Category: Logic

Introduction

It should be noted that David L. Hull, Karl Popper, and Percy Bridgman have contributed greatly to the existing body of knowledge. Their works have been reviewed by many other scholars, and they are appreciated by members of the scientific community despite the criticism of some of the texts. The purpose of this paper is to reflect on the writings of these three scholars and generate three questions that can be discussed in class.

Discussion

The main query that the author will strive to address is related to operations and their ontological status. Operationism is a philosophical domain, which has been put forward by Bridgman (1927). He suggested a proposition that the meanings of scientific concepts were synonymous to the multitude of operations by which their content was determined. In particular, the philosopher argued that the experimental procedures of a phenomenon represented such operations (Bridgman, 1927).

Consequently, his idea was concluded to an understanding that the meaning of physical concepts should be determined by the totality of experimental operations. Nevertheless, this approach could not be universally applied to all scientific and theoretical knowledge.

Notably, scholars have repeatedly stressed the importance of discovery operations. However, as a rule, they were discussed in the light of unsuccessful operationism. Such cases were covered in the works by Bridgman (1927) and Popper (1959). The overall difficulty of discovery operations was linked to the way they were perceived. To be more precise, the researchers relied on theories, frameworks, and hypotheses and connected them to reality. However, discovery operations have a different nature. The first instance is empirical in its character, which implies that it explicates certain facets of reality. In their turn, operations are a number of principles that should be utilized to select an empirical statement among a multiplicity of them.

Therefore, the interpretation of operations should go beyond the propositions suggested by Bridgman (1927). The article by Hull (1968) strongly supports this statement. Operational and theoretical justifications can be contraposed. According to Hull (1968), operations should not be combined with the artifacts that the study is seeking. One of the reasons for it lies in the fact that operational justifications should be logically consistent solely.

Moreover, based on the analysis of the three texts, it can be assumed that a research providing theoretical definitions solely cannot be considered strong. This inference is fundamental for the scope of the course and the authors professional endeavors since it should serve as a construct for the further philosophical reasoning and justification. Theory is a part of a reliable study; therefore, the works that have proved a phenomenon using only theoretical instruments are not rigorous enough (Hull, 1968). Their weakness lies in the fact that such researches cannot provide real-life examples.

Conclusion

Thus, it can be concluded that the three philosophical texts have expanded the existing body of knowledge. Despite the fact that some of them have been subjected to criticism and the scholars have recognized the weaknesses of the claims made, these writings have advanced the comprehension of operationism. The main derivation that can be drawn from the reflection is that operational and theoretical justifications should not be regarded as a single method.

Questions for In-Class Consideration

Based on the discussion and the assumptions made, the three questions for in-class consideration are as follows:

1. How can scholars make sure that their operations are scientifically valid and optimum?
2. What kind of philosophical tests can be applied to operations?
3. How do operations push the advancement of knowledge?

References

Bridgman, P. W. (1927). The logic of modern physics. New York, NY: MacMillan.

Hull, D. (1968). The operational imperative: Sense and nonsense in operationism. Systematic Zoology, 17(4), 438-457.

Popper, K. (1959). The logic of scientific discovery. New York, NY: Basic Books.

What are syllogisms?

A syllogism can be defined as a type of logical argument. However, syllogisms differ from standard logical arguments considerably. As a rule, a traditional logical inference has two basic elements, i.e., a premise and a conclusion. A standard syllogism contains three basic elements, which are two premises and the following conclusion. A typical syllogism is also different from a traditional logical inference in that the conclusion that follows its two premises does not coincide with the supposed result. The conclusion of a syllogism interferes with the minor premise from a major one with the help of mediation.

What constitutes a formal fallacy?

The argument whose premises do not support the conclusion in any way and in which the chain of logical conclusions is always wrong is typically referred to as a formal fallacy. When speaking about a formal fallacy, it is important to realize that it does not matter in the given case whether a specific argument is true or false; it might as well be true with a formal fallacy in it. Traditionally, the following pattern is used to demonstrate the specifics of a formal fallacy:

• Logical statement: 1. If A then B. 2. A. 3. Therefore, B.
• Formal Fallacy: 1. If A then B. 2. B. Therefore, A.

Examples of a formal fallacy:

1. If one is ashamed, ones face will turn red. A mans face is red. Therefore, he is ashamed.
2. Some men can drive a car. Mr. Johnson is a man. Therefore, he can drive a car.

What is the difference between Conjunction and Disjunction?

In logical operations, conjunction is used to denote an and operand; in other words, it denotes the situation in which both operands (or all those included) are true. In its turn, a logical disjunction, known as or, is an operand that shows if one or more of the operands involved is true.

Herein lies the difference between the two operands. In the case of Conjunction, the statement under consideration can be regarded as a universal truth; otherwise, the Conjunction does not make sense. The Disjunction operand works differently; in contrast to Conjunction, Disjunction serves to denote that only some of the operands in question are true, yet not all of them.

From a mathematical standpoint, conjunction can be interpreted as the inclusion of a specific subset into another set. Disjunction, on the contrary, presupposes the exclusion of one of the sets.

How Does Truth Table work?

Often defined as a template for analyzing the forms and relations of the elements in logical expressions, a Truth Table consists of several columns in which a corresponding variable is placed. The final column is left for defining and marking the outcome of a logical operation.

It would be a mistake to believe that a Truth Table can only deliver the results for the operations involving only two variables. On the contrary, as it has been stressed above, the number of types of input variables can be rather big. The result, however, is necessarily restricted to the truth-or-false answer.

It should also be mentioned that a Truth Table allows for dealing with the logical operations that include conjunctions, disjunctions, negations, or implications.

A Truth Table can also help in analyzing the relations between different elements of the logical operation in question, therefore, structuring the task and allowing for a better understanding of the problem.

Rene Descartes

Rene Descartes is one of the most significant philosophers who contributed significantly to modern philosophical science. For instance, Descartess philosophical views on educations and schooling remain essential and widely discussed until nowadays. In the first part of the present paper, Descartess evaluation of education will be reviewed and discussed. Moreover, my schooling system will be evaluated in terms of its value and knowledge of society. In the second part, four rules of logic will be presented and discussed. Furthermore, it will be demonstrated how these rules may help in everyday life.

Descartes and Education

Rene Descartes admitted that school education is an essential part of a persons socio-biological development. It is impossible to reject schooling, and unfortunately, there are no suitable practical alternatives. Descartes noted that in school, children learn how to socialize and further how to enter adulthood. The philosopher himself attended boarding school at the Jesuit college of Henri IV in La Fleche. Descartes suggested several recommendations for the schooling system, such as introducing ideas of meliorism (Descartes and Education, n. d.). He believed that the learning process is an experience, which involves practical experience and thinking process. It is essential to mention that Descartes paid special attention to practical experience rather than theoretical knowledge. Consequently, school education alone is not sufficient to feel confident in a real-life setting.

Concerning my personal schooling experience, it was essential and valuable. I learned being in a group, communicating, problem-solving, and being responsible for myself. Apart from socializing, I received vital academic knowledge for my future university education. However, I should say that education lacked practical wisdom, the same way that Descartes mentioned. We concentrated mostly on theoretical knowledge and seldom on its practical implication. I believe it is a considerable drawback of schooling, and it should be fixed in the near future, as young adults need to learn how to apply the knowledge they get.

Rules of logic

Rene Descartes developed four rules of logic, which help to gain knowledge. The first rule sounds as follows: Never to accept anything for true which I did not clearly know to be such (Introduction to Descartess method). This rule implies that it is essential to avoid any prejudice and believe only in that knowledge or facts that are clear to ones mind. The second principle Descartes suggested is To divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution (Introduction to Descartess method). The following rule is valid for every difficulty in everyday life, whether it is an intellectual dilemma or a daily recurring problem. The third rule sounds as follows: To conduct my thoughts in such order that, by commenting with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex (Introduction to Descartess method). It refers to the process of analysis and synthesis. The last rule is To make enumerations so complete, and reviews so general that I might be assured that nothing was omitted (Introduction to Descartess method). Enumerating allows us to have a road map, which helps to solve complex issues because our memory is often unable to remember too many facts.

Works Cited

Descartes and Education. N.d. Web.

Introduction to Descartess method.Austoaarya.wordpress.com, 2010. Web.

Logic is any inference or judgment made on some issue, which may be linked to intense reasoning and justification. Anything that occurs in our lives, and all our surroundings, are based on some form of logic. There lies a reason behind everything, and this notion was brought about by famous thinkers and philosophers of the olden days.

Amongst the great philosophers of all time, are the famous names of Aristotle, Socrates, and Plato. They each came up with their own philosophies regarding logic, and all the resulting philosophies were pertaining to each of their own unique way of looking at things and opining on them. Aristotle begins the history of logic, with his discussions of principles underlying various avenues of life (Ontology and History of Logic, 2008).

The history of logic relates to the progress of the science of valid inference (Wikipedia, 2008). Numerous cultures have developed and executed varying methods of reasoning, but the most prominent ones that are known to us today, are those associated with China, India, and Greece. The theories concerning logic date back to the 4^th century BC, and the most significant logical concepts developed were those of ancient Greece.

Aristotle gave his idea of logic, which was known as dialectic or analytic in those times. According to the Greek meaning, the term logic is derived from logos, which means sentence. Aristotle and Plato initially came up with their studies of logic, and it is assumed that the need for the reasoning of things aroused with the advent of geometry in that era. Geometrical evaluations had begun as early as the 6^th century, with the pyramids playing an empirical role in the Pythagoras studies, which introduced demonstrative science (Wikipedia, 2008).

The logic of Aristotle was of importance during the period of the Renaissance too. His famous works, which are of the highest eminence in the history of logic include, The Categories, Topics, and Prior Analytics, to name a few. There were five treatises present in his collection, which was named the Organon (King, P. & Shapiro, S., 1995). He is considered the first logician, giving reasoning and justifications for arguments.

Plato was the first thinker to put forth philosophical logic. He also raised three eminent questions relating to logic, firstly, if something can be called true or false, secondly, the connection between valid arguments and conclusions, and thirdly, the nature of definition.

After the philosophies of the former two thinkers, comes the Stoic form of logic. This dates back to the 5^th-century thinking and liked to the thinking of Socrates. In fact, the philosopher Euclid, who came up with these teachings with his fellow men, was a pupil of Socrates. The Stoic school contributed three main aspects, which were, modality, theory of conditional statements, and truth and meaning.

Coming back to Aristotle, he stated that the logical form of a substance is known by its quantity, as well as quality. The greatest contribution he had made to the element of logic was syllogistic, a combination of opposing thoughts and converting thoughts.

Whatever is taught today is based on logic, and the logical forms taught to us by famous philosophers of the past. Everything that we encounter has meaning, and the branch of philosophy has given us the greatest connotation of the term logic, like no one else before.

References

1. King, P. & Shapiro, S. The History of Logic. The Oxford Companion to Philosophy 1995, 496-500. Web.
2. Ontology and the History of Logic 2008. Web.
3. History of logic. Web.

Introduction

Aristotle, the great Greek philosopher, considered dialectic to be the search for the philosophic basis of science. Very often, he used this term as the synonym for logic. In addition, the prominent thinker estimated rhetoric in the context of logic, because logic, as well as rhetoric and dialectic, point out the studying of persuasion methods. The outstanding Aristotles works Poetics and Rhetoric had a great influence on the art of rhetoric and its development. Not only writers and thinkers, but also prominent teachers of rhetoric used some elements from Aristotles doctrine. Aristotle considered rhetoric to be the ability to find all possible methods of persuasion to every single object (Garver, 1995). Thats why Aristotle interpreted rhetoric to be the science about means of persuasion.

Main body

Aristotle told that rhetoric could be regarded as the branch of politics, but at the same time, it could be understood like the part of dialectic, because both rhetoric and dialectic try to find proof for persuasion. Aristotle explained the general concept of persuasion with the help of rhetorical syllogism, which consists of probabilistic conclusions. He rose important arguments and concepts in his ethical, logical, and psychological writings.

Hegel had his own conception of dialectic. His aim was to state a philosophical system so that it would combine the thoughts and ideas of Hegels predecessors. Moreover, he wanted it to be formed in such a conceptual framework in which both the future and past could be understood from the philosophical point of view. Thats why Hegel perceived that the study of philosophy was reality as a whole. Such reality he regarded as the Absolute or Absolute Spirit. According to Hegel, the Absolute had to be referred to as pure Spirit, Thought, or Mind in the long process of self-development. Traditionally the mensuration of his thought was dissected in the categories of thesis, antithesis, and synthesis. Though Hegel tried not to use those terms, still they are very important for realizing his notion of dialectic. So the thesis had to be a historical movement or a certain idea with incompleteness within itself. Such incompleteness led to opposition or antithesis, a contradictory movement or idea. Synthesis was the result of the conflict. The synthesis became a newly appeared thesis, which in its turn gave rise to another antithesis, generating a new synthesis. Such dialectical process of historical and intellectual development led to the evolution of ideas. Hegels views were based on the idealistic concept of the universal mind, which due to evolution could occupy the highest stage of self-actualization and freedom (Hegel, 1812).

Karl Popper had a similar to Hegel approach to dialectic. According to him, dialectic was a theory that maintained that something  for instance, human thought  developed in a way characterized by the so-called dialectic triads: thesis, antithesis, and synthesis (Popper, 2002, p. 421). Usually, dialectic was associated with three laws of dialectic: the law of the interpenetration of opposites (struggle and unity of opposites); the law of the transition of quantity into quality and vice versa; the law of the negation. Popper considered that logic dealt with notions of things prescinded from the real ones themselves. Though dialectic admitted contradictions, for Popper contradictions were logical contradictions. Thats why dialectic is opposed to logic.

Conclusion

In the modern philosophical literature, dialectic is represented as a kind of new logic. A newly appeared term dialectical logic is even used to depict that new type of logic (Stavinsky, 2003). Such an approach towards dialectic and logic leads to the confusion of understanding Poppers treatment of the problem. But a lot of todays scientists consider that logic, dialectic, and rhetoric belong to different spheres and cant be accepted as potential replacements for each other.

Works Cited

Haack, S. Philosophy of logics. Cambridge University Press: Cambridge, 1978.

Hegel, G. Hegels Science of Logic. London: Allen and Unwin, 1812.

Garver, E. Aristotles Rhetoric: An Art of Character. The University of Chicago Press, 1995.

Lakoff, G. Women, Fire and Dangerous Things: What Categories Reveal about the Mind. Chicago: University of Chicago Press, 1987.

Popper, K. Conjectures and Refutations: The Growth of Scientific Knowledge. London: Routledge Classics, 2002.

Stavinsky, I. Philosophical Researchers. Moscow, 2003.

Introduction

Philosophy is part and parcel of our lives. The term philosophy is derived from a Greek phrase which literally means, The love of wisdom (Soccio, 2009). Philosophy can today be used to refer to persons beliefs, values and general way of life. In this case, we will be talking of someone having a philosophy and not someone being a philosopher. The first philosophers were considered to be wise for their boldness in asking some questions like what lifes meaning was, or where our origin was. One such philosopher is Aristotle whose arguments have come to be known as the Aristotle logic (Robin, 2007). Aristotle is reputed to be the first man to study the logic concept although there have been other numerous contributions to the concept over the years.

Logic and Philosophy

Philosophy generally deals with the interpretation, meaning, evaluation as well as logical consistency. There are at least two hundred areas of study in philosophy (Soccio, 2009). Because there are so many branches of study, there is usually conflict of interest and some philosophers even suggest that some of those arrears should not be considered as philosophical disciplines. For example, a philosopher that is a logician may have a hard time embracing metaphysics. The main reason would be that metaphysics is at best confused and abstract.

Only until very recently, the philosophy from the west has been characterized by logical reasoning which involves written arguments. This in a way blocked out any other expressions of philosophical wisdom. After the eighteenth century, philosophers were no longer considered to be a certain clique of highly literate men who were able to fend for themselves or who were associated to the church. Today, learning institutions have made it possible for other people to study philosophy including women who were not considered worthy of the tile of philosophers (Soccio, 2009).

The author defines philosophy as the love for wisdom. Ideally, it means that philosophy is not a career. On the contrary, a philosopher is someone is in pursuit of knowledge and wisdom because he wants to know and not because he has to know. Philosophy is therefore not merely a means to the end. In fact, Liddell & Scott describe it as a passion for wisdom. This would imply that philosophy is not to be looked at as a career but as a hobby. It is however interesting to note that while todays philosophers have more wisdom than the olden day philosophers. They are not necessarily wiser than they (Kimura, 2006).

One other important issue that the author deals with is the fact that the tides have changed as far as archetypes are concerned. Philosophy was considered to be a privileged position that only a few people from the elite class held. This is hoverer changing with time. Philosophy is now available as a field of study at universities and it is an open course for any one with the minimum admission requirements.

Conclusion

Aristotles concept of Logic has been a major building block for logic over the years. He developed the concept of Logic as formal epistemology. This was known as oragan. He by so doing became the first thinker to develop a systematic approach to proof. He paved the way into further research by becoming he first philosopher to come up with formal deductions and independence proofs (Creed et al., 2003). The logic concept is widely used in mathematics and desings of computer algorithms.

References

Creed, L. et al. (2003). The Philosophy of Aristotle. New York: Penguin.

Kimura, G. (2006). Philosophy as Wisdom of Love: Vision in Action Leadership Institute. Web.

Robin, S. (2007). Aristotles Logic. Stanford Encyclopedia of philosophy.

Soccio, J. (2009). Archetypes of Wisdom: an introduction to Philosophy. London: Cengage Learning.

Mathematical Platonism is the concept that describes the existence, abstractness, and independence as adjectives for mathematics routine practices. The philosophy insinuates that some objects exist independently of external forces, such as language and thoughts (Park, 2018). However, the truth is not asserted regarding the formal existence and the role of Platonism in pure mathematics. Besides, the concept of independence is shallow and does not make sense to true realists because of its idea that objects occur regardless of the existence of other practices. Studying Platonism provides alternative thinking that reality extends beyond the physical world and includes objects not part of the casual and spatiotemporal order studied in biological sciences (Ruloff, 2020). The study will help understand how mathematical Platonism influences the naturalists theories school of thought because there is little or no doubt on mathematical philosophies. Freges argument that mathematical language is quantifiable gives Platonism a lifeline and true meaning (Paul, 2020). However, little is known about the objectiveness of the mathematical concepts, the level of accessibility, the metaphysical problems it seeks to address. This paper will discuss realism and true realism as concepts that help understand mathematical Platonism and answer the question of existence, abstractedness, and independence.

Keywords:Existence, abstract, independence, Platonism

Mathematical Platonism

Platonism is a mathematics philosophy insinuating that some objects exist independent of external variables, such as people, thoughts, and routine practices. Mathematical Platonism is described in three conjunctions, including existence, abstractness, and independence, which are the traditional variables of the topic. In 1953, Gottlob Frege posted a strong argument that the language of mathematics tends to refer to and quantify the mathematical objects and the corresponding theories are true (Park, 2018). However, the approach cannot be valid unless the first expression comes after and gives meaning to the statement. Consequently, the mathematical theory of Platonism has developed objections based on Freges argument (Ruloff, 2020). Classical semantics states that the singular language of mathematics refers to the first order of quantifiers and objects that range over such entities. Similarly, the truth indicates that most of the sentences accepted in mathematics are true. Thus, the mathematical concepts are epistemologically inaccessible and metaphysically problematic that attract long debate on Platonism.

Definition of Platonism

Mathematical Platonism is that mathematical adjectives replace the idea that arises from existence, abstractness, and independence. For instance, the formal structure of reality can be xMx, where Mx represents the predicate x is a mathematical object and is acceptable in all objects studied in pure mathematics. Second, the mathematical abstract of abstractedness occurs when an object is deemed abstract in the case of spatiotemporal and casual inefficacious. Lastly, claims of independence are the least clear compared to the first two claims because they ascribe to the autonomy of an object where regardless of the occurrence of other practices. However, the claim of sovereignty is still schematic and not well structured. Thus, mathematical Platonism indicates that objects exist abstractly, independent of intelligent agents such as language and believes.

Significance of Mathematical Platonism

Mathematical Platonism puts pressure on the physicality idea that reality is exhausted. Exhaustion is due to the physical objects that provide alternative thinking that reality extends beyond the physical world and includes objects that are not part of the casual and spatiotemporal order studied in biological sciences (Plebani, 2017). In addition, if mathematical Platonism is true, it puts pressure on the naturalists theories school of thought because there is little or no doubt on mathematical philosophies. Further, an in-depth understanding of the mathematics of Platonism will establish the knowledge of abstract objects leading to rediscovery, which many naturalist theories struggle to accommodate. The philosophical consequences are similar to the mathematical Platonism, but the forms are suited to accommodate such effects (Park, 2018). The resemblance is due to the mathematical concept of owning the rights as a scientific tool. Few philosophers are against the Platonism ideas with strong core claims whose scientific credentials are as strong as mathematics.

Mathematical Significance of Platonism

Platonism defends specific mathematical ideas such as the classical first-order language, impredicative definitions, and Hilbertian optimism, which are the core values in mathematical philosophy. However, according to working realism, more classical methods support mathematical reasoning but require philosophical defense based on Platonism. Therefore, while Platonism is a philosophical view, realism is a view within mathematics about the methodology of disciplines, making the two concepts distinct (Park, 2018). Furthermore, there is a positive correlation between the two views because realism receives strong acceptance from mathematical Platonism. In addition, Platonism ensures that mathematical concepts are discovered rather than invented because there is no need to restrict the idea to construction methods that establish a powerful argument (Park, 2021). Therefore, Platonism has mathematical significance because it indicates that mathematics is about independently occurring objects with unique answers, which motivates the Hilbertian optimism.

Object Realism

Object realism assumes that a mathematical abstract exists and acts as a conjunction of the existence and abstractness. Unlike nominalism, which defines the view that there are no abstract objects, object realism is abstract, and a universe exists (Plebani, 2017). However, object realism leaves out independence because it is logically weak in the concept of mathematical Platonism. The argument of object realism is stronger than mathematical Platonism because many scientists believe in non-physical objects as long as they are dependent on material things (Paul, 2020). For instance, physicalisms accept the law, poems, and corporations as a mystery of epistemic access to non-physical items and the processes constituting them. Other scientists believe that the philosophy of mathematics revolves around the objects outside the Platonism theory, such as traditional intimism. These ideas support the existence of mathematical objects that are dependent on mathematicians and their activities.

Truth Value Realism

True value realism statement involves unique objects with actual value independent of its logical order in the current mathematical theories. The idea also notes that mathematical objects are deemed accurate and vice versa, making the concept a metaphysical view that is non-ontological (Park, 2021). However, despite indicating that every mathematical statement has an actual value, it does not conform with the Platonist ideas that the actual values occur in the ontology of known mathematical objects. Mathematical Platonism promotes the concept of natural value realism by enhancing the platform where the mathematical objects acquire their truth value (Paul, 2020). However, mathematical Platonism does not include the true value realism unless further clauses are provided.

Mathematical Platonism motivates truth realism because it gets the actual value of objects and endorses at least one branch of mathematics, such as arithmetic. Nominal believers commit to the odd-sounding idea that the ordinary math statements that; there are multiples of itself between 10 and 20. In this case, it is essential to differentiate the mathematical language Lm and the nominalists and other philosophers who believe in the Lp format. Nominalist believes prime numbers exist, but no abstract objects are made in the Lp format (Park, 2021). Thus, they indicate that the actual value of the Lm values is in a fixed manner that does not make mathematical sense. Furthermore, for the existence to have the desired effects, it must occur in the Lp language used by the mathematicians and accepted by the nominalists contrary to the purpose of the claim (Paul, 2020). Philosophers argue that true realism ideologies are ideal for Platonism debate because it gives clear and tractable evidence.

Mathematical Platonism involves the ideas of existence, abstractness, and independence as adjectives for mathematics routine practices. The philosophy insinuates that some objects exist independently of external forces, such as language and thoughts. Similarly, the truth is not clear about the existence and the role of Platonism in pure mathematics. This paper agrees with the naturalists concept that independence is shallow because of its idea that objects occur regardless of the existence of other practices. Studying Platonism helps to understand its role in explaining how mathematical objects extend beyond the physical world. In addition, the study discusses how mathematical Platonism influences the naturalists theories school of thought because there is little or no doubt on mathematical philosophies. Frege argues that mathematical language is quantifiable, and the objects exist in true realism regardless of language and thoughts. Mathematics of Platonism implies that mathematical entities are valid and live and are abstract, independent of rational human activities.

References

Park, W. (2018). Philosophys loss of logic to mathematics. Studies in Applied Philosophy, Epistemology and Rational Ethics, 43. Web.

Park, W. (2021). On abducing the axioms of mathematics. Studies in Applied Philosophy, Epistemology and Rational Ethics, 161-175. Web.

Paul, T. (2020). Mathematical entities without objects. On realism in mathematics and a possible Mathematization of (Non) Platonism: Does Platonism dissolve in mathematics? European Review, 29(2), 253-273. Web.

Plebani, M. (2017). Does mathematical Platonism meet ontological pluralism? Inquiry, 63(6), 655-673. Web.

Ruloff, C. (2020). Theism, explanation, and mathematical Platonism. Philosophia Christi, 22(2), 325-334. Web.

Logic

Studies show that the radix sort algorithm was first used in 1887 by Herman Hollerith to perform computations on tabulating machines. Dalton et al. claim that radix is a sorting algorithm that uses passes to sort numbers or integers instead of using the classical method of comparisons (25). Radix sort can use the bucket sort or bin sort logic. The logic of operation involves sorting a series of numbers repeatedly by utilizing the digital properties of numbers. The sorting process starts from the rightmost digit based on the key (string or word) or the positions of the numbers being sorted. Each key is determined by its base number representation. Because different pieces of keys are fixed in size, each key holds a fixed number of values. If R represents different possible values, then the sizes vary according to the series 0, 1, 2…, R-1. Typically, “the key can be defined as a radix-R number, with digits numbered from the left (starting at 0)” (Dalton et al. 26). It has been suggested that good hardware support provides an appropriate environment to implement the radix sort algorithm.

Reasoning

The radix sorting algorithm has two specific modes of operation. The first one involves examining the key with its corresponding digits in a left-to-right order. This technique is referred to as the most-significant-digit (MSD) radix sorts (Albutiu et al. 1065). Often, the MSD approach is the most preferred sorting technique. MSD sort optimizes the lexicographical order based on the minimum amount of information. The original order of the duplicate keys needs not be kept but it follows a sequence that begins with the most significant digit, which is followed by the left most digit before shifting to the least-most digit and gradually to the right most digit. The files can be sorted recursively by partitioning them into sub-files using the sorted digits.

LSD Radix Sort

The second method is the least significant digit (LSD) radix sorts. LSD radix sort works in the opposite way to MSD radix sort. LSD radix sorts the integers from the least to the most significant digit. With LSD, short keys are given a higher priority than long keys. By considering a typical example like “b, c, d, e, f, g, h, i, j, ba” characters, it lexicographically becomes “b, ba, c, d, e, f, g, h, i, j”. The original order of the keys is usually kept when using the LSD sorting technique. LSD is non-recursive while MSD is recursive. Besides, MSD consumes more memory than LSD.

For the LSDRadixSort(R) algorithm, suppose a set of input values is supplied consisting of R = , whose length is m in the alphabetical range of [0…α], the output occurs in the lexicographical order of the following pseudo code:

for l ← m − 1 to 0 do CountingSort(R, l)

Return R

Example: Suppose the original unsorted number is: 171, 45, 75, 92, 802, 2, 25, 66, using the least significant digit results in 171, 92, 802, 2, 25, 45, 75, 66, while noting that 802 has been kept because 802 comes before 2. If sorted by 10 digits, it comes to 802, 2, 25, 45, 66, 171, 75, 92, and if sorted by 100, it becomes 2, 25, 45, 66, 75, 92, 171, 802.

The time complexity of the above sorting algorithm is O (|R| + α). Here, CountingSort(R, l) sorts the strings identified in R. Often, the strings are similar in length, m for sorting short strings and integers can. To sort N distinct numbers where d= log N digits, the time taken to sort N is given by O (Size) = O (d N) = O (N log N), which does not conflict with theory. For a word of size z, the radix sort complexity is O (z n) for n keys that make integers of size z. However, for very large n, if z is taken as a constant, the performance increases further.

Pseudo code

Radix_SORT (A, d)

for i=1 to d

Stable_Sort (A) on digit i

Example

Consider the following array: A [10]

Pass 1

Pass 2

Pass 3

Applications

According to Dalton et al., the radix sorting algorithm was developed to sort large integers and perform parallel computing (27). A set of participants can use it to securely compute multi-party computation (MPC) protocols in sorting networks whose functions take the form of (y₁… y_m) = (x₁,…,x_m). Radix sort is used in computational molecular biology, plagiarism detection, and data compression because its data redundancy detection abilities. Comparisons are not used. Radix is a stable algorithm that works in linear constant sorting time and cannot be used on long sorting keys because it requires more sorting memory.

Works Cited

Albutiu, Martina-Cezara, et al. “Massively Parallel Sort-Merge Joins in Main Memory Multi-Core Database Systems.” Proceedings of the VLDB Endowment, vol. 10, no. 5, 2012, pp. 1064-1075.

Dalton, Steven, et al. “Optimizing Sparse Matrix—Matrix Multiplication For The Gpu.” ACM Transactions on Mathematical Software (TOMS), vol. 4, no. 41, 2015, pp. 25-35.

According to Bolton, “a computer program is a set of instructions for a computer to perform a specific task” (2012, p.1). Data processing is the process by which information is obtained from data (Articlebase.com, 2012, p. 1). There are four main methods used by a computer program (or application) to process data. These are batch, online, real-time and distributed processing.

In the batch method, a program begins to process data once it has been fully collected and organized into a batch (Jones, 2009, p.8). An example where this method of data processing is particularly effective is in computerized payroll cheque processing programs. In such, it is imperative that the program has enough data as this ensures correct debiting and crediting.

In the online processing method, processing of data takes place as it is input into the program, that is, unlike in batch processing it does not wait for the data to be organized into a batch (Jones, 2009, p.14). Thus, the computer program responds immediately to the data being input. Examples where online data processing is applied include booking systems for hotels and word-processing programs.

In real-time processing, as with online processing, data processing takes place as the data is input into the program (Jones, 2009, p.20). The difference, however, is that the processing has to complete in time because the output it produces affects the next data input to the program (Jones, 2009, p.3). An example where real-time processing is effective is in patient monitoring programs.

In distributed processing, data processing is done on more than one computer typically on a server and remote workstations (Dephoff, 2012, p.4). An example where distributed processing is effective is in ATM applications.

Having discussed the methods above this paper argues that the methods used to process data in a program do not change as the quantity of data increases.

The reason for adopting this argument is that if the methods of data processing changed then there would be a high risk of programs becoming unreliable and inefficient in carrying out their tasks. To discuss the logic behind this argument we will consider two cases in which we will investigate the effect of changing the data processing method.

The first case is that of a computerized payroll program. To get an accurate payroll, data has to be collected over a specified period and processed as a whole. This is why the batch processing method is preferred in computerized payroll programs. Let us assume that online processing is used instead of batch processing.

The payrolls produced in this case will be inaccurate since online processing does not support collection of data over time and thus, computerized payroll systems will be unreliable.

In the second case, we consider a patient monitoring system that is being used to administer a drug to a patient when factoring in the patient’s heart bit rate. The data processing solution required in this case is the one that provides the program with real-time output so that it can determine if changes in dosage are needed.

Real-time data processing is apt in this case. Now if for instance batch processing was used in this case instead of real-time processing the consequences will be fatal since batch processing does not give real-time outputs. Thus, in such a case the patient monitoring system becomes unreliable.

To avoid program unreliability and inefficiency program designers do not design data processing methods in a program to change as data quantity increases. This paper therefore concludes that the methods used to process data in a program do not change as the quantity of data increases.

References

Articlesbase. (2012). Definition of data processing. Web.

Bolton, D. Definition of program. About.com. Web.

Dephoff, J. (2012). Methods of data processing. Web.

Jones, R. (2009). Types of processing. ib-computing.com. Web.

Introduction

Digital electronic devices have tremendously revolutionized the world. Many electronic devices have been invented due to the increase in the state of technology day by day. Programmable logic devices offer a wide range of features, speed and characters. In most of cases, the PLD used for a given prototyping, is the same PLD that will be put into use in the final invention of the end equipment, like games.

There are a number of PLDs that have been discovered, and mostly used by the designers. These PLDs includes, field programmable gate arrays and complex programmable logic devices (Sprankle & Hubbard 2012).FPGAs provide a wide range of logic capacity, with numerous features and offer peak performance, whereas the CPLDs offers lower amount of logic gates.

Therefore, these are the two types of programs that are the most ideal for developing and designing games. Game designers often use these programs because they offer a large volume of applications, and are the most relevant in the game designing.

Another benefit that can be derived from these PLDs is that, they are economical and where the designer need a high performing PLD, the fixed programmable device will always be used.

Since the game designer must be a person with high level of artistic and technical skills, designing skills are taught in many colleges and universities across the world. Mostly, game designers are also writers and editors. They must be well versed with the system design, content design and excellent game writing skills. Therefore, many video games have been developed due these acquired designing skills.

Many people, young and adults have now embraced watching or playing several video games. The PLDs are very flexible, hence, whenever designers need to make an alteration during the design period, they simply change the programming files and effects in the design changes will be seen straight away. The most interesting part of the benefits is that PLD can be programmed when already in the field (Zimmermann 2001).

Programming steps

New features can easily be added to the product that has been released in the market, hence making it more interesting. It is very imperative for the programmer to make clear the programming requirements. Otherwise the program may not be successful and accomplish the target. The designer should also know the purpose of the program; verify the end user and determine how the program shall function.

At this time, the designer must also establish the type of the data needed for the successful operation. The designer thereafter will design the program, in our case the computer game. They will use algorithms, which are simply the commands and equations that tells the computer what to execute (Constantin 1995).Algorithms system are mostly used in forms of logical hierarchical.

When the designer has designed a program, it is important for him to follow a syntax rule appropriately, in order to develop a programming language which must be coded. The syntax rule must be followed without any deviation. At this juncture, the program must therefore be tested and documented for use. Another popular program is light wave 3D.

This program is mostly used by video editors, who are rooted in the entire film and TV industry. It has three powerful futures that have made it to be popular among the designers. It can handle 3D modeling and 3D scene building and animation, which are commonly used by designers.

It has advantages over most of the design programs because it is easy to use, it does not consume much time, and designers always have an opportunity to make corrections in the project before it is finally produced to the public.

These great packages have tremendously made this program override other programs in the market today (Poole2000).The 3D light wave is also very cheap and readily available in the markets. In conclusion, because of its simplicity, it makes learning easy, even if the designer has no much prior experience in the game designing field.

References

Constantin, V. A. (1995). Fuzzy logic and NeuroFuzzy applications explained. Upper Saddle River, NJ: Prentice Hall PTR.

Poole, S. (2000). Trigger Happy. New York, NY: Time Warner Book Group.

Sprankle, M., & Hubbard, J. (2012) Problem Solving and Programming Concepts (9^th Ed.). New Jersey, NJ: Prentice-Hall.

Zimmermann, H. (2001). Fuzzy set theory and its applications. Boston: Kluwer Academic Publisher.n Wolfram. A New Kind of Media, 2