In this paper, we study when a set-continuous operator has a fixed-point that is the intersection of a directed family. The framework of our study is the Kelley-Morse theory KMC– and the Gödel-Bernays theory GBC–, both theories including an Axiom of Choice and excluding the Axiom of Foundation. On the one hand, we prove a result concerning monotone operators in KMC– that cannot be proved in GBC–. On the other hand, we study conditions on directed superclasses in (...) GBC– in order that their intersection is a fixed-point of a set-continuous operator. Finally, we illustrate our results with a solution to the liar paradox and a construction of maximal bisimulations. (shrink)

We prove a definable analogue to Brouwer's Fixed Point Theorem for o-minimal structures of real closed field expansions: A continuous definable function mapping from the unit simplex into itself admits a fixed point, even though the underlying space is not necessarily topologically complete. Our proof is direct and elementary; it uses a triangulation technique for o-minimal functions, with an application of Sperner's Lemma.

In a recent paper by M. Rathjen and the present author it has been shown that the statement “every normal function has a derivative” is equivalent to $\Pi ^1_1$ -bar induction. The equivalence was proved over $\mathbf {ACA_0}$, for a suitable representation of normal functions in terms of dilators. In the present paper, we show that the statement “every normal function has at least one fixed point” is equivalent to $\Pi ^1_1$ -induction along the natural numbers.

ABSTRACT A computational logic, PLPR (Predicate Logic using Polymorphism and Recursion) is presented. Actually this logic is the object language of an automated deduction system designed as a tool for proving mathematical theorems as well as specify and verify properties of functional programs. A useful denotationl semantics and two general deduction methods for PLPR are defined. The first one is a tableau algorithm proved to be complete and also used as a guideline for building complete calculi. The second is a (...) sound and complete natural deduction system. Moreover a fixed point induction rule is introduced for formulas called continuous. The strategies for mechanizing the proofs of the final automated system are based on the previous deduction methods. As the examples of the use of the system show, the implemented theorem prover outperforms humans to a certain extent, retaining logic and calculi generality. (shrink)

Some years ago, Yablo gave a paradox concerning an infinite sequence of sentences: if each sentence of the sequence is 'every subsequent sentence in the sequence is false', a contradiction easily follows. In this paper we suggest a formalization of Yablo's paradox in algebraic and topological terms. Our main theorem states that, under a suitable condition, any continuous function from 2N to 2N has a fixed point. This can be translated in the original framework as follows. (...) Consider an infinite sequence of sentences, where any sentence refers to the truth values of the subsequent sentences: if the corresponding function is continuous, no paradox arises. (shrink)

We consider separably closed fields of characteristic $p > 0$ and fixed imperfection degree as modules over a skew polynomial ring. We axiomatize the corresponding theory and we show that it is complete and that it admits quantifier elimination in the usual module language augmented with additive functions which are the analog of the $p$-component functions.

We work with weakly precomplete equivalence relations introduced by Badaev. The weak precompleteness is a natural notion inspired by various fixed point theorems in computability theory. Let E be an equivalence relation on the set of natural numbers $$\omega $$, having at least two classes. A total function f is a diagonal function for E if for every x, the numbers x and f(x) are not E-equivalent. It is known that in the case of c.e. relations (...) E, the weak precompleteness of E is equivalent to the lack of computable diagonal functions for E. Here we prove that this result fails already for $$\Delta ^0_2$$ equivalence relations, starting with the $$\Pi ^{-1}_2$$ level. We focus on the Turing degrees of possible diagonal functions. We prove that for any noncomputable c.e. degree $${\textbf{d}}$$, there exists a weakly precomplete c.e. equivalence E admitting a $${\textbf{d}}$$ -computable diagonal function. We observe that a Turing degree $${\textbf{d}}$$ can compute a diagonal function for every $$\Delta ^0_2$$ equivalence relation E if and only if $${\textbf{d}}$$ computes $${\textbf{0}}'$$. On the other hand, every PA degree can compute a diagonal function for an arbitrary c.e. equivalence E. In addition, if $${\textbf{d}}$$ computes diagonal functions for all c.e. E, then $${\textbf{d}}$$ must be a DNC degree. (shrink)

This paper continues investigations of the monotone fixed point principle in the context of Feferman's explicit mathematics begun in [14]. Explicit mathematics is a versatile formal framework for representing Bishop-style constructive mathematics and generalized recursion theory. The object of investigation here is the theory of explicit mathematics augmented by the monotone fixed point principle, which asserts that any monotone operation on classifications (Feferman's notion of set) possesses a least fixed point. To be more precise, (...) the new axiom not merely postulates the existence of a least solution, but, by adjoining a new constant to the language, it is ensured that a fixed point is uniformly presentable as a function of the monotone operation. Let T 0 + UMID denote this extension of explicit mathematics. [14] gave lower bounds for the strength of two subtheories of T 0 + UMID in relating them to fragments of second order arithmetic based on Π 1 2 comprehension. [14] showed that T $_0 \upharpoonright$ + UMID and T $_0 \upharpoonright$ + IND N + UMID have at least the strength of (Π 1 2 - CA) $\upharpoonright$ and (Π 1 2 - CA), respectively. Here we are concerned with the exact reversals. Let UMID N be the monotone fixed-point principle for subclassifications of the natural numbers. Among other results, it is shown that T $_0 \upharpoonright$ + UMID N and T $_0 \upharpoonright$ + IND N + UMID N have the same strength as (Π 1 2 - CA) $\upharpoonright$ and (Π 1 2 - CA), respectively. The results are achieved by constructing set-theoretic models for the aforementioned systems of explicit mathematics in certain extensions of Kripke-Platek set theory and subsequently relating these set theories to subsystems of second arithmetic. (shrink)

This paper continues investigations of the monotone fixed point principle in the context of Feferman's explicit mathematics begun in [14]. Explicit mathematics is a versatile formal framework for representing Bishop-style constructive mathematics and generalized recursion theory. The object of investigation here is the theory of explicit mathematics augmented by the monotone fixed point principle, which asserts that any monotone operation on classifications possesses a least fixed point. To be more precise, the new axiom not (...) merely postulates the existence of a least solution, but, by adjoining a new constant to the language, it is ensured that a fixed point is uniformly presentable as a function of the monotone operation. Let T$_0$ + UMID denote this extension of explicit mathematics. [14] gave lower bounds for the strength of two subtheories of T$_0$ + UMID in relating them to fragments of second order arithmetic based on $\Pi^1_2$ comprehension. [14] showed that T$_0 \upharpoonright$ + UMID and T$_0 \upharpoonright$ + IND$_\mathbb{N}$ + UMID have at least the strength of $\upharpoonright$ and, respectively. Here we are concerned with the exact reversals. Let UMID$_\mathbb{N}$ be the monotone fixed-point principle for subclassifications of the natural numbers. Among other results, it is shown that T$_0 \upharpoonright$ + UMID$_\mathbb{N}$ and T$_0 \upharpoonright$ + $IND_\mathbb{N}$ + UMID$_\mathbb{N}$ have the same strength as $ $\upharpoonright$ and, respectively. The results are achieved by constructing set-theoretic models for the aforementioned systems of explicit mathematics in certain extensions of Kripke-Platek set theory and subsequently relating these set theories to subsystems of second arithmetic. (shrink)

A function is recursive (in given operations) if its values are computed explicitly and uniformly in terms of other "previously computed" values of itself and (perhaps) other "simultaneously computed" recursive functions. Here, "explicitly" includes definition by cases. We investigate those recursive functions on the structure $\mathbf{N} = \langle \omega, 0, \operatorname{succ,pred}\rangle$ that are computed in terms of themselves only, without other simultaneously computed recursive functions.

In this book the authors introduce and study the following notions: Neutrosophic Crisp Points, Neutrosophic Crisp Relations, Neutrosophic Crisp Sets, Neutrosophic Set Generated by (Characteristic Function), alpha-cut Level for Neutrosophic Sets, Neutrosophic Crisp Continuous Function, Neutrosophic Crisp Compact Spaces, Neutrosophic Crisp Nearly Open Sets, Neutrosophic Crisp Ideals, Neutrosophic Crisp Filter, Neutrosophic Crisp Local Functions, Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals, Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity, Neutrosophic Topological Region, Neutrosophic Closed Set and Neutrosophic Continuous (...) Function, etc. They compute the distances between neutrosophic sets and extend it to Neutrosophic Hesitancy Degree. The authors also generalize the Crisp Topological Space and Intuitionistic Topological Space to the notion of Neutrosophic Crisp Topological Space. At the end, they present applications to Neutrosophic Database, and show a security scheme based on Public Key Infrastructure (PKI) using Neutrosophic Logic Manipulation. The authors utilize neutrosophic sets in order to analyze social networks data conducted through learning activities, and for the Geographical Information Systems (GIS) they employ fundamental concepts and properties of a Neutrosophic Spatial Region. Keywords: Neutrosophic Crisp Points; Neutrosophic Crisp Relations; Neutrosophic Crisp Sets; Neutrosophic Crisp Continuous Function; Neutrosophic Crisp Compact Spaces; Neutrosophic Crisp Nearly Open Sets; Neutrosophic Crisp Ideals; Neutrosophic Crisp Filter; Neutrosophic Crisp Local Functions; Neutrosophic Crisp Sets via Neutrosophic Crisp Ideals; Neutrosophic Crisp L-Openness and Neutrosophic Crisp L-Continuity; Neutrosophic Topological Region; Neutrosophic Closed Set and Neutrosophic Continuous Function; Neutrosophic Hesitancy Degree; Neutrosophic Crisp Topological Space; Neutrosophic Database; Neutrosophic Logic Manipulation; Neutrosophic Spatial Region. (shrink)

The study aimed at measuring the dominant pattern of leadership and its relation to the performance of the administrative staff in the Palestinian universities. The study community consists of all the administrative staff from Al-Azhar University and the Islamic University, and through the census of the study society it was found to consist of (655) administrative staff. In order to achieve the objectives of the study, the researchers used the method of random sample in the study, and the study was (...) conducted on a sample of (221) administrative staff of the surveyed universities and the response rate was (82.35%). The study found that there is a high degree of satisfaction with the Dominant Pattern of Leadership in the Palestinian universities in Gaza Strip from the point of view of the administrative staff, which reached (71.67%). There is a high level of performance from the point of view of administrative staff, with a percentage of (82.53%). There is a direct correlation between the dominant pattern of leadership and the functional Performance of Administrative Staff, the absence of differences between the sample according to the gender variable in their perception of the dominant pattern of leadership and the functional Performance of Administrative Staff, the absence of differences in the perception of employees of the dominant pattern of leadership and the functional Performance of Administrative Staff depending on the age variable. There are differences of statistical significance according to the variable of scientific qualification in the Dominant Pattern of Leadership, while there were no differences in performance, the differences in the dominant pattern of leadership according to the scientific qualification were in favor of those who obtained the diploma degree compared to other practical qualifications, the absence of differences in the perception of employees of the dominant pattern of leadership and the functional Performance of Administrative Staff depending on the variable years of service, the absence of differences in the perception of employees of the dominant pattern of leadership and the functional Performance of Administrative Staff depending on the variable level of career (Director, Head of Department, and Administrative Officer). There were differences in the perception of workers to the dominant pattern of leadership depending on the variable of the workplace, where there were differences in favor of workers in deanships and colleges compared with the workers in the technical departments. While there were no differences in job performance according to the workplace variable, the existence of differences in the perception of workers to the dominant pattern of leadership depending on the university in which they work in favor of the Islamic University and the absence of differences in performance between the Islamic University and Al-Azhar University. The study reached a number of recommendations, the most important of which is that the interest of the managements of the Palestinian universities in improving the dominant pattern of leadership, to give universities the opportunity to participate in decision-making, the continued administration of universities interest and continuous improvement of the performance of its employees, enhance the periodic evaluation of job performance and to inform employees and express their opinion, solving workers' problems and giving them the opportunity to contribute to solving their own problems, the use of the staff rotation method periodically and strengthening the democratic the dominant pattern of leadership and empowering university staff. -/- . (shrink)

A formalism developed in previous papers for the description of continual observations of some quantities in the framework of quantum mechanics is reobtained and generalized, starting from a more axiomatic point of view. The statistics of the observations of continuous state trajectories is treated from the beginning as a generalized stochastic process in the sense of Gel'fand. An effect-valued measure and an operation-valued measure on the σ-algebra generated by the cylinder sets in the space of trajectories are introduced. (...) The properties of the characteristic functional for the “operation-valued stochastic process” are discussed and, through a suitableansatz, a significant class of such processes is explicitly constructed, which contains the examples of the preceding papers as particular cases. (shrink)

Two central assumptions of current models of language acquisition were addressed in this study: (1) knowledge of linguistic structure is "mapped onto" earlier forms of non-linguistic knowledge; and (2) acquiring a language involves a continuous learning sequence from early gestural communication to linguistic expression. The acquisition of the first and second person pronouns ME and YOU was investigated in a longitudinal study of two deaf children of deaf parents learning American Sign Language (ASL) as a first language. Personal pronouns (...) in ASL are formed by pointing directly to the addressee (YOU) or self (I or ME), rather than by arbitrary symbols. Thus, personal pronouns in ASL resemble paralinguistic gestures that commonly accompany speech and are used prelinguistically by both hearing and deaf children beginning around 9 months. This provides a means for investigating the transition from prelinguistic gestural to linguistic expression when both gesture and language reside in the same modality.\nThe results indicate that deaf children acquired knowledge of personal pronouns over a period of time, displaying errors similar to those of hearing children despite the transparency of the pointing gestures. The children initially (ages 10 and 12 months) pointed to persons, objects, and locations. Both children then exhibited a long avoidance period, during which one function of the pointing gesture (pointing to self and others) dropped out completely. During this period their language and cognitive development were otherwise entirely normal, and they continued to use other types of pointing (e.g., to objects). When pointing to self and others returned, it was marked with errors typical of hearing children; one child exhibited consistent pronoun reversal errors, thinking the YOU point referred to herself, while the other child exhibited reversal errors inconsistently. Evidence from experimental tasks conducted with the first child revealed that pronoun errors occurred in comprehension as well. Full control of the ME and YOU pronouns was not achieved until 25-27 months, around the same time when hearing children master these forms. Thus, the study provides evidence for a discontinuity in the child's transition from prelinguistic to linguistic communication. It is argued that aspects of linguistic structure and its acquisition appear to involve distinct, language-specific knowledge. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

Graph polynomials are graph parameters invariant under graph isomorphisms which take values in a polynomial ring with a fixed finite number of indeterminates. We study graph polynomials from a model theoretic point of view. In this paper we distinguish between the graph theoretic (semantic) and the algebraic (syntactic) meaning of graph polynomials. Graph polynomials appear in the literature either as generating functions, as generalized chromatic polynomials, or as polynomials derived via determinants of adjacency or Laplacian matrices. We show (...) that these forms are mutually incomparable, and propose a unified framework based on definability in Second Order Logic. We show that this comprises virtually all examples of graph polynomials with a fixed finite set of indeterminates. Finally we show that the location of zeros and stability of graph polynomials is not a semantic property. The paper emphasizes a model theoretic view. It gives a unified exposition of classical results in algebraic combinatorics together with new and some of our previously obtained results scattered in the graph theoretic literature. (shrink)

In this paper we continue the study of Girard's Linear Logic and introduce a new Linear Logic with modalities. Our logic describes not only the consumption, but also the presence of resources. We introduce a new semantics and a new calculus for this logic. In contrast to the results of Lincoln [7] and Kanovich [4] about the NP-completeness of the problem of the construction of a proof for a given sequent in the multiplicative fragment of Girard's Linear Logic, we present (...) here a non-exponential algorithm to construct a proof for a given sequent and a given point of a given model in our Linear Logic. (shrink)

Is the exemplar of modern ethical theory estranged from their intimates because the motive of duty dominates their motivational psychology? While this challenge against modern ethical theory is familiar, I argue that with respect to a certain strand of Kantian ethical theory, it does not so much as make sense. I explain the content and functional role of the motive of duty in the psychology of the moral exemplar, stressing in particular how that motive shapes and informs the content of (...) others, including those characteristic of intimacy. I argue that to the extent that a subject does not integrate their motive of duty with their other motives, their moral and intimate relationships are compromised, and on the same grounds, because intimate relationships are interpersonal relationships and the motive of duty just is the motive to respect another person as a separate person. (shrink)

Working in an o-minimal expansion of the real field, we investigate when a germ of a complex analytic function has a definable analytic continuation to its Mittag–Leffler star. As an application we show that any algebro-logarithmic function that is complex analytic in a neighborhood of the origin in $\mathbb {C}$ has an analytic continuation to all but finitely many points in $\mathbb {C}$.

We study the non-wellfounded sets as fixed points of substitution. For example, we show that ZFA implies that every function has a fixed point. As a corollary we determine for which functions f there is a function g such that . We also present a classification of non-wellfounded sets according to their branching structure.

In several experiments of survival analysis, the cause of death or failure of any subject may be characterized by more than one cause. Since the cause of failure may be dependent or independent, in this work, we discuss the competing risk lifetime model under progressive type-II censored where the removal follows a binomial distribution. We consider the Akshaya lifetime failure model under independent causes and the number of subjects removed at every failure time when the removal follows the binomial distribution (...) with known parameters. The classical and Bayesian approaches are used to account for the point and interval estimation procedures for parameters and parametric functions. The Bayes estimate is obtained by using the Markov Chain Monte Carlo method under symmetric and asymmetric loss functions. We apply the Metropolis–Hasting algorithm to generate MCMC samples from the posterior density function. A simulated data set is applied to diagnose the performance of the two techniques applied here. The data represented the survival times of mice kept in a conventional germ-free environment, all of which were exposed to a fixed dose of radiation at the age of 5 to 6 weeks, which was used as a practice for the model discussed. There are 3 causes of death. In group 1, we considered thymic lymphoma to be the first cause and other causes to be the second. On the base of mice data, the survival mean time of mice of the second cause is higher than the first cause. (shrink)

We develop a functional abstraction principle for the type-free algorithmic logic introduced in our earlier work. Our approach is based on the standard combinators but is supplemented by the novel use of evaluation trees. Then we show that the abstraction principle leads to a Curry fixed point, a statement C that asserts C ⇒ A where A is any given statement. When A is false, such a C yields a paradoxical situation. As discussed in our earlier work, this (...) situation leaves one no choice but to restrict the use of a certain class of implicational rules including modus ponens. (shrink)

The article is about one of the vital problem for analytic philosophy which is how to define truth value for sentences which include their own truth predicate. The aim of the article is to determine Saul Kripke’s approach to widen epistemological truth to create a systemic model of truth. Despite a lot of work on the subject, the theme of truth is no less relevant to modern philosophy. With the help of S. Kripke’s article “Outline of the Theory of Truth” (...) and R. L. Kirkham’s work “Theories of Truth: A Critical Introduction” the author tried to represent a non-classical approach which is now known as Saul Kripke’s truth value gaps theory. Considering his solving of the Liar Paradox, as well as the Strenghened Liar, it is obvious that there could be the circumstances (or facts) that make sentences have no truth value. In that case the solving of the paradox attracts Kleene’s non-classical three-valued logic which contains the third way and the solution falls into the gap between truth and falsity. Hence there are no relevant and full satisfactory ways to solve the Liar’s Paradox by the language-levels ap- proach. The task consists in an extension of the approach to natural languages and elimination of an ad hoc element as well. Besides that, the language-levels approach refers to the speaker that means that only the last one is allowed to define the hierarchy of the levels and truth value of sentence, but often he does not know what level he is speaking of. As Kripke stated, contingent facts can lead to a paradox which isn’t allowed for a logical point of view. However usage of mathematical apparatus allows the theory in question to be universalized and moreover paves the way to futher epistemological develop- ment of the problem in question. As Kripke’s theory is formalized and presented as a functional series, it gives access to a system model of truth whose elements would be epistemological theories (concepts) of truth. Such a model, for instance, confirms the validity of the deflationary concept of truth. Refs 7. (shrink)

Freud seems to have been torn between a literary and a scientific model for his enterprises. On the one hand he stresses the scientific nature of his researches to an extent which makes the suspicious reader wonder whether he protests too much. On the other hand it is well known that he regarded many writers, though predominantly Shakespeare, as anticipating his findings on the unconscious. In one famous passage in the Introductory Lectures on Psycho-analysis he places his discovery of the (...) unconscious on a par with the discoveries of Darwin and Copernicus in their effect upon man's picture of himself. He is justified, of course, and if we add Marx to this triumvirate we add a figure even closer to Freud in claiming a scientific status for his work, a scientific status which is, to the uncommitted, dubious. Theodore Mischel argues that Freud increasingly construes neurotic behaviour upon the model of ordinary intentional behaviour and, though he continued to show interest in the view that the unconscious impulses which are repressed are physiological in nature, this ideal of a reduction of the psychological to the physiological became a less active ingredient in his published work as his collaboration with Fliess receded into the past. So although he may have paid lip service to some form of psycho-physical identity, believing that mental phenomena are ultimately no more or less than physical happenings in the neurones of the brain, in mature Freud this seems to have been an idly spinning wheel. Roy Schafer has recently pointed out that many of Freud's followers use the concepts of natural science , whilst simultaneously retaining traces of anthropomorphism in their metapsychology. For instance Heinz Hartmann emphasizes the concept of a ‘higher organizing function’ which resists formulation in the mechanistic metapsychology he favours. Similar difficulties obtrude in the work of Waelder and Kohut. The significance of these conflicts leads Schafer to frame basic Freudian insights in terms of the theory of action, stressing the manner in which an action may be described in differing ways and thus allowing us to present the fact that a patient's behaviour may both tell and not tell us of his deepest anxieties. Yet curiously Schafer denies that freedom plays any part in his account whereas we would have expected a concept so central to agency to have an equally central role in any recasting of psycho-analysis in terms of the theory of action. (shrink)

I would like to stress Vadim Mikhailovich's [Mezhuev's] position and clarify our conversation about culturology. It is constantly repeated that culturology is a science. It is my profound conviction that culturology is not a science. Culturology is a distinctive phenomenon of Russian culture and represents a certain intellectual movement. If one briefly surveys the history of its emergence, its philosophical origin becomes obvious. This intellectual movement consists of three levels, if one takes into account the "-logy" ending. First, the philosophical (...) level, from which in the 1970s culture began to be conceived as a special field of knowledge in our country. Then, humanistic knowledge: a great many representatives of the humanities in Russia-historians, art specialists, art critics, essayists-studied culture. Finally, there is the socioscientific tendency, which is just beginning to form in Russia and carries the internationally accepted name of social and cultural anthropology. All of us are synergistically attracted to these three tendencies, which comprise what is called culturology. The question of how these three tendencies of knowledge are correlated in the framework of the given intellectual movement is, in my view, extremely important. For quite some time now, there has been no reflection in Russia on the foundations of scientific and philosophical knowledge, but such reflection is necessary. To advance along the road of rational knowledge it is important to reflect in what cognitive space we find ourselves, what we are doing within its boundaries, and for what reason. From this point of view, neither philosophers nor representatives of the humanities or the social sciences will renounce their positions of observer. Moreover, I agree with Mezhuev that there is no single philosophy, humanistic conception, or theory of culture. Anyone who is engaged professionally in the study of cultural phenomena can choose his initial foundations. As Vadim Mezhuev correctly notes, the significance of philosophy for other types of knowledge lies in the fact that there are borderline areas of man's existence in the world. However, they are identified in different ways by different philosophies: positivism, phenomenology, classical Platonism, Aristotelianism, Kantianism, and so forth. Representatives of humanistic and socioscientific knowledge are free to choose any metaphysics. Philosophers will continue to attend to their business in their subject area, and scientists in theirs. But it is important periodically to determine rationally when there must be close and complementary relations between the three components of this intellectual movement and when they must exist in parallel. Then questions such as who has priority and who is the guardian of truth will not arise. If the tendencies have diverged in parallel, then the representatives of each of them are occupied within their domains with questions which are irrelevant in other fields of knowledge or for other theoretical models. At the end of the twentieth century, to pose the question of scientism or antiscientism is senseless because today we know that there are different forms of rationality and that science is not the only, and is quite a narrow, form of rationality. Myth too is rational. It is expressed in categories and has a particular inner logic. We recognize myth as a rational cultural entity, because it is represented in symbolic form as an ordered sequence of judgments, as an artifact. But it differs from scientific theory. That is why it is fruitful to reflect on what forms of rationality are relevant to what levels of knowledge. I agree with Ogurtsov, who says that these forms penetrate in one way or another into every culturally institutionalized form of knowledge. Indeed, in philosophical knowledge there are elements of everyday, mythological, and scientific knowledge, but this does not negate the distinctive nature of the philosophical form of knowledge. In science there are elements of metaphysics, mythology, and everyday knowledge, but this does not cancel the particularities of the scientific form of knowledge. The same is true of the humanistic form, which is in principle irremovable from the framework of institutionalized knowledge, at least for now. I do not agree with Ogurtsov that I give the humanistic form of knowledge a negative evaluation. Humanistic knowledge begins to be significant in a period of a cognitive paradigm shift. This, we can say, is apparent today, at a time of transition from the grand style of modernism in its postmodern mode to the building of the foundations for a new whole. The point is that the humanistic form of knowledge enables us to isolate at the outset those areas of the unknown at which we arrive because of the limitations inherent in other forms of rationality. It is closest to everyday and empirical categories of knowledge and forms of ideas; hence, particularism, image syncretism, and mobility are its distinctive features. But without this humanistic level no further step is possible in either scientific or philosophical knowledge. The breakdown into these forms of knowledge- philosophical, humanistic, and scientific-may be primitive, but we have to start our reflection on the foundations of our cognitive relationship to our surroundings somewhere. The identification of the forms of knowledge makes it possible to draw the conclusion that, unlike philosophical and humanistic knowledge, socioscientific knowledge is modeled on the natural sciences. From this it becomes obvious that the distinctive features of the object of social sciences determine also the special nature of the categorial apparatus, operationalization, selection method, and information analysis. I do not insist that the model I suggest must be accepted. Other models can be constructed. But let us start with a simpler comparison of types of knowledge and later we shall differentiate them. I started from this level because in our culture such a division is apparent and generally accepted. There are the philosophical, humanistic, and scientific forms of knowledge. They are irreducible to one another, they perform entirely different functions in the knowledge of man's relationship to the environment, and express different views about how man lives in culture. I agree that philosophy is exactly existence in culture with a singling out of the limits of this existence. But representatives of humanistic and socioscientific knowledge also deal with existence in culture. What is important for the philosopher is the direction of knowledge from within to the outside; for the representative of humanistic knowledge it is the description of how he exists among a multitude of seemingly diverse and divergent artifacts and processes; and for the scientist it is the order of the philosophically and humanistically defined reality in order to control it the better. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Teaching Aesthetics and Aesthetic Teaching:Toward a Deweyan PerspectiveDavid A. Granger (bio)The educational writings of John Dewey continue to be invoked by scholars in education on a regular basis and in relation to a wide variety of issues, from social learning theory and situated cognition to constructivism and whole-language literacy instruction. More recently, this scholarship has begun to expand to include books and essays that look to tie Dewey's aesthetics (...) to his work in education in a substantive way. Notably, this is not something that Dewey attempted himself, since his major work in aesthetics, Art as Experience, was not published until he was seventy-five, and he seemingly had neither the time nor means at that point in his life to develop this link to his satisfaction. In addition, many educators are only familiar with Dewey's more explicitly educational writings, most of which came earlier in his career and tend to speak more of the merits of science than of art. As a result, scholars in education have only recently begun to examine the possible significance of Dewey's aesthetics for the practices of teaching and learning.1It is still the case, however, that writers on Dewey have traditionally focused their critical energies on his expansive claims for "the method of science" as a vehicle for solving numerous educational and social problems, and as the only authentic means of learning about our everyday world. Such critical attention is not, I believe, without warrant; though Dewey's use of "science" was a very loose and liberal one, he was a staunch critic of the positivistic model of science often presumed by these writers. Nonetheless, this critical focus has unfortunately led many writers to dismiss or marginalize the Dewey who, for instance, proclaims in "Art in Education—and Education in Art" that theModern preoccupation with science and with industry based on science has been disastrous; our education has followed the model that [End Page 45] they have set. It has been concerned with intellectual analysis and formularized information.... It is disastrous because it has fixed attention upon competition for control and possession of a fixed environment rather than upon what art can do to create an environment.... It is disastrous because civilization built upon these principles cannot supply the demand of the soul for joy, or freshness of experience; only attention through art to the vivid but transient values of things can effect such refreshment.2As Dewey sees it, science and other forms of knowledge are properly "handmaidens" to art, intellectual tools for enhancing the overall quality and value of human life and activity.3 This means that they are largely subordinate to the direct qualitative meaning of experience. They are, Dewey says, transformed in aesthetic experience in that they are "merged with non-intellectual elements to form an experience worth while as an experience."4 Art objects may well be the most potent and ready source of such enhanced, aesthetic experience, being intentionally created to refine and intensify in certain ways the experience of the perceiver. But they are not, to Dewey's way of thinking, the sole or even principal medium of the aesthetic. Art, he tells us, is best seen more liberally as "a quality that permeates an experience," whereby, in any number of life contexts, the meanings of objects and events become "the matter of a clarified, coherent, and intensified or 'impassioned' experience" (AE, 329, 295). If all of this can be taken to mean that art or the aesthetic, and not science, is paradigmatic of optimal human experience, then current efforts to integrate Dewey's aesthetics with his thinking about education are an important endeavor and one that should bear considerable fruit. Then, too, much of the popular literature in art and aesthetic education, which situates art and the aesthetic squarely within the cognitive domain of experience, is significantly at odds with Dewey's radically holistic and vigorously anti-elitist aesthetics.5Accordingly, this article will explore the idea of aesthetic education—conceived in its broadest sense—using a mainly Deweyan lens. Moreover, it will do so by examining everyday classroom practices as they are informed by the general... (shrink)

In this paper, we present an intensive investigation of the finite volume method compared to the finite difference methods. In order to show the main difference in the way of approaching the solution, we take the Burgers equation and the Buckley–Leverett equation as examples to simulate the previously mentioned methods. On the one hand, we simulate the results of the finite difference methods using the schemes of Lax–Friedrichs and Lax–Wendroff. On the other hand, we apply Godunov’s scheme to simulate the (...) results of the finite volume method. Moreover, we show how starting with a variational formulation of the problem, the finite element technique provides piecewise formulations of functions defined by a collection of grid data points, while the finite difference technique begins with a differential formulation of the problem and continues to discretize the derivatives. Finally, some graphical and numerical comparisons are provided to illustrate and corroborate the differences between these two main methods. (shrink)

In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming ...

On Bohm''s formulation of quantum mechanics particles always have determinate positions and follow continuous trajectories. Bohm''s theory, however, requires a postulate that says that particles are initially distributed in a special way: particles are randomly distributed so that the probability of their positions being represented by a point in any regionR in configuration space is equal to the square of the wave-function integrated overR. If the distribution postulate were false, then the theory would generally fail to make (...) the right statistical predictions. Further, if it were false, then there would at least in principle be situations where a particle would approach an eigenstate of having one position but in fact always be somewhere very different. Indeed, we will see how this might happen even if the distribution postulate were true. This will help to show how loose the connection is between the wave-function and the positions of particles in Bohm''s theory and what the precise role of the distribution postulate is. Finally, we will briefly consider two attempts to formulate a version of Bohm''s theory without the distribution postulate. (shrink)

Recent years have seen a certain impatience with John Rawls's approach to political philosophy and calls for the discipline to move beyond it. One source of dissatisfaction is Rawls's idea of a well-ordered society. In a recent article, Alex Schaefer has tried to give further impetus to this movement away from Rawlsian theorizing by pursuing a question about well-ordered societies that he thinks other critics have not thought to ask. He poses that question in the title of his article: “Is (...) Justice a Fixed Point?.” Though Schaefer is critical of Rawlsian political theorizing, I shall contend that his arguments also suggest two paths forward for those who would follow the Rawlsian approach. First, the intellectual devices Schaefer deploys help those who would continue the Rawlsian project to see, and precisely to chart, the next step that that project needs to take—a step necessitated by a concession Rawls himself made late in the development of political liberalism. Second, the clarity and economy with which Schaefer lays out his alternative to the Rawlsian approach make it possible to state some fundamental Rawlsian challenges to a form of theorizing that has considerable appeal to many critics of that approach. (shrink)

We can evaluate laws as better or worse relative to different normative standards. One might lament the fact that a law violates human rights or, in a different register, marvel at its ease of application. A question in legal philosophy is whether some standards for evaluating laws are fixed by—or grounded in—the very nature of law. I take Raz’s discussion of the distinctively legal virtues, those that fall under the rubric of the “Rule of Law” such as clarity, generality, (...) and non-retroactivity, as my starting point for exploring a very general puzzle about the relationship between law’s essence and its virtue. -/- The claim that there are some virtues that laws have qua laws invites a comparison between law and other “goodness-fixing kinds.” A kind is goodness-fixing if what it is to be a member of the kind fixes a standard for evaluating instances as better or worse. For example, if an object belongs to the kind CLOCK, whether it keeps time accurately provides a basis for evaluating it as better or worse as a clock. Furthermore, the relevant normative fact—if a clock does not keep time accurately, it is a bad clock—is at least partly explainable in terms of the nature of clocks (clocks are things that are supposed to be keep time accurately). Hence, for any goodness-fixing kind, K, that sets a standard, S, for evaluating Ks as Ks, we can ask: (1) How does the nature of Ks explain S? (2) Does being a K depend on meeting a minimum threshold of S-relative goodness? In the case of law and its constitutive standard defined by the Rule-of-Law virtues, these questions lack settled answers. Although Raz offers some discussion, I argue that his answers have the surprising upshot of rendering law sui generis relative to other goodness-fixing kinds, and that preserving continuity with other goodness-fixing kinds involves revising the general picture. (shrink)

The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality -- these are the so-called "dangerous" directed graphs. Building on Rabern, et. al (2013) we reformulate this problem in terms of fixed points of certain functions, thereby boiling it down to (...) get a purely mathematical problem. (shrink)

On Bohm's formulation of quantum mechanics particles always have determinate positions and follow continuous trajectories. Bohm's theory, however, requires a postulate that says that particles are initially distributed in a special way: particles are randomly distributed so that the probability of their positions being represented by a point in any regionR in configuration space is equal to the square of the wave-function integrated overR. If the distribution postulate were false, then the theory would generally fail to make (...) the right statistical predictions. Further, if it were false, then there would at least in principle be situations where a particle would approach an eigenstate of having one position but in fact always be somewhere very different. Indeed, we will see how this might happen even if the distribution postulate were true. This will help to show how loose the connection is between the wave-function and the positions of particles in Bohm's theory and what the precise role of the distribution postulate is. Finally, we will briefly consider two attempts to formulate a version of Bohm's theory without the distribution postulate. (shrink)

The Continuous Parameter Estimation Model is applied to develop individual genomic-level heritabilities for the latent hierarchical structure and developmental dynamics of Life History (LH) strategy LH strategies relate to the allocations of bioenergetic resources into different domains of fitness. LH has moderate to high population-level heritability in humans, both at the level of the high-order Super-K Factor and the lower-order factors, the K-Factor, Covitality Factor, and General Factor of Personality (GFP). Several important questions remain unexplored. We developed measures of (...) genome-level heritabilities employing an American sample of 316 monozygotic (MZ) and 274 dizygotic (DZ) twin dyads and a Swedish sample of 863 MZ and 475 DZ twin dyads. This novel heritability index measures individual genetic transmissibility, therefore opening new avenues for analyzing complex interactions among heritable traits inaccessible to standard structural equations methods. For these samples: (1) moderate to high heritability of factor loadings of Super-K on its lower-order factors is demonstrated, evidencing biological preparedness, genetic accommodation, and the gene-culture coevolution of biased epigenetic rules of development; (2) moderate to high heritability of the magnitudes of the effect of the higher-order factors upon their loadings on their constituent factors, evidencing genetic constraints upon phenotypic plasticity; and (3) that heritability of the LH factors, of factor loadings, and of the magnitudes of the correlations among factors are weaker among those with slower LH speeds, demonstrating that inter-individual variation in transmissibility is a function of individual socioecological selection pressures. (shrink)

Many writers suggest that managed care had a brief life and that we are now in a post-managed care era. Yet managed care has had a long history and continues to thrive. Writers also often assume that managed care is a fixed entity, or focus on its tools, rather than the context in which it operates and the functions it performs. They overlook that managed care has evolved and neglect to examine the role that it plays in the health (...) system.This article argues that private actors and the state have used managed care tools to promote diverse goals. These include the following: increasing access to medical care; restricting physician entrepreneurialism; challenging professional control over the medical economy; curbing medical spending; managing medical practice and markets; furthering the growth of medical markets and private insurance; promoting for-profit medical facilities and insurers; earning bounties for reducing medical expenditures; and reducing governmental responsibility for, and oversight of, medical care. Struggles over these competing goals spurred the metamorphosis of managed care internationally. (shrink)

A closely reasoned, although overly long study of the somewhat less than revolutionary contributions of Moore, Stevenson, Toulmin, and Hare to meta-ethical theorizing. The final chapter moves beyond commentary to a balanced analysis of the problems of analyzing moral language. Kerner argues, following Austin, that the bifurcation of moral language into description and evaluation is crude and misleading. Rather, moral judgments differ from descriptive utterances because of their characteristic "performative force," their use or function. Hence moral philosophy properly does (...) not offer pseudo-descriptive definitions, but rather explores in an empirical way the criteria of application and the performatory forces of moral utterances. However, Kerner recognizes that the relevant criteria of application, as well as the specification of the performative forces, are fixed only by our decisions, which in turn can be supported only by arguments which attempt to establish the competence of the person making such decisions. In other terms, Kerner argues that since moral principles are neither descriptions of a nonnatural world of values nor empirical generalizations, they must be treated as enunciations by a legislator. Unfortunately, as Kerner points out, the concept of being well qualified as a moral legislator lacks clear-cut applicability if developed outside a particular moral system.--S. A. S. (shrink)

In Aczel [1], the existence of largest fixed points of set continuous operators is proved assuming the schema version of dependent choices in Zermelo-Fraenkel set theory without the axiom of Foundation. In the present paper, we study whether the existence of largest fixed points of set continuous operators is provable without the schema version of dependent choices, using Boffa's weak antifoundation axioms.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Unmodern Philosophy and Modern Philosophy by John DeweyCharles A. HobbsJohn Dewey. Unmodern Philosophy and Modern Philosophy. Carbondale and Edwardsville: Southern Illinois University Press, 2012, 351 pp., index.John Dewey’s latest publication marks a watershed moment for scholarship in American philosophy, and, in addition to Dewey himself, we have editor Phillip Deen to thank for discovering it (among the Dewey papers in Special Collections at Morris Library of Southern Illinois (...) University) and editing it. We see Dewey late in life (early 1940s) engaged mainly in a critique of the modern, ancient, and (fragmentarily) medieval philosophical periods, which Dewey argues, are eras not nearly as distinct as traditional understanding admits. In the Introduction, Deen helpfully explains how we are now bequeathed incomplete but in most [End Page 122] cases quite robust chapter drafts that amount to another substantial work by Dewey. While published by Southern Illinois University Press, this volume is not itself part of The Collected Works of John Dewey. Still, the careful editing (of what are actually a number of manuscripts) is comparable in its excellence. There is also a well-done Index.The scope is twofold: retrospective and prospective. Chapters one through seven trace the development of so-called modern philosophy along with its central epistemological problem, with the aim being to demonstrate how thoroughly “unmodern” such philosophy has been. Then, chapters eight through fourteen constitute a genuinely modern approach that naturalistically and functionally undercuts the epistemic problem of subject/object and points to a revolution in the process of knowing.We turn to the retrospective, beginning in the first chapter with the acknowledgement that Dewey comes to philosophy itself as a kind of anthropologist, something we note as consistent with the influence of Franz Boas on Dewey (with whom Dewey was a colleague and intellectual ally at Columbia for about thirty-five years). This is further underscored by a lengthy quotation of anthropologist Bronislaw Malinowski on the meaning of culture (p. 290). The ongoing history of philosophy is itself a cultural activity. Indeed, citing James, Dewey declares that “The sickliest way in which a student of philosophy can approach his subject-matter is that of a search for ultimate impersonal revelation of truth.” (p. 16) Rather, let the philosopher have the pragmatic attitude of openness “... to truth from whatever source it comes” (ibid).With that, Dewey once again turns to the Greeks, who initiated “The Discovery of Rational Discourse” (Ch. III) as underscored by the Socratic means of cooperative discourse, with the dialogues—not lectures—being evidence of the Athenian philosophical revolution in turning “from discussing nature and giving an account of it to the examination of the nature and procedure of discussion and report” (p. 38). Yet this project, despite its initial promise, failed for lack of a genuine logic of experimentation or inquiry. Then philosophy focused on going beyond the natural, beginning with the medieval “Search for Salvation” (Ch. IV, a significantly less developed and unified chapter draft). “Modern” philosophers then rightly replaced grand cosmic schemes with a focus on human nature (Ch. V), but they went too far with their introspective methods, gradually resulting in the same consequence supernaturalism had produced: a dualism of mind and nature, as if human nature is somehow not a part of nature. As we recall from Human Nature and Conduct (1922), human nature is not independent of but rather interdependent (or, using Dewey’s later term, transactional) with the rest of nature. The key is to avoid hypostatizing mind and better to talk of culture as nature. [End Page 123]With the Renaissance onward, humans have been “Wandering between Two Worlds” (Ch. VI), and endless arguments between “rationalists” and “empiricists” overlook what these camps share, namely a psychology assuming a fundamental split between subjective/objective and assumptions about certainty as founded upon various first principles or substances. The result is the stagnation of philosophy while science flourishes. Dewey cites Bertrand Russell as an example of continued insistence on such a priori principles (p. 106).We find ourselves in an epoch split between scientism and moral and religious fundamentalism, the result of a lingering tenacious investment in bad elements from ancient and medieval... (shrink)

The realist belief in the primacy of the world and its underlying structure answers the question ‘why is there something rather than nothing.’ The world, and all things contained in it exists because of God’s creative act. Personal death in Christian philosophy continues the gift of human existence by shifting that temporal existence into eternal life. The death and resurrection of Christ lays the foundation for the possibility of eternal life, while the will of God provides an answer to the (...) why of human existence. The aim of this paper is to examine the effects of the death and resurrection of Christ on the metaphysical strings of human existence. The phenomenon of human death takes place on the arms of consciousness and being’s unconcealment. The subjective correlate of human death is the irreversible loss of consciousness, while the objective correlate of human death presents as the infolding of the gift of existence, namely, of being’s unconcealment from consciousness. These correlates function as a dynamic unit to explain human death and resurrection. The attempt to justify a belief in the existence of life after death from the point of view of consciousness alone is dualistic and leads to several absurdities and confusions about the nature of the afterlife state. The explanation of the resurrection of Christ as a continuation of the dialogue between being and consciousness begun on earth avoids those absurdities while maintaining personal identity. (shrink)

Constructivist research in Science and Technology Studies is committed to revealing the heterogeneity of technological change and the fluid boundaries between the elements involved. Its major theories, the Social Construction of Technology and Actor Network Theory, have however both been criticized for limiting themselves to the micro-level of cases, impeding a structural analysis of technological systems. This article seeks to bridge any such divides. We research the recent changes in the viticulture of Mendoza, Argentina, which underwent radical changes over the (...) past decades: once governed by low-cost yield maximization, grape production now revolves around “quality.” To show how the particular quality definition developed, we depart from a social-constructivist framework, following the sociotechnical shaping of problem-solution relationships across the wine production system. To include relevant social groups from different settings around the world, we gradually incorporate the ANT concepts of obligatory passage points, enrollment, convergence, delegation, and codes into the analysis. Combined into the concept of “sociotechnical alliance,” our analysis follows the dual process of creating agreement while establishing heterogeneous practices across settings at different levels. It shows that functioning involves alliance building and highlights the hybridity and continuous dynamics of systems at large. (shrink)

An article by T. Rockmore, published in the journal “Epistemology and Philosophy of Science” in 2009 (Vol. XXII. No. 4, pp. 14‒29), claim that naturalism is by its nature an example of anti-Kantianism, for it treats philosophy as a continuation science and recognizes science as a legitimate source of knowledge, does not allow a priori, relies on an a posteriori approach, empiricism in the pre-Kantian sense, and insists on the possibility of revising the knowledge acquired. This article has a goal (...) to show that T. Rockmore point of view should be revised due to the progress of modern cognitive research and, first of all, neuroscience, in which all the features of the naturalistic approach are implemented and in which the “Kantian program” of brain research is developed. In the context of this program, the existence on the ontological level (i.e., in the brain) of certain neural structures that make it possible and play a crucial role in the cognitive activity of a person is recognized. Those concepts that Kant treated as components of cognitive activity in modern neuroscience acquired ontological status in the form of the activity of certain neural structures, which turn out to be prerequisites and components of this activity. We claim that in the context of the Kantian research program in neuroscience, the metaphor “Kantian brain” naturally entered the vocabulary of neuroscientists, and certain specific operations and functions of the brain began to be associated with individual elements of Kant's ideas. It is in this context attempts are made to comprehend the mechanisms of the brain in the “stimulus – activity” mode, when an external effect leads to the excitation of certain neural structures. The brain is capable to anticipate the long-term results of certain actions of the subject. In the case of foresight, the brain generates “internal” models and uses for their correction external data that constantly provided from reality across the subject. At the same time, some kind of self-correcting mechanisms implements, which from a formal point of view described by the Bayes theorem, using a priori evaluations of upcoming events and changes in these evaluations as result of experience. Thus, naturalism and Kantianism understood in the context of the progress of modern science, despite T. Rockmore idea, are completely compatible. (shrink)

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise (...) algorithmic computation and to offer foundations for scientific computing. The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal. (shrink)

A. H. Louie's More Than Life Itself is an exploratory journey in relational biology, a study of life in terms of the organization of entailment relations in living systems. This book represents a synergy of the mathematical theories of categories, lattices, and modelling, and the result is a synthetic biology that provides a characterization of life. Biology extends physics. Life is not a specialization of mechanism, but an expansive generalization of it. Organisms and machines share some common features, but organisms (...) are not machines. Life is defined by a relational closure that places it beyond the reach of physicochemical and mechanistic dogma, outside the reductionistic universe, and into the realm of impredicativity. Function dictates structure. Complexity brings forth living beings. (shrink)

By an unfounded chain for a function f:X→X we mean a sequence nω of elements of X s.t. fxn+1=xn for every n. Unfounded chains can be regarded as a generalization of fixed points, but on the other hand are linked with concepts concerning non-well-founded situations, as ungrounded sentences and the hypergame. In this paper, among other things, we prove a lemma in general topology, we exhibit an extensional recursive function from the set of sentences of PA into (...) itself without an unfounded chain, and we prove that every term in a Magari algebra has an unfounded chain. (shrink)

Purpose. The paper considers the fear of social alienation of love. It is within the limits of psychoanalytic epistemology, the analysis of which will be presented in the article, the tendencies to monotony and universal solutions with an emphasis on ensuring the objectivity of the problem of gender alienation, to be more exact, the fear of love, which causes the gender process, are viewed most reliably. In view of the above the purpose of the paper is to investigate the conceptual (...) contradictions associated with the reconstruction of basic measurements of the fear of alienation of love within different ideological approaches; to reveal the most significant contradictions that manifest themselves in the differences between secular and religious frames; to determine a philosophical and fundamental foundation for the types of fear: metaphysical, transcendental and social, which to some extent have influenced the development of a gender tradition. The paper investigates the fear of alienation of love, not as an instinct or psychological experience, or as a social factor, but as a correlation between the functional types of fear and the peculiarities of social and cultural processes, and it acts as a dependence of the European societies on the various functional forms of fear of love that influence the processes of social transformations. Theoretical basis. The authors determine that in the gender approach the subject, who is cognized, has specific desires and interests. The process of cognation is local, contextual, in which physiologically and spiritually the fear of alienation of love is closely linked to the conditions of existence of people, with the arrangement of social and individual life. In modern civilization, true love with some exceptions, is fleeting. It is now hindered by the burdens of life, and ideological settings, which go only from the "I", and not from the common "I and You", contributing to frustration and alienation. Originality. The emphasis is placed on the fact that the fear of alienation of love, as a way of identifying the essential characteristics of "I", acts as an existential, which concentrates on the sense-life range of problems. The range of problem in a single topic is in the "point I", surrounded by gender boundaries, it contains as a condition for its manifestation the personality distancing – free or forced consolidation and assertion of the autonomy of the individual. Alienation of love as an existential admits in the register of the intimate, intentional for self-perception, internal state to organize and identify with the "authentic I". Conclusions. The article establishes that gender identity under the conditions of modern socio-psychological crisis is associated with forming a special "picture of fear, anxiety, loneliness" as a part of that internal and external world, generated by alienation from society. The fear of alienated love acts as the essential existential of human being, which is a necessary existential condition of the existential tension that occurs as an antipode and a characteristic of courage, asceticism, and the "beginning of wisdom". The considered phenomenon of the fear of alienation of love is interpreted as the result of the ontological and gender alienation of a person who has lost a sense of security and plunged into a continuous interindividual rivalry. (shrink)

We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract computational content from proofs about abstract structures specified by arbitrary classically true disjunction free formulas. The interpretation is shown to be sound with respect to a domain-theoretic denotational semantics and a corresponding lazy operational semantics of a functional language for extracted programs. We also (...) show how extracted programs can be translated into Haskell. As an application we extract a program converting the signed digit representation of real numbers to infinite Gray code from a proof of inclusion of the corresponding coinductive predicates. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Rhetoric, Hermeneutics, and Translation in the Middle AgesMichael CalabreseRhetoric, Hermeneutics, and Translation in the Middle Ages, by Rita Copeland; xiv & 295 pp. Cambridge: Cambridge University Press, 1991, $64.95 cloth, $22.95 paper.In this deeply learned book, Rita Copeland studies the history of rhetoric and grammar and their shifting roles in the history of translation, commentary, and interpretation from classical antiquity through the Middle Ages. Copeland examines the ideological (...) nexus of history, authority, and power in which commentary and vernacular translation function. “Vernacular writing,” she says, can “authorize itself by taking over the function of academic discourse” (p. 8). Her book then traces the history of this “authorization” and this “dis-placement” of Latin sources by the increasingly academically privileged vernacular. All in all, Copeland tells the story of how medieval literary culture articulated its translatio studii by confronting and preserving its Classical inheritance and also developing a role for the vernacular as an active, creative agent in the production of authoritative works. [End Page 413]Ultimately “rhetoric” is the star of Copeland’s book, and in essence she is telling its Roman and medieval life stories. By “rhetoric” we are to understand critical academic language that points toward ethics and practical action. Throughout the Middle Ages every modification or appropriation of critical tools expands the role of commentary and adds new forms of interpretive invention to the translation process. As Copeland puts it, “The medieval practice of translation as a form of appropriation and substitution will be conditioned, as in Roman contexts, by rhetorical theories of invention” (p. 36).The hermeneutical costar is grammar, for as part of the complex appropriation of classical practice, medieval readers recoup the “debased” Roman category of grammar, so that by the time of Martianus Capella it can “claim for itself the whole compass of literary activity” (p. 56). As grammar expands its power, so does rhetoric, a civic Roman art which gets “revalued in terms of service to theology” (p. 59). Medieval commentary now “assumes the character of rhetorical performance” (p. 86) and takes on a “primary productive character,” as it “continually refashions the [studied] text for changing conditions of understanding” (p. 64). What is emerging from all these developments is a medieval translation theory—and practice—which is informed by both academic and practical, ethical goals, that is, a hermeneutics forged by the link of grammar and rhetoric.The rest of the book studies the shifting status and the evolving role of the vernacular in this medieval hermeneutical drama. Copeland addresses the Ovide moralisé and the French translations of the Consolatio, and then Chaucer’s Legend of Good Women and Gower’s Confessio Amantis. We witness here how vernacular products take on authority by “inventing themselves” through authoritative discourse. In Gower’s Confessio we see the fusion of hermeneutics and rhetoric; the poem uses academic modes of discourse in the service of ethics or action. We thus see that by the late Middle Ages vernacular literature plays an authoritative role in the medieval translatio studii, as Gower seeks to “open the institution of learning to the widest possible audience and thereby empower it as a persuasive tool, leading to knowledge of the good” (p. 220). Overall, Copeland has told the story of the “leveling” of academic and vernacular discourse, so that the later, while not dispelling or overthrowing the former, can claim access to its traditional authority.Copeland’s prose is Latinate, at times pedantic and, at times, just plain Latin; reading the book can be a wearing experience. But it is all part of a history she knows in remarkable detail, a history that lies behind many assumptions we have about medieval ethical poetics. To have presented this history is a major scholarly feat. Copeland allows us to see medieval authors as both products and producers of methods of appropriation, imitation, conquest, and preservation—all strategies for “translating” the past and creating a present that can leave its intellectual mark on the future. One might now want to employ Copeland’s history of classical and medieval hermeneutics as a tool for [End Page 414] examining our own, contemporary academic rhetorics and for analyzing the “state of... (shrink)

We prove a completeness criterion for quasi-reducibility and generalize it to higher levels of the arithmetical hierarchy. As an application of the criterion we obtain Q-completeness of the set of all pairs such that the prefix-free Kolmogorov complexity of x is less than n.

This manuscript investigates fixed point of single-valued Hardy-Roger’s type F -contraction globally as well as locally in a convex b -metric space. The paper, using generalized Mann’s iteration, iterates fixed point of the abovementioned contraction; however, the third axiom of the F -contraction is removed, and thus the mapping F is relaxed. An important approach used in the article is, though a subset closed ball of a complete convex b -metric space is not necessarily complete, the (...) convergence of the Cauchy sequence is confirmed in the subset closed ball. The results further lead us to some important corollaries, and examples are produced in support of our main theorems. The paper most importantly presents application of our results in finding solution to the integral equations. (shrink)