The starting point for the contemporary debate about theories of health should be the holistic theory of Lennart Nordenfelt, claims George Khushf, not the refuted theory of Christopher Boorse. The present paper is an attempt to challenge Nordenfelt and to present an alternative theory to his and other theories, including Boorse’s. The main problems with Nordenfelt’s theory are that it is relativistic, that it leads to counter-intuitive results as to what goals can count as healthy, that (...) it focuses on the wrong kind of abilities, that it makes measuring health extra difficult, and that it does not give us a sufficient account of health, at most a necessary one. The alternative theory proposed is two-dimensional. First, health is to have developed the abilities and dispositions that members of one’s culture typically develop, and be able to use them, in acceptable circumstances; and second, health is to experience positive moods and sensations, the kinds that have internal causes. The theory solves the problems attached to Nordenfelt’s theory by not being individual relativistic, by eliminating the goals in the definition, by giving an alternative interpretation of “ability,” by making health easier to measure, and by adding the dimension of well-being that, together with health as ability, not only gives us a necessary, but also a sufficient, account of health. (shrink)

Scientific representation is an interesting topic for philosophers of science, many of whom have recently explored it from different points of view. There are currently two competing approaches to the issue: cognitive and non-cognitive, and each of them claims its own merits over the other. This article tries to provide a hybrid theory of scientific representation, called Two-Dimensional Theory of Scientific Representation, which has the merits of the two accounts and is free of their shortcomings. To do (...) this, we will argue that although scientific representation needs to use the notion of intentionality, such a notion is defined and realized in a simply structural form contrary to what cognitive approach says about intentionality. After a short introduction, the second part of the paper is devoted to introducing theories of scientific representation briefly. In the third part, the structural accounts of representation will be criticized. The next step is to introduce the two-dimensional theory which involves two key components: fixing and structural fitness. It will be argued that fitness is an objective and non-intentional relation, while fixing is intentional. (shrink)

What determines whether an object is an artwork? In this paper I consider what I will call ‘social’ theories of art, according to which the arthood of objects depends in some way on the art-related social practices that we have. Though such a dependence claim is plausible in principle, social theories of art tend to unpack the determining link between artworks and social practices in terms of intentional relations between the objects in question and the people involved in the relevant (...) practices. This intentionalism has unappealing upshots. Drawing on two-dimensional approaches in social ontology, I show how social theories of art can be done differently, improving their prospects. (shrink)

The theories that form the heterogeneous family of two‐dimensional or 2D semantics are rooted in the tradition of possible‐worlds semantics made popular by Saul Kripke and David Lewis. Advocates of 2D semantics agree that recognizing a dependence of truth on fact is not enough. Advocates of two‐dimensional semantics share a second trademark idea. They agree that the familiar apparatus of worlds‐cum‐intensions can be modified so as to capture both the dependencies they see. The commitments of all 2D theories (...) can basically be captured by one and the same formal framework of worlds‐cum‐intensions. David Kaplan's semantics aims to cover pure indexicals such as 'today' alongside impure indexicals such as 'you' and demonstratives such as 'this'. Kaplan starts off with two 'obvious principles': The referent of an indexical systematically depends on the respective context; and Indexicals are directly referential. (shrink)

Graeme Forbes (2011) raises some problems for two-dimensional semantic theories. The problems concern nested environments: linguistic environments where sentences are nested under both modal and epistemic operators. Closely related problems involving nested environments have been raised by Scott Soames (2005) and Josh Dever (2007). Soames goes so far as to say that nested environments pose the “chief technical problem” for strong two-dimensionalism. We call the problem of handling nested environments within two-dimensional semantics “the nesting problem”. We show that (...) the two-dimensional semantics for attitude ascriptions developed in Chalmers (2011a) has no trouble accommodating certain forms of the nesting problem that involve factive verbs such as “know” or “establish”. A certain form of the nesting problem involving apriority and necessity operators does raise an interesting puzzle, but we show how a generalized version of the nesting problem arises independently of two-dimensional semantics—it arises, in fact, for anyone who accepts the contingent a priori. We, then, provide a two-dimensional treatment of the apriority operator that fits the two-dimensional treatment of attitude verbs and apply it to the generalized nesting problem. We conclude that two-dimensionalism is not seriously threatened by cases involving the nesting of epistemic and modal operators. (shrink)

. David Chalmerss version of two-dimensional semantics is an attempt at setting up a unified semantic framework that would vindicate both the Fregean and the Kripkean semantic intuitions. I claim that there are three acceptable ways of carrying out such a project, and that Chalmerss theory does not coherently fit any of the three patterns. I suggest that the theory may be seen as pointing to the possibility of a double reading for many linguistic expressions (a double (...) reading which, however, is not easily identified with straightforward semantic ambiguity). (shrink)

Two-dimensional semantic theories distinguish between two different aspects, or ‘dimensions’, of the meaning of linguistic expressions. Many other theories identify the meaning of an expression with a dependency of its extension on the state of the world. (The extension of a sentence is its truth-value, and the extension of a sub-sentential expression … Continue reading Semantics, Two-Dimensional →.

This paper is about two requirements on wish reports whose interaction motivates a novel semantics for these ascriptions. The first requirement concerns the ambiguities that arise when determiner phrases, such as definite descriptions, interact with ‘wish’. More specifically, several theorists have recently argued that attitude ascriptions featuring counterfactual attitude verbs license interpretations on which the determiner phrase is interpreted relative to the subject’s beliefs. The second requirement involves the fact that desire reports in general require decision-theoretic notions for their analysis. (...) The current study is motivated by the fact that no existing account captures both of these aspects of wishing. I develop a semantics for wish reports that makes available belief-relative readings but also allows decision-theoretic notions to play a role in shaping the truth conditions of these ascriptions. The general idea is that we can analyze wishing in terms of a two-dimensional notion of expected utility. (shrink)

According to two-dimensional semantics, primary intension and secondary intension can play the role of reflecting the cognitive aspect of an expression like Fregean sense does. The aim of this paper is to argue that this role is likely a myth. To argue for this, I attempt to show that cognitive aspects of fictional names cannot be explained within the framework of two-dimensional semantics. To be more specific, I consider four ontological theories about fictional characters that two-dimensional semanticists (...) might be tempted to choose. And then, I argue that none of them can be combined with two-dimensional semantics in a satisfactory way. (shrink)

In contrast to standard possible worlds semantics, possible worlds in a two-dimensional semantic framework play two kinds of roles, rather than just one. This allows the framework to assign two kinds of intensions to expressions, rather than just one. Its fruitful use in explicating modal operators and the meanings of referential expressions like indexicals has led to two-dimensional accounts that seek to revive the Fregean conception of meaning, or more specifically the descriptivist view of reference, which has fallen (...) into disrepute due to intense criticisms, most famously, by Saul Kripk’s seminal work Naming and Necessity (1972). This entry provides a critical overview of the two most prominent of such accounts, proposed by Frank Jackson and David Chalmers. Unfortunately, there is not space to describe either account in detail, so I rely largely on brief descriptions and plenty of references to primary and secondary sources. More importantly, I rely on focusing on how the accounts explain the phenomenon of necessary a posteriori identity that Kripke’s well-known examples (such as ‘Hesperus is Phosphorus’) have brought to light. Focusing on and structuring our discussions around this phenomenon is by no means just an expository convenience. These cases are of central importance in themselves. They epitomize a large part of the contribution of Naming and Necessity to the theory of reference. This is why section 2 outlines Kripke’s critique of the Fregean theory of referential expressions and section 3 explains rigid designation and identity statements. Section 4 discusses rigidification and the notion of a world considered as actual, leading to the introduction of two-dimensional functions in Section 5. I discuss, finally, Frank Jackson’s and David Chalmers’ two-dimensionalism in Sections 6 and 7. Section 8 makes a few critical remarks on Jackson’s handling of the semantic argument. I conclude (Section 8) by discussing the important distinction between semantics and metasemantics. (shrink)

Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional (...) semantics. I also describe some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem. (shrink)

Two-dimensional (2D) semantics is a formal framework that is used to characterize the meaning of certain linguistic expressions and the entailment relations among sentences containing them. 2D semantics has also been applied to thought contents. In contrast with standard possible worlds semantics, 2D semantics assigns extensions and truth-values to expressions relative to two possible world parameters, rather than just one. So a 2D semantic framework provides finer-grained semantic values than those available within standard possible world semantics, while using the (...) same basic model-theoretic resources. The 2D framework itself is just a formal tool. To develop a semantic theory for someone’s language, a proponent of 2D semantics must do three things: (i) explain what exactly the two possible world parameters represent, (ii) explain the rules for assigning 2D semantic values to a person’s words and sentences, and (iii) explain how 2D semantic values help in understanding the meanings of the person’s words and sentences. (shrink)

This paper presents a new two-dimensional Multiple-Choice Model accounting for Omissions (MCMO). Based on Thissen and Steinberg multiple-choice models, the MCMO defines omitted responses as the result of the respondent not knowing the correct answer and deciding to omit rather than to guess given a latent propensity to omit. Firstly, using a Monte Carlo simulation, the accuracy of the parameters estimated from data with different sample sizes (500, 1,000, and 2,000 subjects), test lengths (20, 40, and 80 items) and (...) percentages of omissions (5, 10, and 15%) were investigated. Later, the appropriateness of the MCMO to the Trends in International Mathematics and Science Study (TIMSS) Advanced 2015 mathematics and physics multiple-choice items was analyzed and compared with the Holman and Glas' Between-item Multi-dimensional IRT model (B-MIRT) and with the three-parameter logistic (3PL) model with omissions treated as incorrect responses. The results of the simulation study showed a good recovery of scale and position parameters. Pseudo-guessing parameters ( d ) were less accurate, but this inaccuracy did not seem to have an important effect on the estimation of abilities. The precision of the propensity to omit strongly depended on the ability values (the higher the ability, the worse the estimate of the propensity to omit). In the empirical study, the empirical reliability for ability estimates was high in both physics and mathematics. As in the simulation study, the estimates of the propensity to omit were less reliable and their precision varied with ability. Regarding the absolute item fit, the MCMO fitted the data better than the other models. Also, the MCMO offered significant increments in convergent validity between scores from multiple-choice and constructed-response items, with an increase of around 0.02 to 0.04 in R 2 in comparison with the two other methods. Finally, the high correlation between the country means of the propensity to omit in mathematics and physics suggests that (1) the propensity to omit is somehow affected by the country of residence of the examinees, and (2) the propensity to omit is independent of the test contents. (shrink)

Pablo Gilabert and Holly Lawford-Smith have, both in collaboration and individually, provided a compelling account of feasibility, which states that feasibility is both ‘binary’ and ‘scalar’, and both ‘synchronic’ and ‘diachronic’. This two-dimensional analysis, however, has been the subject of four major criticisms: it has been argued that it rests upon a false distinction between ‘hard’ and ‘soft’ constraints, that it ignores the importance of intentional action, and that diachronic feasibility is incoherent and insensitive to the existence of epistemic (...) limitations. In this paper, I will argue that such objections do not undermine the persuasiveness of Gilabert and Lawford-Smith’s analysis. Nevertheless, I will contend that the latter is susceptible to two other challenges. First, it mistakenly appeals to morality, and, second, it lacks an analysis of ability. I will maintain, however, that such criticisms can be addressed and that a revised version of the account should be adopted. (shrink)

The paper identifies two major strands of truth theories, ontological and epistemological ones, and argues that both are of equal primacy and find their home within two-dimensional semantics. Contrary to received views, it argues further that epistemological truth theories operate on Lewisian possible worlds and ontological truth theories on Wittgensteinian possible worlds and that both are mediated by the so-called epistemic-ontic map the further specification of which is of utmost philosophical importance.

Philosophical views about the logical structure of time are typically divided between proponents of A and B theories, based on McTaggart's A and B series. Drawing on Paul Ricoeur's hermeneutic phenomenology, I develop and defend McTaggart's thesis that the C series and the A series working together give a consistent description of temporal experience, provided that the two series are treated as distinct dimensions internal to time. In the proposed two-dimensional model, the C series expresses a nesting order of (...) the constitutive states of a world, whereas ontological continuity and change are properties of the A series. This, I argue, allows limited backward causation. (shrink)

David’s epistemic understanding of two-dimensional semantics has these two features. First, although he considers at least two construals of epistemically possible worlds, on one of them they are centered metaphysically possible worlds. Second, David intends epistemic two-dimensional semantics to yield a theory of propositional-attitude content, as well as having application to the semantics of natural language expressions. These two features come together in David’s “The Components of Content,” where he deploys the apparatus of epistemic two-dimensional semantics (...) to provide an account of propositional-attitude content, and where, for reasons of simplicity and familiarity, epistemically possible worlds are taken to be centered metaphysically possible worlds. My talk is about this account of content. (shrink)

Tout le monde ne sait pas que l’eau est du H2O. Supposons qu’Alice soit l’une de ces personnes. Alice dit : « Pour autant que je sache, l’eau pourrait ne pas être du H2O. » Intuitivement, il semble qu’Alice ait dit quelque chose de vrai. Autrement dit, il semble qu’il soit épistémiquement possible (pour Alice) que l’eau ne soit pas du H2O. Pourtant, les conceptions traditionnelles de la modalité en linguistique et en philosophie du langage prédisent que tout énoncé métaphysiquement (...) impossible est également épistémiquement impossible (pour qui que ce soit). Or, il y a des arguments plausibles, venant de Kripke et d’autres, qui prétendent montrer qu’il est métaphysiquement impossible pour l’eau d’être quoi que ce soit d’autre que du H2O. Selon ces conceptions standards de la modalité, Alice a donc en fait dit quelque chose de faux. Ce résultat est hautement contre-intuitif. Je propose une nouvelle théorie de la modalité qui est capable de représenter ce que j’appelle des IMEPs : des impossibilités métaphysiques épistémiquement possibles. Des phrases comme : « L’eau pourrait ne pas être du H2O» et « Hesperus pourrait ne pas être Phosphorus » sont des exemples d’IMEPs, et d’autres peuvent être facilement trouves (y compris certains qui ne reposent pas sur des considérations kripkéennes touchant a la possibilité métaphysique). Ma théorie explique l’existence d’IMEPs tout en conservant la souplesse et la puissance explicative des conceptions standards. (shrink)

Two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. Usually, this theory is presented in an informal manner. In this thesis, I take first steps in formalizing it, and use the formalization to present some considerations in favor of two-dimensional semantics. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, (...) actuality, and apriority that captures the relevant ideas of two-dimensional semantics. I use this to show that some criticisms of two-dimensional semantics that claim that the theory is incoherent are not justified. I also axiomatize the logic, and compare it to the most important proposals in the literature that define similar logics. To indicate that two-dimensional semantics is a plausible semantic theory, I give an argument that shows that all theorems of the logic can be philosophically justified independently of two-dimensional semantics. (shrink)

In this paper I put forward a representationalist theory of conscious experience based on Robert Stalnaker's version of two-dimensional modal semantics. According to this theory the phenomenal character of an experience correlates with a content equivalent to what Stalnaker calls the diagonal proposition. I show that the theory is closely related both to functionalist theories of consciousness and to higher-order representational theories. It is also more compatible with an anti-Cartesian view of the mind than standard representationalist (...) theories. (shrink)

Moral realists can, and should, allow that the truth-conditional content of moral judgments is in part attitudinal. I develop a two-dimensional semantics that embraces attitudinal content while preserving realist convictions about the independence of moral facts from our attitudes. Relative to worlds “considered as counterfactual,” moral terms rigidly track objective, response-independent properties. But relative to different ways the actual world turns out to be, they nonrigidly track whatever properties turn out to be the objects of our relevant attitudes. This (...) theory provides realists with a satisfactory account of Moral Twin Earth cases and an improved response to Blackburn’s supervenience argument. (shrink)

In this paper we revisit Pavel Tichý’s novel distinction between one-dimensional and two-dimensional conception of inference, which he presented in his book Foundations of Frege’s Logic (1988), and later in On Inference (1999), which was prepared from his manuscript by his co-author Jindra Tichý. We shall focus our inquiry not only on the motivation behind the introduction of this non-classical concept of inference, but also on further inspection of selected Tichý’s arguments, which we see as the most compelling (...) or simply most effective in providing support for his two-dimensional account of inference. Main attention will be given to exposing the failure of one-dimensional theory of inference in its explanation of indirect (reductio ad absurdum) proofs. Lastly, we discuss shortly the link between two-dimensional inference and deduction apparatus of Tichý’s Transparent Intensional Logic. (shrink)

We discuss two interpretations of two-dimensional semantics (2DMS) due to D. Chalmers and R. Stalnaker. The main problem with both interpretations of the formal framework is the relinquishng of rigidity for terms. They are in a sense unfaithful to an agent's beliefs. We present alternative principles to capture what we take to be agents's beliefs, namely: the principles of hyper-rigidity and backward reference to actuality. We propose then to go back to a one-dimensional semantics which affords a satisfactory (...) model of beliefs reports. Our proposal, like 2DMS, addresses typical problems of representation for beliefs and epistemological difficulties related to modal knowledge. (shrink)

This theoretical note proposes a two-dimensional cognitive architecture for dual-process theories of reasoning and decision making. Evans (2007b, 2008a, 2009) distinguishes between two types of dual-processing models: parallel-competitive , in which both types of processes operate in parallel, and default-interventionist , in which heuristic processes precede the analytic processes. I suggest that this temporal dimension should be enhanced with a functional distinction between interactionist architecture, in which either type of process influences the content and valence of the other, and (...) independent architecture, in which they do not. Override architecture is a special case of the latter, which postulates statistical interaction, but no interaction of valence and content. I show that this added dimensional distinction casts doubt on two assumptions of statistical modelling that Evans makes: independence and linearity. However, Evans' (2007b) point, that statistical modelling is underspecified vis- -vis the verbal theory, is given further support. The functional dimension is crucial to interpreting the statistical model, as well as to theoretical understanding of the cognitive architecture and its educational applications. (shrink)

This paper endeavors to establish foundations for the interaction between hyperintensional semantics and two-dimensional indexing. I examine the significance of the semantics, by developing three, novel interpretations of the framework. The first interpretation provides a characterization of the distinction between fundamental and derivative truths. The second interpretation demonstrates how the elements of decision theory are definable within the semantics, and provides a novel account of the interaction between probability measures and hyperintensional grounds. The third interpretation concerns the contents (...) of the types of intentional action, and the semantics is shown to resolve a puzzle concerning the role of intention in action. Topic-sensitive two-dimensional truthmaker semantics can be interpreted epistemically and metasemantically. (shrink)

The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it has (...) a polynomial-space lower bound for the domains of type, and has a #P lower bound for the domains of type. (shrink)

In somatic medicine, diagnostic terms often refer to the disease processes that are the causes of patients' symptoms. The language used in some clinical textbooks and health information resources suggests that this is also sometimes assumed to be the case with diagnoses in psychiatry. However, this seems to be in tension with the ways in which psychiatric diagnoses are defined in diagnostic manuals, according to which they refer solely to clusters of symptoms. This paper explores how theories of reference in (...) the philosophy of language can help to resolve this tension. After the evaluation of descriptive and causal theories of reference, I put forward a conceptual framework based on two-dimensional semantics that allows the causal analysis of diagnostic terms in psychiatry, while taking seriously their descriptive definitions in diagnostic manuals. While the framework is presented as a solution to a problem regarding the semantics of psychiatric diagnoses, it can also accommodate the analysis of diagnostic terms in other medical disciplines. (shrink)

In contemporary scholarship on Chinese ideological debates, both pro-system Chinese intellectuals and Western-based academics present China’s future as a binary choice between a “China Model” of authoritarian statism and a “Western” vision of democratic liberalism. This article deconstructs this dichotomy by proposing a new heuristic for conceptualizing ideological cleavage. Informed by interviews with twenty-eight leading Chinese intellectuals, the case is made for a two-dimensional spectrum allowing for ideological co-variation, on one axis, between two contending socioeconomic roads of national revival, (...) capitalism and socialism, and on the other axis between paternalism and fraternalism as conflicting ideals for the political system. This model not only resonates with Chinese intellectual history, but also allows us to uncover two crucial ideological tendencies that disappear with the China Model/western Path dichotomy: (i) the emerging hybrid of Confucian politics and free market economics, and (ii) the tabooed fraternalist-socialist legacy of the 1989 movement. (shrink)

In this paper, we describe a framework for studying social agents’ individual decision making, that takes account of the environment and social dynamics. We describe a study in which we explored the efficiency of foraging strategies within a group of individuals faced with a resource-limited environment. We investigated to what extent cooperative and non-cooperative behaviors impacted on the survival rates of a population of individuals. In the experiment presented here, we considered two different types of individuals: selfish individuals who gather (...) energy for their own use, and cooperative individuals who share the energy they gather with others, thus reducing their own individual chances of survival. In order to study the trade-off between non-cooperative and cooperative behaviors in a pseudo-realistic two-dimensional environment, we introduced an agent-based modeling and simulation tool called ACACIA-ES, which simulated local interactions and spatial behavior for large numbers of individuals in complex environments. The main result from our simulation was that a group of cooperative individuals displayed better survival strategies than groups of selfish individuals when faced with a variety of environmental pressures; however, it was very unlikely that such cooperative strategies could resist competition from selfish individuals, if the outcome of past social interactions was memorized, even when a very small group of selfish individuals was introduced. (shrink)

Nondeterministic models of collective choice posit convergence among the outcomes of simple-majority decisions. The object of this research is to estimate the extent of convergence of majority choice under different procedural conditions. The paper reports results from a computer simulation of simple-majority decision making by committees. Simulation experiments generate distributions of majority-adopted proposals in two-dimensional space. These represent nondeterministic outcomes of majority choice by committees. The proposal distributions provide data for a quantitative evaluation of committee-choice procedures in respect to (...) outcome convergence. Experiments were run under general conditions, and under conditions that restrict committee choice to several game-theoretic solution sets. The findings are that, compared to distributions of voter ideal points, majority-adopted proposals confined to the solution sets demonstrate different degrees of convergence. Second, endogenous agenda formation is a more important obstacle to convergence than the inherent instability of simple-majority rule. Third, if members maximize preferences in respect to agenda formation, a committee choice that approximates the central tendency of the distribution of voter preferences is unlikely. The conclusion is that the most effective way to increase the convergence of majority choice is to restrict the role of individual preferences in agenda formation: identification of proposals to be voted up or down by a committee. (shrink)

In the course of the last thirty years, feminist theories of gender have shifted from quasi-Marxist, labor-centered conceptions to putatively “post-Marxist”culture- and identity-based conceptions. Reflecting a broader political move from redistribution to recognition, this shift has been double-edged. On the one hand, it has broadened feminist politics to encompass legitimate issues of representation, identity, and difference. Yet, in the context of an ascendant neoliberalism, feminist struggles for recognition may be serving to less to enrich struggles for redistribution than to displace (...) the latter. I aim to resist that trend. In this essay, I propose an analysis of gender that is broad enough to house the full range of feminist concerns, those central to the old socialist-feminism as well as those rooted in the cultural turn. I also propose a correspondingly broad conception of justice, capable of encompassing both distribution and recognition, and a non-identitarian account of recognition, capable of synergizing with redistribution. I conclude by examining some practical problems that arise when we try to envision institutional reforms that could redress gender maldistribution and gender misrecognition simultaneously. (shrink)

Ontological commitments and other problems concerning existence arise in connection with various aspects of logical theories. The semantics of quantification theory is usually formulated in such a manner that theorems are all and only those formulae which come out true under all interpretations in all non-empty domains. There are several approaches to include the empty domain. Paradoxically this apparent semantic extension means surrendering several formulae which are valid and intuitively plausible.

We develop the theory of symmetry for a two-level quantum system in oder to illustrate the main ideas of the general theory of symmetry in quantum theory. It is based on the diffeomorphism of the two-dimensional sphere S 2 onto the space of states ℂP 1 and the isomorphism between the groups Pℳ(2) and SO 3 (ℝ). In particular, rotational invariance leads to the appearance of the spin1/2 in a natural way.

I argue that dimensional analysis provides an answer to a skeptical challenge to the theory of model mediated measurement. The problem arises when considering the task of calibrating a novel measurement procedure, with greater range, to the results of a prior measurement procedure. The skeptical worry is that the agreement of the novel and prior measurement procedures in their shared range may only be apparent due to the emergence of systematic error in the exclusive range of the novel (...) measurement procedure. Alternatively: what if the two measurement procedures are not in fact measuring the same quantity? The theory of model mediated measurement can only say that we _assume_ that there is a common quantity. In contrast, I show that the satisfaction of dimensional homogeneity across the metrological extension is independent evidence for the so-called assumption. This is illustrated by the use of dimensional analysis in high pressure experiments. This results in an extension of the theory of model mediated measurement, in which a common quantity in metrological extension is no longer assumed, but hypothesized. (shrink)

Previous theories of early vision have assumed that visual search is based on simple two-dimensional aspects of an image, such as the orientation of edges and lines. It is shown here that search can also be based on three-dimensional orientation of objects in the corresponding scene, provided that these objects are simple convex blocks. Direct comparison shows that image-based and scene-based orientation are similar in their ability to facilitate search. These findings support the hypothesis that scene-based properties are (...) represented at preattentive levels in early vision. (shrink)

One of Kripke's fundamental objections to descriptivism was that the theory misclassifies certain _a posteriori_ propositions expressed by sentences involving names as _a priori_. Though nowadays very few philosophers would endorse a descriptivism of the sort that Kripke criticized, many find two-dimensional semantics attractive as a kind of successor theory. Because two-dimensionalism needn't be a form of descriptivism, it is not open to the epistemic argument as formulated by Kripke; but the most promising versions of two-dimensionalism are (...) open to a close relative of that argument. (shrink)

Close insight into mathematical and conceptual structure of classical field theories shows serious inconsistencies in their common basis. In other words, we claim in this work to have come across two severe mathematical blunders in the very foundations of theoretical hydrodynamics. One of the defects concerns the traditional treatment of time derivatives in Eulerian hydrodynamic description. The other one resides in the conventional demonstration of the so-called Convection Theorem. Both approaches are thought to be necessary for cross-verification of the standard (...) differential form of continuity equation. Any revision of these fundamental results might have important implications for all classical field theories. Rigorous reconsideration of time derivatives in Eulerian description shows that it evokes Minkowski metric for any flow field domain without any previous postulation. Mathematical approach is developed within the framework of congruences for general four-dimensional differentiable manifold and the final result is formulated in form of a theorem. A modified version of the Convection Theorem provides a necessary cross-verification for a reconsidered differential form of continuity equation. Although the approach is developed for one-component (scalar) flow field, it can be easily generalized to any tensor field. Some possible implications for classical electrodynamics are also explored. (shrink)

The present paper develops arguments for the need to formulate the basic theories of physics in terms of a six-dimensional manifold, as opposed to the four-dimensional space-time continuum of conventional theory. Employing a purely classical approach, some of the dynamical consequences of such a formulation with regard to both electrodynamics and gravitation are evaluated. The results lead to interesting implications with regard to various questions such as the occurrence and importance of superluminal particles, the existence of two (...) or more physically distinct time scales, and the variation of the gravitational coupling constant G and the law of energy conservation. The analysis also suggests a physical interpretation of the additional coordinates that occur in the metric. (shrink)

We generalize two of our previous results on abelian definable groups in p-adically closed fields [12, 13] to the non-abelian case. First, we show that if G is a definable group that is not definably compact, then G has a one-dimensional definable subgroup which is not definably compact. This is a p-adic analogue of the Peterzil–Steinhorn theorem for o-minimal theories [16]. Second, we show that if G is a group definable over the standard model $\mathbb {Q}_p$, then $G^0 = (...) G^{00}$. As an application, definably amenable groups over $\mathbb {Q}_p$ are open subgroups of algebraic groups, up to finite factors. We also prove that $G^0 = G^{00}$ when G is a definable subgroup of a linear algebraic group, over any model. (shrink)

Scott Soames’ Reference and Description contains arguments against a number of different versions of two-dimensional semantics. After early chapters on descriptivism and on Kripke’s anti-descriptivist arguments, a chapter each is devoted to the roots of twodimensionalism in “slips, errors, or misleading suggestions” by Kripke and Kaplan, and to the two-dimensional approaches developed by Stalnaker (1978) and by Davies and Humberstone (1981). The bulk of the book (about 200 pages) is devoted to “ambitious twodimensionalism”, attributed to Frank Jackson, David (...) Lewis, and me. After a quick overview of two-dimensional approaches, I will focus on Soames’ discussion of ambitious twodimensionalism. I will then turn to a system advocated by Soames that is itself strikingly reminiscent of a two-dimensional approach. Two-dimensional semantic theories are varieties of possible-worlds semantics on which linguistic items can be evaluated relative to possibilities in two different ways, yielding two sorts of intensional semantic values, which can be seen as two “dimensions” of meaning. The second dimension is the familiar sort of Kripkean evaluation in metaphysically possible worlds, so that necessarily coextensive terms (such as ‘Hesperus’ and ‘Phosphorus’ or ‘water’ and ‘H2O’) always have the same semantic value. The first dimension behaves differently, so that there are typically at least some cases where necessarily coextensive terms have different semantic values on the first dimension. For this reason, the two-dimensional framework is sometimes seen as a way of granting many of the insights of a Kripkean approach to meaning (on the second dimension), while retaining elements of a Fregean approach to meaning (on the first dimension). (shrink)

This paper begins by asking a simple question: can a farmer own and fully utilise precisely five tractors and precisely six tractors at the same time? Of course not. He can own five or he can own six but he cannot own five and six at the same. The answer to this simple question eventually led this author to Alfred Marshall's historically-ignored, linguistically-depicted 'cardboard model' where my goal was to construct a picture based on his written words. More precisely, in (...) this paper the overall goal is to convert Marshall's ('three-dimensional') words into a three-dimensional picture so that the full import of his insight can be appreciated by all readers. After a brief digression necessary to introduce Euclidean three-dimensional space, plus a brief digression to illustrate the pictorial problem with extant theory, the paper turns to Marshall's historically- ignored words. Specifically, it slowly constructs a visual depiction of Marshall's 'cardboard model'. Unfortunately (for all purveyors of extant economic theory), this visual depiction suddenly opens the door to all manner of Copernican heresy. For example, it suddenly becomes obvious that we can join the lowest points on a firm's series of SRAC curves and thereby form its LRAC curve; it suddenly becomes obvious that the firm's series of SRAC curves only appear to intersect because mainstream theory has naively forced our three-dimensional economic reality into a two-dimensional economic sketch; and it suddenly becomes obvious that a two-dimensional sketch is analytically useless because the 'short run' (SR) never turns into the 'long run' (LR) no matter how long we wait. (shrink)

The paper argues that (i) the notion of epistemic reliability, as it is standardly defined within mainstream epistemology, is a multidimensional concept, and that (ii) paying attention to reliability’s multidimensional nature can significantly expand reliabilism’s purview both in the theoretical and practical domain. Reliabilist theories of knowledge and justification agree that a process is reliable just in case it leads to a ‘sufficiently high preponderance of true over false beliefs.’ Given this straightforward definition, reliability appears to be, and so far (...) has been implicitly treated by epistemologists as, a mono-dimensional concept. Nevertheless, the terminology and formulas that statisticians and computers scientists have developed for assessing the reliability of binary classification processes reveal that for any belief-forming process whose aim is to identify the presence or the absence of some quality ι, there are at least four different interpretations of the above definition. These interpretations correspond to four separate dimensions of reliability: Precision, Negative Predictive Value (NPV), Recall and Specificity. Though epistemologists do not explicitly specify how they interpret the above definition of reliability, due to their main interest in ‘know-that’, their mono-dimensional focus seems to have so far been mainly directed at Precision alone (or, at best, to both Precision and NPV—but without distinguishing between the two). As it transpires, however, the (entirely) neglected dimensions of Recall and Specificity can guide the satisfaction of another important epistemic goal, best captured by the locution ‘know-most/all.’ The upshot is that different epistemic goals call for high levels of reliability along different dimensions (and, often, their combinations too). This observation invites upgrading reliabilism into dimensional reliabilism, according to which assessing whether a process is knowledge-conducive depends on whether it manifests high reliability along the appropriate dimension(s), given the epistemic goal at hand. (shrink)

This article introduces and explores a distinction between multi-dimensional and one-dimensional consequentialist moral theories. One-dimensional consequentialists believe that an act's deontic status depends on just one aspect of the act, such as the sum total of wellbeing it produces, or the sum total of priority- or equality-adjusted wellbeing. Multi-dimensional consequentialists believe that an act's deontic status depends on more than one aspect. They may, for instance, believe that the sum total of wellbeing produced by an act (...) and the degree to which the wellbeing is equally distributed in the population affect the act's deontic status independently of each other. These two aspects cannot be reduced into any single (composite) aspect. Wellbeing and equality are two separate considerations that cannot be merged into some novel entity that accurately reflects both intuitions. On the multi-dimensional view I defend, such clashes between separate aspects are irresolvable and are best accounted for by claiming that moral rightness and wrongness are non-binary concepts. Some acts are, literally speaking, a little bit right (because they maximise wellbeing) and a little bit wrong (because they do not maximise equality).1. (shrink)

The field theory of free strings is analyzed in gauges in which the two-dimensional metric along the string worldsheet remains as a dynamical variable. Hamiltonian-based BRST methods are used. The cohomology of the complete BRST charge is computed. Equivalence with the usual approach is explicitly established.

This work is a two-division study of twentieth century philosophies of history in Europe. Fields engaged in the study are transcendental philosophy, speculative metaphysics, theology, historiographical theory, and intellectual history. The main question concerns the historical finitude of History and its temporal horizon. The work explores the unsolved consequences of G.W.F. Hegel's Phenomenology of Spirit and Martin Heidegger's Being and Time in twentieth-century German and French philosophies of History.

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we (...) ask the question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)