Aristotle 's Ideas Of Potential Infinity

2000 years ago the Greek philosopher Democritus came up with the idea that if he cut an object in half, for example a rock, that he could eventually cut it until he reached a tiny piece that could no longer be cut or divided. Democritus named this unbreakable piece ‘atomos’ which in greek meant ‘indivisible/ uncuttable’. However this idea was rejected in favour of another philosopher, Aristotle, whose theory was that all matter was made up of 4 elements, fire, water, air and earth.

An additional defining factor of Aristotle’s universe is that the terrestrial elements -being earth, water, air, and fire- existed in their select parts of the universe and try to return to their sectors; For example fire climbs upwards to try and reach the heavens where it belongs, while rock obeys gravity and returns to the lower section of the earth . This is why when things are removed from their natural habitat, or space, they will try to return their; this tries to explain the geocentric model, because the laws of physics tries to return the elements to their natural place, and the Earth return to the center of the universe . In consolidating thoughts, it is concluded that the main issue with Aristotle’s theories at the time is that there was not enough evidence to neither justify nor counterevidence to disprove his theories . This differs greatly from the Christian model because in Christian ideology the Earth is the center of focus, of God’s focus, thusly the Earth must be the center of the universe

The simplest explanation is to say infinity exists because you can continually reduce a cake by half, however, we know infinity does not exist, sometimes to get to truth you have to throw the materialistic cake away and face the facts, its hard but rewarding.

First scientist to suggest that all matter is composed of small, indivisible particles called atoms

effect…and that what is more perfect cannot derive from what is less perfect”, the idea of an infinite

The premise behind the paradoxes was that the method of describing motion using Pythagorean thought, treating numbers solely as discrete, arguably demonstrated the impossibility of motion. His four paradoxes illustrating this line of thinking are The Dichotomy, Achilles and the Tortoise, The Arrow, and The Stadium. The paradox presented in The Dichotomy is that a race, from beginning to end, is a finite distance. Zeno purported that there are infinitely many half distances, which meant that you could never reach the end, according to Pythagorean thought. This paradox offered a precedent to the idea of the limit of an infinite sequence, in that an infinite number of half distances can add to a finite distance. Achilles and the Tortoise presented a similar paradox about infinite measures within a finite distance, and demonstrated that the boast of Achilles, that he could beat the tortoise even when the tortoise had a head start, could not come to fruition based on Pythagorean thought. The Arrow presented a paradox between the Pythagorean thought, that discrete units of instances make up time, and the premise that if Pythagoreans were correct then the arrow could not move. Thus, claimed Zeno, time must be continuous and not discrete. The Stadium presents a situation which proves that there is no smallest unit of time, as Pythagoreans believed, and therefore time must be both finitely divisible and infinitely divisible (Andrews, Development of calculus: More about the paradoxes, 2016). Although Zeno’s arguments were sound, they did not negate the influence that Pythagoras had on the study of mathematics. Indeed, another famous Greek philosopher, Plato, professedly transferred his knowledge of Pythagorean mathematics to one of his students, Eudoxus (Lahanas,

Aristotle is an ancient genius Greek philosopher who spent most of his life studying, writing, and teaching his ways of knowledge by tutoring future leaders. Several Greek people looked up to him as a role model who had all the questions answered. Aristotle was a man of poetic justice and he proposed the idea to inform humans into studying poetry in a specific way. The study Aristotle was teaching was to analyze constitutive sections, that way it could be easier to draw general conclusions. Aristotle poetry heavily shocked the world with his methods; he influenced other early roman philosophers to write with knowledge that poetry is mimetic. His legacy would inspire young Roman writers because it created a focus on objects within the world.

Aristotle’s belief in ends can be reconciled, at least to an extent, to Christian teaching. God made humans for a purpose and humans can be said to be good when they achieve their God-ordained purpose. Similarly, Aristotle’s emphasis on cultivating good character and his belief that moral actions must be accompanied by good motives also adheres to Christian teaching. However, many critics say that Aristotle’s method for determining the human end is flawed. As apposed to what he believes, it seems inadequate to determine the human end by observing what it is that humans strive after because, since the Fall, every facet of humanity has been corrupted by sin. Consequently, humans often desire and try to attain things that are sinful and that God

The impression that all matters are made up of a tiny and indivisible particles called atom, is believed to have originated from the Greek philosopher Leucippus of Miletus and one of his student called Democritus from Abdera around the 5th century. The word atom, was formed from the Greek word atomos which means indivisible. Atoms are unchangeable and cannot be divided into a small particles. Atoms are said to be too small and are completely solid with no internal structure, and they came in

Accordingly, from the beginning of infinity history, from the Greeks, into the works of Newton, Plato, Aristotle, Galileo and Cantor’s ultimate discovery of the actual infinite. Starting from the beginning of the “What” is Infinity, not just a number, but can ultimately be anything that can be compared in a one to one correspondence without counting. Moreover, the “How” is infinity used in mathematics, encompassing most areas of modern mathematical fields, religion and physical infinities. Specifically, surrounding the areas of space, time, Metaphysics, Calculus, and Fractals. Then finally, ending with the “Now” of Infinity used in three distinct genres. That being mathematics, physical and the third metaphysical infinities. For instance, mathematically using set theory, or counting numbers. Physically, utilized in the occupations of Cosmology and Physics. Metaphysically searching for the ultimate possibilities of the One or a God of choice. These sections, What, How, and Now of Infinity have brought up many areas to continue studying and to reflect on that constant discovery of infinity. Since the essence of the word, infinity means endlessness, limitlessness or boundlessness. Leaving the research and discovery of infinity into the same state of the

According to Descartes a mind cannot be divisible but the body can. He says that it is not humanly possible that someone can live with a divided brain. The argument also says that is it possible to divide our bodies into different part. Therefore scientists attacked this argument and figured they would test to see if it was true. Descartes divisibility argument is not correct, in fact it seems as if it has been proven by scientific experiments that his argument is wrong.

Anaxagoras of Clazomenae was a very influential Pre-Socratic philosopher and scientist who spoke out against the common belief of the society and formed many different views in philosophy. He had a very strong impact, as he is credited with introducing philosophy to Athens when he moved there. Despite introducing philosophy to Athens, his thoughts were also what led to his execution. He openly claimed that the sun was not a God, and the moon reflected the Sun’s light, this view was highly offensive to the religious Greeks. One of his well-known views in philosophy was derived from the structure of things, that there was “everything in everything.” In this metaphysical principle, it stated that everything is in everything at all times.

Humans have many methods to describe large numbers mathematically. Ever since the invention of the concept of zero -- essential to the ancients in keeping good records of various transactions -- humans have been using mathematics to describe ever larger quantities of items. The ancient story of the king and the chessboard of wheat demonstrates that humans have been using large numbers since time immemorial. In the story, a king tells a

Transcendent) and was the totality of everything that is immanent. He explained that our infinite

The implications of infinity (co) are actualiy not that old. The Greeks were some of the first mathematicians recorded to have imagined the concept of infinity. However, they did not actuaily delve into the entirety of this number. The Greeks used the term “potentially infinite," for the concept of an actual limitless value was beyond their comprehension. The actual term “infinity” was defined by Georg Cantor, a renowned German mathematician, in the late nineteenth century. It was originally used in his Set Theory, which is a very important theory to the mathematical world. The value of infinity can get a bit confusing, as there are different types of infinity. Many claim that infinity is not a number. This is true, but it does have a value. So, infinity may be used in mathematical equations as the greatest possible value. i The value of infinity Infinity (00) is the greatest possibleivalue that can exist. However, there are different infinities that, by logic, are greater than other forms of itself. Here is one example: to the set of ait Naturai numbers Z43, 2, 3, 4,...}, there are an infinite amount of members. This is usualiy noted by Ko, which is the cardinality of the set of alt natural numbers,