First off, I am very pleased at the responses. They were both interesting and enlightening. The purpose of this is to spark some out of the box thinking and I think that goal has succeeded in some respects. Let me be the first to say that none of these questions require long drawn out philosophical responses. They are difficult at first but some critical thinking and research will see you through. What was before creation (assuming a Christian creation)? As it turns out this is a meaningless question. St. Augustine is credited to have saying in response to this question, "God was thinking of what he would do to people who would ask these questions." Creation entails the creation of time so therefore that question is meaningless as before time is absurd. What was before the Big Bang? Again, meaningless. This question does not make any sense. The singularity contained all of time. Time is needed for a before. So to have a 'before the singularity' you require a 'before time' which does not make sense. Does original sin imply a sinful birth? Yes it does. If you believe in the moniker. Credited to St. Augustine sinful birth is directly and implicitly implied in his written works on original sin. Original sin has many different meanings to many different people but if you believe the original, the true original sin argument then yes it does. Can god create unlimited things? By no fault of his own, no. Calling something a 'thing' limits it. It's like saying can God create an unlimited limited thing? This argument is credited to Thomas Aquinas. Can some infinities be larger than others? Let's explore: 1-1 Correspondence is a matching of numbers on a number line. A = { 0, 1, 2, 3, 4, 5...} i+1 Z = { 1, 2, 3, 4, 5, 6...} i These have one to one correspondence because you can draw a line from the number above to the number below infinitely. Z = {...-1, 0, 1...} N = { 1, 2, 3...} We maintain correspondence by arranging the numbers thus: N = { 1 , 2, 3, 4, 5...} Z = { 0, 1, -1, 2, -2...} We have to do this because N did not stretch backwards to infinity. This means that |N| = |Z| even though Z stretches in both directions to infinity which should have made it doubly as large they are equal. So does this mean that there is no greater infinity? A real number N between zero and one that, by its construction, differs from every real number on the list in at least one decimal place. Ergo, it cannot be on the list. The one-to-one correspondence between the reals and the naturals fails, as there are simply too many reals—they are "uncountably" numerous—making real infinity somehow larger than natural infinity. Basically real numbers out pace natural numbers if you get the gist of what I mean.
This well-intended and nicely planned debate isn't exactly taking off. I unfortunately don't have much of a response to the topics you included - they all either agree with my answers from the other thread, or explain better and make more sense. IOW.... I agree with all of the above too much to offer a useful response. But - there is one topic from the first set of questions that I differ from most everyone else on, and have stronger feelings towards. Maybe we could use it to jump-start this a little better?
I was going to post this in the answering thread, but here is better. Defining the extent of inifinity If we assume the value of a line equals [infinity] then we can imagine that the line is the side of an "infinite square" and by detemining the area of a square "Area=side squared," then the value of a plane is "[infinity] squared." FLAW: With defining infinity, we are struck with the notion that "[infinity]=[infinity] squared" due to the fact that we cannot measure said inifinity COUNTERARGUMENT: If we assume that infinity has a positive value, we can conclude that the square of any positive number (whether we can measure it or not) is greater than the original number. We MUST assume that infinity has positive value due to the fact that we are talking about distances of a geometric figure. If we view the white space as a plane or an "infinite square" with each of its sides expanding infinitely, then the total area of the plane is [infinite]squared whilst the line is just infinite. Proved-Infinites can be different sizes. Naming infinites in geometry Linear infinite (line) Planar infinite (plane) =infinite squared Spatial infinite (space) =infinite cubed (to the third power) Spatial infinence is a true infinence, meaning that it expands in all three spatial dimensions (length, width and height)
No there are infinite numbers of infinitely large infinities. Simply, 2^aleph-zero, 2^(2^aleph-zero), 2^(2^[2^aleph-zero]). . . That pattern repeats to infinity giving you infinitely larger and larger infinities as you go.
Infinity x Infinity = Infinity. Infinity + Infinity = Infinity. Infinity - Infinity = 0. Infinity / Infinity = 1. Infinity ^ 2 = Infinity. Infinity ^ 3 = Infinity. "Infinity + 1" = Infinity. "Infinity + 2" = Infinity. That is how Infinity works, it is a changing value depending on previously existing numbers. Infinity is endless, you cannot add too it.
I am talking about Geometric infinity within the first three dimensions, not the amount of infinites we can create using numbers. because if we have infinite number of places and infinite numbers we can fill those places with, we have an infinite number of infinites. In geometry, there are Three (i reiterate, three) spatial dimensions, three different directions that we can measure infinity in (diagonals are the sum of two vectors on one of these planes. TO be more specific, the distance between two points is the absolute value of the difference (this is the definition of distance in geometry) and for every x such that x>0, x squared > x. So if we have two points infinite distance apart, their distance is a positive number because every absolute value is a positive value, and squaring said value results in a larger value. ANYWAY, that is my attempt to prove infinities can be different, sizes. I think we can all agree that some can, because we have many examples of then doing so. MOVING ON- About what is before the big bang, I believe that the singularity existed before the big bang. It contained all of time, and all mass.
Changing implies that the values can change in either direction. Infinity is a constant value. It's just that value is always bigger than we can grasp. If we grasp the sheer size of the newly "discovered" biggest number, we will not be any closer to grasping infinity, as the number has no end. Is that infinity squared?
infinity / infinity 1. infinity-infinity 0 Regular rules of math don't apply to infinity, we learned this in my Calc class. The other four rules you have work though. Infinity is not a constant value. It isn't even a number. It is just a way of stating that what you have never ends.
The only way that infinity-infinity doesn't equal 0, and that infinity / infinity doesn't equal 1, is if Infinity doesn't equal Infinity, which is an impossibility.
One theory is the Kaleidoscope effect. That the universe will continue to end where it begins and begin again where it ends. I am not religious, well not in the conventional sense, rather I believe that God's power is less magic and more scientific. I believe the laws of nature are the limitations of God's power. I believe that creation works by trial and error. Consider how very hard it is to produce the ideal conditions to create life. How many stars are out there? And how many of them could produce life in their systems? It is a rare anomaly. Furthermore, the laws of nature cannot create things like plastic without a third party, us. Human Beings. Consider how many lifeforms have inhabited this world until we claimed the Earth. Again, trial and error. In this context, it would indicate that evolution was not only true, but infact was God's plan. Now, why is it that we believe we are created in the image of the creator. Some people believe that in the literal sense. I do not believe it means that God looks human, I believe rather that he/she/it is the creator, and in that sense so are we. We have the ability to create life, energy, heat, etc. People believe that man should not play God. But, I believe we were put here to do God's work, or rather what God or the Universe itself cannot do on it's own. We are the first, but I doubt we'll be the last. We are clearly imperfect. But, again with trial and error, give it another million years or so and maybe the next super species will be unique by ten fold.
infinity doesn't equal infinity. Say you have the graph of x[sup]2[/sup] and the grapgh of x[sup]3[/sup]. As the X values of both the graphs goes to infinity, the Y values of both graphs also go to infinity. But, X cubed is going to be bigger than X squared, even though they both go to infinity.
No it doesn't! Infinity / Infinity can equal anything you want it to equal. It can equal 1, it can equal 100, it can equal 23. Same with subtraction. Examine the following. A/B = C therefore A = B*C A/0 = C (=) a=0 c=0 0/0 = C (=) 0=0*C - - - - C could equal anything. ----- Using the grandi series we get this equation. S= A/1-r 1 + (1/2) + (1/4) + (1/8) . . . = 2 a= 1, r = (1/2) S = 1/ [1-(1/2)] = 2 Both answers are the same. ----- (3/10) + (3/100) + (3/1000) . . . = (1/3) a= (3/10) r = (1/10) S= (3/10) / [1-(1/10)] = (1/3) ----- Apply to infinity 1+2+4+8 . . . = INFINITY a = 1, r = 2 S = 1/ (1-2) = 1/(-1) = -1 INFINITY = -1
Yay! We're arguing about math!!!! @Nitrous, "My Name is Jonas" Anyways, Pred I agree/disagree. I doubt that people have fought or will ever fight purely for the sake of fighting. So in a sense there is no such thing as just war, but in some cases there are individuals that are seduced by it and become enamored with it. Alexander the Great?
In order to decide if there is such thing as a just war, we must decided what "just" means. Just in this sense means "based on or behaving according to what is morally right and fair" KEYWORDS - Morally Right, Fair If these apply to a war, then yes, it can be a just war. If both sides of the wars motivations for their actions in the war are morally right, then there actions can be justified, and it is a just war. I believe that it is not ethically acceptable to kill a person, unless they have been sentenced to the death penalty, so yes killing can be justified, but we would have to follow this back to the "first" incident, which would not be justifiable. The very first "Kill" in a war would not be justifiable, but all the others after that, could in theory be, if everyone was sentenced to the death penalty by a court.
madz333 - I like that you stick to your guns all the way to your conclusion. Try to think of some cases that would fit outside your laws. What if there is no court to give justice? My argument is two-sided. The first is that human behavior is highly explainable. This is deeply rooted in the field of cultural anthropology, of which I am but a student. The following is an excerpt from a review of a book called Cows, Pigs, Wars, and Witches by Marvin Harris: source The basic idea here is that war, like many human practices, is fueled by reasons that are hard to understand from an outside point of view, but reasons present nonetheless. I can't put it as convincingly as the book did myself, but the Maring example really gives some insight as to what drives tribal warfare (in much greater detail than the review provides obviously). Modern warfare even has one strange example. World War II was an historic anomaly in that it approached a comparison to good vs evil to an unprecedented degree [Thom Hartmann]. It's true that it takes two to tango but for the Allies at least, that was a justified war if ever there was one by traditional definitions of justice. I'm not necessarily vouching for most modern wars (too much work) but the question was is war ever justified, so we must include all versions. The second part of my argument is that justice is a human construct. For this I'm going to try out my new Moral Realism boots I just bought, see if I can break them in a bit. “You know as well as we do that right, as the world goes, is only in question between equals in power, while the strong do what they can and the weak suffer what they must” -Thucydides, 416 BC Where is authority for justice derived from? What is the right balance between retribution and rehabilitation? These questions have been answered differently by every distinct culture in history. Justice, as all other moral issues are, is a construct of human minds.
Predicide- I believe from your example that we can justify wars in certain circumstances, like the Maring. BUT we cannot unless we truly understand what is happening and WHY it is happening is said war. In conclusion, yes war is justifiable, but in very rare circumstances. "Is there such thing as a just war?" Yes