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.

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)

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.

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 (...) class='Hi'>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)

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.

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)

Neo-Fregeans such as Bob Hale and Crispin Wright seek a foundation of mathematics based on abstraction principles. These are sentences involving a relation called the abstraction relation. It is usually assumed that abstraction relations must be equivalence relations, so reflexive, symmetric and transitive. In this article I argue that abstraction relations need not be reflexive. I furthermore give an application of non-reflexive abstraction relations to restricted abstraction principles.

Exemption from blameworthiness is often bound to implicit or explicit claims of diminished agency, or even non-agency. This poses a dilemma in navigating moral relationships affected by mental illness. While it is crucial for assessments of responsibility to be responsive to the significance of mental illness, must this responsiveness come at a cost to symmetrical moral relations? In this paper we argue, contra recent critiques, that Strawsonian accounts of responsibility are able to navigate this dilemma, and can accommodate significant (...) exculpation on the basis of mental illness while maintaining symmetrical relations. We understand this to be part of the larger recognition that while we have certain fundamental entitlements within our moral relationships, it is also possible to be over-entitled, and to expect too much of others. Our account draws, in particular, on the moral significance of difficulty. Difficulty is inherently scalar, and in drawing on this explanatory framework we explicate a theory of both excuse and exemption by degree. We argue for a significant realm of excuse on the basis of mental illness that is fully compatible with symmetrical relations. However, we also acknowledge the limits of this accommodation on Strawsonian grounds, and argue that these limits are justified and appropriate. (shrink)

I consider a problem for functional reductionism, based on the following tension. Say that b is functionally reduced to a. On the one hand, a and b turn out to be identical, and identity is a symmetric relation. On the other hand, functional reductionism implies that a and b are asymmetrically related: if b is functionally reduced to a, then a is not functionally reduced to b. Thus, we ask: how can a and b be asymmetrically related if they (...) are the same thing? I propose a solution to this tension, by distinguishing between ontological levels and levels of description. (shrink)

We put forward a new, ‘coherentist’ account of quantum entanglement, according to which entangled systems are characterized by symmetric relations of ontological dependence among the component particles. We compare this coherentist viewpoint with the two most popular alternatives currently on offer—structuralism and holism—and argue that it is essentially different from, and preferable to, both. In the course of this article, we point out how coherentism might be extended beyond the case of entanglement and further articulated.

In this paper we argue that reflection on the patterns of practical concern that agents like us exhibit strongly suggests that the same person relation comes in continuous degrees rather than being an all or nothing matter. We call this the SP-degree thesis. Though the SP-degree thesis is consistent with a range of views about personal-identity, we argue that combining desire-first approaches to personal-identity with the SP-degree thesis better explains our patterns of practical concern, and hence gives us reason to (...) endorse such an approach. We then argue that the combination of the SP-degree thesis and the desire-first approach are best modelled by a stage-theoretic view of persistence according to which temporal counterpart relations are non-symmetric relations that come in continuous degrees. Ultimately, we think that the overall appeal of this package of views provides reason to accept the package: reasons that outstrip the reasons we have to endorse any particular member of the package. (shrink)

In philosophical reflections on geoethics, it is primarily the question of what it means to be ‘part’ of the Earth system that is critically reflected upon. As the current geological era of the Anthropocene disrupts the dichotomy between Human agency and the Earth system, philosophers criticise a humanist account of geoethics and call for a post-humanist account. In this chapter, we critically engage with one specific proponent of the post-humanist position, Timothy Morton. We introduce his version of the post-humanist position (...) by focussing on his call for the ‘end-of-the-world’ in the Anthropocene. We subsequently criticise Morton’s rejection of the World for three reasons. We show that the emergence of the Anthropocene is primarily an ontological phenomenon, namely a shift in our ‘being-in-the-world’ and that the concept of World is needed to understand the meaning of our ‘being-in-the-Anthropocene’ in contrast with our ‘being-in-the-Holocene’. We introduce a twofold between our ‘being-in-the-world’ as a symmetric relation and our ‘being-on-Earth’ as an asymmetric relation that constitutes our ‘being-in-the-Anthropocene’. This asymmetry disrupts the post-humanist position and calls for a conceptualisation of the human ethos beyond the post-humanist position. This conceptualisation of the human ethos also has consequences for our understanding of geoethics as geo-ethos. (shrink)

In this volume Axel Honneth deepens and develops his highly influential theory of recognition, showing how it enables us both to rethink the concept of justice and to offer a compelling account of the relationship between social reproduction and individual identity formation. Drawing on his reassessment of Hegel’s practical philosophy, Honneth argues that our conception of social justice should be redirected from a preoccupation with the principles of distributing goods to a focus on the measures for creating symmetrical relations (...) of recognition. This theoretical reorientation has far-reaching implications for the theory of justice, as it obliges this theory to engage directly with problems concerning the organization of work and with the ideologies that stabilize relations of domination. In the final part of this volume Honneth shows how the theory of recognition provides a fruitful and illuminating way of exploring the relation between social reproduction and identity formation. Rather than seeing groups as regressive social forms that threaten the autonomy of the individual, Honneth argues that the ‘I’ is dependent on forms of social recognition embodied in groups, since neither self-respect nor self-esteem can be maintained without the supportive experience of practising shared values in the group. This important new book by one of the leading social philosophers of our time will be of great interest to students and scholars in philosophy, sociology, politics and the humanities and social sciences generally. (shrink)

A necessarily true sentence is 'brute' if it does not rigidly refer to anything and if it cannot be reduced to a logical truth. The question of whether there are brute necessities is an extremely natural one. Cian Dorr has recently argued for far-reaching metaphysical claims on the basis of the principle that there are no brute necessities: he initially argued that there are no non-symmetric relations, and later that there are no abstract objects at all. I argue (...) that there are nominalistically acceptable brute necessities, and that Dorr's arguments thus fail. My argument is an application of Gödel's first incompleteness theorem. (shrink)

We put forward a new, ‘coherentist’ account of quantum entanglement, according to which entangled systems are characterized by symmetric relations of ontological dependence among the component particles. We compare this coherentist viewpoint with the two most popular alternatives currently on offer—structuralism and holism—and argue that it is essentially different from, and preferable to, both. In the course of this article, we point out how coherentism might be extended beyond the case of entanglement and further articulated.

This paper defends the view that Newtonian forces are real, symmetrical and non-causal relations. First, I argue that Newtonian forces are real; second, that they are relations; third, that they are symmetrical relations; fourth, that they are not species of causation. The overall picture is anti-Humean to the extent that it defends the existence of forces as external relations irreducible to spatio-temporal ones, but is still compatible with Humean approaches to causation (and others) since it denies (...) that forces are a species of causation. (shrink)

I outline a heretofore neglected difference between manipulation scenarios and merely deterministic ones. Plausible scientific determinism does not imply that the relevant prior history of the universe is independent of us, while manipulation does. Owing to sensitive dependence of physical outcomes upon initial conditions, in order to trace a deterministic history, a microphysical level of analysis is required. But on this level physical laws are time-symmetrically deterministic, and causality, conceived asymmetrically, disappears. I then consider a revised scenario to resurrect the (...) threat of manipulation even in the presence of time-symmetry and sensitive dependence upon initial conditions. To do so we posit a manipulator containing all the information of the manipulated and time-symmetrically related to him. The new scenario violates special relativity, but even waiving that objection, the scenario faces a dilemma. I argue that the manipulator either lacks agency enough to manipulate the target, or can integrate thoughts separated by long time spans into a single decision. In the latter case, the 'manipulated agent' disappears into the manipulator, making it the story of just one agent. (shrink)

Rom Harré thinks that the Emergence–Reduction debate, conceived as a vertical problem, is partly ill posed. Even if he doesn’t wholly reject the traditional definition of an emergent property as a property of a collection but not of its components, his point is that this definition doesn’t exhaust all the dimensions of emergence. According to Harré there is another kind (or dimension) of emergence, which we may call—somewhat paradoxically—“horizontal emergence”: two properties of a substance are horizontally emergent relative to each (...) other if they cannot be displayed in the same conditions. Contrary to vertical emergence, horizontal emergence is a symmetrical relation. Harré endorses horizontal emergentism. I argue that this position faces a principled difficulty: it makes it impossible to bind different horizontally emergent discourses in an interesting way. Physics and biology for example become “island” discourses, each speaking of a distinct kind of entities. The only way to ensure that two different discourses can relate to the same entity is to reintroduce verticality into the picture. (shrink)

According to the truth-functional analysis of conditions, to be ‘necessary for’ and ‘sufficient for’ are converse relations. From this, it follows that to be ‘necessary and sufficient for’ is a symmetric relation, that is, that if P is a necessary and sufficient condition for Q, then Q is a necessary and sufficient condition for P. This view is contrary to common sense. In this paper, I point out that it is also contrary to a widely accepted ontological view (...) of conditions, according to which if P is a necessary and sufficient condition for Q, then Q is in no sense a condition for P; it is a mere consequence of P. (shrink)

This paper defends the view that Newtonian forces are real symmetrical and non-causal relations. In the first part, I argue that Newtonian forces are real; in the second part, that they are relations; in the third part, that they are symmetrical relations; in the fourth part, that they are not causal relations, (but causal relata) by which I mean that they are not species of causation. The overall picture is anti-humean to the extent that it defends (...) the existence of forces, irreducible to spatio-temporal relations, but is still compatible with humean approaches to causation (and others) since it denies that forces are species of causation. (shrink)

The mathematical structure of realist quantum theories has given rise to a debate about how our ordinary 3-dimensional space is related to the 3N-dimensional configuration space on which the wave function is defined. Which of the two spaces is our (more) fundamental physical space? I review the debate between 3N-Fundamentalists and 3D-Fundamentalists and evaluate it based on three criteria. I argue that when we consider which view leads to a deeper understanding of the physical world, especially given the deeper topological (...) explanation from the unordered configurations to the Symmetrization Postulate, we have strong reasons in favor of 3D-Fundamentalism. I conclude that our evidence favors the view that our fundamental physical space in a quantum world is 3-dimensional rather than 3N-dimensional. I outline lines of future research where the evidential balance can be restored or reversed. Finally, I draw lessons from this case study to the debate about theoretical equivalence. (shrink)

In the pure powers ontology (PPO), basic physical properties have wholly dispositional essences. PPO has clear advantages over categoricalist ontologies, which suffer from familiar epistemological and metaphysical problems. However, opponents argue that because it contains no qualitative properties, PPO lacks the resources to individuate powers, and generates a regress. The challenge for those who take such arguments seriously is to introduce qualitative properties without reintroducing the problems that PPO was meant to solve. In this paper, I distinguish the core claim (...) of PPO: (i) basic physical properties have dispositional essences, from a hitherto unnoticed assumption: (ii) the dispositional essences of basic physical properties exclusively involve type-causal relations to other basic physical properties. I reject (ii), making room for a structuralist ontology in which all basic physical properties are pure powers, individuated by their places in a causal structure that includes not only other powers, but also physically realized qualitative properties such as shapes, patterns and structures. Such qualities individuate pure powers in the way that non-mental input and output properties individuate realized mental properties in functionalist theories of mind, except that here it is basic physical powers that are individuated by relations to realized non-powers. I distinguish one Platonic and two Aristotelian version of this theory, and argue that the Aristotelian versions require that grounding is not always a relative fundamentality relation, because the powers ground the qualities that individuate them. By considering ontic structural realism, I argue that symmetric grounding is the best way to make sense of relational individuation in structuralist ontologies, and is therefore no additional commitment of the one proposed here. (shrink)

In Chronopathologies, the Australian philosopher Jack Reynolds gives an exciting analysis of the intimate connection between time and politics in three trajectories of contemporary philosophy: analytic philosophy, poststructuralism and phenomenology. These trajectories are incompatible in the sense that internalizing the norms of any one of them 'makes taking the other(s) seriously very difficult' (p. 225). Given this incompatibility, Reynolds convincingly argues that the only way forward is to draw out the differences between these trajectories, in order to address the problems (...) and limitations of each from the perspective of the others. Reynolds's fruitful approach uncovers that each trajectory is threatened by a disease of time or 'chronopathology' (a key term that is never fully defined). Such a chronopathology can be characterized as a pathological condition that is the result of two factors: the reduction of the plurality of time to only one of its dimensions; a biased and one-sided view on ethics and politics. Reynolds convincingly identifies the root of the threat. He develops his diagnosis in three steps. 1. Analytic philosophy over-emphasizes the synchronic dimension of time, without making any room for its diachronic dimension. 2. Poststructuralism acknowledges the necessity of a reciprocal relation between the synchronic and the diachronic dimension of time, but ultimately privileges the latter (i.e., the relation remains asymmetrical). 3. An embodied phenomenology opens up a way to bring the synchronic and diachronic dimension of time in a reciprocal and symmetrical relation that does not privilege the one over the other. (shrink)

Kit Fine (2000) breaks with tradition, arguing that, pace Russell (e.g., 1903: 228), relations have neither directions nor converses. He considers two ways to conceive of these new "neutral" relations, positionalism and anti-positionalism, and argues that the latter should be preferred to the former. Cody Gilmore (2013) argues for a generalization of positionalism, slot theory, the view that a property or relation is n-adic if and only if there are exactly n slots in it, and (very roughly) that (...) each slot may be occupied by at most one entity. Slot theory (and with it, positionalism) bears the full brunt of Fine's (2000) symmetric completions and conflicting adicities problems. I fully develop an alternative, plural slot theory (or pocket theory), which avoids these problems, key elements of which are first considered by Yi (1999: 168 ff.). Like the slot theorist, the pocket theorist posits entities (pockets) in properties and relations that can be occupied. But unlike the slot theorist, the pocket theorist denies that at most one entity can occupy any one of them. As a result, she must also deny that the adicity of a property or relation is equal to the number of occupiable entities in it. By abandoning these theses, however, the pocket theorist is able to avoid Fine's problems, resulting in a stronger theory about the internal structure of properties and relations. Pocket theory also avoids a serious drawback of anti-positionalism. (shrink)

The paper attempts to outline the actual academic debates around the concept of PR ethics. The first part aims to show the intimate link between professionalism and ethics as well as their bearing on the reputation of the PR field. Whether and how ethical public relations are possible is the main issue analyzed in the second part of the article. The two paradigms of public relations, “the attorney-adversary system” and “the two-way symmetrical model”, are put face to face (...) in order to better understand the arguments of their proponents as to the way of approaching to the ethical matters. A main concern of the third part is to answer the question if something is wrong with situational ethics. The problem is approached in the light of virtue ethics, which is itself situational in Aristotel’s sense of the term. In the final part, the paper suggests the possibility to use W. D. Ross’s pluralist deontology as a conceptual structure from which to build a practical model for the analysis of moral dilemmas in the PR practice. (shrink)

Tallant (2007) has challenged my recent defence of no-futurism (Button 2006), but he does not discuss the key to that defence: that no-futurism's primitive relation 'x is real-as-of y' is not symmetric. I therefore answer Tallant's challenge in the same way as I originally defended no-futurism. I also clarify no-futurism by rejecting a common mis-characterisation of the growing-block theorist. By supplying a semantics for no-futurists, I demonstrate that no-futurism faces no sceptical challenges. I conclude by considering the problem of (...) how to interpret the relation 'x is real-as-of y'. -/- (NB: A correction to this article appears in Analysis 68.1.). (shrink)

It is commonly assumed that grounding relations are asymmetric. Here I develop and argue for a theory of metaphysical structure that takes grounding to be nonsymmetric rather than asymmetric. Even without infinite descending chains of dependence, it might be that every entity is grounded in some other entity. Having first addressed an immediate objection to the position under discussion, I introduce two examples of symmetric grounding. I give three arguments for the view that grounding is nonsymmetric (I call (...) this view ‘metaphysical interdependence’). These arguments are: (i) that metaphysical interdependence is the only theory able to reconcile competing intuitions about grounding; (ii) that it is the only theory consistent with both ‘gunk’ and ‘junk’; and (iii) that offers a satisfactory solution to the problem concerning whether or not grounding is itself grounded. (shrink)

A logic of intervals is proposed akin to the one published by Hamblin (Hamblin (1969) and (1971)). Like Hamblin's, the present system is also based on a single primitive. However, the work presented here differs from Hamblin's in a number of respects. Most importantly, the present system is explicitly based on mereological ideas in such a way that not only are the two notions of abutment and temporal order involved in Hamblin's primitive two-place relation "abuts at the earlier end" distinguished (...) ; the temporal ordering itself is built up from a symmetric mereological primitive. The present system is shown to be complete. (shrink)

Our ordinary causal concept seems to fit poorly with how our best physics describes the world. We think of causation as a time-asymmetric dependence relation between relatively local events. Yet fundamental physics describes the world in terms of dynamical laws that are, possible small exceptions aside, time symmetric and that relate global time slices. My goal in this paper is to show why we are successful at using local, time-asymmetric models in causal explanations despite this apparent mismatch with fundamental (...) physics. In particular, I will argue that there is an important connection between time asymmetry and locality, namely: understanding the locality of our causal models is the key to understanding why the physical time asymmetries in our universe give rise to time asymmetry in causal explanation. My theory thus provides a unified account of why causation is local and time asymmetric and thereby enables a reply to Russell’s famous attack on causation. (shrink)

A widespread assumption in debates about trust and trustworthiness is that the evaluative norms of principal interest on the trustor’s side of a cooperative exchange regulate trusting attitudes and performances whereas those on the trustee’s side regulate dispositions to respond to trust. The aim here will be to highlight some unnoticed problems with this asymmetrical picture – and in particular, how it elides certain key evaluative norms on both the trustor’s and trustee’s side the satisfaction of which are critical to (...) successful cooperative exchanges – and to show that a symmetrical, ‘achievement-first’ approach to theorising about trust and trustworthiness (and their relation to each other) has important advantages by comparison. The view I develop is guided by a structural analogy with practical reasoning. Just as practical reasoning is working as it should only when there is realisation (knowledge and action) of states (belief and intention) with reverse directions of fits (mind-to-world and world-to-mind), likewise, cooperation between trustor and trustee is functioning as it should only when there is an analogous kind of realisation on both sides of the cooperative exchange – viz., when the trustor ‘matches’ her achievement in trusting (an achievement in fitting reliance to reciprocity) with the trustee’s achievement in responding to trust (an achievement in fitting reciprocity to reliance). An upshot of viewing cooperation between trustor and trustee as exhibiting achievement-theoretic structure is that we will be better positioned to subsume trustworthiness (and its cognates on the trustee’s side), like trust, under a wider suite of evaluative norms that regulate attempts, dispositions, and achievements symmetrically on both sides of a cooperative exchange, with ‘matching achievements’ as the gold standard. (shrink)

In this paper, we use antecedent-final conditionals to formulate two problems for parsing-based theories of presupposition projection and triviality of the kind given in Schlenker 2009. We show that, when it comes to antecedent-final conditionals, parsing-based theories predict filtering of presuppositions where there is in fact projection, and triviality judgments for sentences which are in fact felicitous. More concretely, these theories predict that presuppositions triggered in the antecedent of antecedent-final conditionals will be filtered (i.e. will not project) if the negation (...) of the consequent entails the presupposition. But this is wrong: John isn’t in Paris, if he regrets being in France intuitively presupposes that John is in France, contrary to this prediction. Likewise, parsing-based approaches to triviality predict that material entailed by the negation of the consequent will be redundant in the antecedent of the conditional; but John isn’t in Paris, if he’s in France and Mary is with him is intuitively felicitous, contrary to these predictions. Importantly, given that the trigger appears in sentence-final position, both incremental (left-to-right) and symmetric versions of such theories make the same predictions. These data constitute a challenge to the idea that presupposition projection and triviality should be computed on the basis of parsing. This issue is important because it relates to the more general question as to whether presupposition and triviality calculation should be thought of as a pragmatic post-compositional phenomenon or as part of compositional semantics (as in the more traditional dynamic approaches). We discuss a solution which allows us to maintain the parsing-based pragmatic approach; it is based on an analysis of conditionals which incorporates a presupposition that their antecedent is compatible with the context, together with a modification to Schlenker’s (2009) algorithm for calculating local contexts so that it takes into account presupposed material. As we will discuss, this solution works within a framework broadly similar to that of Schlenker’s (2009), but it doesn’t extend in an obvious way to other parsing-based accounts (e.g. parsing-based trivalent approaches). We conclude that a parsing-based theory can be maintained, but only if we adopt a substantial change of perspective on the framework. (shrink)

The paper contains a novel realist account of causal production and the necessary connection between cause and effect. I argue that the asymmetric relation between causally connected events must be regarded as a product of a symmetric interaction between two or more entities. All the entities involved contribute to the producing, and so count as parts of the cause, and they all suffer a change, and so count as parts of the effect. Cause and effect, on this account, are (...) two different states of the very same compound substance, or system, one coming to exist out of the other. (shrink)

It is tempting to think that a process of choosing a point at random from the surface of a sphere can be probabilistically symmetric, in the sense that any two regions of the sphere which differ by a rotation are equally likely to include the chosen point. Isaacs, Hájek, and Hawthorne (2022) argue from such symmetry principles and the mathematical paradoxes of measure to the existence of imprecise chances and the rationality of imprecise credences. Williamson (2007) has argued from (...) a related symmetry principle to the failure of probabilistic regularity. We contend that these arguments fail, because they rely on auxiliary assumptions about probability which are inconsistent with symmetry to begin with. We argue, moreover, that symmetry should be rejected in light of this inconsistency, and because it has implausible decision- theoretic implications. -/- The weaker principle of probabilistic invariance says that the probabilistic comparison of any two regions is unchanged by rotations of the sphere. This principle supports a more compelling argument for imprecise probability. We show, however, that invariance is incompatible with mundane judgments about what is probable. Ultimately, we find reason to be suspicious of the application of principles like symmetry and invariance to nonmeasurable regions. (shrink)

The paper is an exercise in descriptive ontology, with specific applications to problems in the geographical sphere. It presents a general typology of spatial boundaries, based in particular on an opposition between bona fide or physical boundaries on the one hand, and fiat or human-demarcation-induced boundaries on the other. Cross-cutting this opposition are further oppositions in the realm of boundaries, for example between: crisp and indeterminate, complete and incomplete, enduring and transient, symmetrical and asymmetrical. The resulting typology generates a corresponding (...) categorization of the different sorts of objects which (complete) boundaries determine or demarcate. The theory is applied first of all in the areas of geography and of administrative and property law. Indications are then given as to how the typology may be applied also in other fields where physical and fiat boundaries are at work, including the field of cognitive linguistics and the related field of the ontology of truth. (shrink)

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

In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF of (...) the same formula. We argue that the first makes use of a too strong metatheory. Although meaningful, this symmetrical reduction does not equate the ontological content of the theories. The strong metatheory levels the two theories. Moreover, we will modernize Shoenfields proof, emphasizing its relation to Herbrands theorem and that it can only be seen as a partial type of reduction. In contrast with symmetrical reductions, we believe that asymmetrical relations are powerful tools for comparing ontological content. In virtue of this, we prove that there is no interpretation of NBG in ZF, while NBG trivially interprets ZF. This challenges the standard view that the two systems have the same ontological content. (shrink)

This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for nonrigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction instead (...) simultaneously defines a collection of distinct abstraction operations, each of which maps a system to its corresponding pure structure. The theory is precisely formulated in an essentialist language. This allows us to throw new light on the question to what extent structuralists are committed to symmetric dependence. Finally, we apply the theory of collective abstraction to solve a problem about converse relations. (shrink)

In this paper I present and evaluate van Inwagen’s famous Consequence Argument, as presented in An Essay on Free Will. The grounds for the incompatibility of freewill and determinism, as argued by van Inwagen, is dependent on our actions being logical consequences of events outside of our control. Particularly, his arguments depend upon, in one guise or another, the transference of the modal property of not being possibly rendered false through the logical consequence relation, i.e. the β-principle. I argue that, (...) due to the symmetric nature of determinism, van Inwagen is exposed to what I call “reversibility arguments” in the literature. Such arguments reverse the β-principle and start from our apparent control over our own actions to our control over the initial conditions. Since van Inwagen does not endorse a particular theory of laws or logical consequence, he is open to such counterarguments. The plausibility of such reversibility arguments depends on what would be called a Wittgensteinian conception of logical consequence. In the _Remarks on the Foundation of Mathematics_, one of Wittgenstein’s main concerns is the normativity of logical inference i.e. proof. Such concerns with normativity and rule-following are generally a feature of his later philosophy. In the _Remarks_ Wittgenstein resists a conception of logical deduction which places the source of normativity outside of human practice. (shrink)

In the paper I propose a definition of higher religions as having their own Holy Scripture. The rating of the higher religions was built on the number of followers, the time of existence and predominance in certain territories. In total, 25 higher religions are identified. Four world religions were chosen as the coordinate basis for building a graphic connection between all 25 higher religions: by rating and by mutual proximity. It turned out that they can be placed in only one (...) specific way. Moreover, all these religions are lined up in the correct absolutely symmetrical matrix—the harmony of the higher religions. This is clear evidence that all higher religions constitute a holistic, mutually reinforcing unity. (shrink)

The principle of Identity of Indiscernibles has been challenged with various thought experiments involving symmetric universes. In this paper, I describe a fractal universe and argue that, while it is not a symmetric universe in the classical sense, under the assumption of a relational theory of space it nonetheless contains a set of objects indiscernible by pure properties alone. I then argue that the argument against the principle from this new thought experiment resists better than those from classical (...) symmetric universes three main objections put forth against this kind of arguments. (shrink)

I argue against the Doctrine of Double Effect’s explanation of the moral difference between terror bombing and strategic bombing. I show that the standard thought-experiment of Terror Bomber and Strategic Bomber which dominates this debate is underdetermined in three crucial respects: (1) the non-psychological worlds of Terror Bomber and Strategic Bomber; (2) the psychologies of Terror Bomber and Strategic Bomber; and (3) the structure of the thought-experiment, especially in relation to its similarity with the Trolley Problem. (1) If the two (...) worlds are not identical, then it may be these differences between the two worlds and not the Doctrine of Double Effect to explain the moral difference; (2a) if Terror Bomber and Strategic Bomber have the same causal beliefs, then why does Terror Bomber set out to kill the children? It may then be this unwarranted and immoral choice and not the Doctrine of Double Effect that explains the moral difference; (2b) if the two have different causal beliefs, then we can’t rule out the counterfactual that, had Strategic Bomber had the same beliefs as Terror Bomber, she would have also acted as Terror Bomber did. Finally, (3) the Strategic Bomber scenario could also be constructed so as to be structurally equivalent to the Fat Man scenario in the Trolley Problem: but then the Doctrine of Double Effect would give different answers to two symmetrical cases. (shrink)

The idea that a being can be identical to its own essence has a long and venerable history in theological speculation. As with many ideas in theology, however, such an idea has never been given an adequate mathematical formulation. The key to such a formulation, I argue, is introducing an essence axiom into non-well-founded set theory. According to such an axiom, for every set, x, there is a set that contains all and only those sets that contain x. With such (...) an axiom, it becomes possible to introduce an essence function that takes each set to its essence. An object that is identical to its essence, then, is simply a fixed point of the essence function. In this paper, I first discuss a theorem according to which any fixed point of the essence function is universally symmetrical with respect to the set membership relation. After proving the theorem, I discuss its theological implications. I go on to argue that the process of counting the members of a set that is identical to its essence is a Sisyphusian process. Such a fact I suggest shows that the absurdity of human existence is not alleviated by the existence of God but rather is entailed by it. (shrink)

The discovery of so-called ‘mirror neurons’ - found to respond both to own actions and the observation of similar actions performed by others - has been enormously influential in the cognitive sciences and beyond. Given the self-other symmetry these neurons have been hypothesized as underlying a ‘mirror mechanism’ that lets us share representations and thereby ground core social cognitive functions from intention understanding to linguistic abilities and empathy. I argue that mirror neurons are important for very different reasons. Rather than (...) a symmetric ubiquitous or context- independent mechanism, I propose that these neurons are part of broader sensorimotor circuits, which help us navigate and predict the social affordance space that we meet others in. To develop both the critical and positive project I analyze the interpretive choices and the debate surrounding the mirror neuron research and show how the field is marred by highly questionable assumptions about respectively motor and social cognition. The discovery of mirror neurons - and the sensorimotor circuits of which these neurons are a part – actually empirically challenge many of these tacit assumptions. Findings of sensorimotor goal representations at levels of abstraction well beyond actual sensory information and kinetic movements challenge the idea of motor cognition as primarily output production. Additionally, the focus on 3rd person mindreading of hidden mental states is misguiding the field of social cognition. Much ‘mind-reading’ seems rooted in sensorimotor representations and a developmentally primary 2nd person understanding of actions and the mental lives of others, which precisely breaks the assumed dichotomy between mind and behavior. I propose a Social Affordance model where parallel fronto-parietal sensorimotor circuits support representations not just of other people’s actions but of the overall social affordance space. It is a process that monitors concrete goals and teleological possibilities that the environment affords respectively oneself and other present agents. With this model I hypothesize that the complex spectrum of sensorimotor integrations are indeed essential not only to normal action choice calibration but also to social cognitive abilities, as the sensorimotor teleological representations let us relate to others and understand their action choices in a shared pragmatic and intentional context. (shrink)

In a recent book and an article, Carl Craver construes the relations between different levels of a mechanism, which he also refers to as constitutive relations, in terms of mutual manipulability (MM). Interpreted metaphysically, MM implies that inter-level relations are symmetrical. MM thus violates one of the main desiderata of scientific explanation, namely explanatory asymmetry. Parts of Craver’s writings suggest a metaphysical interpretation of MM, and Craver explicitly commits to constitutive relationships being symmetrical. The paper furthermore explores (...) the option of interpreting MM epistemologically, as a means for individuating mechanisms. It is argued that MM then is redundant. MM should therefore better be abandoned. (shrink)

Axel Honneth reconstructs Hegel’s social and political philosophy on the basis of the concept of recognition. For Honneth, recognition is a constitutive relation between individuals that is in principle symmetrical. By conceiving recognition through symmetry, Honneth effectively bans the inclusion of power within recognitive relation. He thus regards the relations of power as cases of non-recognition or misrecognition. In this paper, I develop an alternative theory of the constitutive relation between individuals for Hegel, one that is based on the (...) asymmetrical relation of power. To this aim, I focus on the chapter of “determinations of reflection” in the Science of Logic. Through a close analysis of Hegel’s Logic, I argue that the most fundamental form of relation between individuals is the relation of opposition, that individuals are solely constituted in and through the relation of opposition, and that the relation of opposition is essentially asymmetrical. Together, these claims establish... (shrink)

The topics approached in the 52 papers included in this book are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single valued (...) trapezoidal neutrosophic number; inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; Maclaurin symmetric mean; pseudo-BCI algebra; hesitant fuzzy set; photovoltaic plan; decision-making trial and evaluation laboratory (DEMATEL); Choquet integral; fuzzy measure; clustering algorithm; and many more. (shrink)

The present paper explores diffident and dissident practices reflected by the political talk at the end of the 19th-century in Romania. Relying on Jacques Rancière’s theories on the ‘aesthetic regime of politics,’ the introduction sketches a historical frame and proposes a focus change: the relation between ‘politics’ and ‘aesthetics’ does not stand on a set of literary cases, but on political scripts as such. Thus, the hypotheses investigated by the next three parts can be formulated as follows: 1. though determined (...) by an ideological direction (Conservative or Liberal), the political speech still preserves his tendency towards aesthetic autonomy. 2. oratorical merits (hinting at aesthetic autonomy) can turn into practices of political autonomy, diffidence and, then, dissidence. Methodologically, two types of aesthetic practices organize the chosen materials; both the diffident script and the theatre of dissidence help us to perceive how the philosophical and moral meaning of these practices could change into an ideology of dissidence. The formalization of diffident practices, their conversion to outspoken dissidence, also corresponds to the symmetrical symptom of unlimited authority; when old-time politicians warned on ‘Caesarism,’ ‘Vizierate,’ ‘Despotism,’ ‘Omnipotence’ or ‘Tyranny,’ the Romanian society had already been training for a long experience of ‘dictatorship.’. (shrink)

This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally defined maps h and (...) s that define a Galois connection on the power set PW of W. These maps can be used to define two distinct boundary operators bd and BD on W. The main theorem of the paper states that higher-order vagueness with respect to bd collapses to second-order vagueness. This does not hold for BD, the iterations of which behave in quite an erratic way. In contrast, the operator bd defines a variety of tolerance principles that do not fall prey to the sorites paradox and, moreover, do not always satisfy the principles of positive and negative introspection. (shrink)

Consciousness may not only be a problem how to know the brain but also a problem how to understand what known. Understanding is always an ontological system created as the explanation of what known by us. And, if all brains, including human brains, may be defined as the mind, consciousness must be part of our understanding of the mind. The author argues that no mind may exist if not be a life or lives, no life may exist if not be (...) a mind or a part of it, and, if it is the mind that needs to be explained, it must finally and fundamentally be explained as a life or a living system. An ontological definition of life is proposed first in this article, which is also applicable to fields such as physics, biology, psychology, and sociology. Based on an analysis of two kinds of lives and their relationship with matter and energy, a living system is modeled as the organization of two system relations, which explains not only consciousness but also wakefulness, emotion, intelligence, language and mind-body relationship. And finally, a semantic theory is reached, which takes lives as the only meaning of all symmetrical and conservative changes, such as the location changes or form changes of consciousness, or the state changes of memories. The concept of life, the model of living systems and the semantic theory together provide a framework for us to understand what and how consciousness is, why there is consciousness, where and when consciousness occurs. (shrink)