A COUNTABLE infinity is a completed infinity as I am using the term.
There are well ordered sets like the whole numbers
And there are scattered sets like when you count the rationals
I’m sorry, I’m throwing lots of jargon at you …
These are considered complete infinities (countable - meaning: enumerable in 1:1 correspondence)
Now… and I must say this: obsrvr: I don’t like your tone with silhouette. Not only that, but you are wrong that a rational number hotel cannot fit everyone in… if a hotel only has 34 rooms, then if you build a new room for every guest, and move everyone up one room, no contradiction occurs.
The problem is not in the finite, time based logic…
The question is “what happens at infinity?”
There are two possibilities:
1.) Either every room is full
2.) no rooms are full
This is how strange infinity is.
Hilbert didn’t understand the infinities he even claimed to undertstand that he claimed not to understand.
Obsrvr: give silhouette a break, he was very deferential to you
“the infinite is nowhere to be found in reality. it neither exists in nature nor provides a legitimate basis for rational thought. the role that remains for the infinite to play is solely that of an idea.” - david ‘the hitman’ hilbert
maybe try this for thought. when comparing the concepts of ‘finite’ and ‘infinite’ with the use of the terms in this thread, the concept of the infinite is thought of as a possible ‘set’, and therefore a concrete thing, like the concept of finite is being thought of here. but a ‘set’ is a completed object… in the sense that we can know where it begins and where it ends… and in this sense its a conceptual object. now here may be the problem; what you guys are doing is conceiving of a potential infinity… which is a collection that is increasing toward infinity but never gets there… as if it were a collection of definite and discrete members whose number is greater than any natural number. but therein lies the rub. if you can always add 1, you never finish the set of which you speak… and if it remains open, its not a set in the same way a finite set is conceived. the potential infinite set - which you are thinking is an actual infinite set - is really only indefinite, not infinite. the moment you finish it… make it a definitive object… it becomes finite. and yet until you finish it, you’re not speaking of a set or an object, but rather a kind of transcendental idea.
take the typical instance of the division of a distance. a finite distance can be subdivided into potentially infinitely many parts or sections. you can just keep dividing parts in half forever, but you will never arrive at an actual ‘infinitieth’ division or end up with a actually infinite number of parts.
any of you folks familiar with ghazali’s example of one of the absurdities of an actual infinity? it’s a swell thought experiment. kay so let’s assume eternity, and then let’s compare two beginningless series of coordinated events. imagine a solar system consisting of planets with coordinated orbital periods. so for every one orbit planet x completes, planet y completes 2.5 as many. the question is; if they’ve been orbiting for eternity, which planet has completed the most orbits? the correct mathematical answer would be that they have completed precisely the same number. but wtf? the longer they revolve, the greater the disparity between them becomes!
now if you understand what just happened here as a result of trying to construct an actual infinity rather than a potential, you’ll hear the same sizzling sound between your ears that you heard when you visited hilbert’s hotel (though i don’t think anyone so far but sil knows how to get there).
please, for the love of sam sneed, do some reading about ‘actual’ and ‘potential’ infinity. this is an understanding that supercedes what mathematics is telling you. you’ve got to wrap your brain around what the mathematics of infinity necessarily implies in the real world. if an actual infinite number of things were possible, hilbert’s hotel would be possible and not just a thought experiment to demonstrate the utter absurdity of actual infinities.
First I would want to know if you read the prior post and saw the error that you have been making. And if not…
That would depend on who I was trying to prove something to. It seems that James tried something that certainly would have worked on me, but not people who merely dodge the truth for sake of politics or perhaps ego. When debating an issue with me, I suggest two things:
ask for point by point agreement. Avoid long complicated paragraphs where many potential disagreements are possible. Without the effort to prove anything, state one concern at a time and ask for agreement - “agree” or “disagree”. The first time I disagree, ask why.
In that way both parties learn much quicker and also learn ways to word things better. James had set up a forum to handle just that method of debating, “Resolution Debating” - seeking how far people can agree and precisely upon what they actually disagree. James liked to organize things. This one is on his list of “new-to-the-world” concepts although he spelled out much greater detail.
Note in the last post I examined and agreed to each step of your process until I found an error. That way you could know what to NOT argue with me about (although perhaps someone else). It brings focus on the “devil in the detail” to straighten out the disagreement or at least point to where more investigation is needed. If wording was the issue, now both parties would know it. “Light is the best disinfectant”.
It is like climbing a mountain. If you can make certain of each footing along the way, you are far more likely to get to the top, more quickly as well. And if either party makes a mistake it is far more quickly resolved before pride gets too involved.
Pride, politics, and stupidity forbids people from doing that, but you asked what I would do if I were you debating with me. When any of those 3 concerns are present, the other person simply refuses to respond and instead gives some distractive lecture. That’s when you know the kind of person you are dealing with.
So, in like kind, do you agree with the correction that I pointed out?
This one:
If you don’t agree, simply say, “I disagree”. If you have a simple reason, state it and ask for agreement. If the reason is complex, state only the beginning of it and ask if I agree.
It would save a whole lot of wall paper.
When you start an ad hom battle, stop it by just taking your hits realizing that you started it.
I would have to disagree with that. Since he clearly did not understand the concept “infinity”, of course he would conclude that it doesn’t apply to reality.
I think that I have detected that to be where all of the confusion about infinity began.
Teachers describe infinity as a list that can always be added to, “no matter the number, you can always add 1”. But when they say that, some people think that infinity is this idea of always being able to add one. That isn’t really what the teacher meant. The teacher meant that if you try to get to the end, you can’t get there because there are always more numbers already accounted for, already there. You can always add 1 to whatever number you pick in order to find the next number that was already in the “set” of numbers. You are not adding to the set. You add to your position within the set. The set already includes ALL numbers potentially involved.
A better, more precise word would have been “a filled infinity”, then he would have been right. The author stated that the hotel was completely filled.
I think in the maths, “countable” just means no irrational or endless numbers. The real numbers between 0 and 2 are not countable.
I’m not sure what he meant by that but it seems to me that the value 2/3 is something that exists in reality and also has a precise mathematical extension = 0.666… So I don’t see the contradiction.
Again “0.666…” is a proposition that seems to “have sense”.
The whole thing appears to be someone wrongly criticizing someone who was wrong. But since I don’t really know those players nor some of the words they use, I’m just guessing.
believe me, bro, i’m not either, but i’m trying to figure this shit out.
yes, ‘2/3’ is a symbol extended in space, and if included in a closed series of calculations, it would be part of a finite set. this statement has mathematical extension. the difference is, you can’t call a set ‘infinite’ and at the same time give it extension, because in performing the infinite, i.e., endless divisions, all you’re giving extension too are the rules of calculation, recursively; divide, and again, and again, and again, etc. being open ended like this it is only intensional and a concept that is categorically different from extension. i can see more than just a rule extended when i see a finite set; i see the form of calculation and the product of it. but in conceiving an infinite set, i only observe the rule and not the product… for there can’t be an infinite set to observe… only the endless process of division, which is only the expression of a rule.
of course, but that’s not an infinite mathematical proposition.
consider this question. a math student performing the task of dividing, hands his paper to the teacher and asks; ‘is it infinite yet?’
how does the teacher answer? he cannot say ‘yes, the set is infinite’ and produce from that statement the same syntactical meaning as he would had he looked at a completed set of calculations and answered ‘yes, the set is finite’. now he could say ‘no, but it would become infinite if you divided forever’. here, it is theoretically and logically possible to divide forever, so the rule of division is extensional insofar as it is sensible, but the product of following that rule would never be extensional. only intensional and recursive.
infinite calculation could never produce a list. it only expresses a mathematical law by intension. one doesn’t observe infinity, but one can do it… or i should say, ‘approach’ it. thus lies the distinction between actual and potential infinity. one mistakes the process of listing with a list itself… one does the rule and then mistakes it as being a product. that erroneous dualism mentioned above that’s to blame for the battle between realists and anti-realists in mathematics.
I have no education on Wittgenstein (even have trouble getting his name spelled correctly) but if what you say is a correct representation of what he actually meant (and I will never have the time to find out), I would say that he seems to be missing the point in having a mind. And I do know that to be a common problem. It is something politically promoted to ensure an ignorant population. And that tactic is as old as the hills.
i want you to go in there, read all that shit, and explain to me what the crap it all means. you’re way smarter than me so you’re gonna have to drive. but look i’m telling you W was a beast, man. if he said sumthin’, a muthafucka sat down and listened. you ax any of the big brains from back in the day and they’ll tell you; when big W came around, he was getting ready to sort you out whether you liked it or not.
go look at his pic on wikipedia. see that crazy left eye that doesn’t match the right one? that’s what i’m talking about. sumthin’ about that dude was sketchy as fuck.
now i need you and sil to get your shit together and stop bickering so we can pull together and make some headway.
planet x has completed 10 orbits today
planet y has completed 12.5 orbits today (2.5 more than planet x)
planet x completed 9 orbits yesterday
planet y compelted 11.5 orbits yesterday
and so on down to… when?
the paradox: if they’ve been orbiting eternally, they never began orbiting. and yet if planet y has always completed 2.5 more orbits for every one orbit planet x completes, there had to be a time when planet y was orbiting before planet x made its first orbit. but that’s impossible, because they’ve both been orbiting for eternity.
fun with actual infinities.
oh damn the POleece just rolled up to the coffee shop. i’ont like the POleece so lemme holla at you in a minute. i gotta roll.
Does “You are not adding to the set. You add to your position within the set” mean something like the following:
Infinite set represented as: {…, x, y, z, …}
Add 1 at position y:
New set looks like: {… x, y+1, z, …}
??
I would like to query the meaning of a series being “infinite”. Skip to the last paragraph if at any point you get frustrated with the following, but coming back to it afterwards will make more sense if you do:
I see no issue in using the synonym “endless” or “boundless” to aid in my explanations, since these are literally what infinite means by derivation as well as definition. Substitute “infinite” back in when I use these terms if you wish, the meaning won’t be changed if you do.
Consider the example (1+1+1+…+1), is it agreed that the “…” represents an endless string of "1+1"s?
If the example of (1+1+1+…+1) is intended to represent an endless string of "1+1"s, any given “1+1” has no specific position relative to any start or end, because an endless string has no start or end. All positions are therefore undefined and cannot be pinpointed as specific, and are therefore arbitrarily interchangeable.
Picking any one non-specific position of a “1+1” and adding a 1 such that it is now “1+1+1”, is the string still endless?
Put another way, picking any non-specific position of a “1+1+1” and removing a 1 such that it is now “1+1”, is the string still endless?
I would say it is endless both before and after in both cases.
I would also say that infinite (endless/boundless) does not communicate quantity by definition - I would say that it does the exact opposite of conveying quantity, which is what infinite means: undefined or quantity-less are synonymous as well.
With or without the “1+1+1” or “1+1” the endlessness is indistinguishable, the endless set is endless before and after the addition or subtraction, the positions picked are equally arbitrary and non-specific, they cannot be counted because there is no “end” from which to begin counting their position.
One (…+1+1+1+…) appears no different from any other, and this representation confers endlessness better than (1+1+1+…+1), which suggests there’s a beginning end and a finishing end, which contradicts the notion of infinity being literally endless. Squeeze a 1 in or take 1 away, the “quality” of endlessness applies either way. The appearance remains the same, the tracability of any change is equally impossible as there is no end from which to check it relative to. It’s both impossible to confirm any change after it has occurred and impossible to equate the series before and after as there is no specific (end) point of reference to use to do so. It’s only possible to present the change as happening as it happens, because it is in finite terms at that point. Even adding in another (…+1+1+1+…) to any given point in the previous one presents the added series as a specific series, representing the infinite with specificity treats it as it was a finite series to inject. Yet afterwards, we see no difference, because it wasn’t finite - it was only represented that way.
Now.
I think I have been hearing protestation this whole time by some that the infinite series of (…+1+1+1+…) was already full, saturated perhaps. If this is the case then I ask what “ends” are resisting any further addition? If all the positions are all already occupied, and there are no empty positions left to fill, how are you judging the beginning and end of these positions? Do these positions have finite ends within this infinite series? Does this suggest that infinite series have finite bounds internally? Finite positions would appear to be a feature of representing infinite series with finite terms like the “1+1+1” in (…+1+1+1+…), or however you wish to represent the set. However, does this “accurately” represent an infinite series? If “infinite” is consistent with itself, including internal consistency, then each “1” would not have a finite bound to its position, it would be a (…+1+1+1+…) in itself, inception style.
Thank you for the compliment but I could write a whole 3 volume book on the request you just made, not on Wittgenstein, on the request to go read that article and all it implies to responsibly do so.
First realize that the article is about what someone thinks Wittgenstein meant to say. It is written by a third party, Victor Rodych. Reading the article is about like watching MSNBC or CNN report the “news”. To know what really happened concerning any news, you really have to go to the source because in the case of CNN, the truth will invariably be different than what was reported, MSNBC a little less so even though they read from the same scripts. They depend very heavily on us not having the time or inclination to check their sources.
That might not be so much the case with Victor Rodych but until I go read Wittgenstein himself, I couldn’t trust what someone else interpreted from him. And that takes a lot more time than I have, much like trying to untwist the true story from whatever CNN might have said. You have to take the time to go to the source (which they often hide if it existed at all).
That is what I am doing regarding James. And it takes a great deal of effort to try to see the world from another person’s perspective just to ensure that you are not mis interpreting what they are trying to say. What was their environment? Who were they speaking or writing to? What were they trying to accomplish? What words did they use? What references? And finally, what did they really intend to relay to their audience at that time? And that isn’t even getting into who the person really was all about.
So who is this Victor Rodych and why should I believe what he says about anything? He was raised to be a liberal in England, got his BA at Brandon, Phd at York. He seems to have focused primarily on Wittgenstein and Popper, both notable anti-logic promoters - “one can only believe the witnessed” , pro-mindless science. And that should be expected from a well published liberal now associated with the elitist Lethbridge University.
So what did the man report that Wittgenstein was trying to say? By just a quick scan of the article, I run across this quip, “the only genuine propositions that we can use to make assertions about reality are contingent (‘empirical’) propositions, which are true if they agree with reality and false otherwise”. Immediately I observed a “contingent” issue - ,“we can only make true assertions about reality if they are true”. And is what we witnessed what was really there?
Without the ability to reason, to use logic, even what we think we see is dubious, especially if it is some video or TV program. A hundred scientists can witness something that never happened. The senses can be easily fooled. And the instruments can be very easily misinterpreted. That is what skeptics and critical thinkers are for. But critical thinking involves logical and rational thinking, not instantly assuming that you have seen the truth.
I noted that James stated that the “Godwannabes” are the cause of ALL the world’s problems. I have always felt that it is assumption that is doing so. But then James also states that “presumption is the seed of all sin.” So in that regard I guess we actually we agree.
But note the reasoning assumed in that one statement, “genuine propositions are empirical and true only if they agree with reality”. Sounds fair upon simpleminded viewing, but there is a problem. He is saying that logical reasoning is not genuine, supposedly then to not be accepted as true (whether reality agrees or not). The only things we should have any faith in is what we see directly. But does what we see directly agree with reality? How could we know? Well that is easy, “if it is true, then believe it, otherwise don’t”. Yeah.
I think as it turns out, we can only know if our empirical evidence agrees with reality through logical thinking. But logical thinking is not allowed, it is mere “pseudo-proposition”, not to be taken seriously.
What it amounts to is that if you try to take logic out of witnessing and observing to discern truth, you can never know if you have discerned truth. But maybe that is the goal, to be never sure to be always in doubt, always insecure. That does sound like things I have heard about Wittgenstein. And it was a part of the political arena during that era.
I really don’t have the time to go find out what Wittgenstein really meant to say. But what our “sources tell us” is that Wittgenstein thought that people should not think (largely paraphrased) but believe whatever they see on face value.
Apparently Wittgenstein proposed (I guess that was a “pseudo-proposition”) that “2+2=4” is only a pseudo-proposition proposed by mathematics advocates and might not actually be true. We must empirically test the proposal before we can believe it. And if we multiply 947 times 627294, we should only believe our calculation after we go count the empirical items on display.
“Wittgenstein maintains that “mathematical propositions” are not real propositions” - Victor Rodych
In essence, he is saying that maths and logic are not to be trusted.
It appears that his argument is that maths and logic are merely language and thus don’t really mean anything because we invent language, implying that we could have invented it differently and caused “2+2=5”. If it is true that Wittgenstein really believed that, I would have to say that the man, as a philosopher, wasn’t very bright (despite his reputation, which is ALWAYS a product of politics, not performance).
As far as the infinities, one particular paragraph stands out in
It seems that early in his philosophical endeavors Wittgenstein rejected the very idea of an infinity (which to me would have been dumb). But later he expressed more acceptance, although insufficient for certainty. Again, that quote indicates that I would have to go read and investigate the mind of Wittgenstein myself in order to MAYBE discern what he eventually ended up believing about something, infinities, that I don’t really have any doubts about. So it is seriously not worth my time. I have a real life to worry about. Normally, I wouldn’t even be taking the time for these discussions.
I always try to keep in mind that reputation is strictly and entirely about politics, not performance.
Stop there. You have already made a mistake. Planet y could never have made only 12.5 orbits - never.
You stated that both planets have been orbiting for all time. That means that no matter how far back in time you go, both planets have already been orbiting a prior infinity of orbits. There was never a first, so there can never be a 12th. You cannot count from 0 orbits upward. The only thing that you can do is start counting at some arbitrary point in time and declare that to be zero. You can count both forward and backward eternally. But you have to start your count at some point that you arbitrarily choose to be “point 0”. The same is true of the calendar. It is only “2019” because it was arbitrarily chosen to start the years 2019 years ago, for whatever fanciful reason.
There is a part of the problem. The “actual infinities” are not what your problems are about. The actual problem is understanding what it means to exist yet never begin.
if what you say is true, the following would make no sense (correct me if i’m missing something):
we pick an arbitrary time ‘now(t1)’ to begin counting the number of times each planet will make a complete orbit, and will stop counting in 24 hours(t2). after 24 hours has elapsed, we observe that planet x has made five orbits, and that planet y has made 2.5 more orbits than planet x, putting it at 7.5 orbits. (btw, obviously ‘.5’ of an orbit would be half way… 180 degrees).
now even though they’ve been orbiting for eternity, we still notice that planet y has made 2.5 more orbits between t1 and t2… and yet we wouldn’t be able to say it despite the fact that we just watched it happen.
even though we pick an arbitrary starting point to begin counting, and one to stop counting, we still observe an unequal number or orbits. now assume a hypothetical being that has also existed for eternity and has been watching these planets make their orbits. any time he picks an arbitrary starting and ending point for counting orbits, he notices planet y orbits 2.5 more times that planet x does.
clearly this would mean that planet y has been eternally orbiting 2.5 more times than planet x… but if they’ve both been orbiting eternally, how could planet y possibly make more orbits, and how could our hypothetical being be mistaken about what he has counted?
furthermore, both planets are approaching a point at which planet x has fallen infinitely behind planet y. and yet, being ‘actually’ infinite, as you suppose, their completed orbits are somehow magically identical?
as a disclaimer, i should inform you that i probably have a fourth grader’s comprehension of math… something i’ve never regretted seeing that i’ve never needed to know much of it, or that any of my philosophical thinking has ever required a knowledge of it. that being said, if you become impatient and feel like you’ve got better things to do, by all means do so. becoming impatient with people is something i’m no stranger to, so i fully understand.
I don’t understand what you mean by “we wouldn’t be able to say it”.
I think that states the crux of your confusion. And let me try to answer your question by asking you a question, - koan for conk. Perhaps realize that neither past nor future actually exist. The universe knows nothing of either. Time is entirely a mind-made invention, as is counting. But still we must keep our minds clear with consistent (logical) thought.
You say that this eternal being has been watching eternally and counting the whole time. Counting is a serial process from 0 up (or down).
When did he begin counting such as to pass the one million mark?
First, there is no “falling behind”. Planet y has always been “behind”. Then secondly, who said that their “completed orbits are identical”? Does that come from the false notion that all infinities are equal? Just because two things are endless doesn’t mean that they are equally endless.
Hey man I’m in a bar right now on a phone so this will be brief. I’ve been reading up on this infinity thing and I gotta tell ya, i think we’re both in over our heads here. This matter is not as simple as it’s being made out to be in this thread, and if the existence of actual infinities was so obvious, I wouldn’t be reading about all these badass mathematicians and shit who say it isn’t. And when I say badass, I mean the kind that don’t hang out at philosophy forums.
Yeah so there’s a unique and turbulent history to this matter and believe me, it’s one hellacious, mind bending rabbit hole.
Just posting this so I don’t leave you hanging. I’ll be back when I have a standard keyboard at my fancy.