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The history and philosophy of science (HPS) is the subject that entails the history of science and philosophy of science. Even though several researchers in the field are taught chiefly as either philosophers or as historians, there are degree-granting faculties of HPS at some of the prominent tertiary institutions (Newman & Clericuzio, 2015). It examines significantly what happen in the past and how people contributed to the evolution of different concepts of matter.

Throughout the seventeenth century, Europe past through a sequence of fluctuations in beliefs, thought and knowledge that impacted the continent significantly, some of the changes that took place were introduction mathematics, Cultural Revolution, Atomism and politics progressed. It was a transformation of the mind that were longing to understand how nature toil and furthermore to comprehend the original decrees (Cohen 2012, p. 183). This era in the antiquity of Europe was referred to Scientific Revolution since nearly every aspect was transforming. During this period, the exploration of the earth and its understanding of the world was discovered on profound mulling, thoughtful over different questions attempting to uncover the aims or enlightenment that provided signs to awareness the phenomena. By the 17th century, the pattern began to move as some natural philosophers were declining the unconfirmed models and using specific devices to attain careful measurements to base their findings on experimentation and observation.

One of the conceptions of the matter that was developed was the varieties of atomism. They were instituted in the seventeenth-century by several philosophers. Epicurus is recognised as one of the major philosophers who existed during the Hellenistic period. His significant contribution to the conceptions of matter was the development of metaphysics (Cohen 2012, p.203). He claimed that the universe consisted of atoms that could not be divided further and that they flew around in the empty space. In his work, Epicurus tried to provide an atomic explanation to all natural phenomena. He explained that ordinary objects were a collection of atoms. He claimed that it was possible to describe all events and properties of macroscopic bodies using entanglements, rebounding, and collisions of atoms.

Epicurus’ theories in metaphysics were based on two statements: we can all see that some bodies are in motion, and it is not possible for something to come into existence from something that never existed (Newman et al. 2015, p. 162). His second phrase is based on the Principle of Sufficient Reason which states that “for everything which occurs there is a reason or explanation for why it occurs, and why this way rather that.” For bodies to move, an empty space or void (as Epicurus calls it) has to exist for the objects to move in. He stated that bodies are made up of smaller bodies. His theory is evident in the possibility of cutting bodies into smaller pieces. However, the division always comes to an end because if it was indefinite, the bodies will dissolve and become nothing. To better explain the irregularities of matter, Epicurus mentions that the building blocks of matter are basic and unchangeable. Such non-compound bodies are the ones referred to as atoms. Epicurus claimed that atoms existed without relying on their existence in other bodies.

Due to Epicurus' belief that it is impossible for something to exist out of nothing, he believes that the universe has always existed and it has no beginning (Newman et al. 2015, p.163). Similarly, atoms can never come into existence since they have always existed. He continued to argue that the universe has an unlimited size. Due to this, Epicurus states that there are unlimited atoms and infinite void. The existence of an endless void is essential to facilitate the movement of the unlimited number of minute particles.

The Atomism conception was of great significance as it was the principle that described multifaceted phenomena regarding combinations of fixed units or particles. This philosophy has discovered its greatest real application in natural science: conferring to the atomistic interpretation; the material space is consist of minute atoms, which are well thought-out to be comparatively immutable and straightforward and very thin to be observable (Newman et al 2015, p.165). The multiplicity of visible types in nature, then, is centred upon alterations in these atoms and their outlines; henceforth, any noticeable variations ought to be reduced to changes in these arrangements.

Aristotle is another philosopher from the 17th century whose thoughts were original and he an influence in both science and religion. For him, metaphysics focused on the first principles of scientific knowledge. It focuses on existence based on its most fundamental state and the essential attributes of existence. Aristotle explained that the universe was located between two extremes: form without matter and matter without form. It is known as the philosophy of nature. He explained that the change from form to matter usually has a purpose.

He introduced several notions about time, space, and motion (Osler 2010, p.82). He described motion as the change from matter to form, and it exists in four different kinds: motion affects the beginning and the end of an object; motion changes the quality; motion increases and decreases the quantity; motion causes changes location by locomotion. Also, he defined time as a measurement of motion depending on what took place earlier and later. Aristotle explained that space is the limit of the surrounded object towards the body that is enclosed. His concepts provided the basis for the study of metaphysics.

Also during this century was extreme undertaking and invention in mathematics. Progresses in numerical solving, the advancement of analytic geometry and symbolic algebra, and the discovery of the integral calculus and differential ensued in a first expansion of the unit categories of mathematics. Analytic geometry which as well is termed as the coordinate geometry-the mathematical substance in which algebraic methods and symbolism are applied to illustrate and work successfully on challenges in geometry. The connotation of analytic geometry is that it establishes a connection between algebraic equations and geometric curves. This linkage makes it imaginable to reformulate difficulties in geometry as correspondent equations in algebra, and the reverse is true; the approaches of either unit can then be employed to provide the solutions to problems in the other. For instance, processers come up with the animations for exhibition in films and games by influencing algebraic equations. From its discovery, calculus has been vital to the progress of several scientific developments, predominantly in the areas of engineering and physics.

Rene Descartes was a well-known philosopher who took part in the Scientific Revolution in the 17th century. He focuses on the field of mathematics in his arguments. He believed that the key to philosophy was based on the facts of mathematics which could not be disputed. He worked on merging geometry and algebra. He even published his work named “Discours de la method.” One of the appendices titled “La Geometrie” is still considered a landmark in the history and philosophy of mathematics (Cohen 2012, p.103). Descartes introduced the incorporation of symbols in mathematical expressions. He used a, b, and c to represent known quantities and the unknown quantities were represented by x, y, and z. These symbols are currently referred to as the standard algebraic notations. His book is quite similar to modern mathematics textbooks.

In “La Geometrie,” Descartes introduced the Cartesian coordinates. He developed the technique of representing a point using two dimensions. One dimension represented the horizontal location, and the other represented the vertical location. He effectively divided a plane into four quadrants using perpendicular lines which met at the origin. It is now possible to represent an equation on a plane by plotting the solution set of the equation. Descartes contribution to analytic geometry allowed the conversion of algebra to geometry and vice versa. It is now possible to solve a pair of simultaneous equations either graphically or algebraically. His theory led to more discoveries of calculus by Newton and Leibniz.

Descartes came up with a technique called “rule of signs” which was used in the identification of negative or positive real roots of a polynomial. It popularised the use of superscript notation to indicate the powers of numbers. Even though the technique did not provide a solution to the polynomial equation, it gives information on the total number of negative and positive roots of the polynomial (Goldstine 2012, p.87). Also, Descartes contributed to the development of modern physics. He came up with conservation principles of motion, several developments in optics and research on refraction and reflection of light, and laws of nature.

Calculus which was developed on seventeenth-century is of significant importance since it makes us get information concerning the movement of astronomical figures, weather designs, electronic and electric systems, and circuits and the flow of light and sound to mention a few (Goldstine, 2012). It has doubtless been convenient in the discovery of the number of matters in every home. Calculus is consequently beneficial for large-scale and small-scale scientific advancements, discoveries and inventions in broad-spectrum. Calculus is furthermost significance since of its enormous applicability, and also calculus is not confined to only analysis and mathematics, but it is used nearly everywhere. It includes the following faculties that calculus is of great importance, Dynamic Systems, physics, Economics, Engineering, Chemistry, and Biology. Infinitesimal calculus as one might know is the learning of rate of adjustment of functions in accordance to elements the role is relying on.

References

Cohen, H.F., 2012. How modern science came into the world: Four civilizations, one 17th-century breakthrough (p. 832). Amsterdam University Press.

Goldstine, H.H., 2012. A History of the Calculus of Variations from the 17th through the 19th Century (Vol. 5). Springer Science & Business Media.

Newman, W.R. and Clericuzio, A., 2015. Atoms and Alchemy: Chymistry and the Experimental Origins of the Scientific Revolution. Aestimatio: Critical Reviews in the History of Science, 4, pp.162-165.

Osler, M.J., 2010. Reconfiguring the world: nature, God, and human understanding from the Middle Ages to Early Modern Europe. JHU Press.

November 13, 2023

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