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Author Topic:   Math's Arbitrary Non-Necessary Necessarily-Disconnected Conventional Link to Reality
Jon
Inactive Member


Message 1 of 24 (544226)
01-24-2010 8:36 PM


Math's Arbitrary Non-Necessary Necessarily-Disconnected Conventional Link to Reality
In the thread "0.99999~ = 1 ?" (Message 1), talk has turned somewhat to a topic slightly different from that first introduced and proposed. Specifically, the issue at point is no longer the distinctness of two numbers, but the foundations of the entire system of Mathematics (what I called MATHSYSTEM) in relation to the real world (what I called REALWORLDSYSTEM).
As I stated in Message 87
... more a matter of definition than a matter of real-world fact.
A consequence of some proofs in Message 110:
P "All #s with property Z are REAL within MATHSYSTEM (i.e., ((R/Z)/M) (M=MATHSYSTEM)"
P "0.9999| has property Z"
P "(The REAL of 0.9999| is True) given MATHSYSTEM is True (i.e., ((R/0.9999|)/M))"
P "[proof of M=True]"
C "(R (the REAL of 0.9999|) is True... period"
Proof that .9999| is not DISTINCT (from 1):
P "It is false that 0.9999| is both REAL and DISTINCT (from 1) (~(RD))"
P "(R (the REAL of 0.9999|) is True... period"
C "0.9999| is not DISTINCT (from 1)"
... which was a consequence of the proofs explained in Message 89:
Proof that .9999| is REAL:
P [P1 for .9999| being a REAL number]
P [P2 for .9999| being a REAL number]
etc.
C [Conclusion that .9999| is a REAL number]
Proof that .9999| is not DISTINCT (from 1):
P1 "It is true that 0.9999| is REAL"
P2 "It is true that 0.9999| is DISTINCT (from 1)"
P3 "It is false that both P1 and P2 are true (~(P1P2))"
P4 "[conclusion from proof of 0.9999| being a REAL number], i.e., P1 is true"
C "P2 is false, i.e., .9999| is not DISTINCT (from 1)"
... along with the definition of REAL I had been given as being ultimately dependent on the MATHSYSTEM (see posts in reply to me, especially by Dr. A.), and as RAZD concurred in Message 117:
RAZD writes:
math does not need to conform to reality
... the MATHSYSTEM appears to have no necessary relationship to the REALWORLDSYSTEM. As was shown in my reply to Dr. A, which was Message 120:
1 = 3/3 = 1/3 + 2/3 = 0.3333| + 0.6666| = 0.9999| ≠ 1
So, the MATHSYSTEM introduces a function that equates 0.9999| with 1 and thereby closes the paradoxical loophole, such that we may continue using the MATHSYSTEM as a representation of the REALWORLDSYSTEM. Of course, just because we can mend one system so that it will represent another, does not indicate a necessary representative property of the former system in regards the latter, i.e., it does not show that the former system represents by necessity the latter system, but merely shows that it represents it, not necessarily by necessity.
Afterall, any system that represented necessarily another system would not need a function to close paradoxical loopholes, as such loopholes would not exist. The fact that the MATHSYSTEM has introduced such a function in an attempt to represent the REALWORLDSYSTEM, shows that the MATHSYSTEM is not necessarily representative of the REALWORLDSYSTEM.
... were there a necessary relationship between the MATHSYSTEM and the REALWORLDSYSTEM, they would both paradoxically collapse in upon themselvesI mean, the paradox related to their existences would cause them to cease existing.
In Message 123, Rrhain writes in response to my question whether there is any reality in the real numbers:
Rrhain writes:
That is a philosophical question, not a mathematical one. You are playing to the distinction between Platonists and non-Platonists.
And that, to most mathematicians:
... the objects that mathematics studies are real.
So, I would like to challenge any mathematicians who hold this view to support such. I am not convinced that the MATHSYSTEM is necessarily linked to the reality that it describes. As I pointed out in Message 120, certain internal operators of the MATHSYSTEM which function to tweak its failures to match the REALWORLDSYSTEM so it can be a better describer are part of the evidence I will offer initially that the MATHSYSTEM could not be a necessary representative of the REALWORLDSYSTEM, i.e., it does not represent it by necessity, but rather by convention. Or, in the words of Rrhain, I'm going to pull a Bert.
Jon
Edited by Jon, : No reason given.

[O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin

Replies to this message:
 Message 3 by Dr Adequate, posted 01-27-2010 10:52 AM Jon has replied
 Message 6 by nwr, posted 01-27-2010 2:59 PM Jon has replied
 Message 15 by Son Goku, posted 01-28-2010 5:51 AM Jon has not replied

  
Jon
Inactive Member


Message 4 of 24 (544616)
01-27-2010 2:27 PM
Reply to: Message 3 by Dr Adequate
01-27-2010 10:52 AM


Re: Math's Arbitrary Non-Necessary Necessarily-Disconnected Conventional Link to Real
Dr. A writes:
we may note that it is trivially the case that the proposition that a mathematical structure forms a good model for some aspect of reality is necessarily a scientific theory to be confirmed or disconfirmed by observation and experiment; a question which is extrinsic to the mathematics as such.
Ahh, and it is the fact that Mathematicslike a scientific theory composed of words in their structure, the units of Languageis falsifiablelike a scientific theory composed of words in their structure, like any Linguistic proposition, i.e., a proposition which relies on Linguistic modes for its conveyancethat shows the arbitrarily disconnected, conventional (i.e., not by necessity) link that Math has with Reality. In an Empirical epistemology1, Reality2and all things which follow by necessity from itis unfalsifiable. Thus Mathematicslike Language, being falsifiable, cannot be saidwithin an Empirical epistemologyto follow necessarily from Reality. And if it is the case that it does not follow by necessity, then any 'following' it appears to do is not part of the epistemological certainty that is Reality within an Empirical epistemology and is therefore not 'knowable' and true but merely an illusion or coincidence, or, in the case of Math, a result of agreed-upon convention.
Now, of course, one could hold to a Mathematical epistemology, in which numbers and their operators were the only things real, with all else being illusory, from the ground below to the very Self. In such a casereally any casethe link between Math and Reality would be completely unnecessary3 to even exist let alone be consistent. One may also attempt to hold to both a Mathematical and Empirical epistemology with the condition that one would have to show the two epistemologies to be consistent both within each other and in relation to each other else be caught in a contradiction, or discard the entire pursuit of the epistemologically certain altogether.
So, as far as Math and Reality go, our options are rather limited to:
1. Deny the possibility of a successful resolution to the pursuit of knowledge.
2. Show the cross-epistemological consistency of Math and Empiricism.
3. Accept Math as real and Reality as illusory.
4. Accept Reality as real and Math as illusory.
Choosing 1 is silly, whether correct or not, it gets us nowhere; choosing 3 or 4 is fine as each one is perfectly consistent within itself, but also admits to a non-necessary link between Math and Reality; choosing 2 requires evidence of cross-consistency. Obviously I stand at 4, maintaining Math's link to Reality to be conventional; this thread is for folk who stand at 2 to back up that stance.
Jon
__________
1 I use this in a broad sense to mean what one accepts as 'real', i.e., what one can be certain is 'knowable' versus what may or may not be 'knowable' and therefore may or may not be 'real', with 'knowable' being loosely equivalent to 'epistemological certainty'. In this sense, anything that is 'real' and thus 'knowable' cannot be falsified, else it is not 'real'. An Empirical epistemology, then, would say that the natural world (Reality, see foot note 2) exists in such a form as to be unfalsifiable.
2 Simply meaning the natural world as opposed to other worlds, any of which may be epistemologically real (lower case) whether part of Reality (the natural world, upper case) or not.
3 Recall, actual existence says nothing of necessary existence; the link may still exist, just not necessarily so.

[O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin

This message is a reply to:
 Message 3 by Dr Adequate, posted 01-27-2010 10:52 AM Dr Adequate has replied

Replies to this message:
 Message 5 by New Cat's Eye, posted 01-27-2010 2:48 PM Jon has replied
 Message 12 by Dr Adequate, posted 01-27-2010 4:33 PM Jon has not replied

  
Jon
Inactive Member


Message 7 of 24 (544622)
01-27-2010 3:00 PM
Reply to: Message 5 by New Cat's Eye
01-27-2010 2:48 PM


Re: Math's Arbitrary Non-Necessary Necessarily-Disconnected Conventional Link to Real
__________
Did you know that if you type </hr>, it becomes a:

?
Of course; but then my footnotes become as separated from the main text as the technical 'who has replied' information on the bottom. I want them set off from the main text, not cut off from it.
Anyway, off topic, please no more on the decision to use underscores in place of line codes.
Jon

[O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin

This message is a reply to:
 Message 5 by New Cat's Eye, posted 01-27-2010 2:48 PM New Cat's Eye has replied

Replies to this message:
 Message 10 by New Cat's Eye, posted 01-27-2010 3:35 PM Jon has seen this message but not replied

  
Jon
Inactive Member


Message 11 of 24 (544632)
01-27-2010 4:22 PM
Reply to: Message 6 by nwr
01-27-2010 2:59 PM


Re: Math's Arbitrary Non-Necessary Necessarily-Disconnected Conventional Link to Real
nwr writes:
You seem to be confused by the fact that mathematicians sometimes say that their mathematics is real. However, as Rrhain tried to point out, that's more of a philosophical issue.
Well, I realize that 'real' numbers are a specific type of numbers within the MATHSYSTEM which do not necessarily have any relation to the 'real' in Reality. My main point in everything has been that 0.9999| is a Mathematical concept which does not exist in the Real world, likewise for 1. Instead, there is a Reality for which Math has two modes of representation, which it must then equate through rules of its own making.
And yes, it is very much philosophical. My point has been rather simple all along; some folk, however, have been confusing what I say and muddling it up so much that I needed to start a separate thread to try to explain my take: "I do not think Math has any necessary relationship to Reality, and I use the 0.9999| example to show it. As far as the Mathematical equivalence of 0.9999| to 1, I think it is True. As far as for their Reality-based equivalence, I think it, like them, does not exist."
Thank you for your informative post. I guess by those standards I too would be a Fictionalist/Intuitionalist. Not sure who could ever claim to be a Formalist, obviously the Math symbols have meaning, even if to just one person.
Thanks,
Jon

[O]ur tiny half-kilogram rock just compeltely fucked up our starship. - Rahvin

This message is a reply to:
 Message 6 by nwr, posted 01-27-2010 2:59 PM nwr has replied

Replies to this message:
 Message 13 by nwr, posted 01-27-2010 5:19 PM Jon has not replied

  
Jon
Inactive Member


Message 20 of 24 (549406)
03-06-2010 10:03 PM


Last night, I sat in my garden. First, I dug up a little dirt; made from it a small pile. Then I dug up some more dirt; made from it another pile, so that I would have one pile and one pile. Then, I grabbed one of those piles, picked it up, and dumped it onto the other pile. Imagine my shock to discover that, contrary to my original suspicion that the addition of my one pile to one other pile would yield two piles, I ended up with only one pile! Shit... that's fewer piles than I started with!
I wish the mathematicians would have warned me of this little glitch in their system before I tried adding them. I ended up having to start all over from nothing.
Jon
Edited by Jon, : No reason given.

"Can we say the chair on the cat, for example? Or the basket in the person? No, we can't..." - Harriet J. Ottenheimer

Replies to this message:
 Message 21 by lyx2no, posted 03-06-2010 10:32 PM Jon has not replied
 Message 23 by nwr, posted 03-06-2010 11:43 PM Jon has not replied
 Message 24 by Dr Adequate, posted 03-07-2010 6:56 PM Jon has not replied

  
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