This paper uses a partially ordered set of syntactic categories to accommodate optionality and licensing in natural language syntax. A complex but well-studied data set pertaining to the syntax of quantifier scope and negative polarity licensing in Hungarian is used to illustrate the proposal. The presentation is geared towards both linguists and logicians. The paper highlights that the main ideas can be implemented in different grammar formalisms, and discusses in detail an implementation where the partial ordering on categories is (...) given by the derivability relation of a calculus with residuated and Galois-connected unary operators. (shrink)

Why do relationships of friendship and love support partiality, but not relationships of hatred or commitments of racism? Where does partiality end and why? I take the intuitive starting point that important cases of partiality are meaningful. I develop a view whereby meaning is understood in terms of transcending self-limitations in order to connect with things of external value. I then show how this view can be used to distinguish central cases of legitimate partiality from cases of illegitimate partiality (...) and how it puts pressure on the traditional way of thinking about partiality. (shrink)

This paper provides a defence of the account of partial resemblances between properties according to which such resemblances are due to partial identities of constituent properties. It is argued, first of all, that the account is not only required by realists about universals à la Armstrong, but also useful (of course, in an appropriately re-formulated form) for those who prefer a nominalistic ontology for material objects. For this reason, the paper only briefly considers the problem of how to (...) conceive of the structural universals first posited by Armstrong in order to explain partial resemblances, and focuses instead on criticisms that have been levelled against the theory (by Pautz, Eddon, Denkel and Gibb) and that apply regardless of one’s preferred ontological framework. The partial identity account is defended from these objections and, in doing so, a hitherto quite neglected connection—between the debate about partial similarity as partial identity and that concerning ontological finitism versus infinitism—is looked at in some detail. (shrink)

Accounts of Hobbes’s ‘system’ of sciences oscillate between two extremes. On one extreme, the system is portrayed as wholly axiomtic-deductive, with statecraft being deduced in an unbroken chain from the principles of logic and first philosophy. On the other, it is portrayed as rife with conceptual cracks and fissures, with Hobbes’s statements about its deductive structure amounting to mere window-dressing. This paper argues that a middle way is found by conceiving of Hobbes’s _Elements of Philosophy_ on the model of a (...) mixed-mathematical science, not the model provided by Euclid’s _Elements of Geometry_. I suggest that Hobbes is a test case for understanding early-modern system-construction more generally, as inspired by the structure of the applied mathematical sciences. This approach has the additional virtue of bolstering, in a novel way, the thesis that the transformation of philosophy in the long seventeenth century was heavily indebted to mathematics, a thesis that has increasingly come under attack in recent years. (shrink)

One of the advantages of my account in the essay “Instantiation as Partial Identity” was capturing the contingency of instantiation—something David Armstrong gave up in his experiment with a similar view. What made the contingency possible for me was my own non-standard account of identity, complete with the apparatus of counts and aspects. The need remains to lift some obscurity from the account in order to display its virtues to greater advantage. To that end, I propose to respond (...) to those who have grappled with it in print. There are various criticisms by commentators: that it is rendered absurd by the transitivity of identity, that it makes instantiation necessary instead of contingent, that it is unclear what counts are, that aspects are simply tropes, that my view does not capture multiple location, that I make an unclear reference to a theory of composition as identity, that the account suffers from problems with polyadicity, and that it is not a realist account of universals after all. I give responses to these objections. (shrink)

Moeser suggested participants default to linear ordering elements but they can be primed to impose either linear or partial ordering. This study seems problematic insofar as ‘greater than’ might be understood to incline participants to favor linear orderings. Recent follow-up studies strongly suggest participants do not default to linear ordering. It seems plausible, moreover, that the observed priming effect is far more pervasive than Moeser countenanced. The present work explores the extent to which priming for linear or partial (...) orders conflicts with the construction of linear or partial ordering lists. Our two experiments suggest friction between priming and task, and also show once the priming tasks are cleared of potentially confounding semantic content, participants perform equally with respect to constructing linear or partial orders under similar priming conditions. (shrink)

We have to gain from recognizing a relation between epistemic agents and the parts of subject matters that play a role in their cognitive lives. I call this relation “grasping”. Namely, I zone in on one notion of having a partial grasp of a subject matter—that of agents grasping part of the subject matter that they are attending to—and characterize it. I propose that giving up the idealization that we fully grasp the subject matters we attend to allows one (...) to more realistically characterize the epistemic life of agents. To show this, I propose an epistemic logic with partial grasp that has in mind considerations from first-order aboutness theory with the aim of avoiding certain forms of logical omniscience, and which provides an alternative to immanent closure (Yablo Aboutness, Princeton University Press, 2014). (shrink)

In her paper, “True Faith: Against Doxastic Partiality about Faith (in God and Religious Communities) and in Defense of Evidentialism,” Katherine Dormandy argues against the view that there is a partiality norm on faith. Dormandy establishes this by showing that partiality views can’t give the right responses to encounters with stubborn counter evidence. Either they (anti-epistemic-partiality views) recommend flouting the evidence altogether in order hold on to positive beliefs about the object of faith or they (epistemic-partiality views) lower the (...) epistemic standards in objectionable ways to alleviate the epistemic pressure imposed by the counterevidence. However, one cannot have praiseworthy faith when one refuses to really grapple with the evidence against the goodness of the faith’s object. So, partiality norms, far from constituting what makes for great faith, importantly stand in its way. Thus, we should reject any partiality norms on faith. We argue that cases of praiseworthy faith involve dispositions to confront the object of faith when presented with stubborn counter evidence against their goodness. Recognizing this enables us to endorse a partiality norm while avoiding Dormandy’s worries. We argue that dispositions to confront the object of faith presuppose positive beliefs about it, thus vindicating partiality. We further argue that the confrontation makes an epistemic demand of the object of faith: produce high confidence in whether it is still worth having faith in, thus carving out a central role for evidentialist norms. (shrink)

Recent scholarship has drawn attention to John Rawls’s concern with stability—a concern that, as Rawls himself notes, motivated Part III of A Theory of Justice and some of the more important changes of his political turn. For Rawls, the possibility of achieving ‘stability for the right reasons’ depends on citizens possessing sufficient moral motivation. I argue, however, that the moral psychology Rawls develops to show how such motivation would be cultivated and sustained does not cohere with his specific descriptions of (...) ‘pluralist ’ doctrines. Considering Rawls’s claims that ‘most’ citizens—both in contemporary liberal democracies and in the well-ordered society—possess such doctrines, this incompatibility threatens to undermine his stability arguments. Despite the enormous importance of pluralist doctrines and the potential difficulties they pose for Rawls’s project, remarkably little attention has been paid to them. By critically examining these difficulties, the article begins to address this oversight. (shrink)

One way to approach the question of whether there are non-derivative partial reasons of any kind is to give an account of what partial reasons are, and then to consider whether there are such reasons. If there are, then it is at least possible that there are partial reasons of friendship. It is this approach that will be taken here, and it produces several interesting results. The first is a point about the structure of partial reasons. (...) It is at least a necessary condition of a reason’s being partial that it has an explicit relational component. This component, technically, is a rela- tum in the reason relation that itself is a relation between the person to whom the reason applies and the person whom the action for which there is a reason concerns. The second conclusion of the paper is that this relational component is also required for a number of types of putatively impartial reasons. In order to avoid trivialising the distinction between partial and impartial rea- sons, some further sufficient condition must be applied. Finally, there is some prospect for a way of distinguishing between impartial reasons that contain a relational component and partial rea- sons, but that this approach suggests that the question of whether ethics is partial or impartial will be settled at the level of normative ethical discourse, or at least not at the level of discourse about the nature of reasons for action. (shrink)

A rather promising value theory for environmental philosophers combines the well-known fitting attitude (FA) account of value with the rather less well-known account of value as richness. If the value of an entity is proportional to its degree of richness (which has been cashed out in terms of unified complexity and organic unity), then since natural entities, such as species or ecosystems, exhibit varying degrees of richness quite independently of what we happen to feel about them, they also possess differing (...) degrees of mind-independent and subject-independent value. In particular, their value is not dependent on the desires or preferences of humans. The fitting attitudes account of value, at least as it is standardly developed, demands isomorphic evaluative responses on the part of all valuers. In particular, it entails that all valuers should have isomorphic preferences. But this seems absurd. I consider three different strategies with which the fitting attitude theorist can deflect this challenge. The first makes use of an account of non-standard value relations in terms of permissible preference orderings. The second appeals to value appearances and the associated notions of value distance and value perspective. The third involves an account of the ultimate bearers of value as properties, rather than as propositions or states of affairs. These strategies are not all mutually incompatible. While it isn’t possible to combine the first and second strategies, it is possible to combine the first and third strategies, and also to combine the second and the third. (shrink)

Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two entanglement measures for all quantum states, however, allows for meaningful conceptualization of sensitivity to entanglement, which will be greater for the entanglement measure that produces the larger numerical values. Here, we have investigated the partial order between the normalized versions of four entanglement (...) measures based on Schmidt decomposition of bipartite pure quantum states, namely, concurrence, tangle, entanglement robustness and Schmidt number. We have shown that among those four measures, the concurrence and the Schmidt number have the highest and the lowest sensitivity to quantum entanglement, respectively. Further, we have demonstrated how these measures could be used to track the dynamics of quantum entanglement in a simple quantum toy model composed of two qutrits. Lastly, we have employed state-dependent entanglement statistics to compute measurable correlations between the outcomes of quantum observables in agreement with the uncertainty principle. The presented results could be helpful in quantum applications that require monitoring of the available quantum resources for sharp identification of temporal points of maximal entanglement or system separability. (shrink)

We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown to (...) be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling. (shrink)

In this paper authors for the first time define a new notion called neutrosophic lattices. We define few properties related with them. Three types of neutrosophic lattices are defined and the special properties about these new class of lattices are discussed and developed. This paper is organised into three sections. First section introduces the concept of partially ordered neutrosophic set and neutrosophic lattices. Section two introduces different types of neutrosophic lattices and the final section studies neutrosophic Boolean algebras. Conclusions and (...) results are provided in section three. (shrink)

Many accounts of the moral duty to obey the law either restrict the duty to ideal democracies or leave the duty’s application to non-ideal societies unclear. This article presents and defends a partial account of the moral duty to obey the law in non-ideal societies, focusing on the duty to obey judicial orders. We need public judicial authority to prevent objectionable power relationships that can result from disputes about private agreements. The moral need to prevent power imbalances in private (...) relationships grounds a qualified moral duty to obey judicial decisions. The parties to a dispute are morally required to comply with a judicial order in their dispute if all of the following conditions obtain: the parties’ dispute was in good faith, the court’s resolution of the dispute is more impartial than either party’s own judgment, the order does not call for violation of important natural duties or important artificial duties that the duty-bearer incurred involuntarily, and the primary aim of disobeying the court order would be to advance an ordinary, non-political project, not to call public attention to an injustice. The moral duty to obey judicial decisions can survive significant departures from ideal fairness. (shrink)

Starting with a partial order on a NeutroAlgebra, we get a NeutroStructure. The latter if it satisfies the conditions of NeutroOrder, it becomes a NeutroOrderedAlgebra. In this paper, we apply our new defined notion to semigroups by studying NeutroOrderedSemigroups. More precisely, we define some related terms like NeutrosOrderedSemigroup, NeutroOrderedIdeal, NeutroOrderedFilter, NeutroOrderedHomomorphism, etc., illustrate them via some examples, and study some of their properties.

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes (parameters)’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for a (...) more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined be-tween each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life. (shrink)

The most familiar philosophical conception of objective chance renders determinism incompatible with non-trivial chances. This conception – associated in particular with the work of David Lewis – is not a good fit with our use of the word ‘chance’ and its cognates in ordinary discourse. In this paper we show how a generalized framework for chance can reconcile determinism with non-trivial chances, and provide for a more charitable interpretation of ordinary chance-talk. According to our proposal, variation in an admissible ‘evidence (...) base’ generates a spectrum of different chance functions. Successive coarse-grainings of the evidence base generates a partial ordering of chance functions, with finer trumping coarser if known. We suggest that chance-attributions in ordinary discourse express different chance functions in different contexts, and we sketch a potential contextual mechanism for making particular chance functions salient. The mechanism involves the idea that admissible evidence is available evidence: propositions that could be known. A consequence is that attributions of objective chances inherit the relatively familiar context-sensitivity associated with the modal ‘could’. We show how this context-dependency undermines certain arguments for the incompatibility of chance with determinism. (shrink)

It is plausible that the universe exists: a thing such that absolutely everything is a part of it. It is also plausible that singular, structured propositions exist: propositions that literally have individuals as parts. Furthermore, it is plausible that for each thing, there is a singular, structured proposition that has it as a part. Finally, it is plausible that parthood is a partial ordering: reflexive, transitive, and anti-symmetric. These plausible claims cannot all be correct. We canvass some costs of (...) denying each claim and conclude that parthood is not a partial ordering. Provided that the relevant entities exist, parthood is not anti-symmetric and proper parthood is neither asymmetric nor transitive. (shrink)

Many approaches to quantum gravity -the theory that should account for quantum and gravitational phenomena under the same theoretical umbrella- seem to point at some form of spacetime emergence, i.e., the fact that spacetime is not a fundamental entity of our physical world. This tenet has sparked many philosophical discussions: from the so-called empirical incoherence problem to different accounts of emergence and mechanisms thereof. In this contribution, I focus on the partial order relation of causal set theory and (...) argue that causation can be characterized as an a-temporal constraint over the kinematic space defined by the theory. The relation constrains the growth of a new element/event with respect to the other elements/events of a given set. Therefrom, the flow of time emerges from the collection of the possible growths of the given set, where each possibility is characterized by a classical probability assigned by the dynamics of the theory. (shrink)

There are at least three vaguely atomistic principles that have come up in the literature, two explicitly and one implicitly. First, standard atomism is the claim that everything is composed of atoms, and is very often how atomism is characterized in the literature. Second, superatomism is the claim that parthood is well-founded, which implies that every proper parthood chain terminates, and has been discussed as a stronger alternative to standard atomism. Third, there is a principle that lies between these two (...) theses in terms of its relative strength: strong atomism, the claim that every maximal proper parthood chain terminates. Although strong atomism is equivalent to superatomism in classical extensional mereology, it is strictly weaker than it in strictly weaker systems in which parthood is a partial order. And it is strictly stronger than standard atomism in classical extensional mereology and, given the axiom of choice, in such strictly weaker systems as well. Though strong atomism has not, to my knowledge, been explicitly identified, Shiver appears to have it in mind, though it is unclear whether he recognizes that it is not equivalent to standard atomism in each of the mereologies he considers. I prove these logical relationships which hold amongst these three atomistic principles, and argue that, whether one adopts classical extensional mereology or a system strictly weaker than it in which parthood is a partial order, standard atomism is a more defensible addition to one’s mereology than either of the other two principles, and it should be regarded as the best formulation of the atomistic thesis. (shrink)

In this paper we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's \cdt\ logic interpreted over partial orders (\nsbcdt\ for short). It (...) combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented. (shrink)

Both Adam Smith's epistemology and his politics head to a stalemate. The former is under the opposing pulls of an essentialist ideal of knowledge and of a pragmatist approach to the history of science. The latter still tries to provide a foundation for a natural law, while conceiving it as non-absolute and changeable. The consequences are (i) inability to complete both the political and the epistemological works projected by Smith; (ii) decentralization of the social order, giving rise to several (...) partial orders, such as that of the market. (shrink)

Introduction. The book is a study in Adam Smith's system of ideas; its aim is to reconstruct the peculiar framework that Adam Smith’s work provided for the shaping of a semi-autonomous new discipline, political economy; the approach adopted lies somewhere in-between the history of ideas and the history of economic analysis. My two claims are: i) The Wealth of Nations has a twofold structure, including a `natural history' of opulence and an `imaginary machine' of wealth. The imaginary machine is a (...) kind of Newtonian theory, whose connecting links are principles; provided either by `partial' characteristics of human nature or by analoga of physical mechanisms transferred to the social world; ii) a domain of the economic, understood as a self-standing social sub-system, was discovered first by Adam Smith. His `discovery' of the new continent of the economic was an `unintended result' of a deviation in his voyage to the never-found archipelago of natural jurisprudence. -/- 1. Imaginary machines and invisible chains: natural philosophy and method. The first chapter reconstructs Smith's views on the method in natural philosophy, presented primarily in the History of Astronomy (HA). The peculiar kind of semi-sceptical Newtonianism which permeates the essay is highlighted. Its reconstruction of the history of one natural science is shown to be based on the assumptions of Hume’s epistemology, and to lead to a self-aware deadlock. Smith's dilemma is between an essentialist realism and sceptical instrumentalism; the Cartesian presuppositions he shares with Hume and with the 18th century as a whole make it impossible for him to overcome his dilemma. The following chapters will show how, on the one hand, Smith's skeptical methodology encourages him in the enterprise to `carve off' a new self-contained discipline and how, on the other hand, his epistemological dilemma is reflected in the inner tensions of his moral and political theory as well as in a number of basic oscillations concerning the status of the new discipline. -/- 2. Chessboards and clocks: moral philosophy and method. -/- The second chapter reconstructs Smith's views on the method in the parallel field of moral philosophy, including the theory of moral sentiments and natural jurisprudence. I argue that The Theory of Moral Sentiments, when considered together with with the Lectures on Jurisprudence, where Smith's peculiar version of a `weaker' form of natural law is presented, wins special interest, not only for the history of ethics but even more for the history of political theory and the social sciences. The two most striking features of Smith's work in this area are highlighted. First, his effort at reformulating the `practical science' is a methodologically self-aware attempt at applying the Newtonian method to moral subjects. Secondly, this attempt ends in a stalemate as two distinguished kinds of normative order are introduced: one ultimate order of Reason, ultimately justifiable but inaccessible, and one weaker order of our `natural sentiments', to which we have empirical access, but which is so variable as to lack any ultimate value as a basis for grounding our normative claims. These two parallel conundrums may arguably account for the author's inability to publish during his lifetime both The History of Astronomy and the projected history and theory of law and government. -/- 3. Wheels, dams, and gravitation: the structure of scientific argument in The Wealth of Nations. -/- The third chapter provides the core of the book, dealing with the structure of the argument in WN. I argue that the main presupposition that makes the shift possible from a `natural history' to a `system' approach is the Newtonian contrast of `mathematical' with `physical' explanation; that is, Smith drops any discussion of the "original qualities" of human nature that could account for economic behaviour, while introducing, as `principles' for the system, a set of `hypothetical' statements of `observed' regularities in human behaviour and of `observed' super-individual self-regulating mechanisms. In bringing this presupposition to light, the coexistence of a teleological with a mechanistic approach is clarified; fresh light is shed on the notion of the invisible hand by a comparison of its occurrence in Smith with the occurrence of the same expression (until now overlooked) in the correspondence between Newton and Cotes. Finally, the peculiar semi-prescriptive and semi-descriptive character of political economy are highlighted, and the consistency of Smith's `impure' semi-prescriptive social science, when understood in his own terms, is defended against familiar charges with inconsistency and against even more familiar strained modernizations. -/- 4. Apples, deer, and frivolous trinkets: the construction of the economic. -/- The fourth chapter draws consequences from the third, examining how Smith's achievement in political economy, marking its transition to scientific status, carried a re-description of the phenomena, creating the comparatively independent and unified field of the economic. Smith's achievement is interpreted not as the `discovery' of an autonomous character already possessed by the economy out there, so much as a Gestalt-switch by which our perception of social phenomena is modified making us `see' the partial order of the economy as an isolated system. To sum up, the autonomy of the economic in social reality and the autonomy of the economic in social consciousness are shown to be two sides of one process. -/- 5. Concluding considerations: Political economy and the Enlightenment halved. -/- A few suggestions on the status of economic theory two centuries after The Wealth of Nations in its relationship to ‘practical philosophy’ are illustrated. (shrink)

In this paper I argue that physics makes metaphysical presuppositions concerning the physical comprehensibility, the dynamic unity, of the universe. I argue that rigour requires that these metaphysical presuppositions be made explicit as an integral part of theoretical knowledge in physics. An account of what it means to assert of a theory that it is unified is developed, which provides the means for partially ordering dynamical physical theories with respect to their degrees of unity. This in turn makes it possible (...) to assess the empirical fruitfulness of (some) metaphysical theses, in terms of the extent to which they play a role in empirically progressive scientific research programmes. A new conception of physics is developed which makes metaphysical theses an integral part of physics and which, at the same time, makes it possible to assess such theses in terms of their empirical fruitfulness. Circularity objections are rebutted. (shrink)

In this paper I argue for a priori conjectural scientific knowledge about the world. Physics persistently only accepts unified theories, even though endlessly many empirically more successful disunified rivals are always available. This persistent preference for unified theories, against empirical considerations, means that physics makes a substantial, persistent metaphysical assumption, to the effect that the universe has a (more or less) unified dynamic structure. In order to clarify what this assumption amounts to, I solve the problem of what it (...) means to say of a theory that it is unified. There are, I argue, eight different kinds of unity important in theoretical physics, all varieties of one basic idea. This provides us with a precise way of partially ordering physical theories with respect to their degree of unity. It also leads to a hierarchical view of physics, according to which physics makes a number of increasingly insubstantial metaphysical assumptions concerning the comprehensibility and knowability of the universe. Two of these are identified as constituting a priori conjectures. I conclude by arguing that the view developed in the paper resolves the traditional clash between empiricism and rationalism in the philosophy of science, and has important implications for science, and for academic inquiry more generally. (shrink)

El objetivo de este artículo es presentar una demostración de un teorema clásico sobre álgebras booleanas y ordenes parciales de relevancia actual en teoría de conjuntos, como por ejemplo, para aplicaciones del método de construcción de modelos llamado “forcing” (con álgebras booleanas completas o con órdenes parciales). El teorema que se prueba es el siguiente: “Todo orden parcial se puede extender a una única álgebra booleana completa (salvo isomorfismo)”. Donde extender significa “sumergir densamente”. Tal demostración se realiza utilizando cortaduras de (...) Dedekind siguiendo el texto “Set Theory” de Jech, y otras ideas propias del autor de este artículo. Adicionalmente, se formulan algunas versiones débiles del axioma de elección relacionadas con las álgebras booleanas, las cuales son también de gran importancia para la investigación en teoría de conjuntos y teoría de modelos, pues estas son poderosas técnicas de construcción de modelos, como por ejemplo, el teorema de compacidad (permite construir modelos no estándar, etc) y el teorema del ultrafiltro, que permite construir ultraproductos (pueden ser usados para investigar problemas de cardinales grandes, etc). Se presentan algunas referencias de problemas abiertos sobre el tema. -/- The objective of this paper is to present a demonstration of a classical theorem on boolean algebras and partial orders of current relevance in set theory, as for example, for applications of model construction method called forcing" (with boolean algebras complete or with partial orders). The theorem to be proved is as follows: Any partial order can be extended to a single complete boolean algebra (up to isomorphism)". Where to extend means embed densely". Such a demonstration is done using Dedekind's cuts following the text Set Theory" of Jech, and other ideas of the author of this article. In addition, some weak versions of the axiom of choice related to boolean algebras are formulated, which are also of great importance for the research in set theory and model theory, since this are powerful model construction techniques, such as the compactness theorem (allows the construction of non-standard models, etc.) and the ultralter theorem, which allows the construction of ultraproducts (can be used to investigate problems of large cardinals, etc). Some references of open problems on the subject are presented. (shrink)

Abstract. The aim of this paper is to show that the topological interpretation of knowledge as an interior kernel operator K of a topological space (X, OX) comes along with a partially ordered family of belief modalities B that fit K in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB logic of knowledge and belief with the exception of the contentious axiom of negative introspection (NI). The new belief modalities B introduced in this paper are (...) defined with the help of the (dense) nuclei of the Heyting algebra OX of open subsets on the topological space (X, OX). In this way, the natural context for the belief operators B related to topological knowledge operator K is shown to be the Heyting algebra NUC(OX) of the nuclei of the Heyting algebra OX.1 More precisely, the dense nuclei of NUC(OX) can be used to define a variety of bimodal logics of knowledge operators K and belief operators B. The operators K and B are compatible with each other in the sense that the pairs (K, B) satisfy all axioms of Stalnaker’s KB system with the exception of the axiom (NI). Therefore, for (X, OX), one obtains a bounded, partially ordered family of belief operators B defined by the elements of NUC(OX). (shrink)

It is argued that colour name strategy, object name strategy, and chunking strategy in memory are all aspects of the same general phenomena, called stereotyping, and this in turn is an example of a know-how representation. Such representations are argued to have their origin in a principle called the minimum duplication of resources. For most the subsequent discussions existence of colour name strategy suffices. It is pointed out that the BerlinA- KayA universal partial ordering of colours and the frequency (...) of traffic accidents classified by colour are surprisingly similar; a detailed analysis is not carried out as the specific colours recorded are not identical. Some consequences of the existence of a name strategy for the philosophy of language and mathematics are discussed: specifically it is argued that in accounts of truth and meaning it is necessary throughout to use real numbers as opposed to bi-valent quantities; and also that the concomitant label associated with sentences should not be of unconditional truth, but rather several real-valued quantities associated with visual communication. The implication of real-valued truth quantities is that the Continuum Hypothesis of pure mathematics is side-stepped, because real valued quantities occur ab initio. The existence of name strategy shows that thought/sememes and talk/phonemes can be separate, and this vindicates the assumption of thought occurring before talk used in psycho-linguistic speech production models. (shrink)

I argue the existence of two tensions in Smith's system of ideas: the first is that between the postulate of an invisible noumenal order of the universe and the imaginary principles by means of which we connect the phenomena; the second is a tension between the noumenal order of the world where 'is' and 'ought' converge, and the various partial orders that may be reconstructed in social phenomena that leave room for irrationality and injustice. My first claim (...) is that these tensions are dialectical tensions in a unitary, albeit rhapsodically presented in writing. My second claim is that, the system’s unanswered question in the moral domain is a ‘metaphysical’ and ‘theological’ question, namely the problem of evil; by implication, I contend also that Smith was no secularist, but instead a post-skeptical fideist or agnostic, who took Bayle's question: "why are men wicked and unhappy?" quite seriously. His private ethics of prudence, justice, benevolence and his public ethics of liberty, justice, equality were modest proposals for coping with the problem of social evil in our imperfect world. (shrink)

The objective of this article is to present an original proof of the following theorem: Thereis a generic extension of the Solovay’s model L(R) where there is a linear order of P(N)/fin that extends to the partial order (P(N)/f in), ≤*). Linear orders of P(N)/fin are important because, among other reasons, they allow constructing non-measurable sets, moreover they are applied in Ramsey's Theory .

In many languages, the same particles build quantifier words and serve as connectives, additive and scalar particles, question markers, existential verbs, and so on. Do the roles of each particle form a natural class with a stable semantics? Are the particles aided by additional elements, overt or covert, in fulfilling their varied roles? I propose a unified analysis, according to which the particles impose partial ordering requirements (glb and lub) on the interpretations of their hosts and the immediate larger (...) contexts, but do not embody algebraic operations themselves. (shrink)

In the course of the eighteenth and nineteenth centuries the paradigm of a new science, political economy, was established. It was a science distinct from the Aristotelian sub-disciplines of practical philosophy named oikonomía and politiké, and emphasis on its character of science not unlike the natural sciences – still called ‘natural philosophy’ – mirrored precisely a willingness to stress its autonomy from two other sub-disciplines of practical philosophy, that is, ethics and politics. However, the new science resulted from a transformation (...) of part of traditional practical philosophy, allowing the inclusion of bodies of knowledge accumulated by experts of commerce and public finance. Such bodies of knowledge were unified by the (true or alleged) discovery of regularities, mechanisms, causal connections making for a new partial order within the overall social order. How far this paved the way to a science similar to mathematics rather left a normative discipline as alive as ever was a recurrent question for at least a century, until the marginalist revolution opened the way for a sharp division, leaving ‘economics’ as a science of causes and effects facing ‘economic policy’ as a discourse on ends. (shrink)

We show that any coherent complete partial order is obtainable as the fixed-point poset of the strong Kleene jump of a suitably chosen first-order ground model. This is a strengthening of Visser’s result that any finite ccpo is obtainable in this way. The same is true for the van Fraassen supervaluation jump, but not for the weak Kleene jump.

In order to decide whether a discursive product of human reason corresponds or not to the logical order, one must analyze it in terms of syntactic correctness, consistency, and validity. The first step in logical analysis is formalization, that is, the process by which logical forms of thoughts are represented in different formal languages or logical systems. Although each thought can be properly formalized in different ways, the formalization variants are not equally adequate. The adequacy of formalization seems (...) to depend on several essential features: parsimony, accuracy, transparency, fertility and reliability. Because there is a partial antinomy between these traits, it is impossible to find a perfectly adequate variant of formalization. However, it is possible and preferable to reach a reasonable compromise by choosing the variant of formalization which satisfies all of these fundamental characteristics. (shrink)

The paper presents an inferential model of explicit communication based on the speaker’s interests and the addressee’s beliefs. After the introduction, the paper sets out some notions concerning explicit communication within the frameworks of truth-conditional pragmatics and relevance theory. The third section describes the phenomenon of semantic underdeterminacy, and the fourth section introduces non-demonstrative inferences in communication. The fifth section presents the model. The main notions involved are the speaker’s intended meaning and the addressee’s intended meaning. The former notion is (...) centered on the speaker’s interest in situation: a speaker intends the meaning of an utterance on the basis of a partial order of preference with respect to a set of contextually plausible meanings. The latter notion is centered on the addressee’s communicative inference, which is based on the addressee’s belief about the speaker’s interest. The paper takes the notion of interest from cognitive social theory, the notion of meaning from semantics, and the notion of explicit meaning from pragmatics; and it uses the notion of communicative inference for explicit meaning in partial accordance with relevance theory. In the sixth section, the paper argues in favor of the inferential approach compared with the associative approach in determination of “what is said.” The paper’s method is conceptual analysis of declarative utterances used in communicative situations. The main finding of the paper has been to show that, in contextual underdeterminacy cases, speaker’s interest is a determining factor in communicative processes. Keywords: states of affairs; truth-conditions; semantic underdeterminacy; contextual underdeterminacy; speaker’s interest; goal-conditions; speaker’s intended meaning; addressee’s belief; communicative inference; addressee’s intended meaning; shared intended meaning; explicit communication. (shrink)

In order to maintain the existence of the business, it always creates and implements various marketingstrategies to maintain and maintain business operations in the midst of fierce business competition. Allbusinesses have competition so this makes the company must have a strategy to be able to excel incompetition. Companies must be able to know how to retain their customers so as not to turn to competitors.Especially in the field of coffee drinks business which is currently being rife in Surabaya. This (...) research usesa Quantitative Approach is a research approach that uses data in the form of figures from survey answersdistributed to research samples and analyzed using statistical analysis techniques. The partial regressionresults (t-test) showed the results of the brand image proved to have a significant effect on the decision topurchase coffee drinks at Janji Jiwa Royal Plaza Surabaya. Value is proven to have a significant effect oncoffee beverage purchase decisions at Janji Jiwa Royal Surabaya. Simultaneous regression analysis (F-test)proved to have a significant effect on brand image and value on coffee beverage purchase decisions at JanjiJiwa Royal Surabaya. (shrink)

This study assessed the mode of test administration, birth variables, and students’ academic performance in Mathematics in Obubra Local Government Area of Cross River State, Nigeria. The study was guided by three null hypotheses following a quasi- experimental research design. Simple random and purposive sampling techniques were employed in selecting a sample of 250 respondents from a population of 5,792 students. Birth Order Checklist (BOC) and Mathematics Achievement Test (MAT) were used for data collection. The experimental group was assigned (...) to take a Computer-Based Test (CBT) while the control group took a Paper-Pencil Test (PPT) in mathematics. The null hypotheses were tested at .05 alpha level using two-way analysis of variance. Major findings revealed that, the interactive effects of gender and mode of test administration on the academic performance of students is non- significant [F(1,249)=0.028, p>.05, partial η2=.000]; the interactive effects of gender and birth order on the academic performance of students was not statistically significant [F(3,249)=0.782, p>.05, partial η2=.010]; the interactive effect of gender and birth order on the academic performance of students in mathematics is statistically significant [F(3,249)=2.854, p<.05, partial η2 =.034]. Based on these findings conclusions and recommendations were made for improved academic performance and school system effectiveness. (shrink)

A general framework for translating various logical systems is presented, including a set of partial unary operators of affirmation and negation. Despite its usual reading, affirmation is not redundant in any domain of values and whenever it does not behave like a full mapping. After depicting the process of partial functions, a number of logics are translated through a variety of affirmations and a unique pair of negations. This relies upon two preconditions: a deconstruction of truth-values as ordered (...) and structured objects, unlike its mainstream presentation as a simple object; a redefinition of the Principle of Bivalence as a set of four independent properties, such that its definition does not equate with normality. (shrink)

How should we understand the relationship between global justice and global democracy? One popular view is captured by the aphorism “No global justice without global democracy.” According to Dryzek and Tanasoca's reading of this aphorism, a particular form of deliberative global democracy is seen as the way to specify and justify what global justice is and requires in various contexts. Taking its point of departure in a criticism of this proposal, this essay analyzes how to best understand the relationship between (...) global justice and global democracy. The aim is not to offer a first-order substantial account of this relationship, but to theorize the normative boundary conditions for such an account; that is, the conditions that any plausible theory should respect. These conditions take the form of what is here called a “three-layered view,” which is specified through three claims. It is argued, first, that global democracy is best seen as a partial normative ideal; second, that global democracy must be grounded in fundamental principles of justice; and third, that global democracy is an ideal through which applied principles of distributive justice are formulated and justified in light of reasonable disagreement about what justice requires. (shrink)

I provide a theory of the metaphysical foundations of identity: an account what grounds facts of the form a=b. In particular, I defend the claim that indiscernibility grounds identity. This is typically rejected because it is viciously circular; plausible assumptions about the logic of ground entail that the fact that a=b partially grounds itself. The theory I defend is immune to this circularity.

Niche construction theory highlights the active role of organisms in modifying their environment. A subset of these modifications is the developmental niche, which concerns ecological, epistemic, social and symbolic legacies inherited by organisms as resources that scaffold their developmental processes. Since in this theory development is a situated process that takes place in a culturally structured environment, we may reasonably ask if implicit cultural biases may, in some cases, be responsible for maladaptive developmental niches. In this paper we wish to (...) argue for an affirmative answer. In order to do so, we first propose to conceptualize implicit bias as embodied perceptual habits, and then proceed to show that these habits are at least partially responsible for maladaptive developmental niches of children with Down syndrome and autism. With this framework we thus hope to bring together two fields of research that haven’t been explicitly connected: implicit bias and niche construction theory. Linking these two theories may bring benefits both to implicit bias researchers, who can extend this concept to characterize other sets of processes as biased, as well as to niche construction theorists, who will have a useful theoretical tool to diagnose maladaptive features of niches brought about by sociocultural biases. (shrink)

In a world of partially overlapping and partially conflicting interests there is good reason to doubt that self-seeking behaviour at the micro-level will spontaneously lead to desirable social outcomes at the macro-level. Nevertheless, some sophisticated economic writers advocating a laissez-faire policy prescription have proposed various 'invisible hand' mechanisms which can supposedly be relied upon to 'educe good from ill'. Smith defended the 'simple system of natural liberty' as giving the greatest scope to the unfolding of God's will and the working (...) out of 'natural' providential processes free of interference by 'artificial' state intervention - the expression not of divine order but of fallible human reason. Hayek, adopting a similar policy stance, based it in an evolutionary process in which those institutional forms best adapted to reconciling individual interests would, he believed, spontaneously be selected for in the inter-group struggle for survival. Keynes shares the holistic approach of Smith and Hayek, but without their reliance on invisible hand mechanisms. If spontaneous processes cannot be relied upon to generate desirable social outcomes then we have to take responsibility for achieving this ourselves by establishing the appropriate institutional framework. Keynes takes a historical view of the role of capitalism and analyses its pathology as rooted in what we would now refer to as a multi-player prisoners' dilemma. The paper draws out the significance of his methodological standpoint here. Keynes's policy standpoint assigns a critical role to his own class, the 'educated bourgeoisie' in the reform process he maps out. A distinction, but also an intimate connection, is highlighted between, on the one hand, micro-level individualism (the 'Manchester System, and, on the other, the macro-level collective action ('planning') required to preserve it. Finally Keynes is considered in relation to the themes of laissez-faire, holism, reductionism, providentialism and the invisible hand. (shrink)

The goal of this article is to understand the concept of poetry in the broad context of Heidegger’s “early” thought, around 1919 and 1930. To that end, we seek to disclose a relation that in Heidegger remains implicit and in the secondary literature absent. This is the relation between poetry and the ways of Being (existence, ready-to-hand, present-at-hand, etc.). Since Heidegger did not explicitly thematize poetry in this broad context, the setup of this article consists of three main steps, in (...) which we make explicit the implicit ontological notion of Heidegger about poetry and, we shall argue, the ontological status of the poeticized. First, we distinguish between the theoretical and the pre-theoretical dimensions of existence, which enable us to explain that for Heidegger poetry is a pre-theoretical letting-see of the various entities that we encounter in the immediate everyday life that is mostly overlooked because of their “self-evident” and “obvious” presence. In this first step we argue that for Heidegger poetry is partially an explicit ontic letting-see. Second, we address the ways of Being in order to secure the systematic horizon for our interpretation regarding the relationship between the ways of Being and poetry. Third, we discuss that an indicative and non-conceptual letting-see of pre-theoretical ways of Being takes place in poetry through the respective poetized entity. In the second and third steps, we exhibit that according to Heidegger poetry results ultimately in an implicit ontological letting-see of the ways of Being. (shrink)

This paper addresses the so-called paradox of fiction, the problem of explaining how we can have emotional responses towards fiction. I claim that no account has yet provided an adequate explanation of how we can respond with genuine emotions when we know that the objects of our responses are fictional. I argue that we should understand the role played by the imagination in our engagement with fiction as functionally equivalent to that which it plays under the guise of acceptance in (...) practical reasoning, suggesting that the same underlying cognitive-affective mechanisms are involved in both activities. As such, our imaginative engagement with fiction un-problematically arouses emotions, but only to the extent that we are not occurrently attending to our epistemic relation to the fiction i.e. fully attending to the fact that the object of our response is merely fictional. In order to illuminate this idea I examine a recent proposal that the phenomenology of attention is partially non-attributive, and I argue that emotional phenomenology too shares this characteristic. (shrink)

The present paper wants to promote epistemic pluralism as an alternative view of non-classical logics. For this purpose, a bilateralist logic of acceptance and rejection is developed in order to make an important di erence between several concepts of epistemology, including information and justi cation. Moreover, the notion of disagreement corresponds to a set of epistemic oppositions between agents. The result is a non-standard theory of opposition for many-valued logics, rendering total and partial disagreement in terms of epistemic (...) negation and semi-negations. (shrink)

We present a theory of human artistic experience and the neural mechanisms that mediate it. Any theory of art has to ideally have three components. The logic of art: whether there are universal rules or principles; The evolutionary rationale: why did these rules evolve and why do they have the form that they do; What is the brain circuitry involved? Our paper begins with a quest for artistic universals and proposes a list of ‘Eight laws of artistic experience’ -- a (...) set of heuristics that artists either consciously or unconsciously deploy to optimally titillate the visual areas of the brain. One of these principles is a psychological phenomenon called the peak shift effect: If a rat is rewarded for discriminating a rectangle from a square, it will respond even more vigorously to a rectangle that is longer and skinnier that the prototype. We suggest that this principle explains not only caricatures, but many other aspects of art. Example: An evocative sketch of a female nude may be one which selectively accentuates those feminine form-attributes that allow one to discriminate it from a male figure; a Boucher, a Van Gogh, or a Monet may be a caricature in ‘colour space’ rather than form space. Even abstract art may employ ‘supernormal’ stimuli to excite form areas in the brain more strongly than natural stimuli. Second, we suggest that grouping is a very basic principle. The different extrastriate visual areas may have evolved specifically to extract correlations in different domains , and discovering and linking multiple features into unitary clusters -- objects -- is facilitated and reinforced by direct connections from these areas to limbic structures. In general, when object-like entities are partially discerned at any stage in the visual hierarchy, messages are sent back to earlier stages to alert them to certain locations or features in order to look for additional evidence for the object . Finally, given constraints on allocation of attentional resources, art is most appealing if it produces heightened activity in a single dimension rather than redundant activation of multiple modules. This idea may help explain the effectiveness of outline drawings and sketches, the savant syndrome in autists, and the sudden emergence of artistic talent in fronto-temporal dementia. In addition to these three basic principles we propose five others, constituting a total of ‘eight laws of aesthetic experience’. (shrink)

This paper argues that functionalist metasemantic views, such as Conceptual Role Semantics and Interpretivism, face a Euthyphro challenge. The challenge, put roughly, is this: functionalist metasemantic views reverse the order of explanation. According to such views, representational mental states have the contents that they do partly because they play certain roles in our mental lives. According to an intuitive picture of the roles that representational mental states play in our mental lives, however, these states play the roles they do (...) partly because they have the contents that they do. Since explanations—even partial ones—are asymmetric (call this principle ‘the Euthyphro Principle’), we can’t accept both this intuitive picture and a functionalist metasemantics. Hence, we should reject all versions of the latter. This paper can be seen as an attempt to better articulate an intuition that has been suggested in various forms in the literature. The paper proceeds as follows. First, it shows that functionalist metasemantic views imply certain ‘partly because’ claims. Second, it argues for the Euthyphro Principle. Third, it defends the intuitive picture of representational mental states and shows that it implies ‘partly because’ claims that conflict with those made by functionalist metasemantic views. Finally, it considers ways of relaxing the intuitive picture and finds them all wanting. (shrink)

We investigate the theory IΔ 0 + Ω 1 and strengthen [Bu86. Theorem 8.6] to the following: if NP ≠ co-NP. then Σ-completeness for witness comparison formulas is not provable in bounded arithmetic. i.e. $I\delta_0 + \Omega_1 + \nvdash \forall b \forall c (\exists a(\operatorname{Prf}(a.c) \wedge \forall = \leq a \neg \operatorname{Prf} (z.b))\\ \rightarrow \operatorname{Prov} (\ulcorner \exists a(\operatorname{Prf}(a. \bar{c}) \wedge \forall z \leq a \neg \operatorname{Prf}(z.\bar{b})) \urcorner)).$ Next we study a "small reflection principle" in bounded arithmetic. We prove that for (...) all sentences φ $I\Delta_0 + \Omega_1 \vdash \forall x \operatorname{Prov}(\ulcorner \forall y \leq \bar{x} (\operatorname{Prf} (y. \overline{\ulcorner \varphi \urcorner}) \rightarrow \varphi)\urcorner).$ The proof hinges on the use of definable cuts and partial satisfaction predicates akin to those introduced by Pudlak in [Pu86]. Finally, we give some applications of the small reflection principle, showing that the principle can sometimes be invoked in order to circumvent the use of provable Σ-completeness for witness comparison formulas. (shrink)

The idea that qualities can be had partly or to an intermediate degree is controversial among contemporary metaphysicians, but also has a considerable pedigree among philosophers and scientists. In this paper, we first aim to show that metaphysical sense can be made of this idea by proposing a partial taxonomy of metaphysical accounts of graded qualities, focusing on three particular approaches: one which explicates having a quality to a degree in terms of having a property with an in-built degree, (...) another based on the idea that instantiation admits of degrees, and a third which derives the degree to which a quality is had from the aspects of multi-dimensional properties. Our second aim is to demonstrate that the choice between these account can make a substantial metaphysical difference. To make this point, we rely on two case studies (involving quantum observables and values) in which we apply the accounts in order to model apparent cases of metaphysical gradedness. (shrink)