide an account of indefinite extensibility that is both metasemantically and metaphysically satisfying. Section 1 introduces the puzzle of indefinite extensibility; section 2 develops and clarifies the metasemantics of quantifier variance; section 3 solves section 1's puzzle of indefinite extensibility by applying section 2's account of quantifier meanings; and section 4 compares the theory developed in section 3 to several other theories in the literature. (shrink)

Quantifier variance faces a number of difficulties. In this paper we first formulate the view as holding that the meanings of the quantifiers may vary, and that languages using different quantifiers may be charitably translated into each other. We then object to the view on the basis of four claims: (i) quantifiers cannot vary their meaning extensionally by changing the domain of quantification; (ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism; (iii) quantifier (...) class='Hi'>variance is not an ontological doctrine; (iv) quantifier variance is not compatible with charitable translation and as such is internally inconsistent. In light of these troubles, we recommend the dissolution of quantifier variance and suggest that the view be laid to rest. (shrink)

The robustness of the classical tests on means (Z, t, and F) and variances (chi square and F) was investigated by obtaining 30,000 (or, sometimes, 10,000 or 150,000) values of the test statistic under assumption-violating conditions and comparing the actual proportion of Type I errors with the proportion expected when all assumptions are met. The sampling and testing conditions investigated were: population shape (L-shape or bell-shape), relative population variance (1 or 4), sample size (8, 16, or 24), nominal significance (...) level (.05,.01, or.001), and location of rejection region (left-tailed, right-tailed, or two-tailed). All tests on means were nonrobust under most of the investigated conditions, and one was nonrobust under all of them. Both tests on variances were extremely nonrobust under virtually all conditions. The worst nonrobustness of the one- and two-independent-sample Z and t tests rivaled or exceeded that of the notoriously nonrobust chi-square and F tests on variances. (shrink)

Attempting to deflate ontological debates, the proponent of Quantifier Variance (QV) claims that there are multiple quantifier meanings of equal metaphysical merit. According to Hirsch—the main proponent of QV—metaphysical merit should be understood intensionally: two languages have equal merit if they allow us to express the same possibilities. I examine the notion of metaphysical merit and its purported link to intensionality. That link, I argue, should not be supported by adopting an intensional theory of semantic content. Rather, I give (...) a general strategy for supporting claims about metaphysical merit and examine whether that strategy can be used to link merit and intensionality. Though I don’t deliver a definitive verdict, the discussion provides a clearer framework for articulating and evaluating claims about metaphysical merit. (shrink)

The ArgumentMost lay users of statistics think in terms of means (averages), variances or the square of the standard deviation, and Gaussians or bell-shaped curves. Such conventions are entrenched by statistical practice, by deep mathematical theorems from probability, and by theorizing in the various natural and social sciences. I am not claiming that the particular conventions (here, the statistics) we adopt are arbitrary. Entrenchment can be rational without its being as well categorical (excluding all other alternatives), even if that entrenchment (...) claims also to provide for categoricity. 1 provide a detailed description of how a science is “normal” and conventionalized. A characteristic feature of this entrenchment of conventions by practice, theorems, and theorizing, is its highly technical form, the canonizing work enabled by apparently formal and esoteric mathematical means. (shrink)

The aim of the paper is to bring clarity regarding the doctrine of quantifier variance (due to Eli Hirsch), and two prominent arguments against this doctrine, the collapse argument and the Eklund-Hawthorne argument. Different versions of the doctrine of quantifier variance are distinguished, and it is shown that the effectiveness of the arguments against it depends on what version of the doctrine is at issue. The metaontological significance of the different versions of the doctrine are also assessed. Roughly, (...) quantifier variance concerns there being different possible existential quantifier meanings, and often the doctrine involves a claim to the effect there is no unique “best” quantifier meaning. Much of the discussion in the paper concerns what it is to be an existential quantifier meaning in the sense at issue. (shrink)

Eli Hirsch recently suggested the metaontological doctrine of so-called "quantifier variance", according to which ontological disputes—e.g. concerning the question whether arbitrary, possibly scattered, mereological fusions exist, in the sense that these are recognised as objects proper in our ontology—can be defused as insubstantial. His proposal is that the meaning of the quanti er `there exists' varies in such debates: according to one opponent in this dispute, some existential statement claiming the existence of, e.g., a scattered object is true, (...) according to the other it is not. This paper argues that Hirsch's proposal leads into inconsistency. (shrink)

This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of semantics, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence of rules. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of Bohr's (...) principle of correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic. (shrink)

When using sample data to decide whether two populations differ, laypeople attend to the difference between group means, but largely overlook within-group variability (Obrecht, Chapman, & Gelman, 2007). We show, first, that laypeople know about and use story-implied variability when making pairwise comparisons. Then we demonstrate that participants' sensitivity to variance in a dataset is boosted when presented in a context that implies consistent variance information. Statistical data were couched in stories about electrical conductivity measurements obtained from element (...) samples (low-variability category) or body weight measurements from samples of peoples (high-variability category). We manipulated, between participants, whether the data variance matched or mismatched the story-implied variability. Participants who received data in a matching context showed high sensitivity to variance, while those in the mismatching condition did not. Laypeople use statistical data to make reasonable inferences when those data are provided in a context that makes sense. (shrink)

Change of logic is typically taken as requiring that the meanings of the connectives change too. As a result, it has been argued that legitimate rivalry between logics is under threat. This is, in a nutshell, the meaning‐variance argument, traditionally attributed to Quine. In this paper, we present a semantic framework that allows us to resist the meaning‐variance claim for an important class of systems: classical logic, the logic of paradox and strong Kleene logic. The major (...) feature of the semantics is that the connectives have the same meanings in these systems, so that the meaning‐variance argument is straightforwardly blocked. We discuss the effects of this semantics for two uses of the argument of meaning variance, and also consider its impact on related issues. (shrink)

This paper gives a formulation of quantum logic in the abstract algebraic setting laid out by Dunn and Hardegree (2001). On this basis, it provides a comparative analysis of viable quantum logical bivalent semantics and their classical counterparts, thereby showing that the truth-functional status of classical and quantum connectives is not as different as usually thought. Then it points out that bivalent semantics for quantum logic - compatible with realism about quantum mechanics - can be maintained, albeit at the price (...) of truth-functionality. Finally, the paper improves on Hellman (1980)'s argument that this lack of truth-functionality entails a change of meaning between classical and quantum logical connectives. (shrink)

Quantifier variantists accept multiple alternative ontological languages in which quantifiers obey the usual inference rules despite having different meanings. But collapse arguments seem to show that these quantifiers would be provably equivalent to one another. Cian Dorr has pushed this discussion forward by formulating the collapse argument in terms of an algebra of meanings that are common amongst the languages. I attempt to show that quantifier variantists can respond. But an important distinction between types of quantifier variance emerges, between (...) those in which quantifier meanings draw on a single objective backbone of “portions of reality,” and those (such as the type that is arguably associated with neo-Fregeanism) in which they do not. (shrink)

Showing that the arithmetic mean number of offspring for a trait type often fails to be a predictive measure of fitness was a welcome correction to the philosophical literature on fitness. While the higher mathematical moments of a probability-weighted offspring distribution can influence fitness measurement in distinct ways, the geometric mean number of offspring is commonly singled out as the most appropriate measure. For it is well-suited to a compounding process and is sensitive to variance in offspring number. The (...) geometric mean thus proves to be a predictively efficacious measure of fitness in examples featuring discrete generations and within- or between-generation variance in offspring output. Unfortunately, this advance has subsequently led some to conclude that the arithmetic mean is never a good measure of fitness and that the geometric mean should accordingly be the default measure of fitness. We show not only that the arithmetic mean is a perfectly reasonable measure of fitness so long as one is clear about what it refers to, but also that it functions as a more general measure when properly interpreted. It must suffice as a measure of fitness in any case where the geometric mean has been effectively deployed as a measure. We conclude with a discussion about why the mathematical equivalence we highlight cannot be dismissed as merely of mathematical interest. (shrink)

Thomas S. Kuhn claimed that the meanings of scientific terms change in theory changes or in scientific revolutions. In philosophy, meaning change has been taken as the source of a group of problems, such as untranslatability, incommensurability, and referential variance. For this reason, the majority of analytic philosophers have sought to deny that there can be meaning change by focusing on developing a theory of reference that would guarantee referential stability. A number of philosophers have also claimed (...) that Kuhn’s view can be explained by the fact that he accepted and further developed many central tenets of logical empiricism. I maintain that the genesis of Kuhn’s meaning theorising lies in his historical approach and that his view of meaning change is justified. Later in his career he attempted to advance a theory of meaning and can be said to have had limited success in it. What is more, recent cognitive science has unexpectedly managed to shed light on Kuhn’s insights on the organisation of information in the mind, concept learning, and concept definition. Furthermore, although Kuhn’s critique of Putnam’s causal theory of reference has often been dismissed as irrelevant, he has a serious point to address. Kuhn thought that the causal theory that works so well with proper names cannot work with scientific terms. He held that conceptual categories are formed by similarity and dissimilarity relations; therefore, several features and not only one single property are needed for determination of extension. In addition, the causal theory requires universal substances as points of reference of scientific terms. Kuhn was a conceptualist, who held that universals do not exist as mind-independent entities and that mind-dependent family resemblance concepts serve the role of universals. Further, at the beginning of his career, Kuhn was interested in the question of what concepts or ideas are and how they change in their historical context. Although he did not develop his theorising on this issue, I demonstrate that this is a genuine problem in the philosophy of history. Finally, Kuhn argued that scientists cannot have access to truth in history because we cannot transcend our historical niche, and as a consequence, the truth of a belief cannot be a reason for theory choice. Instead of truth, we can rely on justification. I also discuss Kuhn’s idea that problem-solving is the main aim of science and show that this view can be incorporated into coherentist epistemology. (shrink)

Statistical models and expected mean squares [E(MS)] are important concepts that facilitate the extensive use of analysis of variance designs. These concepts were developed in the basic statistics area from 1939 through the 1950s. They were introduced into psychological statistics during the late 1950s and have been useful in attacking some statistical problems. Also, they simplify the teaching of ANOVA designs.

In this paper I examine cases in which we attach different meanings to words and in which we litigate or argue about the best way of defining the term in dispute. I reject the idea that this is just a matter of imposing our will on our interlocutors – I think that the process of litigation is normative. To some extent recent work in the theory of argumentation has shed considerable light on this process, but we will need to retrofit (...) that work for the kinds of considerations we are engaged with here. I’ll begin in Section 1, with some important terminological preliminaries. Then in Section 2, I will offer a general description of how we come to notice that there are disputes about meaning and how we engage the meaning variance once it is recognized. In section 3 I’ll then take up a case that is relatively less controversial – the definition of ‘planet’ – and use it to construct a model for our meaning litigation works. Finally, in section 4 I’ll then turn to more contentious and substantial issues – the definition of ‘rape’ and the definition of ‘person’ and begin exploring how disputes about the meanings of those terms can be normative and fail to be normative. (shrink)

This article looks at Galton's regression to the mean from several traditionally unrelated but interwoven venues: as a law of trait heredity; as a statistical artifact infiltrating careless research designs; as an illustration of cognitive bias. Hereditarians argue for the first of these, disputed by biogeneticists, who view R to M as a mere correlate of generational traits decline. Research designers busy themselves with the second perspective, but to explain the concept, cavalierly adduce various organismic states that sum as "error (...) variance" Research on subjective probability finds R to M in unexpected places. Across these contexts, the weight of argument falls on R to M's confounding rather than causal role in vexing data analysis. 2012 APA, all rights reserved). (shrink)

Although mind‐wandering research is rapidly progressing, stark disagreements are emerging about what the term “mind‐wandering” means. Four prominent views define mind‐wandering as (a) task‐unrelated thought, (b) stimulus‐independent thought, (c) unintentional thought, or (d) dynamically unguided thought. Although theorists claim to capture the ordinary understanding of mind‐wandering, no systematic studies have assessed these claims. Two large factorial studies present participants (N = 545) with vignettes that describe someone's thoughts and ask whether her mind was wandering, while systematically manipulating features relevant to (...) the four major accounts of mind‐wandering. Dynamics explains between four and 40 times more variance in participants' mind‐wandering judgments than other features. Our third study (N = 153) tests and supports a unique prediction of the dynamic framework—obsessive rumination contrasts with mind‐wandering. Our final study (N = 277) used vignettes that resemble mind‐wandering experiments. Dynamics had significant and large effects, while task‐unrelatedness was nonsignificant. These results strongly suggest that the central feature of mind‐wandering is its dynamics. (shrink)

Many men who have sex with men (MSM) express feeling marginalized by discourses within public health and sexual health nursing that determine bareback sex is deviant and unsafe. Their resistance to risk‐based discourses can be seen within radical sex practices such as deliberately becoming‐infected with HIV (bug‐chasing) and breeding‐infection (gift‐giving). The metaphors of bug‐chasing and gift‐giving, particularly those spread across global online spaces, can influence the sexual experiences and practices of MSM. A metaphor analysis was conducted of Internet forums discussing (...) HIV chasing and gifting metaphors, and showed a variety of discursive meanings, tactics and effects to the radical sex practice. A radical research approach was used to explore the processes of becoming‐infected and breeding‐infection as determinant steps in the symbolic resistance of risk‐based discourses, as well as the creation of new forms of life and community among MSM. Our analyses demonstrate how the gifting/chasing metaphors express MSM's marginalization as well as their lines of flight from having their practices captured within public health discourses. We hope to offer alternative nursing approaches for thinking through and engaging with transgressive and queer sexual practices. (shrink)

This paper discusses the reliance of numerical analysis on the concept of the standard deviation, and its close relative the variance. It suggests that the original reasons why the standard deviation concept has permeated traditional statistics are no longer clearly valid, if they ever were. The absolute mean deviation, it is argued here, has many advantages over the standard deviation. It is more efficient as an estimate of a population parameter in the real-life situation where the data contain tiny (...) errors, or do not form a completely perfect normal distribution. It is easier to use, and more tolerant of extreme values, in the majority of real-life situations where population parameters are not required. It is easier for new researchers to learn about and understand, and also closely linked to a number of arithmetic techniques already used in the sociology of education and elsewhere. We could continue to use the standard deviation instead, as we do presently, because so much of the rest of traditional statistics is based upon it (effect sizes, and the F-test, for example). However, we should weigh the convenience of this solution for some against the possibility of creating a much simpler and more widespread form of numeric analysis for many. (shrink)