I feel as this article is trying to discredit some of the great theologians such as Gottfried Wilhelm Leibniz who attempted to use reason to prove the need for a being to begin the universe(an unseasoned reasoner). Let me explain why these philosophers are right about the non-existence of infinities. The most basic of these arguments was made by the Christian philosophers and perfected by Muslim philosophers and was called the Kalam argument. It attempts to prove that the universe had a beginning and is not infinite. So, first, what is an infinity? An infinity is a limitless quantity, in other words, an infinity, by definition, cannot be quantified. The kalam argument looks at two types of infinities: potential and actual. A potential infinity is like a stop watch, if you hit start it could, potentially, continue adding numbers onto each other for a limitless amount of time. but as soon as you hit stop the number that the watch has counted to becomes quantifiable and no longer an infinity. The other type of infinity, an actual infinity, is an unquantifiable amount of something, something that cannot be calculated because it goes on and on forever. The argument then proves that time had to have a beginning and is not infinite. the best way to do this is to observe that there is a "now". If now exists time cannot be infinite. Ok, picture "now" as a destination on a set of train tracks. now picture time as the train tracks that are infinitely long. How far would you have to travel to reach your destination? if you fell into a bottomless pit, how far would you have to jump to get out of the pit? what would you jump off of? There is no point of reference in an infinity because it is unquantifiable. Ok, so time isn't infinite, so what? The impact of this is that there had to be a point when NOTHING existed. So then why does the universe exist, did it one day in its nonexistence decide to pop into existence. This is impossible because A) the universe is not personal and cannot decide B) something that does not exist cannot reason itself into existence. This brings us to the conclusion that there is something that is immaterial, personal, self existent, "outside" of time, and logically necessary that started the universe.
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