Infinite Divisibility Essay

In other words, maybe Descartes could think up the idea of infinity, because he is

For, in fact, what is man in nature? A Nothing in comparison with the Infinite, an All in comparison with the Nothing, a mean between Nothing and Everything. Since he is infinitely removed from

‘I think prime numbers are like life. They are very logical but you can never work out the rules, even if you spent all your time thinking about them.’

Mathematics is a logical and precise subject. Without precision in math everything is imprecise. A modest inaccuracy can produce a catastrophe. For example, if a doctor fails to calculate the correct amount of medicine to give a patient, it could result in a serious complication, such as death. A further example is the logic and precision it takes to construct a building. If there is one minor miscalculation the whole building could collapse, causing mass destruction.

Imagine the number eight. People would probably think that it’s just eight and nothing but eight. Now imagine the number eight tilted 90° to the left. People now see the infinity symbol. Now, people would probably think of it as an expanding number that never ends.

It is vital to the nature of thought to move out into infinity and to go beyond all restrains of time and space. This seems to be the absolute meaning of the teacher in the text. “Also, he hath set eternity in their heart, yet so that man cannot find out the work that God hath done from the beginning even to the end.”3 The abiding mind of man is an alteration, not an accomplishment. We cannot apprehend the immeasurable, and yet we feel the immense force of it. We must adhere to the endless adventure because God is an infinite creature, and he has set eternity in our

These arguments are strong ones for the existence of God, built upon clear and apparently true observations of the world around us. However, there are many criticisms. Hume argued that both Thomas Aquinas and William Lane Craig contradict themselves by firstly denying the possibility of the infinite, but then claiming that there must have been an infinite being. How can this be so?

I will begin with a convenient distinction described by Hume: the difference between relations of ideas and matters of fact. To alter any relation of ideas is to entail a contradiction, and therefore impossible. Thus, “the sciences of Geometry, Algebra, and Arithmetic” as well as analytic propositions are off limits for even an omniscient deity.

The tortoise did not optate to rush through anything to just be done and beat the hare. Adam takes his time and ascertains he does everything veridical. He doesn’t want to rush through anything thing just to be done with

The example of Hilbert’s Hotel to prove his point that an actual infinite cannot exist is a valuable argument because it demonstrates how implausible an actual infinite of physical objects. However, it does not demonstrate the implausibility of an actual infinite amount of time or knowledge. The second scientific confirmation that Craig uses does demonstrate the impossibility of an infinite amount of time in the past but does not in this paper, add anything about an actual infinite of time in the

Additionally, in his essay, History, Ralph Waldo Emerson also reconciled the many with the one: “There is, at the surface, infinite variety of things; at the centre there is simplicity of cause.” Customarily, New Thought teachers profess this same Truth, proclaiming that the infinite is simply one: the cause and effect, the stuff and substance of all that is. For that reason, we believe that everything we see, and all that we do not see, is one reality: an infinite energy moving in a pattern. Although we cannot see the energy, or the pattern, all that we can see is a consequence of the way It moves within Itself, and upon Itself, bringing forth an increasingly greater manifestation of Itself. Albert Einstein quantified this principle by stating

These lead us to the implicit premises underlying the argument about Achilles and the Tortoise. First, Achilles always takes some amount of time to cover a certain distance. And though the Tortoise is slow, it is always moving ahead. Because the animal covers some distance in every interval of time, it seems impossible to know the time at the end of which Achilles has caught the Tortoise. Therefore, we can infer from the premises that in each moment that Achilles must be catching up the distance between them, the Tortoise will be adding a new distance however

This kind of division also can be called as “Hume’s fork”. Relation of ideas are a priori which are “intuitively or demonstratively certain” and “discoverable by the mere operations of thoughts” (Hume, 1748, p.422). In this group, we can include mathematical ideas and math proofs, for example, statement like two plus two equals four. So, the denial of such statements is inconceivable and logically impossible. For example, we can think about the triangle and we all know that it has three sides. Later, we can imagine a triangle with four sides and immediately face a contradiction because four-sided figure is rectangle. This statement is a priori true for the reason that it has nothing to do with the external world and gives us no information back about the world. The second kind is “matters of facts” which is a posteriori. “Matters of facts” are statements that give us knowledge about the world and the sources providing knowledge for these statements are “the present testimony of our senses” and “the record of our memory” (Hume, 1748, p.423). Statements of this group and the denial of these statements are not self-contradictory and conceivable. For example, we can tell that the house of my neighbors is yellow, and we can easily conceive this statement as true, but we can at the same time conceive it as false, and imagine their house in blue

The philosopher Zeno of Elea (495-435 B.C.E.) came up with the idea of “infinite divisibility”. The basic concept of the theory was that you could take any object, cut it in half, cut those halves in half, and so on until you reached the end of the divisibility process and were left with only particles, or “elements” as he called them. The first conclusion he drew from this theory was that the elements were essentially nothing, which meant that the sum of all the pieces made the whole object nothing. The second conclusion was that the elements were something but that they had no size, which meant that the sum of the whole object also had no size. The last conclusion was that the elements are something and they do have a size. But that would mean that you would never reach the end of the

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,