John Corcoran. 1979 Review of Hintikka and Remes. The Method of Analysis (Reidel, 1974). Mathematical Reviews 58 3202 #21388. -/- The “method of analysis” is a technique used by ancient Greek mathematicians (and perhaps by Descartes, Newton, and others) in connection with discovery of proofs of difficult theorems and in connection with discovery of constructions of elusive geometric figures. Although this method was originally applied in geometry, its later application to number played an important role in the early (...) development of algebra [Jacob Klein, English translation, Greek mathematical thought and the origin of algebra, especially pp. 154–157, M.I.T. Press, Cambridge, Mass., 1968]. -/- It is universally agreed that the method of analysis begins by “assuming the thing sought after” (e.g., in geometry, the truth of the proposition to be proved or the existence of the geometric figure to be constructed). Aside from this, little else can be taken for granted. There is disagreement concerning the “direction of analysis”, i.e. whether one is to seek implications of the assumption or whether one is to seek implicants of it. There is also disagreement concerning what is to be “anatomized” (analyzed), i.e., whether one analyzes mathematical objects (figures), mathematical propositions (the axioms, known theorems, and analytic assumption) or an imagined proof (of the analytic assumption from axioms and known theorems). (shrink)

FROM THE HISTORY OF PHYSICS TO THE DISCOVERY OF THE FOUNDATIONS OF PHYSICS By Antonino Drago, formerly at Naples University “Federico II”, Italy – drago@unina,.it (Size : 391.800 bytes 75,400 words) The book summarizes a half a century author’s work on the foundations of physics. For the forst time is established a level of discourse on theoretical physics which at the same time is philosophical in nature (kinds of infinity, kinds of organization) and formal (kinds of mathematics, kinds of (...) logic). This double side of the two dichotomies assures a deep comprehension of theoretical physics by avoiding both a purely philosophical analysis and a purely formal analysis, each manifestly insufficient for representing all the aspects of theoretical physics. Among the many formulations of a physical theory, e.g. Mechanics, also Mach(1) recognized technical differences only, Instead my suggestion is to consider their differences as revealing the characteristic features of their foundations. No more radical differences may exist than those concerning both their kinds of Mathematics and their kinds of Logic. As a fact, after the 20th Century within each of these sciences there exist two antagonist foundations, within Mathematics either the classical one or the constructive one(2); within Mathematical Logic either the classical logic or the intuitionist one(3). Let us take Mechanics as an instance. Being the choices of the Newton’s formulation respectively the actual infinity of the differential equations relying on the infinitesimals and the classical logic, a formulation based on the alternative choices is Lazare Carnot’s,(4) whose mathematics is no more than algebraic-trigonometric and the logic is the intuitionist one, because this formulation makes use of doubly negated propositions, whose corresponding affirmative propositions are idealistic or false; i.e. in these cases the law of double negation fails, as in intuitionist logic occurs. By considering these two dichotomies as the foundations of the physical theories, each couple of choices upon them fashions one out four models of scientific theory, which are baptized through the authors of their most representative theories: Newtonian, Carnotian, Lagrangian, Descartesian. In correspondence four versions of the principle of inertia are recognized, as suggested by respectively: Descartes. Lazare Carnot, Enriques and Cavalieri.(5) All that suggests that the four models of scientific theory may be graphically represented as a compass orientating our minds amid the so numerous physical theories. By taking these dichotomies as interpretative categories, a new interpretative history of Physics including both classical and modern physics results according to a quadrilinear development. The birth of modern physics is characterized by the two theories - Einstein’s paper on special relativity and Einstein’s first paper on quanta - whose choices are the alternative ones to those of the previously dominant physical theory, Newtonian mechanics: in the latter paper Einstein i) declares the dichotomy on the kinds of mathematics (“Introduction”) and then he chooses the discrete mathematics; ii) by using doubly negated propositions he organizes his theory in an alternative way to the deductive-axiomatic one.(6) Moreover, a new history of Philosophy of knowledge results. Kant’s first two a priori transcendental categories represent the physical interpretation of the two choices out of the four pairs of choices on the two dichotomies, i.e. the choices of the dominant theory of mechanics, Newton’s. Hegel’s dialectic was a misleading attempt of anticipating the subsequent intuitionist logic. The book starts by a comparison of different formulations of thermodynamics in order to recognize the first dichotomy on the kind of organization. In chapter 2 the dichotomy on the kind of infinity is recognized through a comparison of Newrton’s mechanics and Lazare Carnot’s. A quickly history of the other classical physical theories is illustrated in chapter 3; it results a foundational conflict between the last two theories, and hence a conflict between their opposite couples of choices. The two main theories of modern physics, special realtivity and quantum mechanics confirm the foundational role played by the two dichotomies which gives reason for the radical change in the history of theoretical physics. Indeed, the opposition of the two main pairs of choices gives reason of the crisis in theoretical physics in the early 1900s. As a global result, the book represents the first interpretation of the entire history of Physics, both classical and modern; This fact proves that the four models of scientific theories can works as a compass (that of the front cover) suggesting a direction among the many physical theories. This new history of physics leads to re-visit both Koyré’s and Kuhn’s historiographies. Their interpretative categories are interpreted and explained through the two dichotomies so that it is possible to suggest à la Koyré categories based on the alternative choices theories to Newton’s as the suitable categories for interpreting the alternative theories to Newton’s mechanics. All that suggests a new interpretation of the crucial step in the history of Western philosophy of knowledge, i.e. the passage from Leibniz to Kant: Leibniz’s suggestion of the two labyrinths of human minds may be seen as a close anticipation of the two above dichotomies. Kant applied them in order to construct the well-known four cosmological proofs, which however he misinterpreted as leading to contradictions, instead to tow different methods of investigation corresponding to the two different kinds of logic.(7) Bibliography 1. Mach E. (1883), Die Mechanik, Leipzig: Brockhaus, Chap. IV, Sect. III. 2. Bishop E. (1967), Constructive Analysis, New York: Mc Graw-Hill. 3. Heyting A. (1962), Intuitionism. An Introduction, Amsterdam: North-Holland. 4. L. Carnot (1783), Essai on the Machines en général, Defay, Dijion (Enlish translation: Springer, Berlin, 2020). Drago A. (2004), “A new appraisal of old formulations of mechanics”, Am. J. Phys., 72(3), pp. 407-9. 5. Vella M.R. (2007), “Le quattro versioni del principio di inerzia”, in M. Leone et al. (eds.), L’eredità di Fermi, Majorana e altri Temi. Napoli: ESI, pp. 147-151. 6. Drago A. (2014), “The emergence of two options from Einstein°s first paper on Quanta”, in Pisano R., Capecchi D., Lukesova A. (eds.), Physics, Astronomy and Engineering. Critical Problems in the History of Science and Society, Scientia Socialis P., Siauliai, 2013, pp. 227-234. 7. This and all in the above points are illustrated by the book Drago A. (2017), Dalla Storia della Fisica ai Fondamenti della Scienza, Roma: Aracne. (shrink)

Mathematical formalism is the the view that numbers are "signs" and that arithmetic is like a game played with such signs. Frege's colleague Thomae defended formalism using an analogy with chess, and Frege's critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue that (...) for Thomae, the formal standpoint is an _algebraic perspective_ on a domain of objects, and a "sign" is not a linguistic expression or mark, but a representation of an object within that perspective. Thomae exploits a shift into this perspective to give a purely algebraic construction of the real numbers from the rational numbers. I suggest that Thomae's chess analogy is intended to provide a model for such shifts in perspective. (shrink)

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, (...) bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, law, medicine, social science, and some more. -/- This book explores the emerging field of Neutrosophic Algebraic Structures, focusing on both their theoretical foundations and practical applications. We apply innovative algorithmic methods to investigate the complex interactions of neutrosophic elements, such as neutrosophic numbers, sets, and functions, within algebraic systems. Our goal is to show how neutrosophic structures challenge and expand traditional algebraic approaches, offering solutions to problems across diverse fields like computer science, engineering, artificial intelligence, and decision-making. (shrink)

The philosophy of mathematics has been accused of paying insufficient attention to mathematical practice: one way to cope with the problem, the one we will follow in this paper on extensive magnitudes, is to combine the `history of ideas' and the `philosophy of models' in a logical and epistemological perspective. The history of ideas allows the reconstruction of the theory of extensive magnitudes as a theory of ordered algebraic structures; the philosophy of models allows an investigation into the (...) way epistemology might affect relevant mathematical notions. The article takes two historical examples as a starting point for the investigation of the role of numerical models in the construction of a system of non-Archimedean magnitudes. A brief exposition of the theories developed by Giuseppe Veronese and by Rodolfo Bettazzi at the end of the 19th century will throw new light on the role played by magnitudes and numbers in the development of the concept of a non-Archimedean order. Different ways of introducing non-Archimedean models will be compared and the influence of epistemological models will be evaluated. Particular attention will be devoted to the comparison between the models that oriented Veronese's and Bettazzi's works and the mathematical theories they developed, but also to the analysis of the way epistemological beliefs affected the concepts of continuity and measurement. (shrink)

This article explores the Foucauldian analysis of the linkage between temporality and politics, addressing mainly two loci of Foucault’s production: the assessment of the post-WWII ordoliberal experience in The Birth of Biopoliticsand the Iran reportage for “Corriere Della Sera”. The article emphasizes the relevance of Foucault’s assessment of ordoliberal Germany for contemporary studies on neoliberalism and inscribes Foucault in a wider tradition of thought on the relevance of history and temporality for the comprehension of political dynamics. In TBoB, (...) Foucault offered a prescient analysis of neoliberal temporality and its de-politicizing effects. In his view, ordoliberal theorists and politicians sought to ground political legitimacy in the economy itself, giving birth to a political-economic “double circuit” which did away with history and made political consensus “permanent” and automatic. The connection between neoliberalism, the re-structuring of state sovereignty, and temporality will be highlighted. Furthermore, by analyzingthe almost-coeval Iranian reportages and the eulogy for Clavel, the article further investigates Fou-cault’s reflection on the link between temporality, politics,and subjectivation processes. If the anal-ysis of ordoliberal temporality in TBoB describes a linkage between de-temporalization and de-politicization, the reportages will be highlighted as a possible “pars construens” –as a way to reinstate the possibility of political action through the appeal to different ways to experience tem-porality. The article concludes that Foucault’s sparse comments on temporality can be read as an attempt, albeit not fully developed, not only to envision the de-politicizing effects of marketization but also to envisage new, re-politicizing modes of experiencing temporality and history. (shrink)

This paper describes a method for the analysis of the evolutionary path of a complex, dynamic, and contingent social phenomenon in an empirical setting. Given empirical evidence of a surprising or anomalous fact, which contradicts the prediction of the wide-acknowledged theory, the goal is to formulate a plausible explanation based on the context of occurrence, taking a holistic and historical point of view. The procedure begins by translating theoretical propositions into grammar rules to describe patterns of either individual action (...) or interaction that may occur within the hypothesized social system. The result is a category of social process in which the objects are types of decision-making events carried by a stable community of actors over time, and the relationships between them are state transitions revealed in the sequences of event outcomes. Therefore, structural comparison between pairs of representative instances result in an extension of the category of social processes, relying on the configurations of contextual conditions that enable the occurrence of the new event outcome in specific empirical settings. (shrink)

Abstract. First-year mathematics education students often face challenges with College and Advanced Algebra assessments. This study aimed to develop and validate a 100-item multiple-choice midterm test for College and Advanced Algebra, ensuring the test's validity and reliability. The test was designed following a structured process that included creating a Table of Specifications (TOS) based on the approved syllabus. To ensure content accuracy and relevance, the test was reviewed by three subject matter experts and evaluated for clarity by 15 (...) students. Pilot testing was conducted with 82 fourth-year Bachelor of Secondary Education Mathematics (BSEd Mathematics) students. The pilot test results underwent detailed item analysis, focusing on metrics such as the difficulty index, discrimination index, and overall reliability using the Kuder-Richardson Formula 20 (KR-20). Of the 100 items, 22 were retained, 48 were revised, and 30 were discarded. The test achieved a reliability coefficient of 0.876, indicating strong internal consistency. The findings suggest that the validated test questionnaire is a dependable tool for accurately assessing students’ knowledge in College and Advanced Algebra, providing valuable feedback for educators and students. (shrink)

If there is an area of discourse in which disagreement is virtually absent, it is mathematics. After all, mathematicians justify their claims with deductive proofs: arguments that entail their conclusions. But is mathematics really exceptional in this respect? Looking at the history and practice of mathematics, we soon realize that it is not. First, deductive arguments must start somewhere. How should we choose the starting points (i.e., the axioms)? Second, mathematicians, like the rest of us, are fallible. Their ability (...) to recognize whether a putative proof is correct is not infallible. In most cases, disagreement over the correctness of a putative proof is, however, evanescent. Once an error is spotted and communicated, the disagreement disappears. But this is not always the case. Sometimes it is recalcitrant; that is, it persists over time. In order to zoom in on this type of disagreement and explain its very possibility, we focus on a single case study: a decades-long (1921-1949) controversy between Federigo Enriques and Francesco Severi, two prominent exponents of the Italian school of algebraic geometry. We suggest that the instability of the mathematical community to which they belonged can be explained by the gap between an abstract criterion of rigor and local criteria of acceptability. It is this instability that made the existence of recalcitrant disagreement over putative proofs possible. We do not condemn speculative mathematics but rather its pretense of being rigorous mathematics. In this respect, we show that the overly self-confident Severi and the more intuitive, visionary Enriques had a completely different attitude. (shrink)

This book places Benjamin’s writing on revolution in the context of his conception of historical knowledge. The fundamental problem that faces any analysis of Benjamin’s approach to revolution is that he deploys notions that belong to the domain of individual experience. His theory of modernity with its emphasis on the disintegration of collective experience further aggravates the problem. Benjamin himself understood the problem of revolution to be primarily that of the conceptualization of collective experience (its possibility and sites) under (...) the conditions of modern bourgeois society. The novelty of his approach to revolution lies in the fact that he directly connects it with historical experience. Benjamin’s conception of revolution thus constitutes an integral part of his distinctive theory of historical knowledge, which is also essentially a theory of experience. Through a detailed study of Benjamin’s writings on the topics of the child and the dream, and an analysis of his ideas of history, the fulfilled wish, similitude and communist society, this book shows how the conceptual analysis of his corpus can get to the heart of Benjamin’s conception of revolutionary experience and distil its difficulties and mechanisms. (shrink)

The logico-algebraic study of Lewis's hierarchy of variably strict conditional logics has been essentially unexplored, hindering our understanding of their mathematical foundations, and the connections with other logical systems. This work aims to fill this gap by providing a comprehensive logico-algebraic analysis of Lewis's logics. We begin by introducing novel finite axiomatizations for varying strengths of Lewis's logics, distinguishing between global and local consequence relations on Lewisian sphere models. We then demonstrate that the global consequence relation is strongly algebraizable (...) in terms of a specific class of Boolean algebras with a binary operator representing the counterfactual implication; in contrast, we show that the local consequence relation is generally not algebraizable, although it can be characterized as the degree-preserving logic over the same algebraic models. Further, we delve into the algebraic semantics of Lewis's logics, developing two dual equivalences with respect to particular topological spaces. In more details, we show a duality with respect to the topological version of Lewis's sphere models, and also with respect to Stone spaces with a selection function; using the latter, we demonstrate the strong completeness of Lewis's logics with respect to sphere models. Finally, we draw some considerations concerning the limit assumption over sphere models. (shrink)

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of (...) K-O comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type. (shrink)

By the middle of the seventeenth century we that find that algebra is able to offer proofs in its own right. That is, by that time algebraic argument had achieved the status of proof. How did this transformation come about?

The passionate and staunch defence of logic of the controversial thinker Ibn Ḥazm, Abū Muḥammad ʿAlī b. Aḥmad b. Saʿīd of Córdoba (384-456/994-1064), had lasting consequences in the Islamic world. Indeed, his book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples (Kitāb al-Taqrīb li-ḥadd al-manṭiq wa-l-mudkhal ilayhi bi-l-alfāẓ al-ʿāmmiyya wa-l-amthila al-fiqhiyya), composed in 1025-1029, was well known and discussed during and after his time; and it paved the way for the studies (...) of his compatriots Ibn Bājjah (d. 1138), Ibn Ṭufayl (1185), and Ibn Rushd (1198), who each gave demonstrative reasoning a privileged place within the methods of attaining knowledge. Unfortunately, as too often in the history of science, Ibn Ḥazm’s innovative perspectives and contributions in logic have been overlooked or considered with an attitude of contempt. On the one hand, his work has been seen, at best, as promulgating the benefits of studying Aristotle’s logic, so that his contribution is assessed as more didactical than conceptual. And on the other hand, those who do examine his innovations often consider them to be mistaken. As indicated by Chejne (1984, p. 2) contempt towards the logical work of Ibn Ḥazm was also present in its reception by the Eastern philosophers who accused him of deviating from Aristotelian logic and of dabbling in things beyond his capability. However, a reassessment of his work on logic has since begun, by delving into the ways the thinker of Córdoba studied the links between deontic and modal qualification of propositions. In this context Lameer’s (2013) paper on the logical sources of Ibn Ḥazm is worth mentioning; the author (p. 417, footnote 1) observes that, although, strictly speaking, it was al-Fārābī who first drew the parallelism between deontic and modal concepts, it was Ibn Ḥazm who developed it and worked it out in a more precise manner. A primary aim of this paper is to help fill some of these gaps by stressing the role of the work of Ibn Ḥazm in developing a notion of deontic necessity deeply rooted in legal normativity, and in explicitly discussing the transference between deontic and modal concepts. According to our view; the basic units of Islamic deontic logic are what we might call, indulging in terminological anachronism, heteronomous imperatives. As it turns out, the heteronomy of imperatives within Islamic legal systems contrasts with those of the purely moral realm, which seem to be closer to an autonomous conception of moral law. There it concurs again with Leibniz’s proposal to define obligatory as “what is necessary for a good person to do”. In the present paper, we will focus on the heteronomous imperatives of legal systems rather than on the imperatives of the purely moral realm. In this context, the work of Ibn Ḥazm extends the parallelism between the necessity of events and that of human actions stressed by his predecessors. According to our understanding, Ibn Ḥazm’s parallelism can be rendered explicit formally by means of a conditional (or hypothetical) structure shared by both deontic and modal propositions. Moreover, this structure makes apparent that this parallelism displays an underlying system of “degrees”. Indeed, while in the domain of events, given some conditions, it makes sense to distinguish between an event that is more likely to happen than another. Ibn Ḥazm speaks of near and distant possibility (such as the higher degree of likelihood of rain, given the condensation of clouds in December, and its lower degree, when the condensation occurs in summer); and, in the domain of actions, the Islamic notion of weighting actions determines degrees of virtue (or of legal and moral value). So whereas the degree of virtue of performing a forbidden act as determined by the distribution of sanction and reward is 0, we obtain the same value by pondering the likelihood of an impossible event to take place. Furthermore, as discussed in section II.3.2, the system of values at work in the parallelism can be seen as opening the way to a more direct correspondence. Thus, while in the realm of nature, likelihood of occurrence of an event is dependent upon the conditions specific to the occurrence of that event; while, in the realm of jurisprudence, likelihood of performing an action is dependent upon the distribution of reward and sanction specific to that action (being that, given the choice to perform or not perform a given action, those that will be rewarded are more likely to be performed than those that are not). According to this perspective, the point of the parallelism is that both deontic and modal qualifications measure the degree of an action or event to become actual; that is – indulging once more in anachronism (but this time from the Leibnizian background) – the degree measures how feasible (facile) an action or event may be. This suggests that Ibn Ḥazm’s perspectives already herald the links to probability and possibility explored by Leibniz six centuries later – see for example Leibniz’s (1671, A VI, I, p. 424-26) use of probability in the context of conditional right. Nevertheless, it also shows a crucial difference to the approach developed in the Elementa Jura Naturalis: whereas Leibniz’s studies seek to define what is to be just or virtuous, the logical system of deontic imperatives within Islamic jurisprudence presupposes that what is to be virtuous has already been settled. Determining what is to be virtuous is not achieved by logical reasoning within the system of legal jurisprudence, but by delving into the higher objectives of the Sharīʿa. While developing our point, we will delve into the logical structure of the heteronomous imperatives. This distinguishes our contribution from the existing literature, such as the papers of Chejne (1984), Lameer (2014), and Guerrero (1997, 2010, 2014), which do not provide a logical analysis of the deontic concepts put into work by Ibn Ḥazm. The true antecedent to the present paper is the work of Farid Zidani (2007, 2015), who, so far as we know, was the first to undertake such a task. Some of our own developments and general epistemological thoughts go beyond Ibn Ḥazm’s framework and motivations; mainly those contained in sections II.3.2 and IV. However, according to our view, these reflections suggest that Ibn Ḥazm’s approach has the substance for a broader and deeper exploration of the logic of norms. The paper is structured as follows:I.Ibn Ḥazm’s Logic of Heteronomous Imperatives. After presenting some extracts of the relevant text, we proceed by providing a formal reconstruction of the five forms of deontic modalities. II. A Landmark in the History of the Logical Analysis of Norms. Duties and Modalities. In this section, we study the transferences from deontic to modal necessity and possibility. We briefly compare the deontic system of Islamic Jurisprudence with that of Leibniz.III. Leibniz and Hypothetical Imperatives in Law.IV. Beyond Ibn Ḥazm: Conclusions and the Work Ahead. We will conclude the paper by discussing briefly some conceptual points that distinguish the logic of heteronomous imperatives from contemporary deontic logic. Our final words will discuss deontic-modal parallelism in the context of Ibn Ḥazm’s rejection of reasoning by conjecture and what we call “the internalization of nature.”. (shrink)

Modifying the descriptive and theoretical generalizations of Relativized Minimality, we argue that a significant subset of weak island violations arise when an extracted phrase should scope over some intervener but is unable to. Harmless interveners seem harmless because they can support an alternative reading. This paper focuses on why certain wh-phrases are poor wide scope takers, and offers an algebraic perspective on scope interaction. Each scopal element SE is associated with certain operations (e.g., not with complements). When a wh-phrase scopes (...) over some SE, the operations associated with that SE are performed in its denotation domain. The requisite operations may or may not be available in a domain, however. We present an empirical analysis of a variety of wh-phrases. It is argued that the wh-phrases that escape all weak islands (i.e., can scope over any intervener) are those that range over individuals, the reason being that all Boolean operations are defined for their domain. Collectives, manners, amounts, numbers, etc. all denote in domains with fewer operations and are thus selectively sensitive to scopal interveners—a “semantic relativized minimality effect”. (shrink)

The main algebraic foundations of quantum mechanics are quickly reviewed. They have been suggested since the birth of this theory till up to last years. They are the following ones: Heisenberg-Born- Jordan’s (1925), Weyl’s (1928), Dirac’s (1930), von Neumann’s (1936), Segal’s (1947), T.F. Jordan’s (1986), Morchio and Strocchi’s (2009) and Buchholz and Fregenhagen’s (2019). Four cases are stressed: 1) the misinterpretation of Dirac’s algebraic foundation; 2) von Neumann’s ‘conversion’ from the analytic approach of Hilbert space to the algebraic approach of (...) the rings of operators; 3) Morchio and Strocchi’s improving Dirac’s analogy between commutators and Poisson Brackets into an exact equivalence; 4) the recent foundation of quantum mechanics upon the algebra of perturbations. Some considerations on alternating theoretical importance of the algebraic approach in the history of QM are offered. The level of formalism has increased from the mere introduction of matrices to group theory and C*-algebras but has not led to a definition of the foundations of physics; in particular, an algebraic formulation of QM organized as a problem-based theory and an exclusive use of constructive mathematics is still to be discovered. (shrink)

Despite being a milestone in the history of statistical causal inference, Sewall Wright’s 1918 invention of path analysis did not receive much immediate attention from the statistical and scientific community. Through a careful historical analysis, this paper reveals some previously overlooked philosophical issues concerning the history of causal inference. Placing the invention of path analysis in a broader historical and intellectual context, I portray the scientific community’s initial lack of interest in the method as a (...) natural consequence of relevant scientific and philosophical conditions. In addition to Karl Pearson’s positivist refutation of causation, I contend that the acceptance of path analysis faced several other challenges, including the introduction of a new formalism, conceptual barriers to causal inference, and the lack of model-based statistical thinking. The presence of these challenges shows that the delayed progress in causal inference in the early twentieth century was inevitable. (shrink)

The classification of algebraic surfaces by the Italian School of algebraic geometry is universally recognized as a breakthrough in 20th-century mathematics. The methods by which it was achieved do not, however, meet the modern standard of rigor and therefore appear dubious from a contemporary viewpoint. In this article, we offer a glimpse into the mathematical practice of the three leading exponents of the Italian School of algebraic geometry: Castelnuovo, Enriques, and Severi. We then bring into focus their distinctive conception of (...) rigor and intuition. Unlike what is often assumed today, from their perspective, rigor is neither opposed to intuition nor understood as a unitary phenomenon – Enriques distinguishes between small-scale rigor and large-scale rigor and Severi between formal rigor and substantial rigor. Finally, we turn to the notion of mathematical objectivity. We draw from our case study in order to advance a multi-dimensional analysis of objectivity. Specifically, we suggest that various types of rigor may be associated with different conceptions of objectivity: namely, objectivity as faithfulness to facts and objectivity as intersubjectivity. (shrink)

The history of the methodology of African philosophy can be divided into two periods: the nascent stage that’s characterized by a rigor-demand, and the contemporary stage that’s characterized by a relevance-demand. In this, paper, I argue for one way to strike the appropriate balance between relevance and rigor in African philosophy. Specifically, I argue that the unconscious rejection of conceptual analysis as a philosophical method by contemporary African philosophers played a major role in how African philosophy came to (...) be characterized by a relevance-demand. Consequently, I submit that even though being only or excessively relevance-oriented is not bad, African philosophy would become rich enough to compete with other regional philosophies—Western, Chinese, and so on—if it re-installs conceptual analysis as part of its methodology. (shrink)

The problem of immigrant migration risk analysis is deeply studied and there are number of issues identified in the selection of country. There exists number of approaches available in the selection of countries towards migration. However, the methods do not produce effective results in the selection of migrant country. To handle this issue, an efficient real-time migrant risk analysis model (RMAM) is presented in this article. The method uses the traces of previos migration histories and data set maintained (...) by the model. Using the migration data set, the method preprocesses the data set for noise removal and normalization. With the normalized data set, the method applies Nation Centric Religious Support Analysis and Psychological Support Analysis. The nation centric religious support analysis algorithm measure the risk factors on religious features by computing National Religious Support (NRS) and the Psychological Support Analysis algorithm computes the value of Psychological Support (PS) for different countries. Based on the result of different analysis, the method computes Migration Support (MS) for various countries towards the selection of migration countries. The proposed model improves the performance of risk analysis and migration control. (shrink)

We investigate the topological properties of scalar field configurations influenced by non-commutative geometry and time-dependent perturbations. Specifically, we analyze the connectedness of level sets of scalar fields, compute the fractal dimensions of generated patterns, and study the impact of varying non-commutative parameters. Utilizing numerical simulations, we provide evidence of topological bifurcations induced by non-commutative corrections. The analysis is framed within point set topology, and the results are formalized using the theorem-proof structure.

This essay aims to adumbrate the relationship between ordinary language, history, and cognition in Joseph Margolis’ pragmatist account of the historical constitution of the human, cultural world. It emphasizes the important connections between his arguments for the essentially practical grounding of all forms of cognitive activity; the existential primacy of the historically evolved ordinary language in the formation of aptly socialized human persons as well as of productively functioning human societies; the transformational role of consciousness in history, including (...) the history of cognition; and the insuperable informality inherent in all philosophical attempts to justify our historically articulated norms of cognition and our way of life. Margolis’ analysis of these relationships claims to show that cultural tolerance and historical plasticity deserve to displace the philosophical ideas of invariance and fixity as the favored resources of conceptual and social stability. This recognition, on Margolis’s view, constitutes pragmatism’s distinctive promise and advantage. (shrink)

An astonishing volume and diversity of evidence is available for many hypotheses in the biomedical and social sciences. Some of this evidence—usually from randomized controlled trials (RCTs)—is amalgamated by meta-analysis. Despite the ongoing debate regarding whether or not RCTs are the ‘gold-standard’ of evidence, it is usually meta-analysis which is considered the best source of evidence: meta-analysis is thought by many to be the platinum standard of evidence. However, I argue that meta-analysis falls far short of (...) that standard. Different meta-analyses of the same evidence can reach contradictory conclusions. Meta-analysis fails to provide objective grounds for intersubjective assessments of hypotheses because numerous decisions must be made when performing a meta-analysis which allow wide latitude for subjective idiosyncrasies to influence its outcome. I end by suggesting that an older tradition of evidence in medicine—the plurality of reasoning strategies appealed to by the epidemiologist Sir Bradford Hill—is a superior strategy for assessing a large volume and diversity of evidence. (shrink)

Standard citation-based bibliometric tools have severe limitations when they are applied to periods in the history of science and the humanities before the advent of now-current citation practices. This paper presents an alternative method involving the extracting and analysis of mentions to map and analyze links between scholars and texts in periods that fall outside the scope of citation-based studies. Focusing on one specific discipline in one particular period and language area—Anglophone philosophy between 1890 and 1979—we describe a (...) procedure to create a mention index by identifying, extracting, and disambiguating mentions in academic publications. Our mention index includes 1,095,765 mention links, extracted from 22,977 articles published in 12 journals. We successfully link 93% of these mentions to specific philosophers, with an estimated precision of 82% to 91%. Moreover, we integrate the mention index into a database named EDHIPHY, which includes data and metadata from multiple sources and enables multidimensional mention analyses. In the final part of the paper, we present four case studies conducted by domain experts, demonstrating the use and the potential of both EDHIPHY and mention analyses more generally. (shrink)

If you have enjoyed any of the 7 (seven) other books I have published over 20 years, including literally thousands of pages of mathematical and topological concepts, Python programs and conceptually expanding papers, please consider buying this book for $20.00 on google play books. -/- Introduction: -/- Though the following pages provide extensive exposition and dedicated descriptions of the phenomenological velocity formulas, theory and mystery, I thought it appropriate to write this introduction as a partial explanation for what phenomenal velocity (...) is, and describe, briefly its theory and applications. Phenomenological Velocity is a method for solving for something that ought cancel out with itself, but there are specific implicit forms for this thing that, “ought cancel out with itself,” namely the Lorentz coefficient ought cancel out with itself when applied to the height of a cone derived from the difference between the circumferences of two circles applied to the Pythagorean Theorem, or, more generally, the height implied by application of the Pythagorean theorem to the difference between two arc lengths’ equaling a third arc length. These difference equations are essential to conceptualizing differentiation, and in these further chapters, I demonstrate that the phenomenological velocity is, indeed the conditional derivative in the chapter, “Conditional Integral of Phenomenological Velocity.” The phenomenological velocity algebraic solution to the velocity within the Lorentz coefficient when applied to the height function in such a way that it ought cancel out with itself is both constructive mathematics and it employs the concept of, “bracketing,” - first introduced by Edmund Husserl in his writings on the phenomenological reduction. Phenomenological Velocity’s algebraic solution from the difference between two arc lengths applied to the Pythagorean Theorem to solve for a theoretical height (which is a projected distance in space), employs bracketing, because we, “set aside,” the existence of an undefined solution, namely due to the presence of necessitated complex analytical forms by the architecture of the equation, or the “mathetecture,” of the algebraic form. -/- With respect to theology, the phenomenological velocity is somehow symbolic of the creation itself; symbolic of creation due to the fact that we find the canceling out of the Lorentz coefficient as, “impotent,” non-existent or non-effecting to the mathetecture of the height function. However, via the modus-ponens work around to phenomenological velocity, which in itself does not require the complex field, but embeds implied complex field solutions to the equation while maintaining logical consistency, we find existence from non-existence. This is directly linguistically applicable to the concept of the big-bang, the resurrection of Yeshua the Messiah, and opens analogies for us to draw relationships between the, “fall,” of Adam and Eve as the generation of error, or the introduction of paradox, as we see the phallus representing paradox topologically. -/- The phenomenological velocity is a gestalt concept, relevant to cosmology, because we find that it is the perfect language-form for discussing dark matter. It does, however, require the reader to re-conceive or re-frame rather, some of the fundamental aspects of assumed physical reality like time, experience, solidity of dark matter, etc. We find the hidden dimension of phenomenological velocity to have been an overlooked aspect of mathematical physics by the researchers of Bell’s theorem and undoubtedly a host of other theorems. Thus, raising awareness about the real existence and necessitated reality of phenomenological velocity is in no way an endeavor deserving further procrastination by the scientific community, for doing so would be intellectually dishonest and further the propagation of incomplete or misleading theories on reality. -/- This work details how the Lorentz coefficient, when applied to the height of a cone in such a way as to cancel out with itself, permits the velocity variable to have a solution to it anyway, even though it ought cancel out with itself. This mathe-tecture, so to speak has consequences for complex analysis, and pave the way for, "transcendental relativity," building an adaptive framework for consciousness and physical reality. (shrink)

It has become a fact that fluency and competency in utilizing the advancement of technology, specifically the computer and the internet is one way that could help in facilitating learning in mathematics. This study investigated the effects of Dynamic Geometry Software (DGS) and Computer Algebra Systems (CAS) in teaching Mathematics. This was conducted in Zamboanga del Sur National High School (ZSNHS) during the third grading period of the school year 2015-2016. The study compared the achievement and attitude towards Mathematics (...) between those students taught with DGS and CAS and those students who were taught without DGS and CAS. A quasi-experimental pretest-posttest control group design was used with two groups which was matched according to their mathematical level. An achievement test was developed and administered to assess the students’ achievement in Mathematics. Aiken’s attitude scale was also used to assess the students’ attitude towards Mathematics. The data were treated with One-Way Analysis of Covariance (ANCOVA) and t-test at 0.05 level of significance. The study revealed a significant difference between the mathematics achievement between students taught with DGS and CAS and those who were taught without it. The integration of DGS and CAS in Mathematics lessons leads to better academic achievement result compared with that of the conventional method of teaching. Moreover, there was no significant difference on the attitude level of the students between the two groups. (shrink)

Staphylococcus aureus ST45 is a major global MRSA lineage with huge strain diversity and a high clinical impact. It is one of the most prevalent carrier lineages but also frequently causes severe invasive disease, such as bacteremia. Little is known about its evolutionary history. In this study, we used whole-genome sequencing to analyze a large collection of 451 diverse ST45 isolates from 6 continents and 26 countries. De novo-assembled genomes were used to understand genomic plasticity and to perform coalescent (...) analyses. The ST45 population contained two distinct sublineages, which correlated with the isolates’ geographical origins. One sublineage primarily consisted of European/North American isolates, while the second sublineage primarily consisted of African and Australian isolates. Bayesian analysis predicted ST45 originated in northwestern Europe about 500 years ago. Isolation time, host, and clinical symptoms did not correlate with phylogenetic groups. Our phylogenetic analyses suggest multiple acquisitions of the SCCmec element and key virulence factors throughout the evolution of the ST45 lineage. (shrink)

In recent decades, perspectivism has developed into an epistemological research program claiming its independence. This autonomy stems from Perspectivism’s potential ability to resolve the contradictions between realist and constructivist programs. Perspectivism is based on the idea that the object depends on perspective, which constitutes any subjective attempt to cognize it. Perspectivists reconstruct and explain the factors involved in the formation of perspective, identifying the conditionality of epistemic acts, using concepts such as “position”, “point of view”, “view”, “angle”, “horizon”, “focus”, “picture”, (...) “context”, “aspect”, etc. Although these concepts are part of the perspectivist’s toolkit, their meanings and interrelation have so far been taken for granted and have not yet been critically and comprehensively analyzed. The purpose of this article is to take steps toward clarifying the conceptual basis for defending perspectivism as an epistemological program. Once consistently uncovered and correlated in a conceptual model, Perspectivist concepts can be used as a tool for a detailed analysis of theories, positions, and beliefs. The article begins with a preliminary description of the concept of perspectivism and its brief history as an epistemological program. In particular, the first modern attempts to outline perspectivist epistemology are described in the works of F. Kaulbach (1990), W. Stegmaier (2008), and M. Massimi (2017, 2020). The problem of identifying the special a priori status of perspectivist notions as a strategy for justifying the autonomy of Perspectivism is then posed. A method for demonstrating such a status, based on Kant’s transcendentalism and P. Strawson’s descriptive metaphysics, is then suggested. (shrink)

In the present article, we are faced with two phenomenological philosophers who, in two different intellectual traditions, namely philosophical hermeneutics and moral phenomenology, have referred to the concept of the Other as the fundamental possibility of the individual. The other, as an ontological and common concept in the thought of Gadamer and Levinas, is the turning point of the condition for the possibility of understanding and ethics. Focusing on the concept of the other, while addressing the points of difference and (...) commonality between Gadamer and Levinas, this article will show that Levinas’s preoccupation with the other as a philosopher refers to the foundations of ethics, and the condition for the possibility of foundations of ethics is encountering the other. In Gadamer, the turning point is the determination of the possibilities of understanding in dialectical and dialogue-oriented relationships. Without the other, in Levinas’s thought, ethics, and moral matter, and in Gadamer’s thought, the process of understanding will not occur in the form of a fusion of horizons. Therefore, this article shows that the other is a common concept between these two philosophers, which both of them cannot avoid in their philosophical analyses of ethics or the process of understanding. Introduction The analysis of ethics is one of the important and innovative achievements of Levinas’s philosophical intellectual structure. Levinas’s concern is to refer to the foundations of morality itself, regardless of institutionalizing the moral in the form of law, and the foundation of morality is in face-to-face relationships with others. Regardless of Levinas’s plan about the concept of the other, Gadamer imagines the determination of understanding in a new way in the face of the other. The other is the comprehensible strain in philosophical hermeneutics, in such a way that the process of understanding is formed by the presence of the other and the face-to-face encounter with it. According to Gadamer, the other is the factor of openness in the process of understanding. The fusion of horizons is the product of openness and mutual encounters in dialogue, which is not possible without the other. The other is the condition of determining the possibility of understanding in each of the parties who are allowed to reveal a part of their being and allow the other to open up and talk. In fact, understanding is a kind of event that is revealed in a two-way conversation in an event-like way. This type of understanding depends on the presence of another. The main focus of the research is the analysis of the concept of the other, which has been done with emphasis on two important works: Truth and method, Totality and infinity. Body & discussion In general, the process of understanding is a dialogical process, whether the other side of the conversation is a text or a person, the foundation of understanding is formed in a relationship with the other. Determining the other as an independent personality and a different perspective is an ontological determination. The other thinks and becomes meaningful beyond the subject or object and even beyond my intellectual position, it belongs to its own independent world and its own experience. In conversation, it plays a significant role in the production of truth. Openness provides the possibility of dialogue and mutual agreement. In dialogue, the final product is not reproduced. The other condition for the production of the final product is dialogue According to Gadamer, facing the other is facing his world. At the moment of facing me, the other makes his abstract aspects concrete and opens his lived experience to me. He believes that the question-and-answer process is a kind of encounter with the world of experience and openness toward it. According to Gadamer, the process of understanding is the result of dialectical-hermeneutic relations between me (the interpreter) and you (the other). The dialogical relationships that allow each other to enter the other’s history are relationships that are formed based on questions and answers. From Gadamer’s point of view, questions and answers are the opening of a new horizon based on tradition and contemporary history. Levinas phenomenologically refers to the philosophical tradition of the West to reread the process of the formation of the concept of the other. Many commentators and interpreters of Levinas’s works believe that it is possible to determine the foundations of ethics from Levinas’s point of view from face-to-face relationships. The condition for the possibility of morality is to pay attention to others. To describe another concept, Levinas analyzes the negative and positive aspects of this concept. In a negative way, Levinas first answers what the other is not, and for this reason, he criticizes the history of Western metaphysics and the criticism of Husserl and Heidegger’s phenomenology. Positively, the other is relative to me and different from me. The other is beyond subject and object. The other is not subjugated by any concept and recognizes its independent identity. The other and the encounter with him are the conditions for determining fundamental ethics from Levinas’s point of view. Another condition of concreteness refers to another person. According to Levinas, it is the condition for the formation of moral form. He believes that ethics is a kind of double encounter in the context of bilateral relations. Many moral concepts are formed in relation to a concrete other. In Levinas’s genealogy of ethics, we are faced with the presence of the other in a concrete way and with the subjectivity of the subject in an abstract and a priori way. Levinas specifies two approaches with the description of the other in the form of an infinite idea. First of all, there is an infinite gap between the other and the same. This issue shows its foreignness and otherness, its independence, and being true to its essence towards me. Second, it is the determination of another in a concrete or abstract form, which in both cases evokes an identity independent of me. Conclusion According to the explanations of the concept of the other in the thought of Gadamer and Levinas, we are faced with two phenomenological philosophers who have paid attention to the ontological aspects of the concept of the other in the fields of philosophical hermeneutics and ethics. In Gadamer’s thought, the other is an ontologically dialectical relationship between I-Thou and the starting point of the conversation process. The fusion of horizons is the turning point of the formation of the relation to the other, which is manifested in another area. The other has its own history, world, tradition, and authority, regardless of the formation of dialogical relationships, and has an independent identity. The other is allowed to share his lived experience in the conversation. The other creates new worlds. The other has opened himself and in return can be self-interpreting and self-revealing. Regardless, the other is the consistency of the complex relationship between language and the world. This form of bilateral relations, which is manifested in the presence of another, is a linguistic form that is the cause of a deep connection between language and the world. The other, whether concrete or abstract, is the turning point of our connection with the world in an ontological way. Regardless of Gadamer’s point of view, Levinas returns to another concept in his new thought project entitled “How to determine the possibilities of ethics.” According to Levinas, finding the foundations of ethics and determining the condition of moral possibilities is in facing the other and in face-to-face relationships. The other is concretely a kind of bilateral encounter which is the basis of many moral events and is manifested abstractly in the form of the subject’s subjectivity. This kind of infinite aspect of the other is revealed in subjectivity is implied in sense. Encountering another in an abstract form within itself is the encounter of the subject’s subjectivity with the sense, and the sense is in the encounter with the other. Sense is the basis of the subjectivity of the subject. Sense is a kind of concrete and visual face-to-face encounter that adds to the importance of determining another. Therefore, both Gadamer and Levinas raise many possibilities about the concept of the other, which shows the importance of this concept in the Western philosophical tradition. (shrink)

Many twentieth-century accounts of history have used geological tropes to describe the phenomenon of historical knowledge, and such terms have been of particular importance in the phenomenological tradition. In Heidegger's references in Being and Time to the "soil of history," Husserl's account in his later work of "sedimentation" in the lifeworld, and the reformulation of this notion in the phenomenology of Merleau-Ponty, geological tropes are used to illustrate important insights into the relation between contingency, a priority and historicity. (...) This paper seeks to contribute to an understanding of history understood phenomenologically as historicity through an analysis of these geological tropes. I argue that such geological tropes help the phenomenologist to describe the way in which history is always determined within a complex interplay between only temporarily fixed determining structures - such as riverbanks, insoluble sediment, soil, etc. - and free-flowing praxis, a situation in which historical events are at once determinant of and themselves determined by human activity. Paradoxically, the constant and "grounding" element in such conceptions of history is not the sediment and hard rock of historical fact, but the the constant change and variability-despite the sense giving continuity - of human experience structured by historicity. I begin with a brief overview of the landscape on the philosophy of history in which these views arose, and then continue to an analysis of the tropes themselves. (shrink)

The concept of similar systems arose in physics, and appears to have originated with Newton in the seventeenth century. This chapter provides a critical history of the concept of physically similar systems, the twentieth century concept into which it developed. The concept was used in the nineteenth century in various fields of engineering, theoretical physics and theoretical and experimental hydrodynamics. In 1914, it was articulated in terms of ideas developed in the eighteenth century and used in nineteenth century mathematics (...) and mechanics: equations, functions and dimensional analysis. The terminology physically similar systems was proposed for this new characterization of similar systems by the physicist Edgar Buckingham. Related work by Vaschy, Bertrand, and Riabouchinsky had appeared by then. The concept is very powerful in studying physical phenomena both theoretically and experimentally. As it is not currently part of the core curricula of STEM disciplines or philosophy of science, it is not as well known as it ought to be. (shrink)

This paper investigates the significance of filmic analysis in the contemporary theoretical paradigm inspired by Slavoj Žižek, which we term ‘Transcendental Materialism’. After characterising its distinct peculiarities within the history of psychoanalysis and film theory, we demonstrate the limitations of previous (possible) answers, arguing they are partly formulated in response to confrontations with other paradigms. Our own approach is then informed by a study of another popular object of analysis in Transcendental Materialism – the joke. We show (...) how Freud’s understanding of the joke was adapted by the paradigm and supported further by certain philosophical insights by (among others) G.W.F. Hegel. Finally, we demonstrate how parallels can be drawn between this adaptation and the significance of the filmic form within Transcendental Materialism, inspired in part by Alain Badiou’s reading of Hegel. (shrink)

Cultural epidemiology is a theoretical framework that enables historical studies to be informed by cognitive science. It incorporates insights from evolutionary psychology (viz. cultural evolution is constrained by universal properties of the human cognitive apparatus that result from biological evolution) and from Darwinian models of cultural evolution (viz. population thinking: cultural phenomena are distributions of resembling items among a community and its habitat). Its research program includes the study of the multiple cognitive mechanisms that cause the distribution, on a cultural (...) scale, of representations and material cultural items. By a detailed analysis of the social cognitive causal chain that occurred in the past, one can find out – and specify – which are the factors of attraction that account for cultural stability as well as historical cultural change. After reviewing recent research and developments in cognitive history, I present the concept of cultural attractor and explain why cultural attractors are historically variable. In doing so, I emphasize the role of historically constituted cognitive mechanisms, which account for much of historical cultural developments. I argue that the framework of cultural epidemiology can better account for these important historical phenomena than either evolutionary psychology accounts of culture or dual inheritance theory. I conclude that describing and explaining the history of cultural attractors is a good research goal for historians. (shrink)

A comparative analysis of the different notions of ‘ways of thinking’ introduced by philosophers. A guiding thread running through historical epistemology in an attempt to unify the researches of its authors. A comprehensive study of Ian Hacking’s ‘project of styles of reasoning’ and its implications for the relativism.

There is a traditional conception of knowledge but it is not the Justified True Belief analysis Gettier attacked. On the traditional view, knowledge consists in having a belief that bears a discernible mark of truth. A mark of truth is a truth-entailing property: a property that only true beliefs can have. It is discernible if one can always tell that a belief has it, that is, a sufficiently attentive subject believes that a belief has it if and only if (...) it has it. Requiring a mark of truth makes the view infallibilist. Requiring it to be discernible makes the view internalist. I call the view Classical Infallibilism. (shrink)

Famously, in the essay Inquiry Concerning the Distinctness of the Principles of Natural Theology and Morality (Prize Essay), Kant attempts to distance himself from the Wolffian model of philosophical inquiry. In this respect, Kant scholars have pointed out Kant’s claim that philosophy should not imitate the method of mathematics and his appeal to Newton’s “analytic method.” In this article, I argue that there is an aspect of Kant’s critique of the Wolffian model that has been neglected. Kant presents a powerful (...) attack of the idea that philosophy should proceed through the analysis of concepts and argues that we should give up the aim of arriving at “complete” concepts as one of its fundamental desiderata. Importantly, this attack of philosophy conceived as conceptual analysis is distinctive and original if one compares it with Kant’s critique of analysis in the Critique of Pure Reason, which rests on the idea that analysis is insufficient to ground substantial metaphysical truths. I also make an additional point: Scholars have debated whether the appeal to Newton’s analytic method involves a form of empiricism. I submit that this debate is ill-conceived because Kant uses a notion of “given concepts” that is indeterminate with respect to their a priori or a posteriori status. (shrink)

Imre Lakatos' conception of the history of science is explicated with the purpose of replying to criticism leveled against it by Thomas Kuhn, Ian Hacking, and others. Kuhn's primary argument is that the historian's internal—external distinction is methodologically superior to Lakatos' because it is "independent" of an analysis of rationality. That distinction, however, appears to be a normative one, harboring an implicit and unarticulated appeal to rationality, despite Kuhn's claims to the contrary. Lakatos' history, by contrast, is (...) clearly the history of a normatively defined discipline; of science and not scientists and their activities. How such history can be written, the historiographic and critical tools available for its construction, and its importance as history, are considered in detail. In an afterword, the prevalence of Lakatos' treatment of history in philosophical discussion is indicated: A related approach is shown to arise in social contract theory. (shrink)

A study of the making of George Peacock's highly influential, yet disturbingly split, 1830 account of algebra as an entanglement of two separate undertakings: arithmetical and symbolical or formal.

Little is know about factors that influence the development of public self-consciousness. One potential factor is exposure to audiences: being repeatedly aware of one's object status could create a high disposition to focus on public self-aspects. To explore this hypothesis public self-consciousness was assessed in two groups of subjects: 62 professors and actors (high exposure to audiences) and 39 people without audience experience. Analysis show that significant differences exist for public self-consciousness in men only. Also, history of frequent (...) exposure to audience is significantly but weakly correlated with high public self-consciousness in men. This supports previous observations indicating that self-consciousness seems to develop differently for men and women. (shrink)

The present yearbook (which is the fourth in the series) is subtitled Trends & Cycles. It is devoted to cyclical and trend dynamics in society and nature; special attention is paid to economic and demographic aspects, in particular to the mathematical modeling of the Malthusian and post-Malthusian traps' dynamics. An increasingly important role is played by new directions in historical research that study long-term dynamic processes and quantitative changes. This kind of history can hardly develop without the application of (...) mathematical methods. There is a tendency to study history as a system of various processes, within which one can detect waves and cycles of different lengths – from a few years to several centuries, or even millennia. The contributions to this yearbook present a qualitative and quantitative analysis of global historical, political, economic and demographic processes, as well as their mathematical models. This issue of the yearbook consists of three main sections: (I) Long-Term Trends in Nature and Society; (II) Cyclical Processes in Pre-industrial Societies; (III) Contemporary History and Processes. We hope that this issue of the yearbook will be interesting and useful both for historians and mathematicians, as well as for all those dealing with various social and natural sciences. (shrink)

This essay critically examines one of the dominant tendencies in recent theoretical discussions of anarchism, postanarchism, and argues that this tradition fails to engage sufficiently with anarchism’s history. Through an examination of late 19th-century anarchist political thought—as represented by one of its foremost exponents, Peter Kropotkin—we demonstrate the extent to which postanarchism has tended to oversimplify and misrepresent the historical tradition of anarchism. The article concludes by arguing that all political-theoretical discussions of anarchism going forward should begin with a (...) fresh appraisal of the actual content of anarchist political thought, based on a rigorous analysis of its political, social, and cultural history. (shrink)

I argue, through appeal to the distinction between analysis and decomposition described by Dummett, that Wittgenstein employs both of those notions in the Tractatus. I then bring this interpretation to bear upon the issue of propositional unity, where I formulate an objection to the views of both Leonard Linksy and José Zalabardo. I show that both Linsky and Zalabardo fail to acknowledge the distinction between analysis and decomposition present in the Tractatus, and that they consequently mischaracterise Wittgenstein’s position (...) with respect to propositional unity. (shrink)

A Fortiori Logic: Innovations, History and Assessments is a wide-ranging and in-depth study of a fortiori reasoning, comprising a great many new theoretical insights into such argument, a history of its use and discussion from antiquity to the present day, and critical analyses of the main attempts at its elucidation. Its purpose is nothing less than to lay the foundations for a new branch of logic and greatly develop it; and thus to once and for all dispel the (...) many fallacious ideas circulating regarding the nature of a fortiori reasoning. -/- The work is divided into three parts. The first part, Formalities, presents the author’s largely original theory of a fortiori argument, in all its forms and varieties. Its four (or eight) principal moods are analyzed in great detail and formally validated, and secondary moods are derived from them. A crescendo argument is distinguished from purely a fortiori argument, and similarly analyzed and validated. These argument forms are clearly distinguished from the pro rata and analogical forms of argument. Moreover, we examine the wide range of a fortiori argument; the possibilities of quantifying it; the formal interrelationships of its various moods; and their relationships to syllogistic and analogical reasoning. Although a fortiori argument is shown to be deductive, inductive forms of it are acknowledged and explained. Although a fortiori argument is essentially ontical in character, more specifically logical-epistemic and ethical-legal variants of it are acknowledged. -/- The second part of the work, Ancient and Medieval History, looks into use and discussion of a fortiori argument in Greece and Rome, in the Talmud, among post-Talmudic rabbis, and in Christian, Moslem, Chinese and Indian sources. Aristotle’s approach to a fortiori argument is described and evaluated. There is a thorough analysis of the Mishnaic qal vachomer argument, and a reassessment of the dayo principle relating to it, as well as of the Gemara’s later take on these topics. The valuable contribution, much later, by Moshe Chaim Luzzatto is duly acknowledged. Lists are drawn up of the use of a fortiori argument in the Jewish Bible, the Mishna, the works of Plato and Aristotle, the Christian Bible and the Koran; and the specific moods used are identified. Moreover, there is a pilot study of the use of a fortiori argument in the Gemara, with reference to Rodkinson’s partial edition of the Babylonian Talmud, setting detailed methodological guidelines for a fuller study. There is also a novel, detailed study of logic in general in the Torah. -/- The third part of the present work, Modern and Contemporary Authors, describes and evaluates the work of numerous (some thirty) recent contributors to a fortiori logic, as well as the articles on the subject in certain lexicons. Here, we discover that whereas a few authors in the last century or so made some significant contributions to the field, most of them shot woefully off-target in various ways. The work of each author, whether famous or unknown, is examined in detail in a dedicated chapter, or at least in a section; and his ideas on the subject are carefully weighed. The variety of theories that have been proposed is impressive, and stands witness to the complexity and elusiveness of the subject, and to the crying need for the present critical and integrative study. But whatever the intrinsic value of each work, it must be realized that even errors and lacunae are interesting because they teach us how not to proceed. -/- This book also contains, in a final appendix, some valuable contributions to general logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox. (shrink)

The claim that Galileo Galilei transformed the spyglass into an astronomical instrument has never been disputed and is considered a historical fact. However, the question what was the procedure which Galileo followed is moot, for he did not disclose his research method. On the traditional view, Galileo was guided by experience, more precisely, systematized experience, which was current among northern Italian artisans and men of science. In other words, it was a trial-and-error procedure—no theory was involved. A scientific analysis (...) of the optical properties of Galileo’s first improved spyglass shows that his procedure could not have been an informed extension of the traditional optics of spectacles. We argue that most likely Galileo realized that the objective and the eyepiece form a system and proceeded accordingly. (shrink)

Szmimary.—The present report investigated the question of how individual differences in self-consciousness devdop. Rimé and LeBon proposed that high self-consciousness follows a history of frequent exposure to selffocusing stimuli, i.e., mirrors, audiences, audio and video devices, and cameras. To explore this hypothesis private and public self-consciousness and past exposure to self-focusing stimuli were assessed in 438 subjects. Analysis indicated that history of frequent exposure to self-focusing stimuli is significantly but weakly related to high private self-consciousness in men (...) and to high public self-consciousness in women. This supports previous observations suggesting that the routes to the development of selfconsciousness seem to differ for the two sexes. (shrink)

Tatiana Ehrenfest-Afanassjewa was an important physicist, mathematician, and educator in 20th century Europe. While some of her work has recently undergone reevaluation, little has been said regarding her groundbreaking work on dimensional analysis. This, in part, reflects an unfortunate dismissal of her interventions in such foundational debates by her contemporaries. In spite of this, her work on the generalized theory of homogeneous equations provides a mathematically sound foundation for dimensional analysis and has found some appreciation and development. It (...) remains to provide a historical account of Ehrenfest-Afanassjewa's use of the theory of homogeneous functions to ground (and limit) dimensional analysis. We take as a central focus Ehrenfest-Afanassjewa's contributions to a debate on the foundations of dimensional analysis started by physicist Richard Tolman in 1914. I go on to suggest an interpretation of the more thoroughgoing intervention Ehrenfest-Afanassjewa makes in 1926 based on this earlier context, especially her limited rehabilitation of a "theory of similitude" in contradistinction to dimensional analysis. It is shown that Ehrenfest-Afanassjewa has made foundational contributions to the mathematical foundations and methodology of dimensional analysis, our conception of the relation between constants and laws, and our understanding of the quantitative nature of physics, which remain of value. (shrink)

Abstract: This research paper presents a novel approach to predict audit risks using a neural network model. The dataset used for this study was obtained from Kaggle and comprises 774 samples with 18 features, including Sector_score, PARA_A, SCORE_A, PARA_B, SCORE_B, TOTAL, numbers, marks, Money_Value, District, Loss, Loss_SCORE, History, History_score, score, and Risk. The proposed neural network architecture consists of three layers, including one input layer, one hidden layer, and one output layer. The neural network model was trained and validated, (...) achieving an impressive accuracy of 100% and an average error of 0.000015, indicating its robust predictive capability. Moreover, we conducted feature importance analysis to identify the most influential features for predicting audit risk. The key features found to be critical for classifying fraudulent activities in audit risk prediction are Sector_score, PARA_A, SCORE_A, PARA_B, SCORE_B, TOTAL, numbers, marks, Money_Value, District, Loss, Loss_SCORE, History, and History_score. This research contributes to the field of audit risk prediction by demonstrating the effectiveness of a neural network-based approach and highlighting the importance of specific features in detecting fraudulent activities. The findings have significant implications for auditors and organizations seeking to enhance their audit risk assessment processes, ultimately leading to improved financial transparency and fraud detection. (shrink)

With fifty-four chapters charting the development of moral philosophy in the Western world, this volume examines the key thinkers and texts and their influence on the history of moral thought from the pre-Socratics to the present day. Topics including Epicureanism, humanism, Jewish and Arabic thought, perfectionism, pragmatism, idealism and intuitionism are all explored, as are figures including Aristotle, Boethius, Spinoza, Hobbes, Hume, Kant, Hegel, Mill, Nietzsche, Heidegger, Sartre and Rawls, as well as numerous key ideas and schools of thought. (...) Chapters are written by leading experts in the field, drawing on the latest research to offer rigorous analysis of the canonical figures and movements of this branch of philosophy. The volume provides a comprehensive yet philosophically advanced resource for students and teachers alike as they approach, and refine their understanding of, the central issues in moral thought. (shrink)