Presupposing that most predicates do not correspond directly to genuine relations, I argue that all genuine relations are symmetric. My main argument depends on the premise that there are no brute necessities, interpreted so as to require logical and metaphysical necessity to coincide for sentences composed entirely of logical vocabulary and primitive predicates. Given this premise, any set of purportedly primitive predicates by which one might hope to express the facts about non-symmetric relations order their relata will (...) generate an objectionable multiplication of possibilities. In the final section I give a different argument, based on the weaker premise that brute necessities should not be multiplied without necessity. (shrink)

It is a metaphysical orthodoxy that interesting non-symmetric relations cannot be reduced to symmetric ones. This orthodoxy is wrong. I show this by exploring the expressive power of symmetric theories, i.e. theories which use only symmetric predicates. Such theories are powerful enough to raise the possibility of Pythagrapheanism, i.e. the possibility that the world is just a vast, unlabelled, undirected graph.

I examine and discuss in this paper Orilia’s theory of external, non-symmetrical relations, that is based on ontological roles (O-Roles). I explore several attempts to interpret O-Roles from an ontological viewpoint and I reject them because of two problems concerning the status of asymmetrical relations (to be distinguished from non-symmetrical relations simpliciter) and of exemplification as an external, non-symmetrical relation. Finally, following Heil’s and Lowe’s characterization of modes as particular properties that ontologically depend on (...) their “bearers”, I introduce relational modes in order to define a new solution to the problems of the ontological status of both external, non-symmetrical relations and O-Roles. I also deal with five objections raised by Fraser MacBride against relational modes and O-Roles and I elaborate an analysis of the relations of being to the left of and being to the right of. (shrink)

There are two ways to characterize symmetric relations. One is intensional: necessarily, _Rxy_ iff _Ryx_. In some discussions of relations, however, what is important is whether or not a relation gives rise to the same completion of a given type (fact, state of affairs, or proposition) for each of its possible applications to some fixed relata. Kit Fine calls relations that do ‘strictly symmetric’. Is there is a difference between the notions of necessary and strict symmetry that (...) would prevent them from being used interchangeably in such discussions? I show that there is. While the notions coincide assuming an intensional account of relations and their completions, according to which relations/completions are identical if they are necessarily coinstantiated/equivalent, they come apart assuming a hyperintensional account, which individuates relations and completions more finely on the basis of relations’ real definitions. I establish this by identifying two definable relations, each of which is necessarily symmetric but nonetheless results in distinct facts when it applies to the same objects in opposite orders. In each case, I argue that these facts are distinct because they have different grounds. (shrink)

Non-symmetric relations like loves or between can apply to the same relata in non-equivalent ways. For example, loves may apply to Abelard and Eloise either by Abelard’s loving Eloise or by Eloise’s loving Abelard. On the standard account of relations, different applications of a relation to fixed relata are distinguished by the direction in which the relation applies to the relata. But neither Directionalism nor its most popular rival, Positionalism, offer accounts of differential application that generalize to (...) class='Hi'>relations of arbitrary symmetry structure. Here, I develop an alternative account, Relative Positionalism, which distinguishes different applications of a relation to fixed relata in terms of the ways in which the relata are characterized relative to one another. In presenting and defending Relative Positionalism, this paper covers some of the same ground as my [2016], but avoids the latter’s algebraic approach and focuses on interpretative issues—in particular, how to make sense of relative property instantiation—that were not addressed in the earlier paper. (shrink)

We study partitions of Fraïssé limits of classes of finite relational structures where the partitions are encoded by infinite binary strings which are random in the sense of Kolmogorov-Chaitin.

In this paper I contribute a further element to the case for admitting non-symmetric relations by dismantling the case against them. Armstrong and Dorr have both argued (1) that asymmetric relations give rise to ‘brute necessities’, whilst Dorr further argues (2) that admitting non-symmetric relations generates spurious possibilities and (3) that exploiting work of Goodman and Hazen, we can do without non-symmetric relations anyway. Against (1) I argue that neither Armstrong nor Dorr succeed in avoiding brute (...) necessities themselves. Against (2) and (3) I argue that admitting non-symmetric relations doesn’t give rise to spurious possibilities and Goodman and Hazen’s work cannot be used to establish that non-symmetric relations are dispensable to science and mathematics. (shrink)

The usual representation of quantum algorithms is limited to the process of solving the problem. We extend it to the process of setting the problem. Bob, the problem setter, selects a problem-setting by the initial measurement. Alice, the problem solver, unitarily computes the corresponding solution and reads it by the final measurement. This simple extension creates a new perspective from which to see the quantum algorithm. First, it highlights the relevance of time-symmetric quantum mechanics to quantum computation: the problem-setting and (...) problem solution, in their quantum version, constitute pre- and post-selection, hence the process as a whole is bound to be affected by both boundary conditions. Second, it forces us to enter into relational quantum mechanics. There must be a representation of the quantum algorithm with respect to Bob, and another one with respect to Alice, from whom the outcome of the initial measurement, specifying the setting and thus the solution of the problem, must be concealed. Time-symmetrizing the quantum algorithm to take into account both boundary conditions leaves the representation to Bob unaltered. It shows that the representation to Alice is a sum over histories in each of which she remains shielded from the information coming to her from the initial measurement, not from that coming to her backwards in time from the final measurement. In retrospect, all is as if she knew in advance, before performing her problem-solving action, half of the information that specifies the solution of the problem she will read in the future and could use this information to reach the solution with fewer computation steps. This elucidates the quantum computational speedup in all the quantum algorithms examined. (shrink)

We consider Borel equivalence relations E induced by actions of the infinite symmetric group, or equivalently the isomorphism relation on classes of countable models of bounded Scott rank. We relate the descriptive complexity of the equivalence relation to the nature of its complete invariants. A typical theorem is that E is potentially Π03 iff the invariants are countable sets of reals, it is potentially Π04 iff the invariants are countable sets of countable sets of reals, and so on. The (...) proofs use various techniques, including Vaught transforms, changing topologies, and the Scott analysis of countable models. (shrink)

Metaphysical orthodoxy maintains that the relation of ontological dependence is irreflexive, asymmetric, and transitive. The goal of this paper is to challenge that orthodoxy by arguing that ontological dependence should be understood as non- symmetric, rather than asymmetric. If we give up the asymmetry of dependence, interesting things follow for what we can say about metaphysical explanation— particularly for the prospects of explanatory holism.

According to Wlodek Rabinowicz's fitting-attitude analysis of comparative value, it is possible to analyse both standard and non-standard value relations in terms of the standard preference relations and two levels of normativity. In a recent article, however, Johan Gustafsson has argued that Rabinowicz's analysis violates a principle of value–preference symmetry, according to which for any value relation, there is a corresponding preference relation. Gustafsson has proposed an alternative analysis which respects this principle and which allegedly accounts for the (...) idea that originally motivated Rabinowicz's analysis, namely, that in some cases different preference relations between a pair of items are equally permissible. The goal of my article is to show that the arguments offered by Gustafsson in favour of his account do not succeed. In particular, I argue that Gustafsson faces a dilemma: either he abandons the principle of value–preference symmetry or he cannot make conceptual room for multiple permissible preferences. (shrink)

Symmetric generalized Galois logics (i.e., symmetric gGl s) are distributive gGl s that include weak distributivity laws between some operations such as fusion and fission. Motivations for considering distribution between such operations include the provability of cut for binary consequence relations, abstract algebraic considerations and modeling linguistic phenomena in categorial grammars. We represent symmetric gGl s by models on topological relational structures. On the other hand, topological relational structures are realized by structures of symmetric gGl s. We generalize the (...) weak distributivity laws between fusion and fission to interactions of certain monotone operations within distributive super gGl s. We are able to prove appropriate generalizations of the previously obtained theorems—including a functorial duality result connecting classes of gGl s and classes of structures for them. (shrink)

Bob hides a ball in one of four drawers. Alice is to locate it. Classically she has to open up to three drawers, quantally just one. The fundamental reason for this quantum speedup is not known. The usual representation of the quantum algorithm is limited to the process of solving the problem. We extend it to the process of setting the problem. The number of the drawer with the ball becomes a unitary transformation of the random outcome of the preparation (...) measurement. This extended, time-symmetric, representation brings in relational quantum mechanics. It is with respect to Bob and any external observer and cannot be with respect to Alice. It would tell her the number of the drawer with the ball before she opens any drawer. To Alice, the projection of the quantum state due to the preparation measurement should be retarded at the end of her search; in the input state of the search, the drawer number is determined to Bob and undetermined to Alice. We show that, mathematically, one can ascribe any part of the selection of the random outcome of the preparation measurement to the final Alice’s measurement. Ascribing half of it explains the speedup of the present algorithm. This leaves the input state to Bob unaltered and projects that to Alice on a state of lower entropy where she knows half of the number of the drawer with the ball in advance. The quantum algorithm turns out to be a sum over histories in each of which Alice knows in advance that the ball is in a pair of drawers and locates it by opening one of the two. In the sample of quantum algorithms examined, the part of the random outcome of the initial measurement selected by the final measurement is one half or slightly above it. Conversely, given an oracle problem, the assumption it is one half always corresponds to an existing quantum algorithm and gives the order of magnitude of the number of oracle queries required by the optimal one. (shrink)

The purpose of this paper is to explore two questions:(1) Is symmetrical communication in public relations practice inherently ethical?(2) Does symmetrical communication contribute to public relations effectiveness and organizational effectiveness? Three surveys are undertaken to test seven research hypotheses for the purpose of cross-validating research findings. The results suggest that symmetrical communication is inherently ethical. Moreover, symmetrical communication indeed contributes to several performance measures, which include positive market performance, overall organizational effectiveness, conflict resolution, crisis (...) management, favorable organizational reputation, and positive media exposure, with the last two measures only partially supported. (shrink)

We articulate the problems posed by the quantum liar experiment (QLE) for backwards causation interpretations of quantum mechanics, time-symmetric accounts and other dynamically oriented local hidden variable theories. We show that such accounts cannot save locality in the case of QLE merely by giving up “lambda-independence.” In contrast, we show that QLE poses no problems for our acausal Relational Blockworld interpretation of quantum mechanics, which invokes instead adynamical global constraints to explain Einstein–Podolsky–Rosen (EPR) correlations and QLE. We make the case (...) that the acausal and adynamical perspective is more fundamental and that dynamical entities obeying dynamical laws are emergent features grounded therein. (shrink)

This chapter examines four special problems involving properties whether universals or tropes. It looks at various accounts of relational facts, facts that involve properties relating two or more particulars. The chapter examines an important special case of relational facts: those that involve nonsymmetric or ordering relations. It focuses on structural properties, those relational properties that enable many things to form a single structure, like a group or a team. Finally, it considers the problem of measurable quantities. Monadism is the (...) view that all relational truths are grounded in the intrinsic character of substances taken individually. The most difficult problem for Leibniz's version of Monadism is giving a full and adequate theory of monadic representation. A monad's representing the world as being a certain way must consist of a set of intrinsic mental acts. The chapter surveys the various metaphysical options for Anti‐Monadism, and considers the most difficult test case: that of non‐symmetric relations. (shrink)

Counterfactuals in quantum theory are briefly reviewed and it is argued that they are very different from counterfactuals considered in the general philosophical literature. The issue of time symmetry of quantum counterfactuals is considered and a novel time-symmetric definition of quantum counterfactuals is proposed. This definition is applied for analyzing several controversies related to quantum counterfactuals.

This article explores the elective affinities between Actor-Network Theory (ANT) and the sociology of critical capacities. It argues that these two research programmes can be understood as symmetrical twins. We show the extent to which the exchange between Bruno Latour and Luc Boltanski has influenced their respective theoretical developments. Three strong encounters between the twin research programmes may be distinguished. The first encounter concerns explanations for social change. The second encounter focuses on the status of objects and their relationship (...) to places. The third encounter is about the concept of critique. Drawing on their long-term mutual readings, we gain insight into how pleas for symmetrical analysis raised in response to Bourdieu’s theory of fields have evolved within both ANT and the sociology of critical capacity. We conclude by relating the development of the respective research programmes to the issue of disciplinary boundaries. (shrink)

According to some representationalists (M. Tye, Ten problems of consciousness, MIT Press, Massachusetts, USA, 1995; W.G. Lycan, Consciousness and experience, MIT Press, Cambridge, Massachusetts, USA, 1996; F. Dretske, Naturalising the mind, MIT Press, Massachusetts, USA 1995), qualia are identical to external environmental states or features. When one perceives a red rose for instance, one is visually representing the actual redness of the rose. The represented redness of the rose is the actual redness of the rose itself. Thus redness is not (...) a property of one’s experience but an externally constituted property of the perceived physical object. In this sense, qualia are out there, in the external world. Here, I argue that the main representationalist arguments to this effect, if successful, establish no more than a symmetrical supervenience relation between representational content and qualia, and that a supervenience relation alone (albeit symmetrical) doesn’t suffice for identity. This supervenience thesis between qualia and representational content leaves open the question as to the essential nature of qualia. (shrink)

In recent years, anthropic reasoning has been used to justify a number of controversial skeptical hypotheses. In this paper, we consider two prominent examples, viz. Bostrom’s ‘Simulation Argument’ and the problem of ‘Boltzmann Brains’ in big bang cosmology. We argue that these cases call into question the assumption, central to Bayesian confirmation theory, that the relation of evidential confirmation is universally symmetric. We go on to argue that the fact that these arguments appear to contradict this fundamental assumption should not (...) be taken as an immediate refutation, but should rather be seen as indicative of the peculiar role that the relevant hypotheses play in their respective epistemic frameworks. (shrink)

The main purpose of this paper is to introduce a class of algebraic structures related to many-valued ukasiewicz algebras. They are symmetrical Heyting algebras with a set of modal operators indexed by a finite completely symmetric poset. A representation theorem is given for these (not functionally complete) algebras.

The article studies two related issues. First, it introduces the notion of the contraposition of quantifiers which is a “dual” notion of symmetry and has similar relations to co-intersectivity as symmetry has to intersectivity. Second, it shows how symmetry and contraposition can be generalised to higher order type quantifiers, while preserving their relations with other notions from generalized quantifiers theory.

We define dual and symmetric combinatory calculi (inequational and equational ones), and prove their consistency. Then, we introduce algebraic and set theoretical relational and operational - semantics, and prove soundness and completeness. We analyze the relationship between these logics, and argue that inequational dual logics are the best suited to model computation.

Theories of scientific representation, following Chakrawartty's categorization, are divided into two groups. Whereas cognitive-functional views emphasize agents' intentions, informational theories stress the objective relation between represented and representing. In the first part, a modified structuralist theory is introduced that takes into account agents' intentions. The second part is devoted to dismissing a criticism against the structural account of representation on which similarity as the backbone of representation raises serious problems, since it has definite logical features, i.e. reflexivity, symmetry and transitivity, (...) which representation lacks. Drawing on the representational relation between quantum and statistical field theories, I argue that scientific representation displays these logical features, although depending on the context they may be used or not. (shrink)

There are three different degrees to which we may allow a systematic theory of the world to embrace the idea of relatedness—supposing realism about non-symmetric relations as a background requirement. (First Degree) There are multiple ways in which a non-symmetric relation may apply to the things it relates—for the binary case, aRb ≠ bRa. (Second Degree) Every such relation has a distinct converse—for every R such that aRb there is another relation R* such that bR*a. (Third Degree) Each one (...) of them applies in an order to the things it relates—with regard to the state that results from R's applying to a and b, either R applies to a first and b second, or it applies to b first and a second. Whereas the first degree is near-indubitable, embracing the second or third generates unwholesome consequences. The second degree embodies a commitment to the existence of a superfluity of distinct converses and states to which such relations give rise. The third degree embodies commitment to recherché facts of the matter about how the states that arise from the application of one non-symmetric relation compare to any other. It is argued that accounts that purport to offer an analysis of the first degree generate unwelcome second or third degree consequences. This speaks in favour of our adopting an account of the application of relations that's not an analysis at all, an account that takes the first degree as primitive. (shrink)

In this paper I provide a state of the art survey and assessment of the contemporary debate about relations. After (1) distinguishing different varieties of relations, symmetric from non-symmetric, internal from external relations etc. and relations from their set-theoretic models or sequences, I proceed (2) to consider Bradley’s regress and whether relations can be eliminated altogether. Next I turn (3) to the question whether relations can be reduced, bringing to bear considerations from the philosophy (...) of physics as well as metaphysics. Finally, (3) I consider in what sense relations have order, and whether to make sense of this we are required to conceive of relations as having direction or argument positions. (shrink)

Do non‐symmetric relations apply to the objects they relate in an order? According to the standard view of relations, the difference between aRb and bRa obtaining, where R is non‐symmetric, corresponds to a difference in the order in which the non‐symmetric relation R applies to a and b. Recently Kit Fine has challenged the standard view in his important paper ‘Neutral Relations’ arguing that non‐symmetric relations are neutral, lacking direction or order. In this paper I argue (...) that Fine cannot account for the application of non‐symmetric relations to their relata; so far from being neutral, these relations are inherently directional. (shrink)

Why must incompatibility be symmetric? An odd question, but recent work in the semantics of non-classical logic, which appeals to the notion of incompatibility as a primitive and defines negation in terms of it, has brought this question to the fore. Francesco Berto proposes such a semantics for negation argues that, since incompatibility must be symmetric, double negation introduction must be a law of negation. However, he offers no argument for the claim that incompatibility really must be symmetric. Here, I (...) provide such an argument, showing that, insofar as we think of incompatibility in normative pragmatic terms, it can play its basic pragmatic function only if it is symmetric. The upshot is that we can vindicate Berto’s claim about the symmetry of incompatibility but only if we, pace Berto, think about incompatibility, in the first instance, as a pragmatic relation between acts rather than a semantic relation between contents. (shrink)

The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as central singularities. On the other hand, if they are extended systems, like (...) in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal geometries seem disfavoured. (shrink)

The trope bundle theories of objects are capable of analyzing monadic inherence (objects having tropes), which is one of their main advantage. However, the best current trope theoretical account of relational tropes, namely, the relata specific view leaves relational inherence (a relational trope relating two or more entities) primitive. This article presents the first trope theoretical analysis of relational inherence by generalizing the trope theoretical analysis of inherence to relational tropes. The analysis reduces the holding of relational inherence to the (...) obtaining of certain other facts about entities of the trope theoretical category system. Moreover, I show that the analysis can deal with asymmetric and non-symmetric relations by assuming that all relation-like tropes are quantities. Finally, I provide an account of the spatial location of tropes in the difficult case in which tropes contribute to determining of the location of other entities. (shrink)

We present a version of system Fω, called image, in which the layer of type constructors is essentially the traditional one of Fω, whereas provability of types is classical. The proof-term calculus accounting for the classical reasoning is a variant of Barbanera and Berardi’s symmetric λ-calculus.We prove that the whole calculus is strongly normalising. For the layer of type constructors, we use Tait and Girard’s reducibility method combined with orthogonality techniques. For the layer of terms, we use Barbanera and Berardi’s (...) method based on a symmetric notion of reducibility candidate. We prove that orthogonality does not capture the fixpoint construction of symmetric candidates.We establish the consistency of image, and relate the calculus to the traditional system Fω, also when the latter is extended with axioms for classical logic. (shrink)

States of affairs involving a non-symmetric relation such as loving are said to have a relational order, something that distinguishes, for instance, Romeo’s loving Juliet from Juliet’s loving Romeo. Relational order can be properly understood by appealing to o-roles, i.e., ontological counterparts of what linguists call thematic roles, e.g., agent, patient, instrument, and the like. This move allows us to meet the appropriate desiderata for a theory of relational order. In contrast, the main theories that try to do without o-roles, (...) proposed by philosophers such as Russell, Hochberg, and Fine, are in trouble with one or another of these desiderata. After discussing some alternatives, it is proposed that o-roles are best viewed as very generic properties characterizable as ways in which objects jointly exemplify a relation. This makes for exemplification relations understood as complex entities having o-roles as building blocks. (shrink)

Students today are habitual users of digital technology. However, they do not examine the nature of their relationship with technology. Even though we are all enduring severe environmental crises including the COVID-19 pandemic, our students do not appear to see the interrelated connections between the environmental crisis and themselves. A case in point is that they have difficulty drawing a connection between environmental crises and their participation in industrial civilization. This is why it is necessary to consider technological literacy seriously (...) for our environmental education. This study seeks to investigate an alternative way to set up the relation of technology for the current environmental education by comparing the views of Heidegger and Latour on technology. Even though the question of the two thinkers starts from the same critics of the instrumentality of technology, their strategies to overcome it are quite different. While Heidegger suggests a human-centered relationship between humans and technology, Latour criticizes the limitation of this approach and maintains that more symmetrical relations with technology are needed as a form of a network between human and nonhuman actors. In this paper, I argue for the urgency of cultivating a sense of connection for our students’ technological literacy in this environmental crisis. For that purpose, I insist Latour’s advice for teachers and researchers to be considered more seriously to encourage students to take symmetrical relationship with technology in these aggravating environmental crises. (shrink)

Journal Name: Semiotica Issue: Ahead of print.

Maureen Donnelly has recently argued that directionalism, the view that relations have a direction, applying to their relata in an order, is unable to properly treat certain symmetric relations. She alleges that it must count the application of such a relation to an appropriate number of objects in a given order as distinct from its application to those objects in any other ordering of them. I reply by showing how the directionalist can link the application conditions of any (...) fixed arity relation, no matter its arity or symmetry, and its converse(s) in such a way that directionalism will yield the correct ways in which it can apply. I thus establish that directionalism possesses the same advantage Donnelly's own account of relations, relative positionalism, has over traditional positionalist accounts of relations, which do not properly treat symmetric relations. I then note some advantages that directionalism has over its closest competitors. This includes Donnelly's relative positionalism, since directionalism is not, like relative positionalism, committed to the involvement of relative properties in every irreducibly relational claim. I close by conceding that, as Donnelly notes, directionalism is committed to the primitive relation of order-sensitive relational application. But I don't find this notion as mysterious as Donnelly does. I conclude that, even if one construes this feature of directionalism as a drawback, the two views are at worst at a draw, other things being equal, since this drawback is mitigated by the advantage directionalism has over relative positionalism. (shrink)

An introduction to our edited volume, The Metaphysics of Relations, covering a range of issues including the problem of order, the ontological status of relations, reasons for ancient scepticism about relational properties, and two ways of drawing the distinction between internal and external relations.

This article identifies the structural and conceptual aspects of a visual construction often used in advertisements to establish a metaphoric or associative relation, that is, symmetric object alignment (SOA). It offers an account of the formal ingredients of SOA, which fall into two groups: object-constitutive factors (like size, shape, and color) and object-depictment factors (like perspective, orientation, and distance from viewing point). Both factors allow us to treat SOA as a visual rhetorical scheme. We also discuss how SOA relates to (...) conceptual structure, metaphoric or otherwise. Four types of relations are distinguished, based on the way in which perceptual and conceptual characteristics interact. Finally, we discuss the way in which these characteristics relate to the processing of such visual messages. One depictment factor will be focused on in particular: one-to-one versus one-to-many alignments. An attempt is made to connect these 2 patterns to the much-discussed topic in verbal metaphor theory, object comparison versus categorization. (shrink)

I shall explore in this article the hypothesis that structures are relations between the components of complex entities. After having introduced hylomorphism, its major advantages and the major views of the nature of structures, I shall introduce the distinctions between external and internal relations and the one between symmetrical and non-symmetrical relations. I shall also describe the theory of non-symmetrical relations that I accept, i.e., the O-Roles theory, as most structures seem to be (...) external and non-symmetrical relations. Later on, I shall develop my hypothesis and I shall deal with one objection, i.e., that relations necessarily come together with Bradley's vicious regress. Finally, I shall also hypothesize that complex entities are different from structures and from their structured components. In this respect, I shall defend a " simple view " of complex entities. Dwelling on this view, I shall also reply to some recent objections against hylomorphism. (shrink)

Fifteen philosophers offer new essays exploring the metaphysics of relations from antiquity to the present day. They address topics as diverse as ancient and medieval reasons for scepticism about polyadic properties; recent attempts to reduce causal and spatiotemporal relations; recent work on the directionality of relational properties; powers ontologies and their associated problems; whether the most promising interpretations of quantum mechanics posit a fundamentally relational world; and whether the very idea of such a world is coherent. From those (...) who question whether there are relational properties at all, to those who hold they are a fundamental part of reality, The Metaphysics of Relations covers a broad spectrum of positions on the nature and ontological status of relations, from antiquity to the present day. (shrink)

Questions of evidence—including the idea, still central to what could be called informal epistemology, that our beliefs and claims are duly corrected by our encounters with autonomously resistant objects —are inevitably caught up in views of how beliefs, generally, are produced, maintained, and transformed. In recent years, substantially new accounts of these cognitive dynamics—and, with them, more or less novel conceptions of what we might mean by “beliefs”—have been emerging from various nonphilosophical fields as well as from within disciplinary epistemology. (...) Because of the distinctly reflexive nature of these developments—that is, new conceptions of concepts, revised beliefs about belief, invocations of evidence said to challenge the operation of evidence, quasi-logical refutations of the authority of logic, and so on—the deployment of positions and arguments becomes extremely difficult here, as does even the description of the relevant events in intellectual history. Indeed, since we are dealing here not merely with shifts of, as it is sometimes put, “vocabulary,” but, often enough, with clashes of profoundly divergent conceptual idiom and syntax, every major term and discursive move is potentially implicated in the problematic itself, and, thereby, open to radical questioning and liable to charges of question-begging.The aim of the present essay is twofold: first, to suggest the more general interest and significance, beyond the fields in which they are being developed, of these emerging reconceptions of belief; and, second, to frame that suggestion in an account which, since it cannot escape the rhetorical difficulties just mentioned, foregrounds them. A number of related themes—notably, symmetry, circularity, reciprocality, and ambivalence—recur throughout and, at various points, are drawn together in accord with the account itself. Barbara Herrnstein Smith is Braxton Craven Professor of Comparative Literature and English at Duke University, and director of its Center for Interdisciplinary Studies and Cultural Theory. Her current work examines contemporary models of cognition and communication. (shrink)

Assuming Martin's Axiom, we compute the value of the cofinality of the symmetric group on the natural numbers. We also show that Martin's Axiom does not decide the value of the covering number of a related Mycielski ideal.