Register | Sign In


Understanding through Discussion


EvC Forum active members: 65 (9162 total)
3 online now:
Newest Member: popoi
Post Volume: Total: 915,806 Year: 3,063/9,624 Month: 908/1,588 Week: 91/223 Day: 2/17 Hour: 0/0


Thread  Details

Email This Thread
Newer Topic | Older Topic
  
Author Topic:   Objective reality
Phage0070
Inactive Member


Message 151 of 172 (560910)
05-18-2010 5:15 AM
Reply to: Message 149 by Peepul
05-18-2010 4:23 AM


Re: Objective Math
Peepul writes:
I think putting 'collectively agreed' in your statement makes it meaningless. Who is to do the agreeing here?
This concept goes back to the extreme basics of philosophy and the way in which we think. For example, put aside everything that you know and start from scratch:
The famous line is "Cogito ergo sum" or "I think, therefore I am." Since you are thinking you can reasonably conclude that you exist in any sense that will be meaningful to yourself. The next step is to consider what other things exist, and this leads us to our senses.
Starting from within our mind, we have no way of determining if our senses are reliable. Most people will readily admit that they can make mistakes, but the more subtle point is that *everything* could be a perfect illusion to our senses ("The Matrix" is often referenced here). There is a certain leap of faith required to conclude that anything we observe can be trusted to be real.
Once we trust our senses to a certain extent, we can determine that there are other thinking beings in the world. This lets us distinguish between consistent and inconsistent observations; for instance if you saw a fairy and 9 other people did not, you could conclude that your senses were simply being unreliable (as they commonly are). Note that this does not strictly prove that these consistent observations are objectively real, only that if they are illusions that they are shared illusions as opposed to solitary ones.
Now for the concept of objective reality; this is again something of a leap of faith. Objective reality is something that exists independent of the mind, and if you will recall up to this point your own mind is the one thing you can most reliably conclude exists. Everything beyond that is to some extent going out on a limb. The concept becomes defined in an awkward fashion; our observations indicate that things happen and exist regardless of them being observed. This again is summed up by a famous saying, "If a tree falls in a forest and no one is around to hear it, does it make a sound?" Our observations indicate that it does, but that sort of negates the whole "lack of observation" concept in the first place.
So to wrap things up we can be reasonably sure that an objective reality exists in the same sense that we can be sure anything exists, including other minds. This is to say we are not completely certain, but sure in every reasonable and useful sense. Determining this objective reality is done through weeding out individual experiences which are obviously not objective, and whatever we are left with is concluded to be objective (although it could technically be a shared illusion).

This message is a reply to:
 Message 149 by Peepul, posted 05-18-2010 4:23 AM Peepul has not replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 152 of 172 (560957)
05-18-2010 8:57 AM
Reply to: Message 150 by Phage0070
05-18-2010 4:46 AM


Re: Mathematical Elegance
The roots of mathematics lie in what I would equate to almost logical rules born of observation; 1 + 1 = 2 would not only be mathematically valid, but also a tautology.
Yeah that is where I started from too. But I am not so sure that things are as simple as that anymore.
Is mathematics rooted in observed reality? Or is observed reality rooted in mathematics? Do we invent maths to reflect observed reality? Or are the observations made in the act of discovering the logical "rules" that objectively exist and underpin what we call "reality"? Is there any actual difference between these two approaches? Or are both approaches saying exactly the same thing really? Maybe it is a bit like asking whether the chicken or the egg came first?
Mathematics is based on being internally consistent with itself, and being based on reality the assumption becomes that reality is internally consistent as well.
I think the difference in approach here is that you are seeing mathematics as being derived from reality whilst the Platonistic approach is essentially to see reality as the result of the underlying mathematical relationships that exist.
Or something like that.
This appears to have born out to this point in time, and the confidence in this trend continuing is the expectation of "elegance" in formula for natural laws.
The fact that we can investigate and discover (subject to empirical verification) aspects of reality purely by working through the maths is what seems to lead those who advocate a more Platonic view to their conclusion.
Whatever the case I find it quite remarkable that we can investigate the world in this way. The fact we can "discover" physical phenomenon like black holes, time dilation, anti-matter etc. etc. in this manner is quite awe inspiring IMHO.

This message is a reply to:
 Message 150 by Phage0070, posted 05-18-2010 4:46 AM Phage0070 has replied

Replies to this message:
 Message 153 by Phage0070, posted 05-18-2010 1:32 PM Straggler has replied

  
Phage0070
Inactive Member


Message 153 of 172 (561026)
05-18-2010 1:32 PM
Reply to: Message 152 by Straggler
05-18-2010 8:57 AM


Re: Mathematical Elegance
Straggler writes:
Is mathematics rooted in observed reality? Or is observed reality rooted in mathematics? Do we invent maths to reflect observed reality? Or are the observations made in the act of discovering the logical "rules" that objectively exist and underpin what we call "reality"? Is there any actual difference between these two approaches?
...
I think the difference in approach here is that you are seeing mathematics as being derived from reality whilst the Platonistic approach is essentially to see reality as the result of the underlying mathematical relationships that exist.
Let me take another stab at explaining what I was getting at.
Some parts of mathematics are based on observation of reality. We would tend to only consider the factual parts (1 + 1 = 2), but there is also the concept of internal consistency that is an assumption of both mathematics and reality. We apply it to the field of mathematics with the expectation that reality is also internally consistent and will share those results.
Consider very simple logical rules from which new, complex logical statements can be derived. This derivation is based on the concept that logic is internally consistent, so that these new statements need not be based on observation at all. There is still the expectation that they will reflect reality however: For instance, if we had derived that since we have thing "A" in this room, some thing in another room we cannot observe must have the quality "not A".
That would be "new information" which we arrived at purely through logic. We might have observation to back up "A=A", but the expansion of logic based upon itself providing accurate results assumes that reality is also based on itself.
Invented maths are not necessarily invented to reflect reality (the observation to back it up may not exist), but they are done so to be consistent with the rest of mathematics. The fact that they do reliably reflect reality is a strong indication that reality is consistent with with the rest of reality. The expectation that undiscovered portions of reality will be consistent with the rest of reality is what makes mathematicians expanding the field confident that those expansions will have any practical application whatsoever.
So if I have managed to make any sense yet, I view mathematics as starting from observations of reality but almost immediately developing independently. What makes it useful is that mathematics develops in a way that inevitably reflects reality because they are both internally consistent; they are two puzzles with pieces that only go together one way, the puzzle being completed cannot help but reflect the master even without reference.

This message is a reply to:
 Message 152 by Straggler, posted 05-18-2010 8:57 AM Straggler has replied

Replies to this message:
 Message 154 by Straggler, posted 05-18-2010 1:37 PM Phage0070 has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 154 of 172 (561027)
05-18-2010 1:37 PM
Reply to: Message 153 by Phage0070
05-18-2010 1:32 PM


Re: Mathematical Elegance
Some parts of mathematics are based on observation of reality.
So we could say that some aspects of mathematics are discovered through observation of empirical reality?
Invented maths are not necessarily invented to reflect reality (the observation to back it up may not exist), but they are done so to be consistent with the rest of mathematics.
So we could say that some maths is simply a case of remaining internally consistent with a set of axioms which were invented and which needn't have any link with physical reality at all?

This message is a reply to:
 Message 153 by Phage0070, posted 05-18-2010 1:32 PM Phage0070 has replied

Replies to this message:
 Message 155 by Phage0070, posted 05-18-2010 5:40 PM Straggler has replied

  
Phage0070
Inactive Member


Message 155 of 172 (561065)
05-18-2010 5:40 PM
Reply to: Message 154 by Straggler
05-18-2010 1:37 PM


Re: Mathematical Elegance
Straggler writes:
So we could say that some aspects of mathematics are discovered through observation of empirical reality?
Yes, that would be correct. Conversely some aspects of empirical reality could be discovered through extrapolation of mathematics, under the assumption that both are internally consistent with themselves.
Straggler writes:
So we could say that some maths is simply a case of remaining internally consistent with a set of axioms which were invented and which needn't have any link with physical reality at all?
A mathematical system which is not based on reality could be constructed and which would yield results without a link to physical reality. However, maths which are consistent with other maths that are based on physical reality are, by that virtue, linked to physical reality and can be expected to yield results consistent with reality.
This is after all why those axioms are not completely arbitrary.

This message is a reply to:
 Message 154 by Straggler, posted 05-18-2010 1:37 PM Straggler has replied

Replies to this message:
 Message 156 by cavediver, posted 05-18-2010 6:00 PM Phage0070 has replied
 Message 158 by Straggler, posted 05-18-2010 6:59 PM Phage0070 has not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 156 of 172 (561069)
05-18-2010 6:00 PM
Reply to: Message 155 by Phage0070
05-18-2010 5:40 PM


Re: Mathematical Elegance
Conversely some aspects of empirical reality could be discovered through extrapolation of mathematics
Could be?
A mathematical system which is not based on reality could be constructed and which would yield results without a link to physical reality.
Or it could yield results with major links to reality - such as with group theory, algebraic topology, the Zeta function, etc...
And the converse of course - physics leading to mathematical results that otherwise had no connection reality, such as topological quantum field theory leading to massive simplification in the calculation of Donaldson polynomials.

This message is a reply to:
 Message 155 by Phage0070, posted 05-18-2010 5:40 PM Phage0070 has replied

Replies to this message:
 Message 157 by Phage0070, posted 05-18-2010 6:10 PM cavediver has not replied

  
Phage0070
Inactive Member


Message 157 of 172 (561070)
05-18-2010 6:10 PM
Reply to: Message 156 by cavediver
05-18-2010 6:00 PM


Re: Mathematical Elegance
cavediver writes:
Could be?
Seems that way don't it?
cavediver writes:
Or it could yield results with major links to reality - such as with group theory, algebraic topology, the Zeta function, etc...
Right, but aren't those also consistent with other branches of mathematics with more concrete links to reality?

This message is a reply to:
 Message 156 by cavediver, posted 05-18-2010 6:00 PM cavediver has not replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 158 of 172 (561078)
05-18-2010 6:59 PM
Reply to: Message 155 by Phage0070
05-18-2010 5:40 PM


Re: Mathematical Elegance
Straggler writes:
So we could say that some aspects of mathematics are discovered through observation of empirical reality?
Yes, that would be correct. Conversely some aspects of empirical reality could be discovered through extrapolation of mathematics, under the assumption that both are internally consistent with themselves.
Yep - I think that is how I see it too.
This is after all why those axioms are not completely arbitrary.
I think we essentially agree.

This message is a reply to:
 Message 155 by Phage0070, posted 05-18-2010 5:40 PM Phage0070 has not replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 159 of 172 (564135)
06-08-2010 1:07 PM
Reply to: Message 130 by Rahvin
05-14-2010 4:59 PM


Re: Numbers
Rahvin writes:
Perhaps another way of saying the same thing would be that 6,7,8,9.... are anticipated to be part of objective reality based on extrapolation of the rules that have been deduced from observation?
Yes, exactly what I'm talking about.

This message is a reply to:
 Message 130 by Rahvin, posted 05-14-2010 4:59 PM Rahvin has not replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 160 of 172 (564139)
06-08-2010 1:34 PM
Reply to: Message 133 by Straggler
05-14-2010 10:01 PM


Re: Platos Cave
First off - sorry for the belated replies. I've been a busy bee the last few... weeks (apparently) and sometimes I just can't post in a timely fashion. Better late than never?
Straggler writes:
Yet when asked which numbers are "known to be part of objective reality" your answer is "I don't know". Can you really not see the contradiction inherent in this position?
Stile writes:
I don't really see the issue.
Erm how can it make sense to not know which numbers are "known to be part of objective reality"? Just read that sentance and think about it.
Think about what?
Remember we're talking about the kind of situation like the man in the box.
"Which are known to be a part of objective reality"
Man in the box = "5"
In reality = "I don't know" (how high have you ever counted stuff?)
What's wrong with this position? Why would I need to know the highest number that is known to be a part of objective reality? Or, to say it another way, why would I need to know the highest number that is actually represented in objective reality? As long as the mathematical rules we rely upon are always verified to be accurate against the reality they are tested on... what does it matter how big "the highest" number is?
Straggler writes:
Stile writes:
"Considering" something is a subjective process. I don't really care what you would like to consider, or not consider.
It seems, to me, that the number 1 has been verified to exist within our reality a lot more than that larger number has, though. But what does it matter?
Well this is exactly your problem. Exactly as you have correctly identified that which you are calling "known to be objective" is actually a subjective conclusion. Hence the innate contradiction in your thinking.
But... I'm calling "known to be objective" that which we have actually counted and verified (likely mutlitple times by multiple different people). How are you calling that a "subjective conclusion"? If that's a subjective conclusion... then what is objective?
So what is the largest number that can be said to exist in our universe? The number of quarks in the universe? Is this number honestly more real than the number of quarks in the universe + 1?
That depends entirely on what you mean by "more real".
If you're talking about "things that have actually been verified to exist in reality".. then yes, of course it is. Like the man in the box, if he only has 5 apples than "5" is "more real" than "6". How is it not? He can extrapolate, or anticipate, or hypothesize about "6". But until he actually has 6 apples... "5" is more real, wouldn't you say? Why would this be any different when we increase 5 and 6 to "some really big number" and "some really big number + 1"? And I still don't see what the point of this is. Who cares if some number is "more real" (in this context) than another number? As long as all numbers are theoretically useful and all verified concepts come back to reality... what does it matter which number happens to be the biggest we're able to verify back to reality?
Straggler writes:
It suggests that we should look at the things we have been discussing in almost exactly the opposite way to the way you have been advocating. It does not affect results as such. But it has enormous implications for our methods of investigation.
Either you do not understand what I'm advocating, or you have not made your own position very clear. Because I still have no idea what you're on about, or what these "enormous implications" may or may not be.
You are treating maths as idealised extrapolation of empirical results. I am attempting to get you to consider the opposite view that the empirical results are in fact nothing more than the shadows on the cave wall and that the maths is in fact the objective reality that underlies it all. You are saying examine empirical reality and the maths will follow. I am proposing (for the sake of argument at least) that we examine mathematical reality and that an understanding of empirical reality will follow from that.
Does that make sense? Do you see the difference that I am trying to get at here?
I should note that I have no idea about the story of Plato, his Cave, or any shadows. So those terms don't really mean anything unless you care to describe the scenario.
Yes, I am treating maths as an idealised extrapolation of empirical results. But I already do also consider the oppostie view that if we examine mathematic reality than an understanding of empirical reality will follow from that... the two go hand in hand, don't they?
1. You get some empirical observations and create a mathematical model...
2. You take your cool mathematical model and some cool mathematical tricks and come up with an awesome mathematical statement about empirical reality.
3. You take your awesome mathematical statement... test it against reality... and see how it does. If it works out, then, congratulations! You just successfully broadened human knowledge of "known to be an objective part of reality" (assuming it can be verified, replicated....).
Why would you assume I'm ignoring step #3?
I still don't really understand what you're attempting to talk to me about.

This message is a reply to:
 Message 133 by Straggler, posted 05-14-2010 10:01 PM Straggler has replied

Replies to this message:
 Message 161 by Straggler, posted 06-08-2010 2:12 PM Stile has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 161 of 172 (564140)
06-08-2010 2:12 PM
Reply to: Message 160 by Stile
06-08-2010 1:34 PM


Re: Platos Cave
Why would I need to know the highest number that is known to be a part of objective reality?
How can it be "known to be part of objective reality" if neither you nor anybody else knows it?
But... I'm calling "known to be objective" that which we have actually counted and verified (likely mutlitple times by multiple different people)
So what is the highest number that "we have actually counted and verified"?
And if I add 1 to this number are you saying that I suddenly leave behind objective known to exist reality and enter a realm of theoretical numbers which may or may not exist?
If so this cutoff point (i.e. the highest "known to be objective" number) would seem to be rather important to ascertain. Because use of any numbers beyond that are just theoretical and may not even exist according to you.
I should note that I have no idea about the story of Plato, his Cave, or any shadows. So those terms don't really mean anything unless you care to describe the scenario.
Plato believed that it is the idealised forms of things that are the true essence of reality. To him a perfect circle is the objectively real circle and all the circles that we see in empirical reality are comparable to looking at shadows of that perfect circle on the wall of a cave. The empirical is derived from the ideal rather than the other way round.
I still don't really understand what you're attempting to talk to me about.
I am trying to get you to see that your assumption that maths is necessarily just an idealised extrapolation of empirical reality is the complete opposite of the Platonic view of mathematics that many mathematicians hold to. AND that this has implications for your view that the only reality that can be objectified is empirical reality.

This message is a reply to:
 Message 160 by Stile, posted 06-08-2010 1:34 PM Stile has replied

Replies to this message:
 Message 162 by Stile, posted 06-08-2010 3:04 PM Straggler has replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 162 of 172 (564147)
06-08-2010 3:04 PM
Reply to: Message 161 by Straggler
06-08-2010 2:12 PM


Re: Platos Cave
I am trying to get you to see that your assumption that maths is necessarily just an idealised extrapolation of empirical reality is the complete opposite of the Platonic view of mathematics that many mathematicians hold to. AND that this has implications for your view that the only reality that can be objectified is empirical reality.
Oh, I see. Then our discussion is simply confusing for no reason. You're accounting a position to me that I do not take.
I've never made the assumption that math is necessarily just an idealised extrapolation of empirical reality. Why do you think I have? I only assume that math can be an idealised extrapolation of empirical reality... and I've shown that it can.
I also do not hold the view that the only reality that can be objectified is empirical reality. Why do you think I do? I only hold the view that certain aspects of empirical reality can be objectified.
I make no all-encompasing claims, such things are rather foolish with the limited knowledge I am constrained by.
All I said was:
All things that are collectively agreed to exist within objective reality (because they can be shown to others) are testable and verifiable through the scientific method.
Message 50
Which is a rather simple and circular statement. I think you've been trying to place things upon this in order to have a conversation with someone who you wish said something else.
You then brought up maths, and I've shown you that indeed there are parts of mathematics that have been shown to others to exist in objective reality and they are also testable and verifiable through the scientific method.
I also quickly admitted that there are parts of mathematics that are not currently demonstrable to others using objective reality, only theoretically objective within the confines of the rules that support those same mathematics. You could try to twist this theoretical aspect into meaning "exist within objective reality" by leaving out the word "theoretical" or "based upon the rules of mathematics" and thereby skewing context and definitions from what I originally intended... but if we're not talking about the same thing it is again rather simple and circular to understand that we're not talking about the same thing.
If you think certain mathematical concepts do exist, which can be shown in physical reality to other people, that cannot be tested by the scientific method... then we may have something to talk about. If you think I am supporting some other position... then we have equally failed in me explaining my position and you attempting to understand it.

This message is a reply to:
 Message 161 by Straggler, posted 06-08-2010 2:12 PM Straggler has replied

Replies to this message:
 Message 163 by Straggler, posted 06-09-2010 11:25 AM Stile has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 163 of 172 (564269)
06-09-2010 11:25 AM
Reply to: Message 162 by Stile
06-08-2010 3:04 PM


Re: Platos Cave
Stile initially says:
quote:
I still stand by the statement of:
All things that are collectively agreed to exist within objective reality are testable and verifiable through the scientific method.
So far, no one has provided any example that goes against this statement.
Stile now says:
I also do not hold the view that the only reality that can be objectified is empirical reality.
So what aspects of an objective reality are both non-empirical and verifiable through the scientific method?
Stile writes:
You then brought up maths, and I've shown you that indeed there are parts of mathematics that have been shown to others to exist in objective reality and they are also testable and verifiable through the scientific method.
Indeed. And in doing so you have led yourself into the rather ridiculous position of advocating that some numbers are known to exist and that some are not but that we don't know which are which.
If you think certain mathematical concepts do exist, which can be shown in physical reality to other people, that cannot be tested by the scientific method... then we may have something to talk about.
You fist need to explain the apparent contradiction in your thinking. Namely that ALL things which can be objectified are verifiable by the scientific method but not necessarily part of empirical reality. How does that work?

This message is a reply to:
 Message 162 by Stile, posted 06-08-2010 3:04 PM Stile has replied

Replies to this message:
 Message 164 by Stile, posted 06-09-2010 12:23 PM Straggler has replied

  
Stile
Member
Posts: 4295
From: Ontario, Canada
Joined: 12-02-2004


Message 164 of 172 (564273)
06-09-2010 12:23 PM
Reply to: Message 163 by Straggler
06-09-2010 11:25 AM


Read the posts, don't create your own
Straggler writes:
So what aspects of an objective reality are both non-empirical and verifiable through the scientific method?
I don't know. I don't know everything. Why do you keep trying to force absolute statements when none are warrented?
And in doing so you have led yourself into the rather ridiculous position of advocating that some numbers are known to exist and that some are not but that we don't know which are which.
You are equivocating again.
I am of the position that some number are known to exist within objective reality (represented by countable, real objects) and others are not. -Do you seriously advocate otherwise?
I also hold the position that I do not know the highest number than any people have ever counted anything. -Do you?
You first need to explain the apparent contradiction in your thinking. Namely that ALL things which can be objectified are verifiable by the scientific method but not necessarily part of empirical reality. How does that work?
Again, that's not what I've said.
This is what I said, you quoted it in the beginning of your own message:
Stile writes:
All things that are collectively agreed to exist within objective reality are testable and verifiable through the scientific method.
This is what you are saying I've said:
Straggler, representing Stile's position writes:
Namely that ALL things which can be objectified are verifiable by the scientific method...
Do you notice the crucial qualifiers you're leaving out?
Do you see how silly your version is when compared to what I'm actually saying and explaining to you?
And now you're also adding on "..not necessarily part of empirical reality" which isn't anywhere contextually near what the original statement is discussing. You ask some follow up questions that I answered honestly. Then you try to force them back onto the original statement with no understanding of context or qualifiers? You seem to bordering on the side of insanity.
As long as you continue to force your own version of what you wish I was saying... your confusion will remain. You can free yourself of this at any time by simply attempting to understand what I've actually said.

This message is a reply to:
 Message 163 by Straggler, posted 06-09-2010 11:25 AM Straggler has replied

Replies to this message:
 Message 165 by Straggler, posted 06-09-2010 1:02 PM Stile has replied

  
Straggler
Member
Posts: 10333
From: London England
Joined: 09-30-2006


Message 165 of 172 (564281)
06-09-2010 1:02 PM
Reply to: Message 164 by Stile
06-09-2010 12:23 PM


Re: Read the posts, don't create your own
Straggler writes:
So what aspects of an objective reality are both non-empirical and verifiable through the scientific method?
I don't know.
Then on what basis are you claiming that there are any non-empirical aspects of reality that can be objectified by means of the scientific method?
Stile writes:
I am of the position that some number are known to exist within objective reality (represented by countable, real objects) and others are not. - Do you seriously advocate otherwise?
Yes I do. Because I am taking the position that objective existence of numbers has nothing to do with "countable, real objects".
You seem to be limiting objective reality to empirical reality (i.e. that which can actually be physically counted). Is this not what you are saying?
Stile writes:
All things that are collectively agreed to exist within objective reality are testable and verifiable through the scientific method.
Once again you seem to be saying that only that which is empirical can be objectified. The scientific method is restricted to that which is empirical is it not?
Stile writes:
I also do not hold the view that the only reality that can be objectified is empirical reality.
Now you seem to be saying that you do not restrict objective reality to that which is empirical.
As long as you continue to force your own version of what you wish I was saying... your confusion will remain. You can free yourself of this at any time by simply attempting to understand what I've actually said.
I am genuinely trying. But at the moment it all seems very contradictory. Can you clarify?

This message is a reply to:
 Message 164 by Stile, posted 06-09-2010 12:23 PM Stile has replied

Replies to this message:
 Message 166 by Stile, posted 06-09-2010 1:40 PM Straggler has replied

  
Newer Topic | Older Topic
Jump to:


Copyright 2001-2023 by EvC Forum, All Rights Reserved

™ Version 4.2
Innovative software from Qwixotic © 2024