The ultimate question?
Moderators: Blip, DarthHelmet86
archibald wrote:Can we do, 'who made elves' next?
Wortfish wrote:Thomas Eshuis wrote:
Colour me surprise. Once again you just assert what you want to be the case, without actually presenting evidence that it is the case.Several people, including me have already refuted this dreck.
That you keep mindlessly regurgitating it without adressing those refutations further serves to demonstrate your trollish intent.
Let's try simple analogies:
Wortfish wrote:
In the first scenario, we never reach anywhere:
1. I take one step forward and then I take a step back. I keep doing this. Where do I end up? That is what it is like to have no beginning...you are always as far from your "destination" as you always were, no matter how long you keep repeating it.
In the second scenario, we have already reached everywhere:
2. I have been taking steps forward forever. How far have I gone? Answer: You have taken all possible steps there could be and there are no more steps you can take. If there were more, you wouldn't have always been taking steps forward.
Greyman wrote:If it is possible to have been walking forever, and you have been doing so until now, then there can still be more steps to take than the countable infinitude taken until now.
Take one more step. How many steps have you taken?
Keep walking. How long have you been walking now?
Why are you walking in circles?
Wortfish wrote:archibald wrote:
Wordfish? Is this not the case? Why does the universe need a creator if god supposedly doesn't?
I mean, giving a reason other than, 'god just doesn't' because any fool can say the same about the universe.
Very simply, God does not need a creator because he has always existed and never began to exist. The universe needs a creator because (as I believe) it began to exist. Of course, if the universe is eternal, then a Creator-God cannot exist. And this is why many of the atheist posters here are determined to defend the possibility, or rather absurdity, of an infinite past. However, just because the universe had a beginning, and presumably a cause, does not mean that God was responsible...but it is consistent with the idea.
Wortfish wrote:Thomas Eshuis wrote:
Colour me surprise. Once again you just assert what you want to be the case, without actually presenting evidence that it is the case.Several people, including me have already refuted this dreck.
That you keep mindlessly regurgitating it without adressing those refutations further serves to demonstrate your trollish intent.
Let's try simple analogies:
In the first scenario, we never reach anywhere:
1. I take one step forward and then I take a step back. I keep doing this. Where do I end up? That is what it is like to have no beginning...you are always as far from your "destination" as you always were, no matter how long you keep repeating it.
In the second scenario, we have already reached everywhere:
2. I have been taking steps forward forever. How far have I gone? Answer: You have taken all possible steps there could be and there are no more steps you can take. If there were more, you wouldn't have always been taking steps forward.
Wortfish wrote:Greyman wrote:If it is possible to have been walking forever, and you have been doing so until now, then there can still be more steps to take than the countable infinitude taken until now.
Take one more step. How many steps have you taken?
Keep walking. How long have you been walking now?
Why are you walking in circles?
Instintively, you might think that. But what Thomas Eshuis cannot get his mind around is that, if you have always been walking, you must have covered all possible ground. If you say that you can take one more step, this means you haven't had enough time to take that extra step which is ridiculous since you have had an infinite amount of time to do so. As paradoxical as it may sound, if you have been walking forever, you can't walk any further. That's infinity for you!
Wortfish wrote:archibald wrote:
Wordfish? Is this not the case? Why does the universe need a creator if god supposedly doesn't?
I mean, giving a reason other than, 'god just doesn't' because any fool can say the same about the universe.
Very simply, God does not need a creator because he has always existed and never began to exist. The universe needs a creator because (as I believe) it began to exist. Of course, if the universe is eternal, then a Creator-God cannot exist. And this is why many of the atheist posters here are determined to defend the possibility, or rather absurdity, of an infinite past. However, just because the universe had a beginning, and presumably a cause, does not mean that God was responsible...but it is consistent with the idea.
Wortfish wrote:But I quite frankly fail to see your point here. You are simply admitting that there are (at least) as many rationals between 0 and 1 as there are positive integers, which (by a sane mathematical definition) there are an infinity of...
My point is that we are engaged in numerical trickery by pretending there is some infinite continuum between 0 and 1 when all we are doing is taking inverses of unbounded positive integers. Unfortunately, abstract maths does entail a lot of this woo!
The so-called "fallacy" comes from the failure to recognize this difference between sets and their members (or between transfinite numbers and integers, for that matter), and we do actually have mathematical models that can explain how such things could work. Your entire counterargument still rests on an insufficient and out-dated model, and simply arguing from the (likewise out-dated) authority of Aristotle doesn't help you.
So you believe Achilles can never catches up with the tortoise and Zeno's arrow never reaches its target?
Aristotle was the one to bring the terms "actual" and "potential" into it, which was what I was talking about. But Democritus may well have been first to the particular conclusion you mention, but he had the same lack of modern mathematical tools, and thus his results are equally out-dated. Without set theory or analytical limits, there is only so much you can do... To put it simply, you need to show how these speculations apply to modern mathematics and/or physics, instead of just making an argument from authority.
Well, in the case of Democritus, his hypothesis became the basis for atomic theory. There is no evidence that we can divide particles indefinitely into infinitely indivisble components.
Wortfish wrote:Calm down. I have already stated that the inverse of all irrational numbers like 1/sqrt(2) lie within 0 and 1 and cannot be definitively expressed in terms of integers. This applies also to sqrt(2) -1 and to PI -3. However, we can always arrive at a rational approximation to any irrational number. Now, the inverse of 2414213565 multiplied by 10^9 is pretty good. I can get ever closer to sqrt(2) -1 by adding more digits. Indeed, the bigger the number, the more accurate the approximation.
Newmark wrote:
First of all, you do realize that there are irrational numbers <1 (including negative ones)? This makes your claim that "the inverse of all irrational numbers [...] lie within 0 and 1" blatantly false. Secondly, you have definitely NOT "always stated" that; here you said "I have shown that any real and rational number between 0 and 1 can be expressed as the inverse of a positive integer multiplied by 10^n and, for >0.5, summed with the inverse of 2" (not to mention your claims about continuums earlier), which directly contradicts your statement above, since the square root of 2 isn't an integer.
But the funniest part is when you try to dismiss irrational numbers by comparing them to "rational approximations". A "rational approximation" is not an irrational number, and there are two subtle clues to this that you may have missed: the term "rational", which indicates that it is not irrational, and the term "approximation", which means "close to", not "equals". That we can construct a rational approximation to an irrational number doesn't really tell us anything; it certainly doesn't tell us that your claim that "any real [...] number between 0 and [0.5] can be expressed as the inverse of a positive integer"* is credible in any way. The only way this could lead us to any interesting conclusions is if you can show that for each possible rational approximation, there is at most one irrational number that is best approximated with that particular approximation. Since there are 2ℵ0 irrationals in the interval between any two rationals, I won't hold my breath waiting for your proof...
Arcanyn wrote:Wortfish wrote:archibald wrote:
Wordfish? Is this not the case? Why does the universe need a creator if god supposedly doesn't?
I mean, giving a reason other than, 'god just doesn't' because any fool can say the same about the universe.
Very simply, God does not need a creator because he has always existed and never began to exist. The universe needs a creator because (as I believe) it began to exist. Of course, if the universe is eternal, then a Creator-God cannot exist. And this is why many of the atheist posters here are determined to defend the possibility, or rather absurdity, of an infinite past. However, just because the universe had a beginning, and presumably a cause, does not mean that God was responsible...but it is consistent with the idea.
So, it's absurd for a universe to have an infinite past, but when it comes to a god having an infinite past that's just dandy.
Wortfish wrote:Newmark wrote:
First of all, you do realize that there are irrational numbers <1 (including negative ones)? This makes your claim that "the inverse of all irrational numbers [...] lie within 0 and 1" blatantly false. Secondly, you have definitely NOT "always stated" that; here you said "I have shown that any real and rational number between 0 and 1 can be expressed as the inverse of a positive integer multiplied by 10^n and, for >0.5, summed with the inverse of 2" (not to mention your claims about continuums earlier), which directly contradicts your statement above, since the square root of 2 isn't an integer.
The square root of 2 does not lie between 0 and 1. Rather, the sqrt(2) -1 lies between 0 and 1.
But the funniest part is when you try to dismiss irrational numbers by comparing them to "rational approximations". A "rational approximation" is not an irrational number, and there are two subtle clues to this that you may have missed: the term "rational", which indicates that it is not irrational, and the term "approximation", which means "close to", not "equals". That we can construct a rational approximation to an irrational number doesn't really tell us anything; it certainly doesn't tell us that your claim that "any real [...] number between 0 and [0.5] can be expressed as the inverse of a positive integer"* is credible in any way. The only way this could lead us to any interesting conclusions is if you can show that for each possible rational approximation, there is at most one irrational number that is best approximated with that particular approximation. Since there are 2ℵ0 irrationals in the interval between any two rationals, I won't hold my breath waiting for your proof...
You're missing the point entirely. If I have a big enough integer I can use its inverse, multiplied by a factor of 10, to get to the approximation of any irrational number that is only infinitesimally inaccurate. Your claim was that there is an infinite continuum of real, including irrational numbers, between 0 and 1. My response was that this is just a charade and that we are just juggling with ever greater integers: 0.1 = 1/10; 0.01 = 1/100; 0.0000000001 = 1/10000000000....and so on. The problem with supposing there can be an infinity within actual bound is that all we end up is just adding more and more zeroes after the decimal place and keep doing so forever. But, all we are really doing is taking the inverse of an integer with one more digit at the end. This gives the illusion that we there is a real infinity within finite space.
Newmark wrote:
...and the inverse of a number that is between 0 and 1 lies in what range? Compare this with your statement that "the inverse of all irrational numbers [...] lie within 0 and 1". And thank you for proving yourself wrong again!
I'm terribly sorry, but I just can't find facepalm picture big enough. You don't really have any clue about what you are talking about, do you? That you are making things up about how you think mathematics work would be cute if I had any reason to assume that you where willing to learn from your errors. Instead, you blindly dismiss well-established mathematical facts as "illusions", which quite frankly is a downright pathetic argument in a mathematical discussion.
For the record, Cantor proved that the reals were uncountably infinite in the late 19th century. Your "objections" only represents an incredibly naive version of set theory, and such issues are address if you actually take the time to properly learn anything about the subject.
And I notice that you dodge a particular one of my questions: now that you've dismissed (among other things) set theory and calculus as "illusion" without "application to reality", what do you think of any technology that is in any way based on them?
Users viewing this topic: No registered users and 1 guest