THE LOGICAL SYSTEM OF FREGE'S GRUNDGESTZE: A RATIONAL RECONSTRUCTION

This paper aims at clarifying the nature of Frege's system of logic, as presented in the first volume of the Grundgesetze . We undertake a rational reconstruction of this system, by distinguishing its propositional and predicate fragments. This allows us to emphasise the differences and similarities between this system and a modern system of classical second-order logic.

Determination of slurry’s viscosity using case based reasoning approach

Case-based reasoning (CBR) is a recent approach to problem solving and learning that has got a lot of attention over the last years. In this work, the CBR methodology is used to reduce the time and amount of resources spent on carry out experiments to determine the viscosity of the new slurry. The aim of this work is: to develop a CBR system to support the decision making process about the type of slurries behavior, to collect a sufficient volume of qualitative data for case base, and to calculate the viscosity of the Newtonian slurries. Firstly in this paper, the literature review about the types of fluid flow, Newtonian and non-Newtonian slurries is presented. Some physical properties of the suspensions are also considered. The second part of the literature review provides an overview of the case-based reasoning field. Different models and stages of CBR cycles, benefits and disadvantages of this methodology are considered subsequently. Brief review of the CBS tools is also given in this work. Finally, some results of work and opportunities for system modernization are presented. To develop a decision support system for slurry viscosity determination, software application MS Office Excel was used. Designed system consists of three parts: workspace, the case base, and section for calculating the viscosity of Newtonian slurries. First and second sections are supposed to work with Newtonian and Bingham fluids. In the last section, apparent viscosity can be calculated for Newtonian slurries.

Application of fuzzy logic for the evaluation of livestock slaughtering

The fuzzy logic admits infinite intermediate logical values between false and true. With this principle, it developed in this study a system based on fuzzy rules, which indicates the body mass index of ruminant animals in order to obtain the best time to slaughter. The controller developed has as input the variables weight and height, and as output a new body mass index, called Fuzzy Body Mass Index (Fuzzy BMI), which may serve as a detection system at the time of livestock slaughtering, comparing one another by the linguistic variables "Very Low", "Low", "Average ", "High" and "Very High". For demonstrating the use application of this fuzzy system, an analysis was made with 147 Nellore beeves to determine Fuzzy BMI values for each animal and indicate the location of body mass of any herd. The performance validation of the system was based on a statistical analysis using the Pearson correlation coefficient of 0.923, representing a high positive correlation, indicating that the proposed method is appropriate. Thus, this method allows the evaluation of the herd comparing each animal within the group, thus providing a quantitative method of farmer decision. It was concluded that this study established a computational method based on fuzzy logic that mimics part of human reasoning and interprets the body mass index of any bovine species and in any region of the country.

Moral reasoning and ethics in educational leadership /

School leaders face difficult decisions regarding discipline matters. Often, such decisions play an important role in determining the moral tone of the school and the health of the school community. Many stakeholders are affected by the outcome of such decisions. Codes of conduct, board and school policies, and discipline meetings are often shrouded under secrecy, making the discipline process mysterious. .; In this study I examined the process of moral reasoning. I sought to determine the extent to which school leaders were aware that they were involved in a process of moral reasoning, and ftirthermore, what kind of moral reasoning they practiced. As well, I investigated the ethical grounds and foundations underlying moral reasoning. Thus, in this study I probed the awareness of the process of moral reasoning and sought to find the ethical grounding of decision making. This qualitative study featured short field research. The process involved individual interviews with three different participants: school leaders of a public. Catholic, and an independent school. It found that each school leader practiced moral reasoning to varying degrees through the discipline process. It also explored the possible democratization of moral reasoning by linking to concepts such as fairness, due process, public accountability, and greater participation in the administering of discipline. This study has implications for practice, theory, and future research. The examination of school leaders as the primary focus for discipline matters opens the door to future research that could explore differences between the school systems and possibly other parties affected by moral reasoning in discipline cases.

Husserl's approach to transcendental intersubjectivity

It is our intention in the course of the development of this thesis to give an account of how intersubjectivity is "eidetically" constituted by means of the application of the phenomenological reduction to our experience in the context of the thought of Edmund Husserl; contrasted with various representative thinkers in what H. Spiegelberg refers to as "the wider scene" of phenomenology. That is to say, we intend to show those structures of both consciousness and the relation which man has to the world which present themselves as the generic conditions for the possibility of overcoming our "radical sol itude" in order that we may gain access to the mental 1 ife of an Other as other human subject. It is clear that in order for us to give expression to these accounts in a coherent manner, along with their relative merits, it will be necessary to develop the common features of any phenomenological theory of consdousness whatever. Therefore, our preliminary inquiry, subordinate to the larger theme, shall be into some of the epistemological results of the application of the phenomenological method used to develop a transcendental theory of consciousness. Inherent in this will be the deliniation of the exigency for making this an lIintentional ll theory. We will then be able to see how itis possible to overcome transcendentally the Other as an object merely given among other merely given objects, and further, how this other is constituted specifically as other ego. The problem of transcendental intersubjectivity and its constitution in experience can be viewed as one of the most compelling, if not the most polemical of issues in phenomenology. To be sure, right from the beginning we are forced to ask a number of questions regarding Husserl's responses to the problem within the context of the methodological genesis of the Cartesian Meditations, and The Crisis of European Sciences and Transcendental Phenomenology. This we do in order to set the stage for amplification. First, we ask, has Husserl lived up to his goal, in this connexion, of an apodictic result? We recall that in his Logos article of 1911 he adminished that previous philosophy does not have at its disposal a merely incomplete and, in particular instances, imperfect doctrinal system; it simply has none whatever. Each and every question is herein controverted, each position is a matter of individual conviction, of the interpretation given byaschool, of a "point of view". 1. Moreover in the same article he writes that his goal is a philosophical system of doctrine that, after the gigantic preparatory work. of generations, really be- . gins from the ground up with a foundation free from doubt and rises up like any skilful construction, wherein stone is set upon store, each as solid as the other, in accord with directive insights. 2. Reflecting upon the fact that he foresaw "preparatory work of generations", we perhaps should not expect that he would claim that his was the last word on the matter of intersubjectivity. Indeed, with 2. 'Edmund Husserl, lIPhilosophy as a Rigorous Science" in Phenomenology and theCrisis6fPhilosophy, trans". with an introduction by Quentin Lauer (New York.: Harper & Row, 1965) pp. 74 .. 5. 2Ibid . pp. 75 .. 6. 3. the relatively small amount of published material by Husserl on the subject we can assume that he himself was not entirely satisfied with his solution. The second question we have is that if the transcendental reduction is to yield the generic and apodictic structures of the relationship of consciousness to its various possible objects, how far can we extend this particular constitutive synthetic function to intersubjectivity where the objects must of necessity always remain delitescent? To be sure, the type of 'object' here to be considered is unlike any other which might appear in the perceptual field. What kind of indubitable evidence will convince us that the characteristic which we label "alter-ego" and which we attribute to an object which appears to resemble another body which we have never, and can never see the whole of (namely, our own bodies), is nothing more than a cleverly contrived automaton? What;s the nature of this peculiar intentional function which enables us to say "you think just as I do"? If phenomenology is to take such great pains to reduce the takenfor- granted, lived, everyday world to an immanent world of pure presentation, we must ask the mode of presentation for transcendent sub .. jectivities. And in the end, we must ask if Husserl's argument is not reducible to a case (however special) of reasoning by analogy, and if so, tf this type of reasoning is not so removed from that from whtch the analogy is made that it would render all transcendental intersubjective understandtng impos'sible? 2. HistoticalandEidetic Priority: The Necessity of Abstraction 4. The problem is not a simple one. What is being sought are the conditions for the poss ibili:ty of experi encing other subjects. More precisely, the question of the possibility of intersubjectivity is the question of the essence of intersubjectivity. What we are seeking is the absolute route from one solitude to another. Inherent in this programme is the ultimate discovery of the meaning of community. That this route needs be lIabstract" requires some explanation. It requires little explanation that we agree with Husserl in the aim of fixing the goal of philosophy on apodictic, unquestionable results. This means that we seek a philosophical approach which is, though, not necessarily free from assumptions, one which examines and makes explicit all assumptions in a thorough manner. It would be helpful at this point to distinguish between lIeidetic ll priority, and JlhistoricallJpriority in order to shed some light on the value, in this context, of an abstraction.3 It is true that intersubjectivity is mundanely an accomplished fact, there havi.ng been so many mi.llions of years for humans to beIt eve in the exi s tence of one another I s abili ty to think as they do. But what we seek is not to study how this proceeded historically, but 3Cf• Maurice Natanson;·TheJburne in 'Self, a Stud in Philoso h and Social Role (Santa Cruz, U. of California Press, 1970 . rather the logical, nay, "psychological" conditions under which this is possible at all. It is therefore irrelevant to the exigesis of this monograph whether or not anyone should shrug his shoulders and mumble IIwhy worry about it, it is always already engaged". By way of an explanation of the value of logical priority, we can find an analogy in the case of language. Certainly the language 5. in a spoken or written form predates the formulation of the appropriate grammar. However, this grammar has a logical priority insofar as it lays out the conditions from which that language exhibits coherence. The act of formulating the grammar is a case of abstraction. The abstraction towards the discovery of the conditions for the poss; bi 1 ity of any experiencing whatever, for which intersubjective experience is a definite case, manifests itself as a sort of "grammar". This "grammar" is like the basic grammar of a language in the sense that these "rulesil are the ~ priori conditions for the possibility of that experience. There is, we shall say, an "eidetic priority", or a generic condition which is the logical antecedent to the taken-forgranted object of experience. In the case of intersubjectivity we readily grant that one may mundanely be aware of fellow-men as fellowmen, but in order to discover how that awareness is possible it is necessary to abstract from the mundane, believed-in experience. This process of abstraction is the paramount issue; the first step, in the search for an apodictic basis for social relations. How then is this abstraction to be accomplished? What is the nature of an abstraction which would permit us an Archimedean point, absolutely grounded, from which we may proceed? The answer can be discovered in an examination of Descartes in the light of Husserl's criticism. 3. The Impulse for Scientific Philosophy. The Method to which it Gives Rise. 6. Foremost in our inquiry is the discovery of a method appropriate to the discovery of our grounding point. For the purposes of our investigations, i.e., that of attempting to give a phenomenological view of the problem of intersubjectivity, it would appear to be of cardinal importance to trace the attempt of philosophy predating Husserl, particularly in the philosophy of Descartes, at founding a truly IIscientific ll philosophy. Paramount in this connexion would be the impulse in the Modern period, as the result of more or less recent discoveries in the natural sciences, to found philosophy upon scientific and mathematical principles. This impulse was intended to culminate in an all-encompassing knowledge which might extend to every realm of possible thought, viz., the universal science ot IIMathexis Universalis ll •4 This was a central issue for Descartes, whose conception of a universal science would include all the possible sciences of man. This inclination towards a science upon which all other sciences might be based waS not to be belittled by Husserl, who would appropriate 4This term, according to Jacab Klein, was first used by Barocius, the translator of Proclus into Latin, to designate the highest mathematical discipline. . 7. it himself in hopes of establishing, for the very first time, philosophy as a "rigorous science". It bears emphasizing that this in fact was the drive for the hardening of the foundations of philosophy, the link between the philosophical projects of Husserl and those of the philosophers of the modern period. Indeed, Husserl owes Descartes quite a debt for indicating the starting place from which to attempt a radical, presupositionless, and therefore scientific philosophy, in order not to begin philosophy anew, but rather for the first time.5 The aim of philosophy for Husserl is the search for apodictic, radical certitude. However while he attempted to locate in experience the type of necessity which is found in mathematics, he wished this necessity to be a function of our life in the world, as opposed to the definition and postulation of an axiomatic method as might be found in the unexpurgated attempts to found philosophy in Descartes. Beyond the necessity which is involved in experiencing the world, Husserl was searching for the certainty of roots, of the conditi'ons which underl ie experience and render it pOssible. Descartes believed that hi~ MeditatiOns had uncovered an absolute ground for knowledge, one founded upon the ineluctable givenness of thinking which is present even when one doubts thinking. Husserl, in acknowledging this procedure is certainly Cartesian, but moves, despite this debt to Descartes, far beyond Cartesian philosophy i.n his phenomenology (and in many respects, closer to home). 5Cf. Husserl, Philosophy as a Rigorous Science, pp. 74ff. 8 But wherein lies this Cartesian jumping off point by which we may vivify our theme? Descartes, through inner reflection, saw that all of his convictions and beliefs about the world were coloured in one way or another by prejudice: ... at the end I feel constrained to reply that there is nothing in a all that I formerly believed to be true, of which I cannot in some measure doubt, and that not merely through want of thought or through levity, but for reasons which are very powerful and maturely considered; so that henceforth I ought not the less carefully to refrain from giving credence to these opinions than to that which is manifestly false, if I desire to arrive at any certainty (in the sciences). 6 Doubts arise regardless of the nature of belief - one can never completely believe what one believes. Therefore, in order to establish absolutely grounded knowledge, which may serve as the basis fora "universal Science", one must use a method by which one may purge oneself of all doubts and thereby gain some radically indubitable insight into knowledge. Such a method, gescartes found, was that, as indicated above by hi,s own words, of II radical doubt" which "forbids in advance any judgemental use of (previous convictions and) which forbids taking any position with regard to their val idi'ty. ,,7 This is the method of the "sceptical epoche ll , the method of doubting all which had heretofor 6Descartes,Meditations on First Philosophy, first Med., (Libera 1 Arts Press, New York, 1954) trans. by L. LaFl eur. pp. 10. 7Husserl ,CrisiS of Eliroeari SCiences and Trariscendental Phenomenology, (Northwestern U. Press, Evanston, 1 7 ,p. 76. 9. been considered as belonging to the world, including the world itself. What then is left over? Via the process of a thorough and all-inclusive doubting, Descartes discovers that the ego which performs the epoche, or "reduction", is excluded from these things which can be doubted, and, in principle provides something which is beyond doubt. Consequently this ego provides an absolute and apodictic starting point for founding scientific philosophy. By way of this abstention. of bel ief, Desca'rtes managed to reduce the worl d of everyday 1 ife as bel ieved in, to mere 'phenomena', components of the rescogitans:. Thus:, having discovered his Archimedean point, the existence of the ego without question, he proceeds to deduce the 'rest' of the world with the aid of innate ideas and the veracity of God. In both Husserl and Descartes the compelling problem is that of establ ishing a scientific, apodictic phi'losophy based upon presuppos itionless groundwork .. Husserl, in thi.s regard, levels the charge at Descartes that the engagement of his method was not complete, such that hi.S: starting place was not indeed presupositionless, and that the validity of both causality and deductive methods were not called into question i.'n the performance of theepoche. In this way it is easy for an absolute evidence to make sure of the ego as: a first, "absolute, indubitablyexisting tag~end of the worldll , and it is then only a matter of inferring the absolute subs.tance and the other substances which belon.g to the world, along with my own mental substance, using a logically val i d deductive procedure. 8 8Husserl, E.;' Cartesian 'Meditation;, trans. Dorion Cairns (Martinus Nijhoff, The Hague, 1970), p. 24 ff.

Beyond g : putting multiple intelligences theory to the test /

The purpose of this study was to investigate Howard Gardner's (1983) Multiple Intelligences theory, which proposes that there are eight independent intelligences: Linguistic, Spatial, Logical/Mathematical, Interpersonal, Intrapersonal, Naturalistic, Bodily-Kinesthetic, and Musical. To explore Gardner's theory, two measures of each ability area were administered to 200 participants. Each participant also completed a measure of general cognitive ability, a personality inventory, an ability self-rating scale, and an ability self-report questionnaire. Nonverbal measures were included for most intelligence domains, and a wide range of content was sampled in Gardner's domains. Results showed that all tests of purely cognitive abilities were significantly correlated with the measure of general cognitive ability, whereas Musical, Bodily-Kinesthetic, and one of the Intrapersonal measures were not. Contrary to what Multiple Intelligences theory would seem to predict, correlations among the tests revealed a positive manifold and factor analysis indicated a large factor of general intelligence, with a mathematical reasoning test and a classification task from the Naturalistic domain having the highest ^- loadings. There were only minor sex differences in performance on the ability tests. Participants' self-estimates of ability were significantly and positively correlated with actual performance in some, but not all, intelligences. With regard to personality, a hypothesized association between Openness to Experience and crystallized intelligence was supported. The implications of the findings in regards to the nature of mental abilities were discussed, and recommendations for further research were made.

Violent Video Game Playing, Moral Reasoning, and Attitudes Towards Violence in Adolescents: Is There a Connection?

In this study of 109 adolescents from the eighth grade of seven public elementary schools in Ontario, the relationship among adolescents’ violent video game playing patterns, habits and attitudes, their levels of moral reasoning, and their attitudes towards violence in real life was investigated. In addition, gender differences were addressed. The mixed-methodology was employed combining qualitative and quantitative data. The research results confirmed that playing video games in general is a very popular activity among those adolescents. Significant negative relationship was found between adolescents’ amount of time playing violent video games during the day and their scores on The Sociomoral Reflection Measure. Significant difference was also found between adolescents who play violent video games and those who do not play violent video games on their scores on The Attitudes Towards Violence Scale. Boys and girls significantly differed in the amount of playing video games during the day, the reasons for playing video games, their favourite video game choices, and their favourite video game character choices. Boys and girls also significantly differed on their choices of personality traits of selected video game characters, the identification with video game characters, and their mood experiences while playing video games. The findings are put into the educational context and the context of normal development, and suggestions are given for parents, for educators, and for future violent video game research.

Equational Reasoning about Object-Oriented Programs

Formal verification of software can be an enormous task. This fact brought some software engineers to claim that formal verification is not feasible in practice. One possible method of supporting the verification process is a programming language that provides powerful abstraction mechanisms combined with intensive reuse of code. In this thesis we present a strongly typed functional object-oriented programming language. This language features type operators of arbitrary kind corresponding to so-called type protocols. Sub classing and inheritance is based on higher-order matching, i.e., utilizes type protocols as basic tool for reuse of code. We define the operational and axiomatic semantics of this language formally. The latter is the basis of the interactive proof assistant VOOP (Verified Object-Oriented Programs) that allows the user to prove equational properties of programs interactively.

Generating Relation Algebras for Qualitative Spatial Reasoning

Basic relationships between certain regions of space are formulated in natural language in everyday situations. For example, a customer specifies the outline of his future home to the architect by indicating which rooms should be close to each other. Qualitative spatial reasoning as an area of artificial intelligence tries to develop a theory of space based on similar notions. In formal ontology and in ontological computer science, mereotopology is a first-order theory, embodying mereological and topological concepts, of the relations among wholes, parts, parts of parts, and the boundaries between parts. We shall introduce abstract relation algebras and present their structural properties as well as their connection to algebras of binary relations. This will be followed by details of the expressiveness of algebras of relations for region based models. Mereotopology has been the main basis for most region based theories of space. Since its earliest inception many theories have been proposed for mereotopology in artificial intelligence among which Region Connection Calculus is most prominent. The expressiveness of the region connection calculus in relational logic is far greater than its original eight base relations might suggest. In the thesis we formulate ways to automatically generate representable relation algebras using spatial data based on region connection calculus. The generation of new algebras is a two pronged approach involving splitting of existing relations to form new algebras and refinement of such newly generated algebras. We present an implementation of a system for automating aforementioned steps and provide an effective and convenient interface to define new spatial relations and generate representable relational algebras.

An interview with Avigail Eisenberg : “Reasoning about the Identity of Aboriginal People”

Document de travail

Deliberative Democracy and Precautionary Public Reasoning : Exploratory Thoughts

article

Étude de situations de validation en algèbre vécues par des élèves de 13 et 14 ans à l’aide et sans l’aide d’un forum électronique

L’un des buts de l’apprentissage des mathématiques est le développement du raisonnement et celui-ci participe à la compréhension des mathématiques. Très liée au raisonnement, la notion de preuve est aussi fondamentale à l’apprentissage des mathématiques, car elle permet d’établir la validité d’arguments mathématiques et de conférer un sens à différents concepts à travers l’explication de l’organisation logique du travail effectué. Toutefois, malgré l’importance accordée au développement de différents types de raisonnements, plusieurs élèves éprouvent des difficultés lorsqu’ils sont appelés à concevoir ou à évaluer des preuves. Dans le cadre de cette recherche, nous avons étudié l’impact de l’utilisation d’un forum électronique sur le développement d’habiletés de validation algébrique ainsi que sur le développement d’habiletés en lien avec l’évaluation de preuves en algèbre chez des élèves de 13 et 14 ans du Nouveau-Brunswick et du Québec. Les résultats laissent supposer que l’utilisation du forum électronique encourage le passage des preuves pragmatiques aux preuves intellectuelles, en plus de favoriser une utilisation adéquate des règles du débat mathématique.