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INTRODUCTION
The ancient Greeks knew that reasoning is a structured process governed, at least partially, by a system of explainable rules. Aristotele codified syllogisms; Euclide formulated geometric theorems; Vitruvius defined the criterion and referential key so that every architectural element could be proportioned according to an ideal model, symbolizing the aspirations and aptitudes of that particular civil society.
In these forms of reasoning it is possible to distinguish contingent aspects with regard to the role which the use of a method and the application of a procedure play within any conceptual process: communicable by virtue of the codes and the prescribed norms, comparable in every time and place by virtue of the reproducibility of the procedures.
Euclidian logic begins with the inductive definition of very simple concepts and gradually constructs a vast body of results, organised in such a way so that each concept depends on the previous. Thus, a strong and rigorous construction is derived that makes all operations perceptible, comprehensible and intelligible. But, unlike processes that are physically constructed, Euclidian reasoning does not materially crumble if its structural elements, that is, its demonstrations, are not coherent with the reality of the empirical world. This explains why deductive-inductive logic, subtended by the philosophical-scientific thought of classical culture, has unconditionally influenced almost all fields of knowledge for almost two thousand years.
Physical-mathematical knowledge was the first to understand the conventional character that is typical of axiomatic reasoning: ".. which firstly, and in the most rigorous manner, became conscious of the symbolic character of its fundamental instruments" [Cassirer, 1929]. The attempt to render Euclid's works without contradictions has caused a review of the form in which scientific work is carried out [Saccheri, 1733]. The verification of the existence of many types of points and lineshas sanctioned the distinction, even in the field of knowledge, between common language and technical language, clarifying once and for all that it is the the type of link established between the symbol and the meaning that provides the symbol with its significance.
Already in antiquity, the criticism raised by the sophists against the use of a ‘common' language had established the premises for the definition of a technical, or pseudo-technical, language, which would be later adopted by Euclid in his Elements. Here, the first twenty-eight propositions, thanks to the uniqueness of the relations that link human intuitions to the properties of geometric entities, define absolute geometry; geometry, that is, which doesn't necessitate any preformulated theorem for its enunciation.
(Hawkins, 2015). Disrespect is not the absence nor necessarily the opposite of respect. For example, a person may demand respect through intimidation and fear, but that does not make the respect they receive positive. Or, a person may be respected for their
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
One source of this interest in method was ancient mathematics. The thirteen books of Euclid's Elements was a model of knowledge and deductive method. But how had all this been achieved? Archimedes had made many remarkable discoveries. How had he come to make these discoveries? The method in which the results were pr...
Galileo’s struggle with the Catholic Church is the essence of the problems people had introducing new ideas to the world. This was a time period during which people were often killed for what they believed by either the state or the church. Perhaps by not killing Galileo outright the church showed that times were starting to change, or maybe not. The episode will no doubt go down in history, however, as a turning point in science, and in religious thought.
And so while the good of Galileo may seem rather subtle and irrelevant to most of us and not nearly as direct and blatant as that of others in history, the impression he laid on humanity is not to be downplayed in any way. There’s a reason he is known as “the father of modern physics/astronomy.” Had Galileo not been such a diligent character with the determination to help society truly understand the world, many other great minds who may not have been quite as brave as to oppose the Church as he was could potentially not have ever shared their works and wouldn't even be a part of history as it’s known today. Without them and Galileo, there’s no telling where technology and science would be and what conceivably could be lacking in this modern age.
...w can there really be any choice at all? The answer is clear- keep your kitty safely inside, and enjoy the years of love that she offers.
Galileo Galilei was an Italian philosopher born in 1564. As an adult, he didn’t believe the universal geocentric theory of the planets and heavens which was established by the Catholic Church. The church taught that the Earth was the center of the universe and everything revolved around our planet. Another theory that the Church supported was that the Earth stood still while the sun rose and set every day. Society in the 1500’s believed that the Pope spoke for God through a divine connection and to against the church was to go against God. To speak out against the church in this time was strictly taboo. If one was to speak against the church was considered to be heresy, which is exactly what happened to Galileo. Galileo invented the telescope and began studying the heavens above and noticed that changes within the stars and planets. He noticed that the “stars” that surrounded Jupiter moved. He came to the conclusion through rational thinking, that the Copernicus’ heliocentric theory was correct. Copernicus was a scientist and philosopher whose theory proposed that the sun was stationary and the heavens orbit around the sun. Galileo tried to convince the church not to aboli...
This essay will consist in an exposition and criticism of the Verification Principle, as expounded by A.J. Ayer in his book Language, Truth and Logic. Ayer, wrote this book in 1936, but also wrote a new introduction to the second edition ten years later. The latter amounted to a revision of his earlier theses on the principle.It is to both accounts that this essay shall be referring.
In the U.S. senate was a heated debate over the issue of slavery. In the South, voices were raised and demanding a separation from the Union. The conflict between the thoos states was also fueled from the upcoming presidential elections. Abraham Lincoln was one of the most promising candidates and an opponent of slavery. Later Abraham Lincoln was elected as the 16th president of the United States on November 1860. He was the first republican president and he received 180 of 303 possible electoralvotes and 40 percent of the popular votes.1 2 The South immediately took political consequences. South Carolina declared to withdraw from the federal government on December 1860. The representatives met six slave states and formed the formation "Confederate States of America" in February 1861. The president of the Confederacy was Jefferson Davis. Five more states joined this confederation a short time later. The capital of the Confederacy was Richmond in Virginia3.
In this book, Samir Okasha kick off by shortly describing the history of science. Thereafter, he moves on scientific reasoning, and provide explanation of the distinction between inductive and deductive reasoning. An important point Samir makes, is the faith that humans put into the inductive reasoning
Aristotle saw logic as a tool that led to probing and eventually to explanations through argumentation rather than deductions alone [6]. In Aristotle’s view, deductions were not sufficient to lead to any type of validity, and most certainly not in the sciences, where arguments should “feature premises which are necessary” in order to avoid false suppositions [6]. He insisted that because science “extends to fields of inquiry like mathematics and metaphysics,” it is essential that not only facts had to be reported, but also explained through their “priority relations” [6].
The Greeks are credited with inventing philosophy and it was believed that whoever pursued a deeper understanding in a subject was a philosopher. Since then, the subject of philosophy has grown and has helped us analyze complicated questions such as what is real and what is beauty. The questions encountered in philosophy can fall under four areas, but in this essay we will focus on one of them, Metaphysics. Metaphysics is the branch of philosophy that deals with questions relating to the physical world. Further, in life we encounter many physical objects in which we can touch and feel. However, what makes these objects real? Plato introduced his metaphysics idea of Theory of Forms, which presents a view of what makes an object real. In this paper, I will touch upon the Theory of Forms and explain that a world of forms does exist separately from concrete/permanent things.
Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
The Nature of Mathematics Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its basic interest. The essence of mathematics lies in its beauty and its intellectual challenge. This essay is divided into three sections, which are patterns and relationships, mathematics, science and technology and mathematical inquiry. Firstly, Mathematics is the science of patterns and relationships. As a theoretical order, mathematics explores the possible relationships among abstractions without concern for whether those abstractions have counterparts in the real world.