All Knowledge

OrdinaryClay
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All Knowledge

Is the set of potential knowledge finite or infinite.


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OrdinaryClay

OrdinaryClay wrote:

nigelTheBold wrote:

... 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.

The power set of all concatenations. A finite alphabet can encode an infinite sequence of sequences.

Only if you allow infinitely long sequences of characters.

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OrdinaryClay

OrdinaryClay wrote:

nigelTheBold wrote:

... 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.

The power set of all concatenations. A finite alphabet can encode an infinite sequence of sequences.

Gotcha. Thanks.


Quote:

Quote:

... 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 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.

No, actually I rely not on feelings, but on math.

The article I linked to describes a universe in which there is a limited set of data. Unlike the alphabet example above, each piece of data is concrete, and cannot be repeated. That is, you don't have an infinite set of letters from which to draw; there is a limited number of each. This is not a feeling; it is mathematics and logic. A finite set of physical properties can only be arranged in a finite number of combinations.

"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


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Okay, third time's a charm:

Okay, third time's a charm: any example of knowledge that exists outside of a brain? Anyone?


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BobSpence1

BobSpence1 wrote:

OrdinaryClay wrote:

BobSpence1 wrote:

Uncertainty or ignorance about changes or updates in knowledge in the future may expand the amount of potential knowledge, but not infinitely.

This sentences is non-sensical (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.

Re-reading my statement, I agree I could re-phrase 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.

My point regarding the expansion of the universe is no different than the inability and impossiblity
to infallibly predict the outcome infinite chaotic events, and the effect of chaos upon what currently exists. Refer back to my example of predictive models of the weather becoming obsolete due to the immeasurable events effecting global warming and
global dimming.

The universe is not static.
Moreover, there is no measure
of the chotic events in it, nor the effect of those chaotic events to forever change the universe in infinite and immeasurable ways that we can not predict in advance. As the universe infinitely evolves, so to does the infinite "information" forever evolve
in unpredictable ways.

As long as there is chaos, there is no limit to what is "created" or what changes.

So too, as the universe expands, it evolves, and that infinite and unpredictable evolution is evidence that
however you may reasonably choose to define knowledge, it is and will always remain
immeasurably "short" of a chotic, non-static, unpredictable universe of knowledge of proportions that
only a Theist would claim is finite, not immeasurable, static, and most importantly, known to God.

I take it the author you referenced also holds Theistic beliefs suggesting that everything, i.e. all that exists is finite because
God knows and will always know it all.

I've nothing more to say abour the matter, and no vested interest to discuss it further, as this thread and the counter-arguments made are no longer honestly being resposive.


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HisWillness wrote:Okay,

HisWillness wrote:

Okay, third time's a charm: any example of knowledge that exists outside of a brain? Anyone?

I can't help thinking that we first need to clarify just what the OP was referring to by the word 'knowledge' - it seems to be becoming more confusing as this thread goes on...

Outside the brain, there is only 'information' in the Information Theory sense, the state of the universe as it is. Knowledge is a sub-set of the information describing that state, plus implications and deductions extracted from that set of 'data', encoded/represented in a particular brain, or a communicating group of brains.

A bit like the way there are fundamental relationships between what we perceive as distinguishable 'things' 'out there', which we codify as 'logic' - the codification we refer to as the 'laws of Logic' exists only in our brains. Our brains assign various symbols to each perceptually discrete entity, and then to coherent abstractions ('memes' ?) derived from our observations and contemplation of the raw objects of perception. There is then a further level of concepts involving ideas about perceived relationships and implications from the first level of abstractions, etc. 

I guess the question in the OP could be thought of as, given an unbounded set of 'ideal' neuronal units, could such a hierarchy of derived concepts extend indefinitely?

EDIT: And if so, would such indefinite extension of relationships from a finite set of raw perceptions 'really' represent new ideas  equal in 'value' to the primary ideas, or some sort of ever-finer 'hair-splitting'?

Leaving 'knowledge' as a purely abstract 'metaphysical' term just allows such open-ended virtually meaningless speculative playing with words and meanings as we have seen here. We really need to nail such things down to some more structured model which allows us to make more fruitful deductions by applying the tools of logic and math.

Anyway, that's how I see it at the moment.

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

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BobSpence1 wrote:Outside the

BobSpence1 wrote:

Outside the brain, there is only 'information' in the Information Theory sense, the state of the universe as it is. Knowledge is a sub-set of the information describing that state, plus implications and deductions extracted from that set of 'data', encoded/represented in a particular brain, or a communicating group of brains.

That was my point. Since there will always be a limited number of brains, with a limited capacity, then pragmatically speaking, the issue is not with "potential" knowledge. If we were really able to stretch our imaginations to a universe with even a nearly infinite number of brains, we still wouldn't hit an infinite amount of capacity. Capacity is intrinsically the "potential knowledge" of a population of brains.

BobSpence1 wrote:
Leaving 'knowledge' as a purely abstract 'metaphysical' term just allows such open-ended virtually meaningless speculative playing with words and meanings as we have seen here. We really need to nail such things down to some more structured model which allows us to make more fruitful deductions by applying the tools of logic and math.

Metaphysics was a branch of philosophy (actually, just a chapter in one of Aristotle's collection of extremely dry writing). Now, it's an unfortunate speedbump.

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BobSpence1 wrote:We really

BobSpence1 wrote:

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.

Information theory (the one which is a branch of applied mathematics and electrical engineering, pioneered by Claude Shannon) by itself is not adequate to answer the question. It is adequate for encoding information. I agree that knowledge can be encoded as information. This is not the same as saying that the state of the universe is encoding all knowledge.  The state of the universe can be parameterized. Knowledge is both the set of all possible states of the universe as well as the totality of all physical laws that can act on this state set.

 


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BobSpence1

BobSpence1 wrote:

OrdinaryClay wrote:

nigelTheBold wrote:

... 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.

The power set of all concatenations. A finite alphabet can encode an infinite sequence of sequences.

Only if you allow infinitely long sequences of characters.

I addressed that already.


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nigelTheBold wrote:The

nigelTheBold wrote:

The article I linked to describes a universe in which there is a limited set of data. Unlike the alphabet example above, each piece of data is concrete, and cannot be repeated. That is, you don't have an infinite set of letters from which to draw; there is a limited number of each. This is not a feeling; it is mathematics and logic. A finite set of physical properties can only be arranged in a finite number of combinations.

The article refers to the finite state and computation ability of the universe. The knowledge in the universe is not the total computation ability of the universe. You are mixing concepts. The computation limits of my laptop do not describe how or why the laptop works.

The state of the universe can be a function of other states of the universe. In this sense the "alphabet" can repeat. Total knowledge is the state plus the laws that govern that state.
 


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HisWillness wrote:Okay,

HisWillness wrote:

Okay, third time's a charm: any example of knowledge that exists outside of a brain? Anyone?

I answered already. Your's is a non-sense question. The world existed with out your brain else your brain would not be here. Our brains allow us to perceive, acquire and understand knowledge.


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BobSpence1 wrote:Outside the

BobSpence1 wrote:

Outside the brain, there is only 'information' in the Information Theory sense, the state of the universe as it is. Knowledge is a sub-set of the information describing that state, plus implications and deductions extracted from that set of 'data', encoded/represented in a particular brain, or a communicating group of brains.

...

Leaving 'knowledge' as a purely abstract 'metaphysical' term just allows such open-ended virtually meaningless speculative playing with words and meanings as we have seen here. We really need to nail such things down to some more structured model which allows us to make more fruitful deductions by applying the tools of logic and math.

To conclude a subset relationship would require total knowledge, which you do not have. Physics exists whether we are here to understand it or not. To believe otherwise is metaphysics.


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OrdinaryClay

OrdinaryClay wrote:

BobSpence1 wrote:

Outside the brain, there is only 'information' in the Information Theory sense, the state of the universe as it is. Knowledge is a sub-set of the information describing that state, plus implications and deductions extracted from that set of 'data', encoded/represented in a particular brain, or a communicating group of brains.

...

Leaving 'knowledge' as a purely abstract 'metaphysical' term just allows such open-ended virtually meaningless speculative playing with words and meanings as we have seen here. We really need to nail such things down to some more structured model which allows us to make more fruitful deductions by applying the tools of logic and math.

To conclude a subset relationship would require total knowledge, which you do not have. Physics exists whether we are here to understand it or not. To believe otherwise is metaphysics.

Shit! goddamn PDA! I think I just lost my response... which I will now shorten.

Agreed. Given the manner in which we are Now referring to "knowledge" as what we are capable and have the capacity to understanding, retain, etc. In several posts, I've made references to humans not as gods, and our limitations to conceive of the amount of information, our limitations with regard to comprehending abstract information far beyond our experience, etc.

I've no disagreement with the
quoted post and quoted post within it.


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OrdinaryClay wrote:I

OrdinaryClay wrote:

I answered already. Your's is a non-sense question. The world existed with out your brain else your brain would not be here. Our brains allow us to perceive, acquire and understand knowledge.

What are you saying, though? Knowing something requires a brain. There are no examples of things known outside of brains that I can think of.

I'm aware that the world existed without my brain. That's obvious. But where can there be knowledge outside of brains?

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That's a compelling statement

That's a compelling statement


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OrdinaryClay

OrdinaryClay wrote:

BobSpence1 wrote:

OrdinaryClay wrote:

nigelTheBold wrote:

... 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.

The power set of all concatenations. A finite alphabet can encode an infinite sequence of sequences.

Only if you allow infinitely long sequences of characters.

I addressed that already.

The number of elements in the power set of a finite set containing n elements contains 2n elements - still finite. Where do you get infinity 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


OrdinaryClay
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BobSpence1

BobSpence1 wrote:

OrdinaryClay wrote:

BobSpence1 wrote:

OrdinaryClay wrote:

nigelTheBold wrote:

... 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.

The power set of all concatenations. A finite alphabet can encode an infinite sequence of sequences.

Only if you allow infinitely long sequences of characters.

I addressed that already.

The number of elements in the power set of a finite set containing n elements contains 2n elements - still finite. Where do you get infinity here??

http://www.rationalresponders.com/forum/17535#comment-242720


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OrdinaryClay

OrdinaryClay wrote:

BobSpence1 wrote:

OrdinaryClay wrote:

BobSpence1 wrote:

OrdinaryClay wrote:

nigelTheBold wrote:

... 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.

The power set of all concatenations. A finite alphabet can encode an infinite sequence of sequences.

Only if you allow infinitely long sequences of characters.

I addressed that already.

The number of elements in the power set of a finite set containing n elements contains 2n elements - still finite. Where do you get infinity here??

Once you've defined a "set of a finite set containing n elements" the set is by definite, a finite set. unless you union it with an infinite number of finite sets. The by definition, resulting set may be of any size.

Set Theory is one of the most boring aspects of mathematics
I've ever encountered and worked with. There's nothing complex about it at all.


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OrdinaryClay

OrdinaryClay wrote:

BobSpence1 wrote:

The number of elements in the power set of a finite set containing n elements contains 2n elements - still finite. Where do you get infinity here??

http://www.rationalresponders.com/forum/17535#comment-242720

... wherein you state, "A finite set of facts is not sufficient to conclude finite knowledge." You have not yet demonstrated that to be true, though. That's even outside of the problem of knowledge being limited to brains, which you have not addressed.

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fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence


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HisWillness wrote:Given that

HisWillness wrote:

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".

Christ! The fucker above answered the question in the 1st response. What the hell are you pea-brains blogging for?

Sit on a vibrator already, for fuck's sake.

Zzzzzzz zzzzzz ....