Science Of Quantity Research Articles

APPLICATION OF LEARNING MATHEMATICS USING WEB BASED LEARNING METHOD

Mathematics is one branch of science that we have learned from an early age. Mathematics is the science of quantity, structure, space, and change. Mathematicians find patterns from rigorous conclusions drawn from consistent axioms and definitions, propose new conjectures, and construct truth. We often encounter a learning approach that becomes a problem in the real world as a context for learning by thinking more critically and skillfully in problem-solving and knowledge and concepts from the material to be learned. The success of learning can be seen from the results of learning. Therefore, learning methods related to technology are indispensable for practical activities with the object of study cannot be separated from theoretical learning. Learning theory makes us bored compared to the practice done directly in front of the computer with existing technology at the moment. One such technology is Web-Based Learning (WBL). Using the Web-Based Learning (WBL) method is expected to help develop its capabilities

Woosuk Park.*Philosophy’s Loss of Logic to Mathematics: An Inadequately Understood Take-Over

Woosuk Park’s book discusses a number of disparate issues which are not on the agenda in the philosophy of mathematics but deserve to be. One is the Aristotelian realist option in the philosophy of mathematics. Since Frege, the philosophy of mathematics has been divided into two opposing schools on the nature of mathematical entities, Platonism and nominalism. ‘Full-blooded’ Platonism holds that entities like sets and numbers are classical acausal ‘abstract objects’, existing in a non-physical Platonic realm. Nominalism holds that mathematical entities do not exist at all and mathematics is merely a language, or manipulation of formal symbols or similar. That neglects the Aristotelian option, that mathematical entities exist in a way, but not as abstract entities, and that mathematics studies certain aspects of the real non-abstract (physical and other) world, for example its structural, or quantitative, or relational aspects [Franklin, 2014; Jacquette, 2014; Thomas, 2008]. As Park points out, the ‘science of quantity’ version of Aristotelian theory was once dominant. He praises in particular Biancani’s De Mathematicarum Natura Dissertatio [1615]. Of most interest is Biancani’s treatment of the question whether scientiae mediae (what we would call applied mathematics, like astronomy and optics) have perfect demonstrations. That is, can mathematics prove truths valid in the physical as well as the abstract world? Biancani’s defence of the affirmative is less than convincing; contemporary readers might be more impressed by Archimedes’ demonstration (or purported demonstration) of the law of the lever and Galileo’s proof that falling bodies cannot have speed proportional to the distance travelled.

The Nature of Scientific Philosophy

The goal of this paper is to explain the nature of philosophy as a distinct science with its own subject-matter. This is achieved through a comparative analysis of mathematical and philosophical knowledge that reveals a profound similarity between mathematics and philosophy as mutually complementary sciences exploring the field of abstract entities that can be comprehended only by purely a priori theoretical inquiry. By considering this complementarity, a general definition of philosophy can be obtained by dualizing the traditional Aristotelian definition of mathematics as the “science of quantity”. Philosophy should thus be interpreted as an a priori science of the pure qualitative attributes of being.

MATEMATIK DAN REALITI: SATU PENELITIAN TERHADAP TAKRIF-TAKRIF MATEMATIK

The role of mathematics as a foundation of other sciences is well acknowledged since the dawn of modern science. This fundamental and important role is then not only limited to the natural and physical sciences but also further extended to the social domains of humanities. This article reviews the many definitions of mathematics as put forth by philosophers and mathematicians, how these definitions are understood, and how they subsequently influence the development of mathematics itself as well as other disciplines influenced by mathematics. These definitions are: mathematics as the science of teaching and learning (ʿulūm al-taʿālim); mathematics as abstraction or the construction of abstracts; mathematics as logic; mathematics as a formal system; mathematics as the science of quantity and structure, mathematics=ontology; and mathematics as intellectual exercise (riyāḍiyyāt). Based on the aforementioned definitions, this article attempts to analyse the ontological status of mathematics and mathematical objects based on the degrees of existence (marātib al-wujūd) framework which orders existence into five levels, namely essential existence (wujūd dhātī), concrete existence (wujūd ‘aynī), mental existence (wujūd dhihnī), verbal existence (wujūd lafẓī), dan formal or written existence (wujūd khaṭṭī).

The Idea of Principles in Early Modern Thought: Interdisciplinary Perspectives ed. by Peter R. Anstey

Reviewed by: The Idea of Principles in Early Modern Thought: Interdisciplinary Perspectives ed. by Peter R. Anstey Daniel Schneider Peter R. Anstey, editor. The Idea of Principles in Early Modern Thought: Interdisciplinary Perspectives. New York: Routledge, 2017. Pp. xvi + 303. Cloth, $140.00. This book is a collection of essays that relate in some way to the notion of a principle as it appears in early modern thought. Essays by James Franklin, J. C. Campbell, Alberto Vanzo, Anstey, and William R. Newman provide a survey of the usage of principles within particular subjects: the principles of early modern mathematics, equity law, corpuscularism, and chemistry or alchemy, respectively. Other essays, by Kristen Walsh and Michael LeBuffe, clarify a particular early modern thinker's understanding and usage of the term 'principle.' Walsh's essay concerns Newton's usage and understanding of the term, while LeBuffe's concerns Spinoza's. Other essays, by Daniel Garber and Kiyoshi Shimokawa, clarify how an early modern thinker, or a pair of thinkers, understand and use a particular principle or set of principles to do philosophical work. Garber's essay considers Leibniz's principle of the equality of cause and effect, while Shimokawa's considers the principles that Grotius and Hume use in their accounts of the origin of justice and its relation to utility. Sophie Roux's essay (a wonderful example of the high level of scholarship found in this collection) examines disputes concerning, and contemporaneous to, the two comets of 1664, and shows the role principles played (and failed to play) in demarcating the positions within these disputes. Scholars looking for a sustained investigation into the idea of principles in the early modern period will be disappointed. This is not on account of any failure on the part of these authors, but rather on account of there being no such thing. As this collection makes clear, the early modern period reveals no single idea of principles. Indeed, the only attempt at offering a broad discussion of various early modern ideas of principles is in the excellent introduction by Anstey. Still, this collection succeeds in satisfying its description within this same introduction, namely, as a "preliminary sounding of the subject" (1) of the nature and role of principles in the early modern period. Of the essays offering a "sounding" of principles as they appear within a particular subject, James Franklin's insightful and fascinating "Early Modern Mathematical Principles and Symmetry Arguments" stands out as particularly useful. Franklin's survey of mathematical principles effectively illustrates a dominant early modern conception of mathematics as a science of quantity that yields deductive knowledge of the real world. Likewise, among the essays offering an analysis of particular thinkers' use of the term 'principle,' Kristen Walsh's essay "Principles in Newton's Natural Philosophy" stands out in its significance. Walsh argues persuasively that, in the Principia, Newton used the term 'principle' to signify the functional role of a proposition within his theories. Walsh argues that if, in the Principia, Newton describes a proposition as a principle, he does so because the proposition satisfies two conditions: one, it has been deduced from the phenomena, and two, it serves as a premise in further deductions. Walsh shows how these two simple constraints systematize Newton's otherwise unsystematic usage of 'principle' in the Principia. Walsh's essay is well argued, well researched, and important. Newton scholars will undoubtedly find it of interest. The essays in this collection are all solid works of scholarship. As a collection however, they do not fit together in a very useful way. On the one hand, it will be the rare scholar who can engage deeply with the material covered in each and every essay. On the other hand, it will be the rare researcher of early modern thought who does not find at least some essays in the collection to be of use. The collection would have benefited from a tightening of its theme or perhaps even a tightening of the approaches with which the essays address the theme. As it stands, this "preliminary sounding" of the study of early modern principles lacks a cohesive focus. But the quality of the essays shows that further volumes investigating principles...

An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure, by Franklin, James

This rich book differs from much contemporary philosophy of mathematics in the author's witty, down to earth style, and his extensive experience as a working mathematician. It accords with the fiel...

An Aristotelian realist philosophy of mathematics: mathematics as the science of quantity and structure

An Aristotelian realist philosophy of mathematics: mathematics as the science of quantity and structure

James Franklin: An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure

James Franklin: An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure

An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure

An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure

Mathematics as a Science of Quantities

Mathematics as a Science of Quantities

Algebra of Conscience: A Comparative Analysis of Western and Soviet Ethical Systems

In this book two ethical systems are described in the language of mathematics. Ordinarily mathematics is thought to be a science of quantity. Indeed, manipulation of quantities constitutes much of mathematics. Elementary applied mathematics deals with reckoning and measurement, where concrete quantities are objects of attention, such as counting sheep or weighing corno But the operations on these quantities are performed with the help of symbols, from which concrete referents have been 'abstracted out': 3 + 5 = 8 regardless of whether the symbols stand for numbers of sheep or tons of corno Thus, the first principle that exhibits the power of mathematics is abstraction. It is one ofthe three pillars on which the edifice of mathematics rests. Another pillar is precision. Ordinarily, man communicates by words. W ords serve communication to the extent that they refer to things, events, states of affairs, feelings of the speaker, and so on. These are the meanings attributed to words. Communication is successful to the extent that the meanings coded upon words by the speaker correspond to the meanings decoded by the hearer. As is weH known, the degree ofthis correspondence varies enormously in different contexts of discourse and with the back grounds or attitudes of the speakers and hearers. Mathematics is a language in which the meanings ofthe symbols (the 'words' ofthis language) are absolutely precise. This precision is achieved by abstraction. Abstract terms are defined by their relations to other terms and by nothing else.