All Knowledge
Posted on: April 27, 2009  11:09am
All Knowledge
Is the set of potential knowledge finite or infinite.
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Given that even if all information could be acquired as knowledge, the capacity of an entire human population is limited, one must say that while "potential" knowledge is infinite, our potential to acquire all information as knowledge is definitely finite.
PS  if you're asking if we can know everything, then the answer is "no".
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum.  Terence
Hah! Speak for yourself.
"Yes, I seriously believe that consciousness is a product of a natural process. I find that the neuroscientists, psychologists, and philosophers who proceed from that premise are the ones who are actually making useful contributions to our understanding of the mind."  PZ Myers
I agree.
No, I'm not asking that.
Well if knowledge is only defined as what humans 'know' then yes it is finite, but always expanding.
If you take knowledge to mean what HisWillness is talking about then I believe it is still finite, that is, if the universe is finite.
Agreed.
Quantum Theory suggests that for a finite Universe, there will only be a finite amount of total information.
Even if our Universe were infinite, which is not consistent with a finite rate of expansion from anything approaching a pointlike singularity for a finite period of time, we would only ever have access to a finite volume of it, out to the event horizon, beyond which it is retreating from us faster than lightspeed.
So, based on current physics and cosmology, we do not have even hypothetical access to an infinite amount of data.
That leaves the hypothetical of what lies beyond the event horizon and before the Big Bang, which both currently seem to be intrinsically beyond our grasp, whether they involve infinities or not.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology
Oh, that too. So guaranteed limited knowledge from both sides (our capacity to hold knowledge, and the information available).
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum.  Terence
Okay. Well, I'm glad we settled that. That is, everyone but nigel, who knows everything already.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum.  Terence
Don't confuse facts with knowledge. New knowledge can be built from multiple facts. If you view each bit of information as a grapheme then we know that the power set of the language built from all concatenations of these graphemes is uncountably infinite. A finite set of facts is not sufficient to conclude finite knowledge.
Don't confuse knowledge with what's knowable.
What? You must be looking for something to be contrary about, because that's hardly a worthy point of contention. Your argument seems to be that potential is infinite, but since we only hold onto facts as knowledge, why would a limited number of facts not limit the already limited capacity of a limited population to know? How is the objection even reasonable?
Have you changed the definition of knowledge or something? What, other than fact, is knowable? I don't even care if the fact is true or false, I'm just wondering what you consider knowable that is somehow infinite.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum.  Terence
No matter how you cut it, we cannot generate an infinite number of combinations from a finite set of facts, unless you allow a proposition to refer to one or more elementary facts an infinite number of times, which is meaningless.
You are certainly confused....
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology
If any segment of existence is infinite, then potential knowledge would also be. If, however, all of existence is finite, then potential knowledge would also be finite.
Given that we do not know whether existence is finite or infinite, this question cannot be definitively answered.
Proud Canadian, Enlightened Atheist, Gaming God.
Does someone smell a fallacious nonsequitor trap comming on here?
Here is the gap argument.
"We don't know, cant know, and probably will go to our death as a species not knowing everything about the universe or it's start, so therefor magic exists and I can fart a Lamborghini out of my ass"
Sorry, whatever we don't know about the universe, and we will not know everything before our self suicide or natural extinction if we don't kill ourselves, does not constitute virgin births or magical harems in the sky because you slammed a plane into a building".
There certainly is allot we dont know, and probibly much more we will never know, but in any case, scientific method is not leading to hocus pokus or wishful thinking.
Quantum mechanics will not get me laid by Angelina Jolie a nanosecond from now, no matter how much I might dream about it.
So I don't know what the intent of this argument is other than the standard fallacy that since we dont know everything a magical being must have done it.
"We are a nation of Christians and Muslims, Jews and Hindus  and nonbelievers."Obama
Check out my poetry here on Rational Responders Like my poetry thread on Facebook under BrianJames Rational Poet also on twitter under Brianrrs37
I'm afraid that scent has become so ambient that I no longer sense it.
Besides, it has no weight, so there's no harm in presenting the idea that knowledge is limited, regardless of the particular angle. If someone can't understand that the godofthegaps argument combines several types of informal fallacy, then it's fair to give up and move on to helping more reasonable people with their questions.
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum.  Terence
I've asked a question and then have been consistent in my position. This is not being a contrarian. Why did you change your mind from one position to another so quickly?
I did not say facts were not knowledge. I'm saying knowledge is more then the irreducible facts. Facts can be combined to produce new knowledge distinct from the facts. Combined facts can be discovered to have new knowledge. Whether we have a limited number of minds to know things is irrelevant.
Knowledge exists even if we have not discovered it. So something can be knowledge, but not yet known. I'm not saying that any given piece of knowledge are infinite.
You are imposing a priori knowledge you do not know. You can not declare what sequence of facts represent knowledge unless you have complete knowledge of the system, which obviously you do not. Your argument is a circular one.
Not at all.
Trap or gap? I'm not sure I understand who is being trapped. In any case, your building a strawman and a simplistic one at that.
The thread started as a question. This then generated a differing position among the posters as to whether knowledge was infinite or not. Do you have any substance to add as to whether knowledge is finite or infinite?
Because I thought about it. You're referring to post #1, where I said: "... while 'potential' knowledge is infinite ...". Well, I thought about it, and I was wrong. If we were in an infinite universe, then we would have an infinite amount of information (no matter how redundant) to potentially process as knowledge. But given a limited universe, that can't be the case. A limited universe limits the amount of information, and thus fact.
But if the facts are limited, then that new knowledge itself is limited. You don't approach infinity that way (at least not philosophically or mathematically).
It's not irrelevant, because people need to be alive to hold facts in their head. Given that zero people means zero knowledge, I'd say it's pretty relevant.
Edit: fixed quote problem
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum.  Terence
The old "gained new knowledge and changed your mind" trick, eh? Very sneaky.
In case anyone's interested, Seth Lloyd has calculated the total informational capacity of the universe. It is indeed limited. Very large, but limited.
"Yes, I seriously believe that consciousness is a product of a natural process. I find that the neuroscientists, psychologists, and philosophers who proceed from that premise are the ones who are actually making useful contributions to our understanding of the mind."  PZ Myers
Yes. I find that all learning is sneaky and underhanded. Also elitist.
Hahahahaha!
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum.  Terence
Your quoting is all messed up in your post.
No, this is not true, because just having a collection of facts does not always tell you how those facts are related. You often need observational knowledge to relate the facts.
No, knowledge exists whether we have a brain to think about it or. If it were not the case then we could not be here since evolution preceded us.
This article is just saying the information(states viewed as bits) in the Universe is finite, and that there is a finite amount of usable energy to change these bits using computational logic. The universe as a computer is very different then knowledge. I never disputed that. This does not tell you if the total knowledge about the bits in the context of the Universe is finite. The total set of relationships between these bits is uncountably infinite as I just showed.
"Uncountably infinite." That makes me smile. Some infinities are more uncountable than others.
Don't let's be silly. Let's ignore the fact that a finite set of elements can only have a finite set of relationships. Very large, but finite. The article also states there's a limit on the computational ability of the universe. The ability to process data is also limited, meaning the universe (and you and me, too) can only process a finite amount of knowledge.
"Yes, I seriously believe that consciousness is a product of a natural process. I find that the neuroscientists, psychologists, and philosophers who proceed from that premise are the ones who are actually making useful contributions to our understanding of the mind."  PZ Myers
In a finite universe, there seems to be no way to generate an infinite amount of knowledge. Because of the finite universe, we cannot in reality put together an infinite sequence of elements of any kind, which is the only way you could generate an infinite number of combinations.
There is another way of resolving the 'problem', even if we allow an infinite number of elements or bits per proposition in principle:
There is a presumption of what a proper measure of quantity of 'knowledge' would mean. Only if you give equal weight to every distinct proposition, no matter how trivial or how little it differs in content or implication from another, would an infinite number of propositions necessarily imply an infinite amount of knowledge. If we take such factors into account, it is easy to see in principle how even allowing for hypothetical infinite combinations of finite elements, there is no necessary implication of infinite knowledge. A bit like the way an infinite sequence of digits with no repeating pattern, like those representing the value of transcendental quantities like pi, represent a finite quantity. Or the way a finite length can be subdivided into an theoretical infinite number of points.
Thus I would see as inevitable that ever more complex propositions based on a finite base of data would just be making ever more subtle and ultimately meaningless distinctions, just like subdividing a finite line into ultimately infinitesimally distinct points. Can't prove it mathematically, but it seems eminently reasonable to me, and reconciles your proposition with a finite universe.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology
Read what nigel said about relationships. Still finite.
I have no idea what you're talking about. Can you give me an example of knowledge that exists outside of a brain?
Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum.  Terence
As long as there is chaos, and unpredictability we can never know, nor reliably predict everything.
I disagree, and posted why above.
I'd be interested in your response though.
I think your previous post addresses a different issue.
Anyway, some thoughts:
My main point here is related to problems with just how you meaningfully measure 'knowledge'. I think the 'size of the set of all possible knowledge' is not an adequately defined or meaningful concept. It would make more sense to refer to the minimum number of bits required to encode all possible valid and nonredundant statements about reality.
Quantum considerations, which also involve uncertainty and unpredictability, are the basis of the assertion that a finite universe can only contain a finite amount of information.
As to the effect of chaotic unpredictability, I don't see that as directly relevant to the argument, although it would provide a further limit on know, although it does imply that there are some things which are unknowable, I guess.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology
One of the fundamental differences between Einstein's Theories and Quantum Mechanics is that Einstein envisioned
that the Universe is predictable and ordered. To the followers of Bohr, Einstein would say "God does not throw dice."
Quantum Mechanics is not based on principles of predictability, but probability instead. Bohr recognized chaos, while Einstein effectively denied it.
Quantum Mechanics although recognized to be applicable on the subatomic level advanced physics beyond Einstein's theories (which are recognized to be applicable to very large objects, and very high speeds.)
Quantum Mechanics was surpassed approximately 2 decades ago by String theories, of which there were five, which was then superseded by MTheory, all of which has had the goal of searching for a Grand Unification Theory applicable to the very small and very large.
Reference Nova Science's web site for a 3 part series on the above.
My point was rather simple, because chaos exists, we can not KNOW everything, simply because there is nothing at the present time to suggest that there will EVER be a Model, Theory, or set of Equations by which we can PREDICT EVERYTHING.
As to the Universe being finite, as you stated. That is not at all certain, and you can find many references to statements by reputable physicists that disagree.
We do NOT know that the Universe is finite, nor do we know if it is infinite. We DO know that we can NOT predict a wide variety of chaos that exists in the universe, and no theory to date even suggests that we can.
My post simply said that as long as there is chaos, and as long as we can not predict what will occur in a variety of chaotic circumstances, THEN we have no basis to conclude that all knowledge is finite, since the number of possibilities insofar as chaos is concerned are infinite.
Now that you more fully understand what I was hinting at, as we've discussed the issue I was addressing, I think you can recognize that I directly addressed the Topic of this thread.
Unpredictability does not imply infinite knowledge in a finite universe except after infinite time, since new data can only be generated at a finite rate.
I fully agree that chaotic effects alone mean that even with Quantum Uncertainty a 'deterministic' universe is still essentially unpredictable.
I am aware that some scientists refer to the possibility of the Universe being infinite, and I am interested to find out why, since it seems inconsistent with the Big Bang, which has our Universe expanding from the infinitely small (a singularity) or something close to that, for a finite time. To be currently infinite, it would seem to require that the singularity was actually infinite already, or expanded at an infinite rate for a finite time. The inflation proposed by Guth has only ever been described as 'exponential', not infinite in any sense, AFAIK.
I subscribe to New Scientist magazine and science podcasts from Scientific American, Science Magazine, the Royal Society, NPR, PRI, the BBC, CBC, Nature, and several others, so I am reasonably across developments in science.
QM superceded by String Theories?? That seems wrong in so many ways.
I will nevertheless have a look at some of those NOVA programs, I have found them quite good when broadcast on TV here.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology
Not in any particular order...
Soz, if I mistyped, I often do far worse...
MTheory superseded the 5 variations of String Theory. It essentially unifies all 5 String theories into a single String Theory, and just designates a different name. But it's String Theory, too.
Forgive my laziness...
"Unpredictability does not imply infinite knowledge in a finite universe except after infinite time, since new data can only be generated at a finite rate."
I suspect two things are going on... 1st) We're debating semantic differences, and 2nd) More importantly, we're talking about two different things. That is to say... While I'm talking about one thing, you are talking about the another, and visaversa.
I'm not going to repeat what I said, as that would be silly.
We're approaching a philosophical subject from 2 different angles, and I can see, that because we are doing so, it makes no sense to attempt to reconcile our 2 different statements. In short, we are saying 2 different things about the same thing. So, I'm not going to build a strawman.
I could REALLY pick apart your first sentence, about the "finite universe except after infinite time, since new data can only be generated at a finite rate.", but I'm not going to, as I find your posts to be original, intelligent, and responsive, despite a misinterpretation (in your first sentence) of what I said.
As to:
"I am aware that some scientists refer to the possibility of the Universe being infinite"
Scientists KNOW that the Universe is expanding, and as such that it the Universe is never finite, as long as time exists in the Universe as a whole (as opposed to the center of a black hole). Opps! (Soz. I began to chip away at something.)
I'm not familiar with Guth and his/her exponents.
BTW. The 3 Part PBS Nova programs on String Theory are 1 hour each. The MTheory is also an hour. I downloaded and viewed the stuff via freeware called vtap, but I'm sure you can grab and view the shows a number other ways. Unfortunately, the 3 parts could have been consolidated into an hour, so expect them have large segments that are redundant.
Not to be patronizing... and understanding that I very often choose not to read your posts in many threads...
Those or your posts within Topics that interest me are enjoyable particularly for their honesty and originality.
Although, sometimes I sense you enjoy venturing pretty far into the rings of Saturn and telling folks what you saw.
BTW. I enjoyed the response.
When you said in the earlier post
"we have no basis to conclude that all knowledge is finite, since the number of possibilities insofar as chaos is concerned are infinite."
That might be true in classical universe, but as mentioned earlier in the thread, QM implies that a finite universe can only have a finite number of states, so the uncertain outcomes of chaotic processes are still going to be limited to that same set of possible states.
A little surprised you aren't aware of Alan Guth's proposal of a period of rapid and exponential inflation shortly after the Big Bang, to explain the relative uniformity of the Universe and some other things. I assumed you had looked into the Big Bang in a little more detail. Perhaps Nova haven't covered that...
I think I have already seen that Nova series on string Theory.
The expansion of the Universe doesn't make the Universe infinite in any sense, if it wasn't already, unless if it is expansion at an infinite rate for a finite time or a finite rate for an infinite time. There is no current theories which suggest that time was significantly affected after the very early stages of the Universe. If you are using words differently here, I would suggest your usage is simply wrong.
On a separate topic, feel free to continue quizzing Eloise, but I doubt you will get anywhere. She appears to live in a different reality from everyone else, I gave up trying to make sense of much of what she says.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology
I'm very tired, as before, so excuse my laziness, I'm waiting for fall asleep at the keybored, but you keep waking me up! Shit!
MTheory denotes a finite universe?
Within how many dimensions?
I'm not a physicist nor studied Mtheory but I suspect one of us is quite mistaken, as String Theories speak of parallel universes, all having different possibilities, NOT replicating each other.
I've also not seen anything in String theories which speak of a finite universe.
I want to digress again to make the same point as before...
We know the universe is NOT finite! It is CONSTANTLY EXPANDING.
We do not and can NOT know the outcome of random chaotic events, as that would take infinite knowledge which we do not have.
HOWEVER, just because we do not know the outcome of all random events does not mean that our knowledge MUST BE finite... rather scientists continually refine their models, refine their equations to account for new variables, ...
Let's put it this way... and I think we can REASONABLY agree on this, even if we are approaching the subject from 2 different angles.
There is so fucking much to know, and learn that not only will nobody EVER know EVERYTHING, nor even be able to make any conclusion with certainty as to how much there IS to know. The important thing to understand is that we as a species DO know that compared to how much there could possible be to know (of which we can NOT quantify), we can quantify that compared to what we do not know, we do no effectively nothing.
Eloise, the Pantheist... Pantheistspeak is rather fascinating. It is entirely misleading unless you've really dedicated yourself to understanding it, which includes getting Pantheist glossaries, reading English interpretations of several examples of Pantheistspeak.
When first reading a definition and explanation of Pantheism
everyone is totally lost, that included myself.
As someone somewhere one this baord said... Pantheists are essentially Atheists... there are 3 or 4 big differences.
They redefine commonly used words to intentionally obfuscate the meaning of the words to suitably account for their claim of the existence of "God". Next, they have a personal need for "God", and a religion. Lastly, understand that when a Pantheist speaks of God, they are using a misnomer for the laws of nature, for example the organization of the various larger components of the Atom, the organization of the Atomic Chart, that Nature is God, that the fact the sky is blue is God, that God decided to give us a glorious day,,, all obfuscation of English.
BTW. I don't try to convince anyone of squat. I tell people what I think, and don't bullshit, although I do obfuscate truth and humor for 1 reason... to attempt to get people to think, perhaps to laugh, get pissed, agree or disagree, or slam them on the head.  As for the Pantheist member, again... I've no objective other than to question and from that point out what can be concluded from the responses.
BTW., I didn't challenge the Pantheist... s/he got pissed and challenged me to some sort of useless "debate".
Lastly, humor and an honest originality keeps one's mind sharp there are certain requirements to fulfill either of them. (I just wrote a goddamn fucking blog.)
That is simply wrong. Are you somehow reading 'finite' as implying of fixed size? Which is simply not a usage of the word in any dictionary I have seen.
It means not infinite. What do you think 'infinite' means?
Even infinite knowledge would still not allow us to know the outcome of a random event in advance.
QM does allow us to quantify at least the amount of raw data required to describe the state of a finite universe.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology
I'm not being silly. You should probably do a quick study om transfinite numbers. Here is something that may be helpful to you  http://en.wikipedia.org/wiki/Uncountable_set
Yes, obviously, I acknowledged that. It says it can only computationally process a finite amount of information. Knowledge is more then information. Knowledge captures the possible relationships between pieces of data. These do not automatically follow from just having the information.
Your two counter arguments are basically the same. You argue that infinity has no meaning in a finite universe. This is not true, you give a counter example in your argument.
All of us know that an infinite sequence can have meaning with out scribbling every bit. There are many examples. Irrational numbers, such as PI, have meaning even if we can not write down every single digit. We know .9* = 1 even if we can not write down every single digit. It is possible to draw knowledge from an infinite sequence via convergence, or associate cardinality with an infinite set. All of these are cases where knowledge is had despite the "limitation" of working in a finite universe.
Right. I'm aware of Cantor's work. I also realize that the cardinality of a set describes how "infinite" it is. It's just that "uncountably infinite" is a redundancy. Any infinite set is, by definition, uncountable. That's what made me smile. And it was an honest, nonironic smile. Really.
I'm also aware that any set with a finite set of elements has a bounded, finite set of relationships. For sets containing information, this is the total number of bits represented by the set, taken as a single binary number. According the paper I linked, the universe has 10^120 bits. This is the total number of potential states at any given instant, including gravitational degrees of freedom. The universe has (so far) performed 10^120 calculations, resulting in 2^(10^240) total pieces of distinct information (note: all number are approximate). This sets the upper bound for all potential knowledge at this point in time, including all the information about the past.
2^(10^240) is very large, but it is hardly infinite. I'd say it's infinitely far away from infinite, in fact, though not nearly as infinitely as far away as 2^(10^120).
[EDIT] Sorry, I messed up. I changed "10^240" to "2^(10^240)," which is the real number of potential information. Sorry. That was a dumb mistake.
The 2^(10^240) number also includes all operations performed on the 10^120 bits. That is, that number includes all the relationships that comprise "knowledge." And, as an added bonus, those 2^(10^240) possible relationships include all the thinking that goes on in your head, as well. It includes what you contain as knowledge.
Strangely, it also sets an upper bound for the number of potential alternate universes, if you take the "many worlds" interpretation of QM seriously (I don't, but there you have it).
"Yes, I seriously believe that consciousness is a product of a natural process. I find that the neuroscientists, psychologists, and philosophers who proceed from that premise are the ones who are actually making useful contributions to our understanding of the mind."  PZ Myers
I can't think of an example of knowledge that exists outside the brain, either.
Wrong again. I did not argue that.
On the one hand, I argue that there is no actual infinite quantity in a finite universe, such as length, volume, number of real entities, subatomic particles , etc.
OTOH, there is certainly meaning to the notion, the concept, of infinity, as in the number of points in a line, the elements in the summation of an infinite series, the digits of PI, all the transfinite numbers of Cantor, etc.
You are conflating these two references to infinity in my argument.
Exactly, and I did not deny any of that.
Nowhere did I invoke the limitation of working in a finite universe. I was making the distinction between the finite number of states that a finite universe can exist in, as Nigel explained, and the entirely valid and useful conceptual infinities, as rigorously defined by Cantor.
The point is, would you describe the knowledge you can draw from a convergent infinite series as 'infinite' in any meaningful way??
My argument was that a more meaningful measurement of knowledge seems to me to better correspond to the value of PI, which is finite, rather than counting the number of digits needed to write out that value in a standard number system.
The value of PI can also be defined by writing out the algorithm which can generate those numbers, and that algorithm uses a finite set of symbols. That seems to me to be a better measure of the information content in that quantity.
That is consistent with the normal way of estimating the information content in any sequence, IOW the length of the shortest algorithm or computer program which could generate that sequence. For example, at one extreme, a string of 10,000 'A's can be described in less than 10 ASCII characters. An infinite sequence of any one thing can be precisely defined by a description of one instance with the appropriate Cantorian Transfinite number attached.
EDIT:
At the other extreme, an infinite sequence of truly random numbers cannot be represented by anything shorter, so by that measure it does contain an 'inifinite' quantity of raw information. The question then is, is that truly worth regarding as representing an 'infinite' amount of knowledge?? This suggests to me that a measure of knowledge should be further constrained to eliminate purely random sequences, but measure the knowledge embodied in such sequences by specifying their mean, standard deviation, etc.
This is what I meant by a more meaningful measure of 'knowledge'.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology
Knowledge is more then just counting or performing computations on finite sets. I'm not conflating anything. You are making an irrelevant distinction so you think I'm conflating things.
No one is arguing that a single piece of knowledge is infinite. We are talking about the total set of knowledge. The point is that given a finite set of elements, and an incomplete understanding of how those elements relate in a meaningful way you can not make an absolute statement about the set of subsets that have meaning.
Knowledge is more then just a set of encoded bits. A set of encoded bits describes the state at a given moment. You are conflating an observation with knowledge. You are still confusing facts with knowledge. It does not tell you how multiple states are related, for example.
No, it is not redundant. I'm not sure you do understand. The set of all odd numbers is infinite and countable.
You have not defined your relationship so no, this is not true.
I understand that very large numbers are not infinite.
I was responding to this from you:
and pointing out that that I agreed with this, because the 'infinity' of the 'infinite set' is in a different category to the 'infinity' of an infinite physical universe. This is a very relevant distinction when discussing "infinity", which you obviously do not see the significance of.
So you haven't actually demonstrate how we can get an infinite set of knowledge from a finite universe.
Anything that can be expressed in language, or a mathematical formula, or a philosophical argument, etc, can be encoded in a sequence of bits.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology
There is not a shread of evidence that the universe is
finite.
More importantly, and much ore to the point of the topic regarding if the is a finite or infinite amount of knowledge...
As long as there are infinite outcomes / possibilities, knowledge remains infinitesas we can never posess the knowledge to predict the outcomes of the chaos in the universe.
In simpler terms, given forever changing conditions, our "knowledge" becomes obsolete, i.e. false. In concrete terms, take as an example our mathematical models to predict the weather.
Already, given a host of chaotic events contributing from global dimming, to global warming, our knowledge
is obsolete. Our previous models to predict the weather or now obsolete / false, due to a wide variety of changes.
NEW MODELS must now be developedTHOSE WHICH PREVIOUSLY WOULD HAVE BEEN INNACCUARATE or FALSE.
This is a simplified example of how knowledge is not finite! It is infinite. Chaos
and random events cannot be predict and knowledge EVOLVES
in a manner that PREVIOUS knowledge does NOT always remain true.
I can't explain the basis of my argument any sinpler than I just did. The evidence
that knowledge is not finite is indisputable.
My apologies. My own ignorance was amusing me. It's been way too long since I studied math and logic; I had completely forgotten the "countable" vs. "uncountable" distinction. Even when you tried to remind me above.
Egg, meet face.
Okay, since I've already proven my ignorance here, could you provide a link or an example of a finite set of elements with an infinite set of relationships? It's not been as long since I've studied information theory, but I seem to recall that a finite set of elements encodes a finite set of information.
I recognize that. But did you get that there is only a certain amount of information in the universe? And that there has only been a certain amount of time in the universe, resulting in a finite (thoough extremely large) set of potential states? This seems to bound the total amount of potential knowledge not just in this universe, but in all the variants of this universe.
"Yes, I seriously believe that consciousness is a product of a natural process. I find that the neuroscientists, psychologists, and philosophers who proceed from that premise are the ones who are actually making useful contributions to our understanding of the mind."  PZ Myers
There is at least strongly suggestive evidence from studies of patterns in the cosmic background radiation, which show 'ripples' at a range of sizes, whose intensity seems to fall off above a certain size, which would be consistent with a maximum, ie finite, size of the Universe.
The Big Bang theory has the Universe expanding in size from an extremely small size at a finite rate for a finite time, which means it cannot, at least now or for any finite time into the future, be infinite in volume. It may indeed continue into an infinite future, at least hypothetically. To be currently infinite would require the Big Bang to have started with an infinitely large singularity, which has severe logical and mathematical problems, AFAICS.
Uncertainty or ignorance about changes or updates in knowledge in the future may expand the amount of potential knowledge, but not infinitely. Continuing expansion of anything  the Universe, or the amount of knowledge  does not equate to infinity within a finite period of time  that would require expansion at an infinite rate.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology
I can see that this particular example I gave earlier was not well phrased, and has obfuscated my point.
For that reason I provided an example of obsoleted weather models as an example of why and how chaos and unpredictable events resulting in infinite possibilities that we can not
predict the outcomes of.
From that example, I derived the point that it would require infinite knowledge to correctly UNDERSTAND infinite chaotic and unpredictable events to the degree that we could ever acquire the infinite knowledge that would be required to infinitely predict the outcomes of infinite chaotic events and the results of those events.
In short, we would have to be what Theists call "God",
to be "all knowing", and understand infinite chaos.
In sum, a we can not understand the infinite chaos
in the universe, we will never acquire the infinite knowledge required to understand / correctly predict the outcomes. We are not "Gods" and never will be.
It is not possible to know anything about the outcome of chaotic or random processes without actually knowing the future, perhaps with a hypothetical time machine. Questions of 'infinite' knowledge do not arise.
Outcomes of finite processes in a finite universe can not have infinite possible outcomes, chaotic or not.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology
I understood your point. Your claim that an infinite set is in a different "category" of infinity because there are examples where infinite sets have alternative representations is not sufficient to prove anything about your spooky notion of "category". "There exists" does not prove "for all".
I believe knowledge is infinite. I can not prove it. I'm showing your demonstration is not sufficient to prove that it be finite.
Obviously, I have not disputed this since I argued from the beginning the power set of a finite set was uncountably infinite. You know full well you have been referring to the state of the universe when referring to encoded bits. This is how you arrived at your finite "snapshot", which is the basis of your argument. My comments regarding the set of encoded bits have been in this context. You stated that the current information in the universe was finite and therefore this was adequate to claim knowledge was finite. Your statement is pointing out what I said from the beginning.
Since knowledge is more then the encoded state of the universe the next question is what is the set of grapheme/token/bit sets that describe this knowledge. We don't know because we don't have complete knowledge of the Universe. Since the set can be uncountably infinite that is the upper bound.
The power set of all concatenations. A finite alphabet can encode an infinite sequence of sequences.
Yes, I do agree the evidence points toward a universe that is bounded and therefore finite. You are relying on feelings not proof when you believe in finite knowledge. Now I suspect you don't like the word faith and I know that some atheists think I use this derogatorily ( I don't. I embrace faith), but you are basically relying on faith to believe in finite knowledge.
This sentences is nonsensical (even in its context). Perhaps you could paraphrase what you mean.
Are you saying future discoveries may increase knowledge, if so, besides being redundant on its face, says nothing about how much knowledge is available to be discovered.
I was addressing a post from treat2. The point was that while I acknowledge the 'redundant' idea that new knowledge will inevitably become available, that in itself does not imply an infinite amount. Treat2 seems to have this fallacious idea that anything growing cannot be considered finite.
Rereading my statement, I agree I could rephrase it to better convey what I had in mind:
"Uncertainty or ignorance about changes or updates in knowledge in the future implies that there is almost certainly more potential knowledge than we currently might estimate, but not infinitely more."
We really need to settle on some way to meaningfully quantify 'amount of knowledge' before any statements about "how much knowledge is available to be discovered" can make be meaningful, and certainly any statements about 'infinite' knowledge.
Formal measurement of information according to Information theory, which is a branch of applied mathematics and electrical engineering, pioneered by Claude Shannon, is what I have been basing my responses on. What are you basing your ideas of 'amount of knowledge' on, and what do you see as the differences between 'information' and 'knowledge'? I acknowledge they certainly have at least different connotations, and arguably more basic differences, but I think they are definitely closely related concepts.
Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality
"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings."  Sam Harris
The path to Truth lies via careful study of reality, not the dreams of our fallible minds  me
From the sublime to the ridiculous: Science > Philosophy > Theology