Four Theoretical Approaches to Metaphysics Essay Example for Free

Four Theoretical Approaches to Metaphysics Essay There are four theoretical approaches to the metaphysics and they include Dualism and the theory that what exists on can do so on two levels the physical or the mental. The next approach is Materialism which theorizes that everything exists on a physical level. Then there is the Idealism approach which states that everything that exists is mental or spiritual. Finally, there is Alternative Views which theorizes that what exists in neither mental nor spiritual but believed that what exists is both, which means that what exists is neutral. In the Materialism theory of metaphysics it is said that everything is made of some kind of structure that are now called atoms. These atoms are governed entirely by physical laws and are thought to make up everything that we know and see. There were and are still many men in the scientific community that feel this way, but the most pronounced one was named Thomas Hobbes. Hobbes implied â€Å"clearly that all things are made of material particles and that all change reduces to motion. † (cite) His theory states that everything is matter in motion to include an individual’s thought process. Hobbes goes into detail about how this process works and called it perception or sense. His way of describing it is the fact that things have different properties and that the properties do not really exist. The properties of an object are based on what we perceive them to be. We perceive a rose to be beautiful, smell nice, and have red pedals. Those properties according to Hobbes are all based on perception and the rose does not actually have any of these traits. â€Å"The things that really are in the world outside us are those motions by which these seemings are caused. † (cite) Hobbes describes perception as motion from the outside effects the motion of the inside of a person. The motion on the outside affected the motion on the inside and leaves a lasting effect after the motion is complete or dispersed then the motion that remains behind on the inside is left as a memory. The motion that is still on the inside is a perception and in turn is the root cause for thinking, imagination, and memory. As humans we describe this reaction by assigning words to these perceptions and Hobbes labeled that as reasoning. The way that people reason is nothing sort of â€Å"adding and subtracting of the consequences of general names. † (cite) The easiest way that this can be explained would be to refer it to a computer. The hard drive is considered as the movement on the inside and the keyboard and mouse as the outside. The hard drive is made up of a disk and magnet and works by taking the disc and spinning is around at a rapid pace. Next the magnet is moved around to encode the data to the hard drive. This whole process is done through movement and if stationary there is nothing that can be done to retrieve or store information. First to store or retrieve information an external source of movement needs to happen. Movement from the outside was represented as a keyboard and mouse. The keyboard and mouse which is movement from the outside affects the hard drive which is the movement from the inside and vice versa. Now that movement has been represented the reasoning of information needs to be considered. Now we understand what movement effect movement means we can now address the fact of reasoning and perception. All of the information that the computer takes in needs to go somewhere and needs to be retrieved again. The computer makes sense of all the data by assigning numbers to all of the data so that it can be retrieved again. This aspect would be considered our perception which is reasoning which as Hobbes stated before is our thinking, memory, and imagination. Now some people would argue that Hobbes theory does not take into accounts decision making and other voluntary actions, but he does go into detail about how that process works. Hobbes addresses the finer points of the decision process by stating that every decision or movement starts of as an â€Å"endeavor† which was caused by perception. He then breaks it down even into two groups consisting of desire and aversion. When the endeavor is toward something then it is considered a desire and when it is away it is considered an aversion. We associate desire and aversion with words like love and hate or good and bad. So according to Hobbes the basic principle of our decision making is like a magnet. Let’s look at the magnet that is in the computer and affects the hard drive. Sometimes data can be corrupted and the information will not take to the hard drive. The process of corrupt data being entered from the outside can be considered as an aversion. Now any information that the system lets in can be considers as desire. If that did not make sense then lets look at a magnet in general. A magnet has a positive and a negative side. Anything that is attracted to the positive side can be considered a desire and anything that is repelled by the negative side can be considered an aversion. In the recent years there has been some advancements in technology that allows us to uncover the mysteries of the universe. Scientists have found matter that is smaller than atoms and they are calling them subatomic particles. It has been discovered that these particles make up every aspect of the universe and are comprised of some type of energy that is connected with everything else. After this discovery a lot of scientists are rattled about their theory and if Materialism is really the right type of metaphysical theory to go with. However, this does not completely rule this theory out it just seems like that needs to some changes or tweaks to the way that we think about Materialism.

The Earth is surrounded by a covering of air which we call the atmosphe

The Atmosphere The Earth is surrounded by a covering of air which we call the atmosphere. It reaches over 384 miles from the surface of the earth, so we can only see what occurs in the troposphere and the tropopause. Nitrogen – 78% Oxygen – 21% Argon – 1% Carbon Dioxide – 0.035% Other – 0.00253% The above information highlights what the atmosphere is composed of. It is clearly visible that Nitrogen is the dominant gas as over three quarters of the atmosphere is made up of this. It is very fortunate that Nitrogen is not a very reactive gas because if it were not, that atmosphere would be far less stable and extremely dangerous. The pie chart refers to the atmosphere today but it was not always made up of these percentages. It seems that carbon dioxide levels have raised a lot and these rises may be down to many causes such as the industrial revolution and constant deforestation. Natural functions of the atmosphere The atmosphere is vital for life and acts as a life support system to al...

Relating Pairs of Non-Zero Simple Zeros of Analytic Functions

Relating Pairs of Non-Zero Simple Zeros of Analytic Functions Edwin G. Chasten June 9, 2008 Abstract We prove a theorem that relates non-zero simple zeros sol and z of two arbitrary analytic functions f and g, respectively. Preliminaries Let C denote the set of Complex numbers, and let R denote the set of real numbers. We will be begin by describing some fundamental results from complex analysis that will be used in proving our main lemmas and theorems.For a description of the basics of complex analysis, we refer the reader to the complex analysis text Complex Variables for Mathematics and Engineering Second Edition by John H. Mathews. The following theorems have particular relevance to the theorems we will be proving later in this paper, and will be stated with out proof, but proofs can be found in [1]. Theorem 1 (Deformation of Contour)(Mathews) If CLC and ca are simple positively oriented contours with CLC interior to ca , then for any analytic function f defined in a domain conta ining both contours, the following equation holds true [1]. F (z)adz -? CLC f (z)adz Proof of Theorem 1 : See pages 129-130 of [1]. The Deformation Theorem basically tells us that if we have an analytic function f defined on an open region D of the complex plane, then the contour integral off long a closed contour c about any point z in D is equivalent to the contour integral of f along any other closed contour co enclosing that same point z. The Deformation Theorem allows us to shrink a contour about a point z arbitrarily close to that point, and still be guaranteed that the value of the contour integral about that point will be unchanged.This property will be instrumental in the proof of a lemma we will be using in proving our main result that relates all ordered pairs (zoo , sol ) of non-zero simple zeros, zoo and sol , of any two arbitrary analytic functions, f and g, each having one of those points as a simple zero. This powerful result is both non-trivial, and counter-intuitiv e: there is no reason to think right owe that all pairs of non-zero simple zeros of analytic functions are related.The result is non-trivial because our result only works for pairs of non-zero simple zeros and does not in general carry over to more than two non-zero simple zeros. All of the statements above will be proven rigorously The author wishes to proper special thanks to Sean Apple, DRP. Edwin Ford, Ryan Mitchell, and Larry Washman for all of their insights and contributions to making this paper possible. Without each one of them, none of what is in this paper, however useful or not, would have been possible. In this paper.But before this, we wish to describe briefly one case where a more general result does hold; namely, that if the non-zero simple zeros of an analytic function g are closed under multiplication, then the non-zero simple zeros of any other arbitrary analytic function, say h, that is defined on a union of open regions in the complex plane containing all of the non-zero simple zeros of said function g, can be related using a slight modification of our main theorem to be proven. All but the last of these statements, too, will be proven rigorously in this paper, as the proof of he last statement is trivial.One particular application of this special case of our main theorem to be proved, is the reduction of the prime factorization problem down to evaluating contour integrals of any number of possible analytic functions over a closed contour. More specifically, the integral is taken over a closed contour containing information about the prime factors of a product of prime numbers. The product to be factored is contained in the argument of a product of analytic functions, f and g, each of whose only zeros in the complex plane occur at the integers, and the result is a factor of the product of prime numbers.This particular result was the main conclusion obtained via our two year research project consisting of the following researchers: Sean App le, DRP. Edwin Ford, Ryan Mitchell, and Larry Washman, math instructor at Pierce Community College. Our collaborative research on the integer prime factorization problem was of great inspiration to the author in the formation of the generalization that is the main theorem of this paper.This main theorem, itself, is a generalization of some machinery we had together developed to reduce the prime factorization problem to evaluating contour integrals of the product f two specially chosen functions in the complex plane during the two year research project. The author wishes to thank Sean Apple, DRP. Edwin Ford, Ryan Mitchell, and Larry Washman, for their inspiration and help in making this generalization possible, for without them, none of this, however useful or not, would have been discovered at this time.For the following discussion, see page 113 of [1] for a formal definition of a contour. Now we shall discuss some more theorems that will be instrumental in proving our main results. The following theorem is called Cauchy Integral Formula. It provides us a way to represent arbitrary analytic functions evaluated at a point z in the domain of definition of the function in terms of a contour integral. This highly famous result is extremely powerful, and has many applications in both physics and engineering [1].It is also instrumental in proving a most counter-intuitive result: that if a function f is determinable on an open subset of the complex plane (I. E. If f is analytic on an open subset of the complex plane), then f has derivatives of all orders on that set [1]. In other words, if a function f has a first derivative on an open subset f complex numbers, then it has a second derivative defined on the same open subset of complex numbers, and it has a third derivative defined on the same open subset of complex numbers and so on ad infinitum [1].Theorem 2 (Cauchy Integral Formula)(Mathews) Let f be analytic in the simply connected domain D, and let c be a simple closed positively oriented contour that lies in D. If zoo is a point that lies interior to c, then the following holds true [1]. adz Proof of Theorem 2: see page 141 of [1]. The following theorem is called Leibniz Rule and along with Cauchy Integral Formula is instrumental in proving what is known as Cauchy Integral Formula for Derivatives, which has as a corollary, that functions that are analytic on a simply connected domain D, have derivatives of all orders on that same set [1].Without this theorem, we would need much stronger assumptions in the premise of our theorem relating pairs of non-zero simple zeros of analytic functions. Although we shall not use Leibniz rule directly in any of our proofs, Leibniz rule together with Cauchy Integral Formula form the back-bone of the machinery in the proof of Cauchy Integral Formula for Derivatives given in [1] on page 144, which we shall only outline. 2 Theorem 3 (Leibniz Rule)(Mathews) Let D be a simply connected domain, and let I : a t 0 b be an interval of real numbers.Let f (z, t) and its partial derivative fez (z, t) with respect to z be continuous functions for all z in D, and all t 2 1. Then the following holds true [1]. B f (z, t)dot fez (z, t)dot is analytic for z 2 D, and Proof of Theorem 3: The proof is given in [2]. The following Theorem is called Cauchy Integral Formula for derivatives and allows one to express the derivative of a function f at a point z in the domain off by a onto integral formula about a contour c containing the point z in its interior.The formula shows up in the remainder term in the proof of Tailor's Theorem. The remainder term mentioned above is used in the proof of Theorem (10), our main result. Theorem 4 [1](Mathews) Let f : D ! C be an analytic function in the simply connected domain D. Let be a simple closed positively oriented contour that is contained in D. If z is a point interior to c, then n! Ads z)n+l Proof of Theorem 4: We give here a sketch of the proof appearing in [1] . The proof is inductive and starts with the parameterization C : s = s(t) ND Ads = s (t)dot for a 0 t 0 b.Then Cauchy Integral formula is used to rewrite f in the form O f (s(t))so (t) dot s(t) z The proof then notes that the integrands in (B) are functions of z and t and the f and the partial derivative off with respect to z, fez , are derived and then Leibniz rule is applied to establish the base case for n = 1. Then induction is applied to prove the general formula. The main point of this is Corollary (5. 1) in [1] on page 144, which states that if a function f is analytic in a domain D, then the function has derivatives 3 of all orders in D, and these derivatives are analytic in D.Without this corollary, we could not relate the non-zero simple zeros of analytic functions as stated in Theorem (10); instead, the best we could do is to relate the non-zero simple zeros of functions whose second derivative exists on the intersection of the domains of the functions that contain the p air of non-zero simple zeros of the pair of given functions. But with Corollary (5. 1), we need only assume analyticity of the functions in question at the non-zero simple zeros, which significantly strengthens the results of our paper.Below we will give the definition of what is known in complex and real analysis as a ere of an analytic function f of a given order k, where k is a non-negative integer. What the order of a zero z tells us is how many of the derivatives of the function f are zero at z in addition to f itself. What is known is that if two functions, f and g, have a zero of order k and m, respectively, at some point zoo in the complex numbers, then the product of the two function f and g, denoted f g, will have a zero of order k + m at the point zoo [1].

Leonardo da Vinci An Introduction - 708 Words

Leonardo da Vinci Introduction Leonardo da Vinci is among the most well known artists, designers, engineers and innovators in the history of the world. He may in fact be the most revered and studied artist / inventor of all time, due to his creative genius and his knack for originality in thinking and design. This paper reviews the impact that Leonardo has had on civilization since his remarkable career ended upon his death in 1519. Leonardos Legacy Leonardos birth (1452) came just two years prior to the invention of the printing press by Gutenberg. As he matured and began painting, he wanted his drawings to be printed, but the printing press in those years was not able to deal with the  ¦complex technical and scientific drawings he had created by the tens of thousands (Veltman, 2008, p. 381). It wasnt until after Leonardos death that the printing technology advanced to the point of being able to reproduce the rough sketches and carefully composed presentation drawings (Veltman, 381). Still, over the next five hundred years or so, Leonardos drawings, notebooks and art have been passed from hand to hand and for the most part preserved. While Leonardos most famous works Mona Lisa and the Last Supper have put his brilliant artistic skills in display for myriad generations of critics and art collectors, it has only been over the past fifty years or so that  ¦our understanding of Leonardos engineering activities has increased considerably (Veltman, 383).Show MoreRelatedAnalysis of Da Vincis Work as Being Reflective and Definitive of the Renaissance Period948 Words   |  4 PagesLeonardo Da Vinci and the Renaissance Period Objective The objective of this work examines the how Leonardo Da Vincis work is reflective and definitive of the Renaissance period and as well, describes some of Da Vincis art. 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