I show that the partial truth of a sentence in a partial structure is equivalent to the truth of that sentence in an expansion of a structure that corresponds naturally to the partial structure. Further, a mapping is a partial homomorphism/partial isomorphism between two partial structures if and only if it is a homomorphism/isomorphism between their corresponding structures. It is a corollary that the partial truth of a sentence in a (...) class='Hi'>partial structure is equivalent to the truth of a specific Ramsey sentence in a corresponding structure. Hence the partial structures approach can be expressed in standard first or second-order model theory, and it can be captured in the received view on scientific theories as developed by Carnap and Hempel. (shrink)

We examine, from the partial structures perspective, two forms of applicability of mathematics: at the “bottom” level, the applicability of theoretical structures to the “appearances”, and at the “top” level, the applicability of mathematical to physical theories. We argue that, to accommodate these two forms of applicability, the partial structures approach needs to be extended to include a notion of “partial homomorphism”. As a case study, we present London's analysis of the superfluid behavior of liquid helium (...) in terms of Bose‐Einstein statistics. This involved both the introduction of group theory at the top level, and some modeling at the “phenomenological” level, and thus provides a nice example of the relationships we are interested in. We conclude with a discussion of the “autonomy” of London's model. (shrink)

This paper is about partially ordered multisets (pomsets for short). We investigate a particular class of pomsets that we call order-deterministic, properly including all partially ordered sets, which satisfies a number of interesting properties: among other things, it forms a distributive lattice under pomset prefix (hence prefix closed sets of order-deterministic pomsets are prime algebraic), and it constitutes a reflective subcategory of the category of all pomsets. For the order-deterministic pomsets we develop an algebra with a sound and (-) complete (...) equational theory. The operators in the algebra are concatenation and join, the latter being a variation on the more usual disjoint union of pomsets. This theory is then extended in order to capture refinement of pomsets by incorporating homomorphisms between models as objects in the algebra and homomorphism application as a new operator. (shrink)

In this paper, we study natural language constructions which were first examined by Barwise: The richer the country, the more powerful some of its officials. Guided by Barwise’s observations, we suggest that conceivable interpretations of such constructions express the existence of various similarities between partial orders such as homomorphism or embedding. Semantically, we interpret the constructions as polyadic generalized quantifiers restricted to finite models. We extend the results obtained by Barwise by showing that similarity quantifiers are not expressible (...) in elementary logic over finite models. We also investigate whether the proposed readings are sound from the cognitive perspective. We prove that almost all similarity quantifiers are intractable. This leads us to first-order variants, which only approximate the strong readings, but are cognitively more plausible. Driven by the question of ambiguity, we recall Barwise’s argumentation in favour of strong readings, enriching it with some arguments of our own. Given that Barwise-like sentences are indeed ambiguous, we use a generalized Strong Meaning Hypothesis to derive predictions for their verification. Finally, we propose a hypothesis according to which conflicting pressures of communication and cognition might give rise to an ambiguous construction, provided that different semantic variants of the construction withstand different pressures involved in its usage. (shrink)

In the paper, original formal-logical conception of syntactic and semantic: intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically: in the spirit of some Husserl’s ideas of pure grammar, Leśniewski-Ajukiewicz’s theory syntactic/semantic categories and in accordance with Frege’s ontological canons, Bocheński’s famous motto—syntax mirrors ontology and some ideas of Suszko: language should be a linguistic scheme of ontological reality and simultaneously a tool of its (...) cognition. In the logical conception of language L, its expressions should satisfy some general conditions of language adequacy. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic, and semantic compatibility, correspondence guaranteed by the acceptance of a postulate of categorial compatibility syntactic and semantic categories of expressions of L. From this postulate, three principles of compositionality follow: one syntactic and two semantic already known to Frege. They are treated as conditions of homomorphism partial algebra of L into algebraic models of L: syntactic, intensional, and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, of course, an idealization, but only expressions with high degrees of precision of their senses, after due justification, may become theorems of science. (shrink)

Three results in [14] and one in [8] are analyzed in Sections 3–6 in order to supply examples on Loeb probability spaces, which distinguish the different strength among three generalizations of k-saturation, as well to answer some questions in Section 7 of [15]. In Section 3 we show that not every automorphism of a Loeb algebra is induced by an internal permutation, in Section 4 we show that if the 1-special model axiom is true, then every automorphism of a Loeb (...) algebra is induced by a point-automorphism, in Section 5 we show that not every measure-preserving homomorphism from a small subalgebra to a Loeb algebra is induced by an internal permutation, without assuming full-saturation, in Section 6 we show that, under some cardinality assumptions, the 1-isomorphism property does not guarantee the compactness of a Loeb space, and in Section 7 an application of the 1-special model axiom is given on the existence of ergodic transformations of a Loeb space, which partially answers Problem 2.3 of [5]. (shrink)

Given a Polish groupG, let$E(G)$be the right coset equivalence relation$G^{\omega }/c(G)$, where$c(G)$is the group of all convergent sequences inG. The connected component of the identity of a Polish groupGis denoted by$G_0$.Let$G,H$be locally compact abelian Polish groups. If$E(G)\leq _B E(H)$, then there is a continuous homomorphism$S:G_0\rightarrow H_0$such that$\ker (S)$is non-archimedean. The converse is also true whenGis connected and compact.For$n\in {\mathbb {N}}^+$, the partially ordered set$P(\omega )/\mbox {Fin}$can be embedded into Borel equivalence relations between$E({\mathbb {R}}^n)$and$E({\mathbb {T}}^n)$.

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and (...) semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions. (shrink)

An algebraization of the notion of topology has been proposed more than 70 years ago in a classical paper by McKinsey and Tarski, leading to an area of research still active today, with connections to algebra, geometry, logic and many applications, in particular, to modal logics. In McKinsey and Tarski’s setting the model theoretical notion of homomorphism does not correspond to the notion of continuity. We notice that the two notions correspond if instead we consider a preorder relation \( (...) \sqsubseteq \) defined by \(a \sqsubseteq b\) if _a_ is contained in the topological closure of _b_, for _a_, _b_ subsets of some topological space. A _specialization poset_ is a partially ordered set endowed with a further coarser preorder relation \( \sqsubseteq \). We show that every specialization poset can be embedded in the specialization poset naturally associated to some topological space, where the order relation corresponds to set-theoretical inclusion. Specialization semilattices are defined in an analogous way and the corresponding embedding theorem is proved. Specialization semilattices have the amalgamation property. Some basic topological facts and notions are recovered in this apparently very weak setting. The interest of these structures arises from the fact that they also occur in many rather disparate contexts, even far removed from topology. (shrink)

After proving, in a purely categorial way, that the inclusion functor |$\textrm {In}_{\textbf {Alg}(\varSigma )}$| from |$\textbf {Alg}(\varSigma )$|⁠, the category of many-sorted |$\varSigma $|-algebras, to |$\textbf {PAlg}(\varSigma )$|⁠, the category of many-sorted partial |$\varSigma $|-algebras, has a left adjoint |$\textbf {F}_{\varSigma }$|⁠, the (absolutely) free completion functor, we recall, in connection with the functor |$\textbf {F}_{\varSigma }$|⁠, the generalized recursion theorem of Schmidt, which we will also call the Schmidt construction. Next, we define a category |$\textbf {Cmpl}(\varSigma )$|⁠, (...) of |$\varSigma $|-completions, and prove that |$\textbf {F}_{\varSigma }$|⁠, labelled with its domain category and the unit of the adjunction of which it is a part, is a weakly initial object in it. Following this, we associate to an ordered pair |$(\boldsymbol {\alpha },f)$|⁠, where |$\boldsymbol {\alpha }=(K,\gamma,\alpha )$| is a morphism of |$\varSigma $|-completions from |${{\mathscr {F}}}=(\textbf {C},F,\eta )$| to |$\mathscr {G}= (\textbf {D},G,\rho )$| and |$f$| a homomorphism of |$\textbf {D}$| from the partial |$\varSigma $|-algebra |$\textbf {A}$| to the partial |$\varSigma $|-algebra |$\textbf {B}$|⁠, a homomorphism |$\varUpsilon ^{\mathscr {G},0}_{\boldsymbol {\alpha }}(f)\colon \textbf {Sch}_{\boldsymbol {\alpha }}(f)\longrightarrow \textbf {B}$|⁠. We then prove that there exists an endofunctor, |$\varUpsilon ^{\mathscr {G},0}_{\boldsymbol {\alpha }}$|⁠, of |$\textbf {Mor}_{\textrm {tw}}(\textbf {D})$|⁠, the twisted morphism category of |$\textbf {D}$|⁠, thus showing the naturalness of the previous construction. Afterwards, we prove that, for every |$\varSigma $|-completion |$\mathscr {G}=(\textbf {D},G,\rho )$|⁠, there exists a functor |$\varUpsilon ^{\mathscr {G}}$| from the comma category |$(\textbf {Cmpl}(\varSigma )\!\downarrow \!\mathscr {G})$| to |$\textbf {End}(\textbf {Mor}_{\textrm {tw}}(\textbf {D}))$|⁠, the category of endofunctors of |$\textbf {Mor}_{\textrm {tw}}(\textbf {D})$|⁠, such that |$\varUpsilon ^{\mathscr {G},0}$|⁠, the object mapping of |$\varUpsilon ^{\mathscr {G}}$|⁠, sends a morphism of |$\varSigma $|-completion of |$\textbf {Cmpl}(\varSigma )$| with codomain |$\mathscr {G}$|⁠, to the endofunctor |$\varUpsilon ^{\mathscr {G},0}_{\boldsymbol {\alpha }}$|⁠. (shrink)

In an earlier paper, we introduced the following pre-order on the subgroups of a given Polish group: if G is a Polish group and \ are subgroups, we say H is homomorphism reducible to L iff there is a continuous group homomorphism \ such that \\). We previously showed that there is a \ subgroup L of the countable power of any locally compact Polish group G such that every \ subgroup of \ is homomorphism reducible to (...) L. In the present work, we show that this fails in the countable power of the group of increasing homeomorphisms of the unit interval. (shrink)

This paper is a critical response to Andreas Bartels’ sophisticated defense of a structural account of scientific representation. We show that, contrary to Bartels’ claim, homomorphism fails to account for the phenomenon of misrepresentation. Bartels claims that homomorphism is adequate in two respects. First, it is conceptually adequate, in the sense that it shows how representation differs from misrepresentation and non-representation. Second, if properly weakened, homomorphism is formally adequate to accommodate misrepresentation. We question both claims. First, we (...) show that homomorphism is not the right condition to distinguish representation from misrepresentation and non-representation: a “representational mechanism” actually does all the work, and it is independent of homomorphism – as of any structural condition. Second, we test the claim of formal adequacy against three typical kinds of inaccurate representation in science which, by reference to a discussion of the notorious billiard ball model, we define as abstraction, pretence, and simulation. We first point out that Bartels equivocates between homomorphism and the stronger condition of epimorphism, and that the weakened form of homomorphism that Bartels puts forward is not a morphism at all. After providing a formal setting for abstraction, pretence and simulation, we show that for each morphism there is at least one form of inaccurate representation which is not accommodated. We conclude that Bartels’ theory – while logically laying down the weakest structural requirements – is nonetheless formally inadequate in its own terms. This should shed serious doubts on the plausibility of any structural account of representation more generally. (shrink)

In this paper, we introduce the notion of intuitionistic fuzzy PMS-subalgebras under homomorphism and Cartesian product and investigate several properties. We study the homomorphic image and inverse image of the intuitionistic fuzzy PMS-subalgebras of a PMS-algebra, which are also intuitionistic fuzzy PMS-subalgebras of a PMS-algebra, and find some other interesting results. Furthermore, we also prove that the Cartesian product of intuitionistic fuzzy PMS-subalgebras is again an intuitionistic fuzzy PMS-subalgebra and characterize it in terms of its level sets. Finally, we (...) consider the strongest intuitionistic fuzzy PMS-relations on an intuitionistic fuzzy set in a PMS-algebra and demonstrate that an intuitionistic fuzzy PMS-relation on an intuitionistic fuzzy set in a PMS-algebra is an intuitionistic fuzzy PMS-subalgebra if and only if the corresponding intuitionistic fuzzy set in a PMS-algebra is an intuitionistic fuzzy PMS-subalgebra of a PMS-algebra. (shrink)

Argues that a pluralistic understanding of truth can foster productive conversations about common concerns involving religion, science, ethics, politics, economics, and ecology without falling into relativism. In this book, Donald A. Crosby defends the idea that all claims to truth are at best partial. Recognizing this, he argues, is a necessary safeguard against arrogance, close-mindedness, and potentially violent reactions to differences of outlook and practice. Crosby demonstrates how “partial truths” are inevitably at work in conversations and debates about (...) religion, science, morality, economics, ecology, and social and political progress. He then focuses on the concept in the discipline of philosophy, looking at a number of distinctions that are taken to be strictly binary—those between fact and value, continuity and novelty, rationalism and empiricism, mind and body, and good and evil—and demonstrates how in all of these cases, each on its own can offer only an incomplete picture. Partial Truths and Our Common Future invites ongoing dialogue with others for the sake of mutual enlargements of understanding rather than mere civility, and provides incentive for continuing open-minded and shared inquiries into the important issues of life. “This is a transdisciplinary philosophical work that moves with grace across traditions, time periods, and thinkers. It is a master class in the existential and public relevance of philosophy and a rare example of a book that is both timely and timeless.” — Michael S. Hogue, author of The Promise of Religious Naturalism. (shrink)

In this article, we investigate the status of the homomorphism preservation property amongst restricted classes of finite relational structures and algebraic structures. We show that there are many homomorphism-closed classes of finite lattices that are definable by a first-order sentence but not by existential positive sentences, demonstrating the failure of the homomorphism preservation property for lattices at the finite level. In contrast to the negative results for algebras, we establish a finite-level relativised homomorphism preservation theorem in (...) the relational case. More specifically, we give a complete finite-level characterisation of first-order definable finitely generated anti-varieties relative to classes of relational structures definable by sentences of some general forms. When relativisation is dropped, this gives a fresh proof of Atserias’s characterisation of first-order definable constraint satisfaction problems over a fixed template, a well known special case of Rossman’s Finite Homomorphism Preservation Theorem. (shrink)

Most of us are partial to our friends and loved ones: we treat them with special care, and we feel justified in doing so. In recent years, the idea that good friends are also epistemically partial to one another has been popular. Being a good friend, so-called epistemic partialists suggest, involves being positively biased towards one's friends – that is, involves thinking more highly of them than is warranted by the evidence. In this paper, I outline the concept (...) of epistemic partiality and its relation to non-epistemic partiality and explore some considerations that speak in favour of and against such partialism in friendships. I finish by suggesting some directions in which this debate could go next. (shrink)

Prospective parents are sometimes partial towards their future children, engaging in what I call ‘pre-parental partiality’. Common sense morality is as permissive of pre-parental partiality as it is of ordinary parental partiality—partiality towards one’s existing children. But I argue that existing justifications for partiality typically establish weaker reasons in support of pre-parental partiality than in support of parental partiality. Thus, either these existing justifications do not fully account for our reasons of parental partiality, or our reasons to engage in (...) pre-parental partiality are indeed typically weaker than our reasons to engage in parental partiality. (shrink)

Say that an audience understands a given utterance perfectly only if she correctly identifies which proposition (or propositions) that utterance expresses. In ideal circumstances, the participants in a conversation will understand each other’s utterances perfectly; however, even if they do not, they may still understand each other’s utterances at least in part. Although it is plausible to think that the phenomenon of partial understanding is very common, there is currently no philosophical account of it. This paper offers such an (...) account. Along the way, I argue against two seemingly plausible accounts which use Stalnaker’s notion of common ground and Lewisian subject matters, respectively. (shrink)

Suppose G is a definably connected, definable group in an o-minimal expansion of an ordered group. We show that the o-minimal universal covering homomorphism equation image: equation image→ G is a locally definable covering homomorphism and π1 is isomorphic to the o-minimal fundamental group π of G defined using locally definable covering homomorphisms.

This paper explores allowing truth value assignments to be undetermined or "partial" and overdetermined or "inconsistent", thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I (...) investigate twelve natural extensions containing nested implications, all of which can be viewed as coming from natural variations on Kripke's semantics for intuitionistic logic. Many of these logics exist antecedently in the literature, in particular Nelson 's "constructible falsity". (shrink)

The foundational conviction of contemporary liberal thought is that all persons possess equal moral worth and are entitled to equal concern and respect by others. At the same time, nation states, as the primary organs of our collective self-governance, frequently pursue policies that are strikingly partial towards the interests of compatriots over those of foreigners. A common strategy for justifying this national partiality is to view it as grounded in associative obligations that we incur by standing in special relationships (...) with our fellow citizens. For instance, according to familiar arguments from ‘fair play’, voluntarily partaking in and benefiting from cooperative relationships with our fellow citizens gives us reciprocal obligations to maintain these social institutions and care for needy compatriots. By contrast, we do not have corresponding associative obligations towards foreigners. I maintain that such arguments from associative obligations face an important stumbling block. I argue for the following “Boundary Principle”, according to which we cannot appeal to special relationships amongst members of a group to justify an attitude of partiality towards them unless the boundaries of this group, and the fact that they exclude other persons from membership, can also be justified. If this is right, arguments from associative obligations, by themselves, are necessarily incomplete. Most modern states severely limit the scope of economic migration, and thereby prevent many would-be contributors to the collective enterprises of affluent societies from entering into those special relationships with us that would give rise to associative obligations on our part. Not only are would-be immigrants excluded from the benefits that participation in the cooperative schemes of affluent nation-states would itself confer; in addition, the fact that they do not stand in such cooperative relationships with us is then appealed to in order to justify the fact that we assign significantly less weight to their interests in the formulation of state policy. The upshot of my discussion is not that a defense of national partiality in terms of associative obligations cannot succeed. It is rather that a successful defense of national partiality in these terms is more closely tied to the question whether principled restrictions can be placed on immigration than most political philosophers have hitherto assumed. (shrink)

We are partial to people with whom we share special relationships--if someone is your child, parent, or friend, you wouldn't treat them as you would a stranger. But is partiality justified, and if so, why? Partiality presents a theory of the reasons supporting special treatment within special relationships and explores the vexing problem of how we might reconcile the moral value of these relationships with competing claims of impartial morality. Simon Keller explains that in order to understand why we (...) give special treatment to our family and friends, we need to understand how people come to matter in their own rights. Keller first presents two main accounts of partiality: the projects view, on which reasons of partiality arise from the place that people take within our lives and our commitments, and the relationships view, on which relationships themselves contain fundamental value or reason-giving force. Keller then argues that neither view is satisfactory because neither captures the experience of acting well within special relationships. Instead, Keller defends the individuals view, on which reasons of partiality arise from the value of the individuals with whom our relationships are shared. He defends this view by saying that we must accept that two people, whether friend or stranger, can have the same value, even as their value makes different demands upon people with whom they share different relationships. Keller explores the implications of this claim within a wider understanding of morality and our relationships with groups, institutions, and countries. (shrink)

African ethical theories tend to hold that moral agents ought to be partial, in the sense that they should favour members of their family or close community. This is considered an advantage over the impartiality of many Western moral theories, which are regarded as having counterintuitive implications, such as the idea that it is unethical to save a family member before a stranger. The partiality of African ethics is thought to be particularly valuable in the context of bioethics. Thaddeus (...) Metz, in particular, argues that his African-derived theory best accounts for a number of plausible intuitions, such as the intuition that health care practitioners ought to be biased towards the patients for whom they are directly responsible. In this article, I claim that the plausible intuitions drawn on in favour of partiality can be satisfactorily explained on the basis of impartial moral theories. Moreover, I argue that blanket acceptance of partiality has problematic consequences for distributive justice in resource allocation in biomedical contexts. By contrast, impartial theories can justify plausible instances of partiality whilst avoiding the pitfalls of fully partial moral theories. Although this provides grounds for abandoning partiality in principle, I claim that this finding should not be seen as damaging to African medical ethics. Instead, it prompts investigation of underexplored possibilities of impartial African moral theories. To demonstrate the value of this direction, I sketch some novel and attractive conceptions that combine impartiality with elements of African ethics. (shrink)

There is a duality in our everyday view of belief. On the one hand, we sometimes speak of credence as a matter of degree. We talk of having some level of confidence in a claim (that a certain course of action is safe, for example, or that a desired event will occur) and explain our actions by reference to these degrees of confidence – tacitly appealing, it seems, to a probabilistic calculus such as that formalized in Bayesian decision theory. On (...) the other hand, we also speak of belief as an unqualified, or flat-out, state (‘plain belief’ as it is sometimes called), which is either categorically present or categorically absent. We talk of simply believing or thinking that something is the case, and we cite these flat-out attitudes in explanation of our actions – appealing to classical practical reasoning of the sort formalized in the so-called ‘practical syllogism’.1 This tension in everyday discourse is reflected in the theoretical literature on belief. In formal epistemology there is a division between those in the Bayesian tradition, who treat credence as graded, and those who think of it as a categorical attitude of some kind. The Bayesian perspective also contrasts with the dominant view in philosophy of mind, where belief is widely regarded as a categorical state (a token sentence of a mental language, inscribed in a functionally defined ‘belief box’, according to one popular account). A parallel duality is present in our everyday view of desire. Sometimes we talk of having degrees of preference or desirability; sometimes we speak simply of wanting or desiring something tout court, and, again, this tension is reflected in the theoretical literature. What should we make of these dualities? Are there two different types of belief and desire – partial and flat-out, as they are sometimes called? If so, how are they related? And how could both have a role in guiding rational action, as the everyday view has it? The last question poses a particular challenge in relation to flat-out belief and desire.. (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)

You can trust your friends. You should trust your friends. Not all of your friends all of the time: you can reasonably trust different friends to different degrees, and in different domains. Still, we often trust our friends, and it is often reasonable to do so. Why is this? In this paper I explore how and whether friendship gives us reasons to trust our friends, reasons which may outstrip or conflict with our epistemic reasons. In the final section, I will (...) sketch some related questions concerning trust based on the trustee’s race, gender, or other social identity. (shrink)

It’s an undeniable fact about our moral lives that we are partial towards certain people and projects. Despite this, it has traditionally been very hard to justify partiality. In this paper I defend a novel partialist theory. The context of the paper is the debate between three different views of how partiality is justified. According to the first view, partiality is justified by facts about our ground projects. According to the second view, partiality is justified by facts about our (...) relationships with the things that we are partial towards. And according to the third view, partiality is justified by facts about the things that we are partial towards. I argue that all three views contain part of the truth. We can see this by adopting a more sophisticated view of the weight of reasons. Once we do this, it will be clear that both facts about individuals and facts about relationships play a role in explaining why we often have stronger reason to act well towards those things we are partial towards. Further, I argue, facts about projects help explain why facts about relationships play the role that they do in determining the strength of our reasons. (shrink)

In 'Aboutness' (MIT Press 2014), Yablo argues for the importance of the notions of partial content and of partial truth. This paper argues that those notions are involved in a much greater range of entities than acknowledged by Yablo. The paper also argues that some of those entities involve a notion of partial satisfaction as well as partial existence (and partial validity).

Parents typically favour their own children over others’. For example, most parents invest more time and money in their own children than in other children. This parental partiality is usually regarded as morally permissible, or even obligatory, but it can have undesirable distributive effects. For example, it may create unfair or otherwise undesirable advantages for the favoured child. A number of authors have found it necessary to justify parental partiality in the face of these distributive concerns, and they have typically (...) done so by appealing to features of the parent–child relationship. Parental partiality is said to be justified, despite its undesirable distributive effects, in part because the parent enjoys a special kind of relationship with her child. In this paper, I raise a problem for such relational defences of parental partiality. I report empirical findings suggesting that parental partiality will frequently create advantages—sometimes undesirable—not only for one’s children, but also for one’s more distant descendants; I argue that the creation of these latter advantages stands as much in need of justification as does the creation of advantages for one’s own children; and I claim that existing relational defences do not clearly contain the resources necessary to deliver such a justification. I then examine three possible responses to this problem. (shrink)

This chapter considers whether our moral entitlement to manifest certain kinds of partiality stems from a morally basic permission to be partial, or whether it can be accounted for in some other way. In particular, it explores the possibility of justifying partial conduct via a general moral prerogative to pursue our own projects. On this approach, in contexts of plural agency, where two or more people together pursue a joint project, we would have permission to favour our co-agents (...) — but only in ways that relate to our joint project. While this approach might limit the scope of morally permissible partiality, it seems more faithful to the concerns that animate the partiality debates than the alternative of claiming an unrestricted basic right to be partial to whomsoever we wish. (shrink)

The partial structures program of da Costa, French and others offers a unified framework within which to handle a wide range of issues central to contemporary philosophy of science. I argue that the program is inadequately equipped to account for simple cases where idealizations are used to construct abstract, mathematical models of physical systems. These problems show that da Costa and French have not overcome the objections raised by Cartwright and Suárez to using model‐theoretic techniques in the philosophy of (...) science. However, my concerns arise independently of the more controversial assumptions that Cartwright and Suárez have employed. (shrink)

In this article we define a logical system called Hybrid Partial Type Theory ( $\mathcal {HPTT}$ ). The system is obtained by combining William Farmer’s partial type theory with a strong form of hybrid logic. William Farmer’s system is a version of Church’s theory of types which allows terms to be non-denoting; hybrid logic is a version of modal logic in which it is possible to name worlds and evaluate expressions with respect to particular worlds. We motivate this (...) combination of ideas in the introduction, and devote the rest of the article to defining, axiomatising, and proving a completeness result for $\mathcal {HPTT}$. (shrink)

We argue for asymmetries between positive and negative partiality. Specifically, we defend four claims: i) there are forms of negative partiality that do not have positive counterparts; ii) the directionality of personal relationships has distinct effects on positive and negative partiality; iii) the extent of the interactions within a relationship affects positive and negative partiality differently; and iv) positive and negative partiality have different scope restrictions. We argue that these asymmetries point to a more fundamental moral principle, which we call (...) Morality’s Harmonious Propensity. According to this principle, morality has a propensity toward preserving positive relationships and dissolving negative ones. (shrink)

Ethical theories normally make room both for global duties to human beings everywhere and special duties to those we are attached to in some way. Such a split-level view requires us to specify the kind of attachment that can ground special duties, and to explain the comparative force of the two kinds of duties in cases of conflict. Special duties are generated within groups that are intrinsically valuable and not inherently unjust, where the duties can be shown to be integral (...) to relationships within the group. Since nations can be shown to meet these conditions, acknowledging special obligations towards compatriots is justified. However for such partiality to be reasonable, it must be balanced against recognition of duties of global justice. These duties include duties to respect human rights and duties of fairness towards non-nationals. Weighing such duties against domestic duties of social justice is not a simple task, and the outcome should depend on the precise specification of the duty at stake. In particular, the duty to respect human rights fragments into four sub-duties whose force when set against local duties is markedly different. (shrink)

Over the years, two models of freedom have emerged as competitors: the alternative-possibilities model and the actual-sequence model. This paper is a partial defense of the actual-sequence model. My defense relies on two strategies. The first strategy consists in de-emphasizing the role of examples in arguing for a model of freedom. Imagine that, as some people think, Frankfurt-style cases fail to undermine the alternative-possibilities model. What follows from this? Not much, I argue. In particular, I note that the counterparts (...) of Frankfurt-style cases also fail to undermine the actual-sequence model. My second strategy of defense consists in revitalizing the original motivation for the actual-sequence model, by revamping it, isolating it from claims that do not fully capture the same idea, and arguing that it can be developed in a successful way. (shrink)

A central theme of the volume is whether impartiality and partiality are really opposed dimensions or if they can be harmoniously reconciled in one picture of ...

Is a belief that one will succeed necessary for an intention? It is argued that the question has traditionally been badly posed, framed as it is in terms of all-out belief. We need instead to ask about the relation between intention and partial belief. An account of partial belief that is more psychologically realistic than the standard credence account is developed. A notion of partial intention is then developed, standing to all-out intention much as partial belief (...) stands to all-out belief. Various coherence constraints on the notion are explored. It is concluded that the primary relations between intention and belief should be understood as normative and not essential. (shrink)

Philosophers and scientists have maintained that causation, correlation, and partial correlation are essentially related. These views give rise to various rules of causal inference. This essay considers the claims of several philosophers and social scientists for causal systems with dichotomous variables. In section 2 important commonalities and differences are explicated among four major conceptions of correlation. In section 3 it is argued that whether correlation can serve as a measure of A's causal influence on B depends upon the conception (...) of causation being used and upon certain background assumptions. In section 4 five major kinds of partial correlation are explicated, and some of the important relations are established among two conceptions of partial correlation, the conception of screening off, the conception of partitioning, and the measures of causal influence which have been suggested by advocates of path analysis or structural equation methods. In section 5 it is argued that whether any of these five conceptions of partial correlation can serve as a measure of causal influence depends upon the conception of causation being used and upon certain background assumptions.The important conclusion is that each of the approaches (considered here) to causal inference for causal systems with dichotomous variables stands in need of important qualifications and revisions if they are to be justified. (shrink)

The debate around epistemic partiality in friendship presents us with several tough philosophical puzzles. One of these has been articulated in two objections to the view that friendship can require epistemic partiality on the grounds it is incompatible with the nature of friendship. The first, owed to Crawford, argues that you should not treat your friends with epistemic partiality because your beliefs about your friends should be responsive to the facts about them, and epistemic partiality is incompatible with this demand. (...) The second, owed to Mason, draws on a Murdochian account of love to argue that loving relationships—such as friendship—are ‘epistemically rich states’, which means that they are constituted by a drive towards ever greater and more intimate knowledge of our loved ones. In this paper, I shall argue that epistemic partiality may indeed limit what we know about our friends, but not in ways that diminish the quality of our love for them, and certainly not in ways that block us from being friends with them. (shrink)

The author contests the claim made independently by F.M. Kamm and Thomas Hurka that combatants ought to assign greater weight to collateral harm done to their compatriot noncombatants then they assign to collateral harm done to enemy non-combatants. Two arguments by analogy offered in support of such partiality, one of which appeals to permissible self/other asymmetry in cases of harming the few to save the many, and the second of which appeals to parents' justifiable partiality to their children, are found (...) wanting. The author also rebuts Kamm's argument that combatants should assign greater weight to collateral harm done to neutrals than to compatriot non-combatants. However, he contends that in some cases a neutral state's right to sovereignty may entail that a combatant ought to choose the act that will collaterally kill a greater number of compatriot non-combatants over one that involves collaterally killing a lesser number of neutrals. (shrink)

The partial structures program of da Costa, French and others offers a unified framework within which to handle a wide range of issues central to contemporary philosophy of science. I argue that the program is inadequately equipped to account for simple cases where idealizations are used to construct abstract, mathematical models of physical systems. These problems show that da Costa and French have not overcome the objections raised by Cartwright and Suárez to using model-theoretic techniques in the philosophy of (...) science. However, my concerns arise independently of the more controversial assumptions that Cartwright and Suárez have employed. (shrink)

Two of the most well-known belief contraction operators are partial meet contractions (PMCs) and kernel contractions (KCs). In this paper we propose two new classes of contraction operators, namely the class of generalized partial meet contractions (GPMC) and the class of generalized kernel contractions (GKC), which strictly contain the classes of PMCs and of KCs, respectively. We identify some extra conditions that can be added to the definitions of GPMCs and of GKCs, which give rise to some interesting (...) subclasses of those classes of functions, namely the classes of extensional and of uniform GPMCs/GKCs. In the context of contractions on belief sets the classes of partial meet contractions, uniform GPMCs and extensional GPMCs are all identical. Nevertheless, when considered as operations on belief bases, the class of uniform GPMCs coincides with the class of partial meet contractions, but the extensional GPMCs constitute a new kind of belief base contraction functions whose characterizing postulate of irrelevance of syntax is extensionality—the same postulate of irrelevance of syntax which occurs in the classical axiomatic characterization of partial meet contractions for belief sets—rather than the postulate of uniformity—which is the irrelevance of syntax postulate used in the axiomatic characterization for partial meet contractions on belief bases. Analogous results are obtained regarding the classes of extensional and of uniform GKCs. We present the interrelations in the sense of inclusion among all the new classes of operators presented in this paper and several well known classes of PMCs and of KCs. (shrink)

The semantic approach to scientific representation is now long established as a favourite amongst philosophers of science. One of the foremost strains of this approach—the model-theoretic approach —is to represent scientific theories as families of models, all of which satisfy or ‘make true’ a given set of constraints. However some authors have criticised the approach on the grounds that certain scientific theories are logically inconsistent, and there can be no models of an inconsistent set of constraints. Thus it would seem (...) that the MTA fails to represent inconsistent scientific theories at all, and this raises concerns about the way it represents in general. In a series of papers and a recent book da Costa and French have developed a variant of the MTA approach which they call ‘partial structures’, and which they claim can accommodate inconsistent theories. I assess this claim, looking to two theories which have been called ‘inconsistent’: Bohr’s theory of the atom and classical electrodynamics. (shrink)

According to a prominent thought, in one’s practical reasoning one should rely only on what one knows. Yet for many choices, the relevant information is uncertain. This has led Schiffer to the following objection: oftentimes, we are fully rational in reasoning from uncertain premises which we do not know. For example, we may decide to take an umbrella based on a 0.4 credence that it will rain. There are various ways proponents of a knowledge norm for practical reasoning can respond. (...) One option is to say that the right way of dealing with uncertain information requires knowledge of probabilities. Another option is to say that credences can be knowledge because they really are beliefs with an unusual kind of content that consists of a set of probability spaces. Mixed accounts are possible as well. On neither of the accounts in the literature, however, can reasoning from uncertain premises be taken as reasoning based on a graded attitude, a credence, toward an ordinary proposition. To make room for this possibility, I argue that reliance comes in degrees. The knowledge norm is only plausible when taken to be concerned with full reliance.Partial reliance, on the other hand, goes hand in hand with credence. (shrink)

Situated within the framework of Confucian family-oriented ethics, this book explores the issue of familial partiality and specifically discusses whether it is morally praiseworthy to love one's family partially. In reviewing the tension between familial partiality and egalitarian impartiality from different perspectives while also drawing on binary metrics to understand the issue - that is, the weak and strong sense of familial partiality in Confucian moral theory - the author carefully discusses the efficacy of three major arguments to justify moral (...) partiality. It is concluded that the tree argument fails to justify moral partiality in Confucianism, the evolutionary argument only justifies moral partiality in the weak sense that we should devote more resources to our family, and the care argument fails to justify moral partiality in the strong sense that family takes priority in any case even at the expense of the principle of justice. Seeking to address the quandary, the author advances an alternative argument based on Thomas Aquinas' theory of love to interpret Confucian view of partial relationships, holding that partial treatment is assumed in partial relationships. The title will appeal to scholars and students interested in Confucianism, Chinese Philosophy, Moral Philosophy, and Comparative Philosophy. (shrink)