Herein I offer a model for understanding the traditional distinction between essentially and accidentally ordered causal series and their function in traditional proofs for the existence of God. I argue that, like the traditional proofs, my model of the causal series in question permits an infinite regress of the accidentally ordered series but not of the essentially ordered series. Furthermore, I argue that on the basis of this model one can avoid Edwards’s criticism (...) that no matter how we conceive of the causal series (as accidental or essential) we still have to deal with the suggestion that arriving at a first cause does not mean that we have an uncaused first cause. Finally, I end with a short speculation on what a successful proof for an uncaused first cause might lead to. (shrink)

Many discussions of per se and per accidens series focus on efficient causality and how a consideration of the metaphysics of the matter can deliver us a primary efficient cause of all that is (God). Drawing on my own previous work on causal series, I offer in this article a model for the understanding of per se causal series wherein the causality involved is that of finality. I then consider whether or not such per se final causal (...) series are infinite. Finally, I consider the implications this has for our conception of God as creator. (shrink)

In this paper, I investigate the variety and richness of the taxonomical practices between the end of the nineteenth and the early twentieth centuries. During these decades, zoologists and paleontologists came up with different quantitative practices in order to classify their data in line with the new biological principles introduced by Charles Darwin. Specifically, I will investigate Florentino Ameghino’s mathematization of mammalian dentition and the quantitative practices and visualizations of several German-speaking paleontologists at the beginning of the twentieth century. In (...) so doing, this paper will call attention to the visual and quantitative language of early twentieth-century systematics. My analysis will therefore contribute to a prehistory of the statistical frame of mind in biology, a study which has yet to be written in full. Second, my work highlights the productive intertwinement between biological practices and philosophical frameworks at the turn of the nineteenth century. Deeply rooted in Kantian bio-philosophy, several biologists sought to find rules in order to apply ordering principles to chaotic taxonomic information. This implies the necessity to investigate the neglected role of Kantian and Romantic bio-philosophy in the unfolding of twentieth-century biology. (shrink)

In this paper, I investigate the variety and richness of the taxonomical practices between the end of the nineteenth and the early twentieth centuries. During these decades, zoologists and paleontologists came up with different quantitative practices in order to classify their data in line with the new biological principles introduced by Charles Darwin. Specifically, I will investigate Florentino Ameghino’s mathematization of mammalian dentition and the quantitative practices and visualizations of several German-speaking paleontologists at the beginning of the twentieth century. In (...) so doing, this paper will call attention to the visual and quantitative language of early twentieth-century systematics. My analysis will therefore contribute to a prehistory of the statistical frame of mind in biology, a study which has yet to be written in full. Second, my work highlights the productive intertwinement between biological practices and philosophical frameworks at the turn of the nineteenth century. Deeply rooted in Kantian bio-philosophy, several biologists sought to find rules in order to apply ordering principles to chaotic taxonomic information. This implies the necessity to investigate the neglected role of Kantian and Romantic bio-philosophy in the unfolding of twentieth-century biology. (shrink)

The history of biological systematics documents a continuing tension between classifications in terms of nested hierarchies congruent with branching diagrams (the ‘Tree of Life’) versus reticulated relations. The recognition of conflicting character distribution led to the dissolution of the scala naturae into reticulated systems, which were then transformed into phylogenetic trees by the addition of a vertical axis. The cladistic revolution in systematics resulted in a representation of phylogeny as a strictly bifurcating pattern (cladogram). Due to the ubiquity of character (...) conflict—at the genetic or morphological level, or at any level in between—some characters will necessarily have to be discarded ( qua noise) in favor of others in support of a strictly bifurcating phylogenetic tree. Pattern analysts will seek maximal congruence in the distribution of characters (ultimately of any kind) relative to a branching tree-topology; process explainers will call such tree-topologies into question by reference to incompatible evolutionary processes. Pattern analysts will argue that process explanations must not be brought to bear on pattern reconstruction; process explainers will insist that the reconstructed pattern requires a process explanation to become scientifically relevant, i.e., relevant to evolutionary theory. The core question driving the current debate about the adequacy of the ‘Tree of Life’ metaphor seems to be whether the systematic dichotomization of the living world is an adequate representation of the complex evolutionary history of global biodiversity. In ‘Questioning the Tree of Life’, it seems beneficial to draw at least four conceptual distinctions: pattern reconstruction versus process explanation as different epistemological approaches to the study of phylogeny; open versus closed systems as expressions of different kinds of population (species) structures; phylogenetic trees versus cladograms as representations of evolutionary processes versus patterns of relationships; and genes versus species as expressions of different levels of causal integration and evolutionary transformation. (shrink)

Avicenna's proof for the existence of God (the Necessary Existent) in the Metaphysics of the Salvation relies on the claim that every possible existent shares a common cause. I argue that Avicenna has good reason to hold this claim given that he thinks that (1) every essentially ordered causal series originates in a first, common cause and that (2) every possible existent belongs to an essentially ordered series. Showing Avicenna's commitment to 1 and 2 allows me (...) to respond to Herbert Davidson's and Richard Swinburne's claim that Avicenna's proof for the Necessary Existent is incomplete and fallacious -/- . (shrink)

Dōgen's views of time are descriptively compared to the modern western philosophical view called "B-theory" and found to contain elements of each of the four main tenets of the B-theory. Furthermore, a fundamental incongruency is discovered. Even accounting for traditional Buddhist approaches to apparent contradictions, Dōgen's problems in this regard call into question the assumption of consistency that has characterized modern interpretations of his views on time.

Several of Thomas Aquinas's proofs for the existence of God rely on the claim that causal series cannot proceed in infinitum. I argue that Aquinas has good reason to hold this claim given his conception of causation. Because he holds that effects are ontologically dependent on their causes, he holds that the relevant causal series are wholly derivative: the later members of such series serve as causes only insofar as they have been caused by and are effects (...) of the earlier members. Because the intermediate causes in such series possess causal powers only by deriving them from all the preceding causes, they need a first and non-derivative cause to serve as the source of their causal powers. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

In this paper, Taylor series is used to solve neutrosophic multi-objective programming problem (NMOPP). In the proposed approach, the truth membership, Indeterminacy membership, falsity membership functions associated with each objective of multi-objective programming problems are transformed into a single objective linear programming problem by using a first order Taylor polynomial series. Finally, to illustrate the efficiency of the proposed method, a numerical experiment for supplier selection is given as an application of Taylor series method for solving neutrosophic (...) multi-objective programming problem at end of this paper. (shrink)

In one of the most stunning Star Wars story lines, the Republic's clone troopers turn on and kill their Jedi generals upon receiving – personally from Darth Sidious – the message, “Execute Order 66.” Animated series such as The Clone Wars, The Bad Batch, and Rebels, novels such as Order 66, and comics such as Star Wars: Republic more deeply explore and explain Order 66. The clones' inhibitor chip degrades or destroys their capacity for independent thought, testifying to the (...) fragility of moral autonomy. The Republic apparently faces many challenges as they turn to the Kaminoans to clone an army that can successfully fight the Separatist droid army. The clones' moral autonomy was indeed quite fragile upon hearing the order. It takes autonomy to make a competent soldier, especially an elite clone trooper. (shrink)

O-minimal structures have long been thought to occupy the base of a hierarchy of ordered structures, in analogy with the role that strongly minimal structures play with respect to stable theories. This is the first in an anticipated series of papers whose aim is the development of model theory for ordered structures of rank greater than one. A class of ordered structures to which a notion of finite rank can be assigned, the decomposable structures, is introduced (...) here. These include all ordered structures definable in o-minimal structures. The principal result in this paper, Theorem 5.1, asserts roughly that a decomposable structure [Formula: see text] can be partitioned into finitely many definable subsets such that on each set the restriction of < is a "twisted lexicographic" order. As a consequence, for all n and linear orders ≺ definable on a subset X ⊆ Mn in an o-minimal structure [Formula: see text], there is a definable partition of X such that the restriction of ≺ to each set in the partition is "lexicographic". (shrink)

In the section of the Antinomy of pure Reason Kant presents three notions of infinity. By investigating these concepts of infinity, this paper highlights important ‘building blocks’ of the structure of the mathematical antinomies, such as the ability of reason of producing ascending and descending series, as well as the notions of given and givable series. These structural features are discussed in order to clarify Ernst Zermelo’s reading of Kant’s antinomy, according to which the latter is deeply rooted (...) in the tendency of the mind of producing “creative progress” and “inclusive closure”. The aim of this paper is to explain in which sense and why Kant’s treatment of the antinomies attracts the attention of Zermelo in the early 1900s and which aspects of his second axiomatic system have been inspired by Kant’s philosophy. Thus, by reading Kant’s antinomy ‘through Zermelo’s eyes’—with emphasis on the concept of regressive series in indefinitum and on that of regressive series ad infinitum – this paper identifies the echoes of Kant’s work in the making of the ZFC set theory. (shrink)

ABSTRACT: This paper argues that the so-called paradoxes of higher-order vagueness are the result of a confusion between higher-order vagueness and the distribution of the objects of a Sorites series into extensionally non-overlapping non-empty classes.

The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer in the first part of the paper a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (...) (like FOL + K)in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. Models of this type are either difficult of impossible to build in terms of relational Kripkean semantics [40].We conclude by introducing general first order neighborhood frames with constant domains and we offer a general completeness result for the entire family of classical first order modal systems in terms of them, circumventing some well-known problems of propositional and first order neighborhood semantics (mainly the fact that many classical modal logics are incomplete with respect to an unmodified version of either neighborhood or relational frames). We argue that the semantical program that thus arises offers the first complete semantic unification of the family of classical first order modal logics. (shrink)

A heuristic proof is given that the divergent QCD perturbation series is, asymptotic. By treating it as an asymptotic expansion we show that it makes sense to keep only the first few terms. The example of e+e− annihilation is considered. It is shown that by keeping only the first few terms one can get within a per cent (or smaller) of the complete sum of the series even at very low momenta where the coupling is large. More generally, (...) this affords an explanation of the phenomena of precocious scaling and why keeping only leading order corrections generally works so well. (shrink)

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of (...) all n-element subsets for each natural number n ≥ 2. Moreover, series ∑β<αf are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic. (shrink)

Aristotle attaches particular significance to the homonymy of many central concepts in philosophy and science: that is, to the diversity of ways of being common to a single general concept. His preoccupation with homonymy influences his approach to almost every subject that he considers, and it clearly structures the philosophical methodology that he employs both when criticizing others and when advancing his own positive theories. Where there is homonymy there is multiplicity: Aristotle aims to find the order within this multiplicity, (...) and believes that doing so is crucial to scientific inquiry and philosophical progress.Christopher Shields investigates and evaluates Aristotle's approach to questions about homonymy, characterizing the metaphysical and semantic commitments necessary to establish the homonymy of a given concept. Then, in a series of case-studies, Shields examines in detail some of Aristotle's principal applications of homonymy--to the body, sameness and oneness, life, goodness, and being. Shields's aim is not only to give a fuller understanding of Aristotle's methodology and to illuminate his specific doctrines in a variety of areas, but to show that this methodology remains fruitful today. (shrink)

In herein article an attempt of problem solution connected with anomaly detection in network traffic with the use of statistic models with long or short memory dependence was presented. In order to select the proper type of a model, the parameter describing memory on the basis of the Geweke and Porter-Hudak test was estimated. Bearing in mind that the value of statistic model depends directly on quality of data used for its creation, at the initial stage of the suggested method, (...) outliers were identified and then removed. For the implementation of this task, the criterion using the value of interquartile range was used. The data prepared in this manner were useful for automatic creation of statistic models classes, such as ARFIMA and Holt-Winters. The procedure of calculation of model parameters’ optimal values was carried out as a compromise between the models coherence and the size of error estimation. Then, relations between the estimated network model and its actual parameters were used in order to detect anomalies in the network traffic. Considering the possibility of appearance of significant real traffic network fluctuations, procedure of updating statistic models was suggested. The results obtained in the course of performed experiments proved efficacy and efficiency of the presented solution. (shrink)

Truth predicates are widely believed to be capable of serving a certain logical or quasi-logical function. There is little consensus, however, on the exact nature of this function. We offer a series of formal results in support of the thesis that disquotational truth is a device to simulate higher-order resources in a first-order setting. More specifically, we show that any theory formulated in a higher-order language can be naturally and conservatively interpreted in a first-order theory with a disquotational truth (...) or truth-of predicate. In the first part of the paper we focus on the relation between truth and full impredicative sentential quantification. The second part is devoted to the relation between truth-of and full impredicative predicate quantification. (shrink)

This book discusses the relationship between democracy and the financial order from various legal perspectives. Each of the nine contributions adopts a unique perspective on the legal and political challenges brought to the fore by the Global Financial Crisis. This crisis and the ensuing sovereign debt crisis in Europe are only the latest in a long series of financial crises around the globe in recent decades. By their very existence, but also as a result of the political turmoil they (...) have created, these financial crises testify to the well-known tensions between democracy and a market-based economic and financial order. However, what is missing in this debate is an analysis of the role of law for reconciling democracy with a market-based financial order. To fill this lacuna, the book focuses on the controversy surrounding the concept of law, thereby adding another variable to the debate on the relation between democracy and capitalism. Each chapter addresses the concept of law from a particular theoretical angle, be it a full-grown legal theory or an approach in political economy that has a particular view of the law. (shrink)

Aristotle attaches particular significance to the homomyny of many of the central concepts in philosophy and science: that is, to the diversity of ways of being that are denoted by a single concept. Shields here investigates and evaluates Aristotle's approach to questions about homonymy, characterizing the metaphysical and semantic commitments necessary to establish the homonymy of a given concept. Then, in a series of case studies, he examines in detail some of Aristotle's principal applications of homonymy--to the body, sameness (...) and and oneness, life, goodness, and being. This first full-length study of a central aspect of Aristotle's thought will interest philosophers working in a number of areas. (shrink)

In some games, the products of the probabilities times the payouts result in a series that is conditionally convergent, which means that the sum can vary based on the order in which the products are summed. The purpose of this paper is to address the question: How should such games be valued? We first show that, contrary to widespread belief, summing in the order determined by the mechanism of the game does not lead to the correct value. We then (...) consider other attempts to value such games. We suggest that games with conditionally convergent series are properly valued by summing the products in increasing order of the absolute values of the game’s payouts. (shrink)

In The Order of Things (OT), Foucault recounts the birth and imminent death of Man as an object of study for science and philosophy. Foucault's point is that this very notion of “Man” is dependent on a particular transformation in the history of Being. The mere formulation of this hypothesis opens up a whole series of questions. First, is it true that Man has only become an object of concern in the late eighteenth century. Secondly, if Man has indeed (...) only recently become an object of theoretical interest, is Foucault's description and explanation of this process correct. Thirdly, why should we overcome the concept of “ Man”. Fourthly, in what sense was structuralism deemed to help us overcoming the limitations of this paradigm. In conclusion, if OT has to be overcome, it seems that it should be on grounds slightly different from those usually advanced. (shrink)

Following Henkin’s discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or “cardinality” quantifiers, e.g., “most”, “few”, “finitely many”, “exactly α ”, where α is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first (...) to a general definition of monotone-increasing (M↑) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwise’s 1979 analysis of the basic case of M↑ POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional 1st-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages. (shrink)

The problem of time appears in the fundamental physics in a context of some attempts to formulate the quantized model of general relativity and it shows the inadequacy of many metaphysical assumptions underlying the principles of classical physics. The author uses the Leibnizian ontological model in order to demonstrate that the conceptual core of this problem could be basically identified in the context of tension between the principle of completeness of the world histories, and the reality of dynamics. He describes (...) shortly modern cosmological model of the growing causets in order to show the similar construction in the area of theoretical physics and the necessity of generalizing the notion of „dynamics”. The author puts the thesis that the ontology of quantum block-universe not only doesn’t exclude some dynamics, but it might also assume it on the fundamental level of description of the nature while preserving the physical general covariance and giving up the external, absolute time. (shrink)

Following Henkin's discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or "cardinality" quantifiers, e.g., "most", "few", "finitely many", "exactly α", where α is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first to (...) a general definition of monotone-increasing (M↑) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwise's 1979 analysis of the basic case of M↑ POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional Ist-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages. (shrink)

This is an introductory paper to a series of results linking generic absoluteness results for second and third order number theory to the model theoretic notion of model companionship. Specifically we develop here a general framework linking Woodin’s generic absoluteness results for second order number theory and the theory of universally Baire sets to model companionship and show that (with the required care in details) a $$\Pi _2$$ -property formalized in an appropriate language for second order number theory is (...) forcible from some $$T\supseteq \mathsf {ZFC}+$$ large cardinals if and only if it is consistent with the universal fragment of T if and only if it is realized in the model companion of T. In particular we show that the first order theory of $$H_{\omega _1}$$ is the model companion of the first order theory of the universe of sets assuming the existence of class many Woodin cardinals, and working in a signature with predicates for $$\Delta _0$$ -properties and for all universally Baire sets of reals. We will extend these results also to the theory of $$H_{\aleph _2}$$ in a follow up of this paper. (shrink)

Vagueness does not necessarily come in with vague predicates, nor need it be expressed by them , but undoubtedly 'vague predicates' are traditionally in the focus of main stream discussions of vagueness. In her current modal logic presentation and discussion of the Sorites paradox Susanne Bobzien[1] lists among the properties of a Sorites series a rather weak modal tolerance principle governing the 'grey zone' containing the borderline cases of the Sorites series, which later proves crucial for her solution (...) of the Sorites paradox by use of epistemic interpreted modal operators in 1st order modal logic. We suggest (for different research interest) instead a non-modal description of the switch in the grey zone (respecting tolerance), by resort to similarity sequences, thus getting tangent to two other areas of research in the field. Let's say -any way- the Sorites paradox vanishes, the Sorites series does not. (shrink)

_Order and History,_ Eric Voegelin's five-volume study of how human and divine order are intertwined and manifested in history, has been widely acclaimed as one of the great intellectual achievements of our age. In the fourth volume, _The Ecumenic Age,_ Voegelin breaks with the course he originally charted for the series, in which human existence in society and the corresponding symbolism of order were to be presented in historical succession. The analyses in the three previous volumes remain valid as (...) far as they go, Voegelin explains, but the original conception proved "untenable because it had not taken proper account of the important lines of meaning in history that did not run along lines of time." _The Ecumenic Age_ treats history not as a stream of human beings and their actions in time, but as the process of man's participation in a flux of divine presence that has eschatological direction. "The process of history, and such order as can be discerned in it," Voegelin writes, "is not a story to be told from the beginning to its happy, or unhappy, end; it is a mystery in process of revelation." In the present volume, Voegelin applies his revised conception of historical analysis to the "Ecumenic Age," a pivotal period that extends roughly from the rise of the Persian Empire to the fall of the Roman. The age is marked by the advent of a new type of political unit—the ecumenic empire—achieved at the cost of unprecedented destruction. Yet the pragmatic destructiveness of the age is paralleled by equally unprecedented spiritual creativity, born from the need to make sense of existence in the wake of imperial conquest. These spiritual outbursts gave rise to the great ecumenic religions and raised fundamental questions for human self- understanding that extend into our historical present. (shrink)

In the article we study the existence predicate \(\varepsilon\) in the context of semantics for first-order modal logic. For a formula \(\varphi\) we define \(\varphi^{\varepsilon}\) - the so called existence relativization. We point to a gap in the work of Fitting and Mendelsohn concerning the relationship between the truth of \(\varphi\) and \(\varphi^{\varepsilon}\) in classes of varying- and constant-domain models. We introduce operations on models which allow us to fill the gap and provide a more general perspective on the issue. (...) As a result we obtain a series of theorems describing the logical connection between the notion of truth of a formula with the existence predicate in constant-domain models and the notion of truth of a formula without the existence predicate in varying-domain models. (shrink)

B- theorists frequently argue that the A- theoretic views are incompatible with the Special Theory of Relativity (STR) and that this is a problem for the A- theoretic views. however, the B- theory needs to be revised in light of implications of STR. in particular, it follows from STR that some events stand in genuine temporal relations to each other while others do not. Consequently, there isn’t a single temporal order of all events. instead, there are multiple B- series. (...) Some B- theorists defend a view of the passage of time according to which passage is simply temporal succession. This paper argues that, in Minkowski spacetime, time passes in each of the multiple B- series, but there is no passage spanning across all events because some events stand in no genuine temporal relations to each other. (shrink)

We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of “logarithmic-exponential series” , which is equipped with a well behaved exponentiation. We show that the LE-series with derivative 0 are exactly the real constants, and we invert operators to show that each LE-series has a formal integral. We give evidence for the conjecture that the field of LE-series is a universal domain for ordered (...) differential algebra in Hardy fields. We define composition of LE-series and establish its basic properties, including the existence of compositional inverses. Various interesting subfields of the field of LE-series are also considered. (shrink)

We consider relational databases organized over an ordered domain with some additional relations — a typical example is the ordered domain of rational numbers together with the operation of addition. In the focus of our study are the first-order queries that are invariant under order-preserving “permutations” — such queries are called order-generic. It has recently been discovered that for some domains order-generic FO queries fail to express more than pure order queries. For example, every order-generic FO query over (...) rational numbers with + can be rewritten without +. For some other domains, however, this is not the case.We provide very general conditions on the FO theory of the domain that ensure the collapse of order-generic extended FO queries to pure order queries over this domain: the Pseudo-finite Homogeneity Property and a stronger Isolation Property. We further distinguish one broad class of domains satisfying the Isolation Property, the so-called quasi-o-minimal domains. This class includes all the o-minimal domains, but also the ordered group of integer numbers and the ordered semigroup of natural numbers, and some other domains.An important difference of this paper from the recent series of related papers is that we generalize all the notions to the case of finitely representable database states — as opposed to finite states — and develop a general lifting technique that, essentially, allows us to extend any result of the kind we are interested in, from finite to finitely representable states. We show, however, that these results cannot be transfered to arbitrary infinite states. (shrink)

The paper focuses on extending to the first order case the semantical program for modalities first introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we offer in the first part of the paper a series of new completeness results for salient classical systems of first order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (...) (like FOL + K)in terms of neighborhood frames with constant domains. The first order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. Models of this type are either difficult of impossible to build in terms of relational Kripkean semantics [40].We conclude by introducing general first order neighborhood frames with constant domains and we offer a general completeness result for the entire family of classical first order modal systems in terms of them, circumventing some well-known problems of propositional and first order neighborhood semantics (mainly the fact that many classical modal logics are incomplete with respect to an unmodified version of either neighborhood or relational frames). We argue that the semantical program that thus arises offers the first complete semantic unification of the family of classical first order modal logics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:First Order Relationality and Its Implications:A Response to David ElsteinRoger T. Ames (bio)David Elstein has asked a series of important questions about Human Becomings that provide me with an opportunity to try to bring the argument of the book into clearer focus. Let me begin by thanking David for his always generous and intelligent reflection on not only my new monograph [End Page 181] but also on Henry (...) Rosemont's and my best efforts to expand upon the idea of "role ethics" as a productive way to read Confucian ethics.David asks: Is relationality truly a part of original Confucian thought? Does relationality rule out any notion of essential human nature, and does it necessarily imply or entail role ethics? Is relationality true or merely a useful way of thinking (if these can be distinguished)? Do we know that it's useful?I think the answer to these questions turns on two very different ways of understanding relationality, namely the doctrines of first and second order relationality. The term 'ontology' as "the science of being per se or in itself" gives us a doctrine of external, second order relations. Ontology was introduced into our philosophical vocabulary as a new term for an old way of thinking at the beginning of the seventeenth century by two German philosophers.1 For the classical Greeks, "the science of being per se" (to on he on) was posited as their "first philosophy" with all of its implications for metaphysics, epistemology, logic, ethics, philosophy of religion, and so on. Ontology is that branch of metaphysics that seeks to classify and explain the things that exist, with its underlying assumption that there are unchanging substances or essences internal to things that are available to us to classify them as this and not that. Ontology privileges "being per se" with its categorical language and its "substance" and "attribute" dualism, giving us a grammar of substances as property-bearers and properties that are borne, respectively.Such ontological thinking animates Plato's pursuit of formal, "real" definitions in his quest for certainty (that is, definitions not of words but of what really is), and underlies Aristotle's taxonomical science of knowing "what is what." For these classical Greek philosophers, only what is real and is thus true can be the proper object of knowledge, giving us a logic of the changeless. Corollary to ontology is causal thinking, formal definitions, and, important for David's question, a doctrine of external, second order relationality in which relations conjoin discrete and self-sufficient things, such as human "beings." As the contemporary philosopher Zhao Tingyang 趙汀陽 avers, this kind of substance ontology defining the real things that constitute the content of an orderly and structured cosmosprovides a "dictionary" kind of explanation of the world, seeking to set up an accurate understanding of the limits of all things. In simple terms, it determines "what is what," and all concepts are footnotes to "being" or "is."2In the Book of Changes, we find a vocabulary making explicit cosmological assumptions that stand in stark contrast to this substance ontology and that brings with it a doctrine of first order, constitutive relations. This alternative "first philosophy" has prompted me to create the neologism "zoetology," with the Greek zoe- "life" and -logia "discourse," as my own new term for an old way of thinking that we might translate into modern Chinese as shengshenglun 生生論: "the art of living." The starting point in this zoetological cosmology, then, is that nothing does anything by [End Page 182] itself; association is a fact. Since the very nature of life is associative and transactional, the vocabulary appealed to in defining Confucian cosmology is irreducibly dyadic and collateral: always multiple, never one.And further, it is the nature of life itself that it seeks to optimize the available conditions for its continuing growth, where such growth has a persistent existential and thus intentional aspect. "Life" is the productive correlation between organism and environment that gives rise to correlative, relational, ecological thinking that many of our best sinologists (Marcel Granet, David Keightley, Tang Junyi, K. C. Chang, A. C. Graham, and many others) would ascribe to the earliest semblances of Chinese... (shrink)