Is knowledge finite?

[dawiyd]

Discuss....

 

[JBrian]

Discuss....

If you don't know, then it should be obvious.

 

[TLFM]

Discuss....

Yes, knowledge must be finite. There could never be infinite knowledge because this would require that there is an infinite amount of things to know. But, if there was an infinite amount of things to know then one could never know them all. As soon as one knew the last thing there was to know, then that would mean there wasn't an infinite amount of things to know.

 

[Born_to_Lose_Live_to_Win]

Discuss....

Knowledge(of __________) is certainly finite.

As long as the knower and the object of knowledge are distinct entities, knowledge has to be finite.

'I'(the knower) can have only finite knowledge about 'myself'(object of knowledge).

How is the knower to be known?

P.S. Since this is a philosophy forum, I took the freedom to indulge in metaphysics. Please bear with me ppl.

 

[one love]

Yes, knowledge must be finite. There could never be infinite knowledge because this would require that there is an infinite amount of things to know. But, if there was an infinite amount of things to know then one could never know them all. As soon as one knew the last thing there was to know, then that would mean there wasn't an infinite amount of things to know.

How about this: we do not know enough to say this is true. There are mathematicians and computer scientist trying to understand the Riemman hypothesis and whether or not it is true. Despite the knowledge you and I have, there is much more to be had.

I'll say this, it sure would be sad to realize that learning is finite. To me, that says that creativity is finite, love is finite and life is finite. If there is a climax, I do not wish to ever achieve that peak.

There is not a finite amount of facts to learn. This would cause a very boring world to exist. I hope it is not true, do not believe it is true and hope to never live to see thee day that it is true.

 

[TLFM]

How about this: we do not know enough to say this is true. There are mathematicians and computer scientist trying to understand the Riemman hypothesis and whether or not it is true. Despite the knowledge you and I have, there is much more to be had.

I'll say this, it sure would be sad to realize that learning is finite. To me, that says that creativity is finite, love is finite and life is finite. If there is a climax, I do not wish to ever achieve that peak.

There is not a finite amount of facts to learn. This would cause a very boring world to exist. I hope it is not true, do not believe it is true and hope to never live to see thee day that it is true.

But the question was is knowledge finite. In order for it to be considered knowledge it must be possesed by someone, otherwise it may be truth, but it is not knowledge. This creates the paradox I tried to illustrate in my first reply. The fact that knowledge must be a subset of truth and that truth cannot be a subset of knowledge requires that knowledge is the one that must be finite whether truth is infinite or not.

Even if we look beyond that and address truth itself, since we live in what is (by current evidence) a finite universe it would necessarily follow that there is only a finite amount of truths contained within it to learn.

 

[Merlin]

If you were to assume that knowledge must be contained in the brain, then it must be finite.
If knowledge can extend beyond the brain, then knowledge may be infinite.

 

[Patzak]

It's not so much an assumption but rather a definition. Knowledge is something that is known. Though I wouldn't say at all that knowing something implies the knowledge to be "contained" in a brain or even anything material for that matter. So yeah, if there is a God, then his knowledge would probably be infinite - I think even if creation is finite, God himself must also be the subject of his own knowledge - and since he's infinite, his knowledge must be infinite as well; though it looks as if this might run into some sort of a recursion problem (in which God would not only have to have a perfect knowledge of himself but a perfect knowledge of himself having perfect knowledge of himself and so forth).

Anyway, as knowledge is a subjective term (in the sense that it neccesarily applies to a subject) it doesn't make sense to ask it in such a general way. A better way of asking would be "Is human knowledge finite?" - in which case: mine is; or "Is God's knowledge infinite?" - in which case: I think it isn't; or "Is there a limit to what we can know?" - in which case: there are obviously practical limits (human lifespan, brain capacity, etc.) but I don't think there are any such limits in principle (except perhaps for infinite self-knowledge: see above).

Anyway, the question posed in the topic needs qualification.

 

[one love]

But the question was is knowledge finite. In order for it to be considered knowledge it must be possesed by someone, otherwise it may be truth, but it is not knowledge. This creates the paradox I tried to illustrate in my first reply. The fact that knowledge must be a subset of truth and that truth cannot be a subset of knowledge requires that knowledge is the one that must be finite whether truth is infinite or not.

Even if we look beyond that and address truth itself, since we live in what is (by current evidence) a finite universe it would necessarily follow that there is only a finite amount of truths contained within it to learn.

You are thinking too much. Knowledge is not truth, as truth is just interpretation of the facts. Facts are what constitute knowledge. It has nothing to do with subsets of truth.

I fail to see what the evidence is that suggest a finite universe. Even evidence is not always necessarily proof for a case.

Despite what anyone or someone or everyone knows, has been known, there is still more to know. The current trend amongst humans is that there is always something new to learn: first, primitive man came down from the tree, picked something up with the hands, walked on hind legs, worked problems in the head, communicated amongst other humans, began to form a number system, mastered the technique of starting a fire, began to smelt, melt and burn anything and everything in sight in order to gage various characteristics. Eventually all of this lead to a birth of science in the 17th century, sparked in large part due to Isaac Newton and the calculus and mechanics he developed.

From what humans have scribed, written and etched in stone, the search for the facts has not ended. The data obtained through research in the various fields of physical sciences leaves far more data for researchers to scrutinize than they know what to do with. Entire new systems have been developed to accommodate for a lack of time to analyze the whole scope of what has been collected. I believe one of the new fields of computer science and biology has emmerged due to this: bioinformatics.

 

[TLFM]

You are thinking too much. Knowledge is not truth, as truth is just interpretation of the facts. Facts are what constitute knowledge. It has nothing to do with subsets of truth.

I fail to see what the evidence is that suggest a finite universe. Even evidence is not always necessarily proof for a case.

Despite what anyone or someone or everyone knows, has been known, there is still more to know. The current trend amongst humans is that there is always something new to learn: first, primitive man came down from the tree, picked something up with the hands, walked on hind legs, worked problems in the head, communicated amongst other humans, began to form a number system, mastered the technique of starting a fire, began to smelt, melt and burn anything and everything in sight in order to gage various characteristics. Eventually all of this lead to a birth of science in the 17th century, sparked in large part due to Isaac Newton and the calculus and mechanics he developed.

From what humans have scribed, written and etched in stone, the search for the facts has not ended. The data obtained through research in the various fields of physical sciences leaves far more data for researchers to scrutinize than they know what to do with. Entire new systems have been developed to accommodate for a lack of time to analyze the whole scope of what has been collected. I believe one of the new fields of computer science and biology has emmerged due to this: bioinformatics.

You seem to be equating knowledge with possible knowledge, which is not how the term is commonly used. Knowledge is defined by dictionary.com as:

Knowledge (n):

1.) The state or fact of knowing.
2.) Familiarity, awareness, or understanding gained through experience or study
3.) The sum or range of what has been perceived, discovered, or learned.
...

So knowledge is not knowledge unless someone "knows" it. This is what makes knowledge finite. Just as one could never count all numbers, one can never acquire all facts if those facts are indeed infinite. We can use knowledge of numbers as an example. If the number string is infinite, one can never know all the numbers, hence, knowledge must be finite.

I categorize knowledge as a subset of truth because, if acquired information is not true, then I do not consider it knowledge. To possess information that is incorrect is not to know something, it is to be mistaken. Even if we think we know something which turns out to be correct, there are still times when this is hard to qualify is knowledge. The Gettier Problem is a problem which questions what we can actually consider knowledge, but that would be straying a little far from the topic.

 

[Patzak]

Just as one could never count all numbers, one can never acquire all facts if those facts are indeed infinite. We can use knowledge of numbers as an example. If the number string is infinite, one can never know all the numbers, hence, knowledge must be finite.

While I agree with the rest of your post, I'm not too sure about this point: you say one could never count all the numbers (and I agree this is analogous to knowing everything) - but the problem is not counting all the numbers, it's counting to infinity. By saying "all" you are effectively putting a limit on the process of counting - while the essence of infinity is precisely that it is not limited; it's true that if we start counting and then stop after an arbitrarily long time, we will not have reached infinity - but that's implied by the fact that we stopped at all. If we were instead to count for an infinite duration, wouldn't we have counted to infinity?

I think your argument is essentially analogous to arguing that the universe must neccesarilly be finite in time because there couldn't have been an infinite number of stages (or moments or whatever) between now and the beginning; but forgetting that an eternal universe would have been eternal precisely by its lack of a beginning.

 

[TLFM]

While I agree with the rest of your post, I'm not too sure about this point: you say one could never count all the numbers (and I agree this is analogous to knowing everything) - but the problem is not counting all the numbers, it's counting to infinity. By saying "all" you are effectively putting a limit on the process of counting - while the essence of infinity is precisely that it is not limited; it's true that if we start counting and then stop after an arbitrarily long time, we will not have reached infinity - but that's implied by the fact that we stopped at all. If we were instead to count for an infinite duration, wouldn't we have counted to infinity?

Yeah, that is the kind of wording problem that it is easy to run into when discussing infinity. The reason I didn't say "count to infinity" is because this makes it sound as if infinity is at a particular location in the number string. There really is no way I know of to speak of infinity that is very useful to our minds. The concept of infinity is just too far removed from anything we can actually perceive.

I think your argument is essentially analogous to arguing that the universe must neccesarilly be finite in time because there couldn't have been an infinite number of stages (or moments or whatever) between now and the beginning; but forgetting that an eternal universe would have been eternal precisely by its lack of a beginning.

Well, if time actually exists, I am quite sure that the universe is eternal, or that it has been around for all of time since time would be contained within the universe. I'm not sure, however, that, even if the universe had no beginning, or was infinite in its existence, that we could not arrive at where we are. It seems to me that, just as one can arrive at the numbers 6 trillion through 800 trillion even though there are numbers stretching out infinitely in both directions, one could arrive at any point on an infinite line of existence regardless of the fact that the line had no beginning and no end. To traverse all points would be impossible, but to arrive at a point would be necessary.

 

[one love]

Ok, here is my example that knowledge is not finite. I know it is rather shoddy and hastely constructed, but...

What are the solutions to the equation x+y=0, given all real numbers?

There are infinitely many solutions. I know it is not a great example, but I hope the idea that I am meaning to get across has been understood to a degree.

 

[Osiris]

I have infinite knowledge.

 

[TLFM]

Ok, here is my example that knowledge is not finite. I know it is rather shoddy and hastely constructed, but...

What are the solutions to the equation x+y=0, given all real numbers?

There are infinitely many solutions. I know it is not a great example, but I hope the idea that I am meaning to get across has been understood to a degree.

An interesting line of thought, but I would contend that while you may know x+y=0 (where y=-x of course), this does not equate to infinite knowledge. It is actually only knowledge of a single mathematical principle which may be demonstrated an infinite number of ways. Unless you know every way in which it may be demonstrated, knowledge would still be finite.

 

[one love]

An interesting line of thought, but I would contend that while you may know x+y=0 (where y=-x of course), this does not equate to infinite knowledge. It is actually only knowledge of a single mathematical principle which may be demonstrated an infinite number of ways. Unless you know every way in which it may be demonstrated, knowledge would still be finite.

Not only is y=-x, but Ry=-Rx, there are infinite possiblities. So why does this not equate to infinite knowledge, because you believe the system has not changed? The thing to do is to prove that knowledge is finite, because as of now I assume knowledge to be infinite based on a thin axiom that human knowledge in mathematics has not reached an end, neither has our language and so neither has our creativity.

 

[EverlastingMan]

Well,
The state or fact of knowing.
1.Familiarity, awareness, or understanding gained 2.through experience or study.
3.The sum or range of what has been perceived, discovered, or learned.
4.Learning; erudition.
By these definitions it is of course clear that we can only learn so much. Even if one believes one will someday be perfect and reunited with god that god is usually defined as being beyond comprehension.

 

[one love]

Well,
The state or fact of knowing.
1.Familiarity, awareness, or understanding gained 2.through experience or study.
3.The sum or range of what has been perceived, discovered, or learned.
4.Learning; erudition.
By these definitions it is of course clear that we can only learn so much. Even if one believes one will someday be perfect and reunited with god that god is usually defined as being beyond comprehension.

Why? Why is it so clear? The range can be infinite: include all real numbers as the set X and let X be put into the function f(x)=y. This is assuming that you choose an arbitrary time from now (somewhere ahead in the future) and plug this into some sort of algorithm and have it repeat infinitely, I do not see why it is so clear that knowledge is then finite.