Explain and evaluate the key argument(s) and concept(s) of one of the Presocratic philosophers covered in Chapter 2 of your textbook (Thales, Pythagoras, Anaximander, Anaximenes, Heraclitus, Parmenides, Empedocles, Anaxagoras, or Democritus). Where does your chosen philosopher's reasoning hold up and where does it fail? What examples can you cite that help make this philosopher's case, and what counterexamples can you come up with showing any flaws in your chosen philosopher's reasoning? book archetypes of wisdom

Pythagoras Of Samos: Where Does His Reasoning Hold Up and Where Does It Fail? Name: Institutional affiliation: Course: Date: Table of Contents TOC \o "1-3" \h \z \u Introduction PAGEREF _Toc163451378 \h 1Key arguments and concepts PAGEREF _Toc163451379 \h 1Where Pythagoras' reasoning holds up PAGEREF _Toc163451380 \h 2Concept of the “Ordered World” PAGEREF _Toc163451381 \h 2Mathematics as a Predictor of Unseen Realities PAGEREF _Toc163451382 \h 3Where Pythagoras' reasoning fails PAGEREF _Toc163451383 \h 3Lapses in the “Music of the Spheres” Concept PAGEREF _Toc163451384 \h 3Lapses in Mathematical Idealism PAGEREF _Toc163451385 \h 4Conclusion PAGEREF _Toc163451386 \h 4References PAGEREF _Toc163451387 \h 5 Introduction Pythagoreanism is attributed to the famous and yet controversial Greek Philosophers who lived from CA 570 to CA 490 BCE in south Italy. Pythagoras ran a worshiping cult where he had staunch followers referred to as Mathematikoi. In his cultic ministry, Pythagoras expected his followers to pray for numbers, especially sacred numbers such as 1, 7, 8, and 10. The number “10” was considered holy to the extent that sacrifices were made to it every time they discovered a mathematical theorem. The basis of Pythagoras' argument is numbers and according to him numbers are important and without them, nothing else held the meaning of life and existence. His philosophy reiterated that numbers are the very first principles of all things and by focusing on the concepts of numerology, he argued that numbers explain the truest nature of the universe. As the first developer of mathematical concepts, Pythagoras discovered that every natural event can be described in a mathematical expression, such as ratios. For this reason, the “principle of numbers” accounts for everything according to the Pythagoras (Soccio, n.d). Pythagoras presented his argument about numbers using the “cosmic music of the sphere” concept, an argument that numbers were not just mental constructs but existed in space. Music of the sphere helped reinforce his philosophical theory by suggesting that there existed a major harmony and order in the cosmos, governed by mathematical principles and only discoverable through intellectual inquiry as human nature is majorly limited. Numbers accordingly are not abstract concepts but key to the nature of human existence. The numbering concept helped them come up with the idea that just as numbers follow rules, then everything in our universe is bound by “rules” and “order.” To describe their perceived “ordered whole” they came up with the Greek word, “Cosmos”. Cosmos was first coined by Pythagoreans as a description of the ordered word. In this paper, I will cover Pythagoras’ philosophy while appraising competence and weakness. Although Pythagoras's accomplishments in the field of mathematics and metaphysics cannot be underrated, I will also discuss where his thinking is flawed and where it is plausible. By providing different examples that agree with Pythagoras' thoughts and examples that are opposite to his theorizing, I hope to offer a complete assessment of his philosophical background. Key arguments and concepts The Pythagorean philosophy, based on metaphysics and number theory, explains the meaning of the world utilizing mathematical thought. Per Aristotle’s thinking, Pythagoreanism, claims that "things are" numbers or "resemble" numbers, meaning that everything can be expressed through numbers and number relationships. This principle offered a foundation for the assertion that the universe falls into a disciplined order of numerical laws. The spirit of Pythagorean thought was to recognize that specific numbers, rather than being tangible quantities, conceptual abstracts have been associated with creating a numerical symbolism that makes it possible to contemplate the essence of reality (Soccio, n.d). Simply put and as reiterated by major Philosophers such as Aristotle, number speculation, which was the Pythagoreans' main point was a great novelty that led to the opening of a new view of the universe as a harmonious and orderly structure. At the core of the Pythagorean cosmology, we find the principle of harmony. This can be nicely illustrated by the mystical capacity of the tetraktys—the sum of the first four numbers—and its subsequent connection to the very idea of cosmic order. As he proclaimed, the spheres of the cosmos were attuned to each other according to their harmony and numbers, for which the entire universe was governed. The Pythagoreans not only realized the harmonic essence of things but also applied numbers to music theory revealing the inseparable relationship between sound and mathematic ratios. This corresponded to the underlying principle of harmony that not only bound nature and humanity but also earth and soul. Pythagoras' mystical reference to "the music of the heavens" is an example argument that cosmic motion aligns with the music of numbers, thus echoing the harmony and orderness of the universe. Additionally, the Pythagorean philosophy combined the numerical symbolism of cosmic dualism with ideas from the Ionian cosmology (Soccio, n.d). They believed that the universe had pairs of cosmic opposites, such as limit and unlimited, odd and even, and light and darkness, which interacted in harmony. This dualistic perception, embodied in the Pythagorean table of 10 opposites, emphasizes the Pythagorean conviction of the unity and reciprocity of principles that operate in the universe.  Of greater significance in Pythagorean philosophy are the mathematics and science ideas brought forth in critical areas such areas as arithmetic, geometry, music, and astronomy. The Pythagoreans' works concerning numerology, exemplified by the odd and even numbers symbolized by geometric figures, were th...