PROOF INFINITY DOES NOT EXIST! Not even ONE type
in [Math]
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From: David Bernier on 12 Jul 2010 21:33 Marshall wrote: > On Jul 12, 12:50 pm, c...(a)kcwc.com (Curt Welch) wrote: >> "K_h"<KHol...(a)SX729.com> wrote: >> >>> No, there are absolute truths of the universe, for example conservation >>> of electric charge. >> >> Not absolute in ANY sense. Our understand of the universe, and these laws >> of nature we created to explain it are all predictions about the future >> derived from past experience. Such predictions NEVER become absolute >> truths. NO matter how many times we flip the coin and see it comes up >> heads, do we _ever_ get to make the claim that the next time we flip it, we >> will get heads again, with ABSOLUTE certainty. > > I see you are absolutely certain that there is no absolute certainty. [...] I don't think there are Laws of measurement for electric charge. To take a census of electric charges, shouldn't there be a census time? And clocks to tell when it is census time? If two different methods of measuring charge always give the same answer, which is the official one for census purposes? How can one make sure that the census was 100% accurate? David Bernier
From: Wolf K on 12 Jul 2010 21:48 On 12/07/2010 18:21, K_h wrote: [...] > No, I correctly claimed that the truth underlying regular arithmetic does exist > and that truth is independent of context. 1+1=2 is true for any two objects: two > cars, two houses, two people, etc. [...] Plato was wrong. wolf k.
From: Nam Nguyen on 12 Jul 2010 22:19 K_h wrote: > "Nam Nguyen" <namducnguyen(a)shaw.ca> wrote in message > news:uNc_n.6705$KT3.5193(a)newsfe13.iad... >> K_h wrote: >>> "Nam Nguyen" <namducnguyen(a)shaw.ca> wrote in message >>> news:MTSZn.2663$Bh2.125(a)newsfe04.iad... >>>> K_h wrote: >>>>> Mathematical truth exists. >>>> Sure. In your mind for example! >>> And also outside of the human mind. >> Did you mean _physically outside of human mind_ ? That's very bizarre to say >> of mathematical abstractions that human thinks of. No? > > The truth underlying the abstractions does exist. Sure. In your mind for example! > > No, I correctly claimed that the truth underlying regular arithmetic does exist > and that truth is independent of context. 1+1=2 is true for any two objects: two > cars, two houses, two people, etc. But 1+1=2 is true in many ... many _modulo arithmetics_ "for any two objects: two cars, two houses, two people, etc.", right? > Those truths exist and are perceived by the human mind so I stated nothing > incorrectly. Of course you did: when you said "Mathematical truth exists ... outside of the human mind"! -- --------------------------------------------------- Time passes, there is no way we can hold it back. Why, then, do thoughts linger long after everything else is gone? Ryokan ---------------------------------------------------
From: Transfer Principle on 13 Jul 2010 02:06 On Jul 11, 10:22 pm, "K_h" <KHol...(a)SX729.com> wrote: > "Curt Welch" <c...(a)kcwc.com> wrote in message > > some internal representation of separate "objects". Once you have one of > > these machines, we get closer to the truth embodied in 2x7=14,. But > > without that machine, that "truth" really doesn't exist at all. > Nonsense. You just claim the truth embodied in 2x7=14 doesn't actually exist and > that is plainly untrue. Marshall, thanks for the heads-up on Nam; it looks like > Curt is another Nam. And therefore, it should come as no surprise that I'm going to defend Curt Welch, just as I defend Nam Nguyen. > > "K_h" <KHol...(a)SX729.com> wrote: > >> In regular arithmetic 4+5=9 is true but Curt was claiming > >> that there is some tiny chance it could be wrong in regular arithmetic.. > >> Curt is obviously wrong there. But there is some tiny chance that PA is inconsistent. Despite K_h and Spight repeatedly calling those who even consider the possibility that PA is inconsistent "loons" and "cranks," the possibly remains that there's a chance, however tiny, that PA is inconsistent. > > and does exist, and all of math takes place in that fairy tale land. It's > > highly useful and important to do math under that belief. But what's > > invalid, is to assume the lies we use to do math, actually happen (or > > exist) in the real world. > Mathematical truth exists in the real world and those truths are not lies.. > Again, this is obvious. But infinite objects aren't known to exist in the real world. So I don't consider any statement concerning an infinite object to be an absolute mathematical truth at all. > > I can produce language that describes a reality where pink flying elephants > > with no mass exist. But no one is going to get confused about whether the > > reality I am talking about actually exists in our universe or not. It's > > just a story I made up by taking things that do exist in our universe, and > > combining them in a way that has never been seen, and which is highly > > unlikely to ever be seen in our universe. That's how the idea of absolute > > truth was created as well. > No, there are absolute truths of the universe, for example conservation of > electric charge. There are absolute _physical_ truths, I admit, but not absolute infinitary _mathematical_ truths. > > But yet, somehow, many people get so engrossed in the stores we make up as > > we talk the language of mathematics, they start to believe the world of > > mathematics is not just a story, but that it actually exists. That it not > > only exists, but that it "lives on" even after all the story tellers die > > off. It is as if they believe the pink elephants exist and live on > > forever, even after everyone that's heard the story has died off. > No, because mathematical truth is discovered not invented. An alien on another > planet must also discover the same prime numbers that humans have. I am loath to bring up analogies about aliens due to their association with JSH (Planet Contary), but since K_h brings up aliens here, so do I. Sure, if an alien defines "primes" the same way that we do, then I admit that they'll discover the same primes. But an alien need not have the same ideas about infinite objects that we do. I'll concede that _finitistic_ mathematical truth is absolute and discovered. But _infinitary_ mathematical truth is, to me, _invented_, with the inventors being Cantor, Zermelo, Frankel -- in other words, those who invented the _axioms_ postulating the existence of any infinite objects. Without the axioms, there's no reason to believe that any infinite object exists, no matter how much K_h and Spight insist upon it. Thus, this is where I draw the line between a defensible poster and an indefensible poster. I won't defend those who contradict the finitistic _theorems_ of PA, which do include K_h's "4+5=9" and "2*7=14." But I will defend those who don't necessarily accept the _infinitary_ proofs, which include the _consistency_ of PA itself. (So I distinguish between the _theorems_ of PA and the _consistency_ of PA.) And so I defend Nguyen, Welch, and even finitists like Herc. Yes, K_h and Spight are definitely biased by their own notions of "absolute truth."
From: Transfer Principle on 13 Jul 2010 02:10
On Jul 10, 6:42 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > Herc's Axiom Of Pseudo Infinity (based on above equation AOF) > There is a set, I, that includes all the natural numbers that could physically be computed > (before the end of the computer sustainable Universe) Out of curiosity, what does Herc consider to the the largest number in I? If Herc is like AP, then his upper bound might be somewhere around 10^500 or so. But I suspect that Herc might be more like WM (who influenced him greatly), and perhaps the set I contains gaps -- so that googolplex is in I, but there exist natural numbers less than googolplex but not in I. |