Can I be an Instantaneous Stage and yet Persist Through Time?

An alternative to the standard endurance/perdurance accounts of persistence has recently been developed: the stage theory (Sider, T. Four-Dimensionalism: an Ontology of Persistence and Time. Oxford: Oxford University Press, 2001; Hawley, K. How Things Persist. Oxford: Oxford University Press, 2001). According to this theory, a persisting object is identical with an instantaneous stage (temporal part). On the basis of Leibniz’s Law, I argue that stage theorists either have to deny the alleged identity (i.e., give up their central thesis) or hold that stages are both instantaneous and continuants. I subsequently show that, although stage theory is flexible enough to accommodate the latter claim, the cost for accommodating it is an excessive proliferation of persistence concepts.     

Non-Symmetrical Relations,O-Roles,and Modes

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.     

Adolescent girls’ construction of moral discourses and appropriation of primary identity in a mathematics classroom

This qualitative study examines the way three American young adolescent girls who come from different class and racial backgrounds construct their social and academic identities in the context of their traditional mathematics classroom. The overall analysis shows an interesting dynamic among each participant’s class and racial background, their social/academic identity and its collective foundation, the types of ideologies they repudiate and subscribe to, the implicit and explicit strategies they adopt in order to support the legitimacy of their own position, and the ways they manifest their position and identity in their use of language referring to their mathematics classroom. Detailed analysis of their use of particular terms, such as “I,” “we,” “they,” and “should/shouldn’t” elucidates that each participant has a unique view of her mathematics classroom, developing a different type of collective identity associated with a particular group of students. Most importantly, this study reveals that the girls actively construct a social and ideological web that helps them articulate their ethical and moral standpoint to support their positions. Throughout the complicated appropriation process of their own identity and ideological standpoint, the three girls made different choices of actions in mathematics learning, which in turn led them to a different math track the following year largely constraining their possibility of access to higher level mathematical knowledge in the subsequent schooling process.     

Persistence of Simple Substances

In this paper, we argue for a novel three-dimensionalist (3D'ist) solution to the problem of persistence, i.e. cross-temporal identity. We restrict the discussion of persistence to simple substances, which do not have other substances as their parts. The account of simple substances employed in the paper is a trope-nominalist strong nuclear theory (SNT), which develops Peter Simons' trope nominalism. Regarding the distinction between three dimensionalism (3D) and four dimensionalism (4D), we follow Michael Della Rocca's formulation, in which 3D explains persistence in virtue of same entities and 4D in virtue of distinct entities (temporal parts). SNT is a 3D'ist position because it accounts for the persistence of simple substances in virtue of diachronically identical ‘nuclear’ tropes. The nuclear tropes of a simple substance are necessary for it and mutually rigidly dependent but distinct. SNT explains qualitative change by tropes that are contingent to a simple substance. We show that it avoids the standard problems of 3D: temporal relativization of ontic predication, Bradley's regress and coincidence, fission and fusion cases. The temporal relativization is avoided because of the analysis of temporary parts that SNT gives in terms of temporal sub-location, which is atemporal part–whole relation.     

A Logical Analysis of the Anselm’s Unum Argumentum (from <Emphasis Type="BoldItalic">Proslogion</Emphasis>)

Anselm of Cantorbery wrote Proslogion (1077–1078), where is formulated the famous ‘Unum argumentum’ about the existence of God. This argument was been disputed and criticized by numerous logicians from an extensional view point. The classical predicate logic is not able to give a formal frame to develop an adequate analysis of this argument. According to us, this argument is not an ontological proof; it analyses the meaning of the “quo nihil maius cogitari posit”, a characterization of God, and establish, by absurd, that “quod non posit cogitare non esse” by using the hypothesis: “to think in re” is taller than “to think in solo intelectu”. We discuss this relation and the difference between the meanings of the elementary predicates ‘to be in re’, ‘to be in intellectu’ and ‘to be in solo intellectu’. We propose a new logical approach of this ‘Unum argumentum’ of Anselm by using Curry’s Combinatory Logic (1958, 1973). Indeed, Combinatory Logic is an abstract applicative formalism of operators applied to operands; in this formalism, the predicates, viewed as specific operators, can be composed and can be transformed, by an intrinsic way, into more complex predicates, by means of abstract operators, called “combinators”, studied by Combinatory Logic. We show that this formalism is a logical frame where it becomes possible to discuss and to formulate cognitive representations of the meanings of predicates used inside of the ‘Unum argumentum’ and to explain how the argument runs.     

A historic overview of the interplay of theology and philosophy in the arts, mathematics and sciences

The etymology of the word “mathematics” can be traced to Greek roots with meanings such “a thing learned” (mathein is the verb “to have learned”) and, from that, ta mathe^matika, “learnable things” and, “to think or have one’s mind aroused. The natural philosophers of the Renaissance did not draw an explicit distinction between mathematics, the sciences and to an extent the arts. In this paper I explore connections forged by the thinkers of the Renaissance between mathematics, the arts and the sciences, with attention to the nature of the underlying theological and philosophical questions that call for a particular mode of inquiry. Recently Robert Root-Bernstein (2003) introduced the construct of polymathy to suggest that innovative individuals are equally likely to contribute both to the arts and the sciences and either consciously or unconsciously forge links between the two. Several contemporary examples are presented of individuals who pursued multiple fields of research and were able to combine the aesthetic with the scientific. Finally, some possibilities for re-introducing university courses on natural philosophy as a means to integrate mathematics, the arts and the sciences are discussed.     

Lewis meets Brouwer: Constructive strict implication

C.I. Lewis invented modern modal logic as a theory of “strict implication” $?$. Over the classical propositional calculus one can as well work with the unary box connective. Intuitionistically, however, the strict implication has greater expressive power than $\square$ and allows to make distinctions invisible in the ordinary syntax. In particular, the logic determined by the most popular semantics of intuitionistic $\mathsf{K}$ becomes a proper extension of the minimal normal logic of the binary connective. Even an extension of this minimal logic with the “strength” axiom, classically near-trivial, preserves the distinction between the binary and the unary setting. In fact, this distinction has been discovered by the functional programming community in their study of “arrows” as contrasted with “idioms”. Our particular focus is on arithmetical interpretations of intuitionistic $?$ in terms of preservativity in extensions of $\mathsf{HA}$, i.e., Heyting’s Arithmetic.     

Energy-Preserving Integrators and the Structure of B-series

B-series are a powerful tool in the analysis of Runge–Kutta numerical integrators and some of their generalizations (“B-series methods”). A general goal is to understand what structure-preservation can be achieved with B-series and to design practical numerical methods that preserve such structures. B-series of Hamiltonian vector fields have a rich algebraic structure that arises naturally in the study of symplectic or energy-preserving B-series methods and is developed in detail here. We study the linear subspaces of energy-preserving and Hamiltonian modified vector fields which admit a B-series, their finite-dimensional truncations, and their annihilators. We characterize the manifolds of B-series that are conjugate to Hamiltonian and conjugate to energy-preserving and describe the relationships of all these spaces.     

Frege on Identity as a Relation of Names

This essay offers a detailed philosophical criticism of Frege’s popular thesis that identity is a relation of names. I consider Frege’s position as articulated both in ‘On Sense and Reference’, and in the Grundgesetze, where he appears to take an objectual view of identity, arguing that in both cases Frege is clearly committed to the proposition that identity is a relation holding between names, on the grounds that two different things can never be identical. A counterexample to Frege’s thesis is considered, and a positive thesis is developed according to which, in contradistinction to the Fregean position, identity is a reflexive, symmetric, and transitive relation holding only between a thing and itself which can be expressed as a relation between names.     

Probabilities and temporal parts

Adopting temporal parts theory is the most popular way of addressing a host of puzzles about diachronic identity. For example, it is not obvious how I am the same person as the baby who shared my name. With the theory, sameness of person, e.g., consists in being comprised by the same temporally extended, four-dimensional object. However, temporal parts theory has unacceptable consequences for notions of freedom and probability. I show that the only acceptable reading of four-dimensionalism entails that the four dimensional object that is me, say, already exists in its entirety. This entails that all of my future properties are already set. This nearly Spinozistic result robs us of familiar notions of choice and possibility. I argue that these notions are more central to our thinking than temporal parts theory, and that on these grounds we must look elsewhere for solutions to our questions about identity across time.     

“Value” of additional information in multicriterion analysis under uncertainty

The expected value of information in classical (monocriterion) decision analysis has been well covered in the literature. One cannot say the same thing about the multicriterion analysis, particularly when one is in the presence of multicriterion aggregation procedures based on outranking relations for a ranking problematic. The objective of this paper is to try to extend the Bayesian approach to a multicriterion analysis in the context of uncertainty. After illustrating the a posteriori analysis, we shall mention some difficulties associated with the pre a posteriori analysis and the concepts of the “expected value” of perfect or imperfect information.     

On the Coherence of Wittgensteinian Constructivism

Michael Dummett presents a modus tollens argument against a Wittgensteinian conception of meaning. In a series of papers, Dummett claims that Wittgensteinian considerations entail strict finitism. However, by a “sorites argument”, Dummett argues that strict finitism is incoherent and therefore questions these Wittgensteinian considerations.In this paper, I will argue that Dummett’s sorites argument fails to undermine strict finitism. I will claim that the argument is based on two questionable assumptions regarding some strict finitist sets of natural numbers. It will be shown that strict finitism entails none of these assumptions. Hence, the argument does not prove that the view is internally incoherent, and consequently, Dummett fails to undermine the Wittgensteinian conception of meaning.     

Ontology of Time and Hyperdynamism

The three alternative ontological theories of time are introduced as well as the three basic temporal phenomena. The different ontological analyses by the different theories are compared and examined. A relational theory of time is advocated as a result of the examination, and an influential misrepresentation and emendation of it by McTaggart is criticized and diagnosed as hyperdynamism. Finally, the problem of the direction of time is addressed. The physicist’s solutions are rejected, and an ontological solution is offered.     

What Makes a Thing What It Is? Aristotle and Hegel on Identity

The notion of identity is investigated through Aristotle and Hegel as supporters of two different ontological conceptions: pluralism of substances and relational holism. Through Aristotle, I examine both the thesis according to which the identity of an object is constituted by its properties and the difficulties which this thesis encounters (e.g., those raised by Max Black). Aristotle easily defines the identity in species, in genus, and in number; some problems arise regarding the identity of individuals: for these, it is not enough to indicate the definition and the proper qualities, but matter is needed. Matter cannot, however, be a criterion for identifying duplicate objects: in this case, it plays at most the role of a “weak individuator.” A weak individuator involves relations with other entities. The use of relations in determining the identity of an entity is extensively treated by Hegel, according to whom, in order to define the identity of an object a multiplicity of particular objects is required and, therefore, relations among entities. I conclude by proposing a notion of the object understood not as an independent, separate, and autonomous item, but as a portion of the world, which is given in a phenomenological context and identifies a dialectical context.     

Contextualism,art, and rigidity: Levinson,Currie and Davies

The topic of this paper is the role played by context in art. In this regard I examine three theories linked to the names of J. Levinson, G. Currie and D. Davies. Levinson’s arguments undermine the structural theory. He finds it objectionable because it makes the individuation of artworks independent of their histories. Secondly, such a consequence is unacceptable because it fails to recognise that works are created rather than discovered. But, if certain general features of provenance are always work-constitutive, as it seems that Levinson is willing to claim, these features must always be essential properties of works. On the other hand, consideration of our modal practice suggests that whether a given general feature of provenance is essential or non-essential depends upon the particular work in question or is “work relative”. D. Davies builds his performance theory on the basis of the critical evaluation of Currie’s action-type hypotheses (ATH). Performances, says Davies, are not to be identified with “basic actions” to which their times belong essentially, but with “doings” that permit of the sorts of variation in modal properties required by the work-relativity of modality. He is also a fierce critic of the contextualist account. Contextualism is in his view unable to reflect the fact that aspects of provenance bear upon our modal judgements with variable force.In the second part of the paper I consider Davies’s “modality principle”. Davies is inclined to defend the claim that labels used for designation of works are rigid designators. Such a view offers a ground for discussion about the historicity of art. What has been meant when people claim that art is an historical concept? I argue that any historical theory implies a two-dimensional notion of “art”. At the end of the paper I suggest that Davies should embrace the theory of contingent identity and not the colocationist view about the relationship that exists between a particular artwork and its physical bearer.     

关于自相似集的一个维数定理

本文对严格自相似集，提出了一个比“开集”条件更弱的“可解”条件，并且证明：在可解条件下，自相似集的Ｈａｕｓｄｏｒｆｆ维数及Ｂｏｕｌｉｇａｎｄ维数与其相似维数一致．     

Routes to chaos in continuous mechanical systems. Part 3: The Lyapunov exponents,hyper, hyper-hyper and spatial–temporal chaos

Third part of the paper is devoted to analysis of the hyper, hyper-hyper and spatial–temporal chaos of continuous mechanical systems using the Lyapunov exponents. The constructed algorithms for the Lyapunov exponents’ computation allowed detecting and analysing novel phase transitions from chaos through hyper chaos to hyper-hyper chaos. In addition, a novel characteristic “maximal deflection versus excitation amplitude” has been introduced to study stability properties of the investigated continuous systems. It should be emphasized that the latter characteristic yields results in full agreements with those obtained via the Lyapunov exponents’ spectrum estimation. The introduced methods and tools of analysis allowed detecting the Sharkovskii windows of periodicity in all continuous mechanical systems investigated in this paper. Finally, the approach to study the space-temporal chaos exhibited by shell structural-members is also proposed.     

Non-branching Clause

The central claim of the Parfitian psychological approach to personal identity is that the fact about personal identity is underpinned by a “non-branching” psychological continuity relation. Hence, for the advocates of the Parfitian view, it is important to understand what it is for a relation to take or not take a branching form. Nonetheless, very few attempts have been made in the literature of personal identity to define the “non-branching clause.” This paper undertakes this task. Drawing upon a recent debate between Anthony Brueckner and Harold Noonan on the issue, I present three candidates for the non-branching clause.     

Persistence, Ontic Vagueness and Identity: Towards a Substantialist Four–dimensionalism

Four-dimensionalism, the stage theory version in particular, has been defended as the best solution for avoiding vagueness in regards to composition, persistence and identity. Stage theory is highly problematic by itself, and the two views usually packed with it, unrestricted composition and counterpart theory, are a heavy burden. However, dispensing with these two views, four-dimensionalism could avoid vague persistence by issuing a criterion that would establish sharp temporal boundaries for the existence of genuine entities (simples, molecules and living organisms). This would avoid vague existence and vague identity, but in a way that is still compatible with endurantism. Nevertheless, a minimal (substantialist) four-dimensionalism, a worm perdurantist ontology, would fit better with the unique way in which organisms persist: by retaining both identity and intrinsic change.