I meant collectively not you specifically and was more or less joking around, nice comeback. I will leave it here as it was not really important.
It is not necessary to be fractionally this rigorous to find the problem here. You did not supply an actual infinite, you supplied a hypothetical infinite. The reason you can do this hypothetically and not in reality is that hypothetical variable have no actual properties or dimensions. The moment you take your hypotheticals and assign them any actual properties they instantly cease to be able to able fit into finites an infinite number of times. I am not saying your hypothetical fails any rigorous test of logic, I am saying it cannot possibly represent an actual thing.
Well you have the right idea but your not stating it as I would. Natural causation always has a time span of finite dimension and is chronological (for the moment let's leave out the theoretical possibility of simultaneous causation because it has not be proven or claimed). Now as long as your hypothetical X1 and X2s are abstract they have no dimensions but any actual causes do. I do not care how small a time span they require you are not going to fit an infinite number of finite's into a total finite. Even if it was only fractions of a pico-second your only going to fit a finite number into a 24 hour day.
Now your on fire, I could not have put it better. We do not have infinite time to put any infinite causal chains in.
I do agree.
Good, if there is a minimal amount of time for causality to take place, then an infinite causal chain will entail an infinite time from its beginning. That is obvious, independently from what causality means.
So, how much is that this minimal time? One picosecond, a femtosecond, a billionth of a femtosecond? A poster suggested Planck time (very very short, but still greater than zero) is a good candidate. For time intervals less than Planck time causality is not applicable because nothing is applicable: our current theories just break down for time shorter than that. Ergo, we do not know anything about what happens at such scale.
Would you agree to take Planck time as a good candidate for the minimal amount of time causality needs,in order to be instantiated?
If not, What other candidates do you have i mind?
A finite universe is the dominant cosmological model. I will give one example of an eminent cosmologist who supports the view but there is a consensus on this matter.
Vilenkin’s verdict: “All the evidence we have says that the universe had a beginning.”
It is said that an argument is what convinces reasonable men and a proof is what it takes to convince even an unreasonable man. With the proof now in place, cosmologists can no longer hide behind the possibility of a past-eternal universe. There is no escape, they have to face the problem of a cosmic beginning (
Many Worlds in One [New York: Hill and Wang, 2006], p.176).
Alexander Vilenkin: “All the evidence we have says that the universe had a beginning.” | Theo-sophical Ruminations
I use his model as my example because it was designed to be so robust that any vagary that people like Hawking can throw in the mix without justification does not affect it, he is not a Christian, and he is very emphatic. The BGV I second only to TBBT in dominance and both pose a finite universe.
What I asked is not "what makes you think that the Universe had a beginning?". What I asked is "What makes you think that the Universe is not infinite?"
I think it is pretty obvious that even if the Universe had a beginning, that does not say anything about it being finite or not. What makes you think that Vilenkin's theorem entails a finite Universe? It is very puzzling to me, what kind of mental processes you might have used to come to this conclusion.
I actually read the Vilenkin's book you posted (
Many Worlds in One [New York: Hill and Wang, 2006]). It does not say anything about the Universe being finite. It actually advertises the existence of INFINITE universes, ours being just one of them (which, by the way provides a good defeater of any fine-tuning argument).
This is a couple of short reviews of his work (source: Amazon), just in case you did not read the book:
"Cosmologists ask many difficult questions and often come up with strange answers. In this engagingly written but difficult book, Vilenkin, a Tufts University physicist, does exactly this, discussing the creation of the universe, its likely demise and the growing belief among cosmologists that there are an infinite number of universes. Vilenkin does an impressive job of presenting the background information necessary for lay readers to understand the ideas behind the big bang and related phenomena. Having set the stage, the author then delves into cutting-edge ideas, many of his own devising. He argues persuasively that, thanks to repulsive gravity, the universe is likely to expand forever.
He goes on to posit that our universe is but one of an infinite series, many of them populated by our "clones." Vilenkin is well aware of the implications of this assertion: "countless identical civilizations [to ours] are scattered in the infinite expanse of the cosmos. With humankind reduced to absolute cosmic insignificance, our descent from the center of the world is now complete." Drawing on the work of Stephen Hawking and recent advances in string theory, Vilenkin gives us a great deal to ponder. B&w illus.
(July)"
"Cosmology has moved from establishing that there was a finite start to the cosmos to theorizing about the initial conditions that kicked off the whole shebang. Vilenkin is a leading theorist whose scenarios about the enigma of the big bang emerge in this estimably clear, personable treatment. Vilenkin explains the idea of inflation, a phenomenal increase in the volume of space in the first infinitesimals of time, propounded by physicist Alan Guth (The Inflationary Universe, 1997). Inflation solved some theoretical problems but left others dangling, such as inducing inflation to stop; if it didn't, life could not have begun. Explaining that his solutions to the "graceful exit problem," as it is whimsically called, involve the concept of "eternal inflation," Vilenkin guides readers through its bizarre and head-spinning propositions. One is that our observed universe is embedded in a suprauniverse that infinitely spawns an infinite number of other universes. This and other gigantic ideas concisely presented will provoke the interest of readers intrigued by the origin of the big bang. "
So, either you never read Vilenkin's work, or you never understood it, or we are not talking of the same Vilenkin.
What is more likely?
Ciao
- viole