Precision, Ideal and Real

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ughaibu
 
Reply Thu 3 Jun, 2010 11:58 pm
@Reconstructo,
Reconstructo;172830 wrote:
That something so counter-intuitional can be proven shows that not all is well when it comes to our relating the continuous with the discreet.
It can be argued that only the area of a point has been proved equal to the area of any circumference. But in any case, mathematics (and logic) are separate from physical reality, that something is mathematically true doesn't imply that it's actually true, or even that it's actually meaningful.
 
Reconstructo
 
Reply Fri 4 Jun, 2010 12:11 am
@ughaibu,
ughaibu;172838 wrote:
It can be argued that only the area of a point has been proved equal to the area of any circumference. But in any case, mathematics (and logic) are separate from physical reality, that something is mathematically true doesn't imply that it's actually true, or even that it's actually meaningful.


I agree that it's not necessary real in a physical sense, but I do think its meaningful. I think concept is real, except it exists in logical space or imagination. In my opinion, the structure of what we call reality also exists here. All of physics is also just concept. Smile

As I have argued before, we only think of the world in parts rather than as continuous because we quantify it conceptually. But this is so automatic that we take it for reality-in-itself. It's we who impose a form upon the flux, but the flux has a structure that encourages certain impositions. We and the flux are man. Man is not separate from what he perceives, except as an abstraction in logical space.
 
ughaibu
 
Reply Fri 4 Jun, 2010 12:20 am
@Reconstructo,
Reconstructo;172845 wrote:
I do think its meaningful.
How did that formal system go? Something like:
a,b
if a then bab
if b then ba

What meaning do the theorems of such a system have?
 
Reconstructo
 
Reply Fri 4 Jun, 2010 12:30 am
@ughaibu,
ughaibu;172848 wrote:
How did that formal system go? Something like:
a,b
if a then bab
if b then ba

What meaning do the theorems of such a system have?


I am talking about our entire conception of the world, which is systematic. We think of the world as an organized system. We project concepts on sensation. We don't see blobs of color, we see a tree. We see a cat. You know your physics. Isn't matter and energy fairly continuous here on earth? But we experience objects, parts, and not continuity. Which is part of my argument that quantity is fundamental.
 
ughaibu
 
Reply Fri 4 Jun, 2010 12:33 am
@Reconstructo,
Reconstructo;172850 wrote:
I am talking about our entire conception of the world, which is systematic.
Okay, but there's no implication from that to the effect that all statements of mathematics, logics or other formal systems are meaningful. There is a view that mathematics is almost entirely pathological, and that it's conceptual doesn't have any bearing on this.
 
Reconstructo
 
Reply Fri 4 Jun, 2010 12:36 am
@ughaibu,
ughaibu;172853 wrote:
Okay, but there's no implication from that to the effect that all statements of mathematics, logics or other formal systems are meaningful. There is a view that mathematics is almost entirely pathological, and that it's conceptual doesn't have any bearing on this.



Just so you know where I am coming from, I think we can divide human experience into discrete concept (logical space) and continuous sensation-emotion. And these are primaries. The other stuff derives from these. Even the idea of the self is an abstraction composed of sub-concepts, sensations, emotions. So for me, concept is a basic kind of being. I think this is why there is argument as to whether existence is a property. All concept already just is. And the primal concept is something like empty is. And I think that numbers are made from this, with just a little added on, a minimal determination added to the otherwise indeterminate. Hence the perfect ideal precision of arithmetic. Just my opinions. I enjoy our dialogue. I hope I don't offend you in any way.
 
Twirlip
 
Reply Fri 4 Jun, 2010 01:42 am
@ughaibu,
ughaibu;172838 wrote:
But in any case, mathematics (and logic) are separate from physical reality, that something is mathematically true doesn't imply that it's actually true, or even that it's actually meaningful.

Take for example the proposition, "The union of a finite set whose cardinal number in 893 with a disjoint, finite set whose cardinal number is 127 is a finite set whose cardinal number is 1,020." Would you say that this proposition is (a) "mathematically true", (b) "actually true", and/or (c) "actually meaningful"?

---------- Post added 06-04-2010 at 08:50 AM ----------

ughaibu;172853 wrote:
Okay, but there's no implication from that to the effect that all statements of mathematics, logics or other formal systems are meaningful. There is a view that mathematics is almost entirely pathological, and that it's conceptual doesn't have any bearing on this.

Do you believe that mathematics is a formal system? Can you say (informally!) what you mean by the term "formal system"? And what do you mean by saying that mathematics is "almost entirely pathological"?

(And is the latter statement related somehow to your description of mathematics, in another thread, as being "useless" - except for those purposes for which it is useful! - and your contention that I misunderstood what you meant? Need I quote that dialogue in detail?)
 
ughaibu
 
Reply Fri 4 Jun, 2010 03:06 am
@Twirlip,
Twirlip;172868 wrote:
Take for example the proposition, "The union of a finite set whose cardinal number in 893 with a disjoint, finite set whose cardinal number is 127 is a finite set whose cardinal number is 1,020." Would you say that this proposition is (a) "mathematically true", (b) "actually true", and/or (c) "actually meaningful"?
On the information given, I'd say "yes" to all three.
Twirlip;172868 wrote:
Do you believe that mathematics is a formal system? Can you say (informally!) what you mean by the term "formal system"? And what do you mean by saying that mathematics is "almost entirely pathological"?
1) yes
2) a language, inference rules and axioms, allowing the construction of theorems
3) I didn't say that maths is almost entirely pathological, I said there's a view that it is.
Twirlip;172868 wrote:
is the latter statement related somehow to your description of mathematics, in another thread, as being "useless" - except for those purposes for which it is useful!
No.
Does this interview have some purpose?
 
Twirlip
 
Reply Fri 4 Jun, 2010 04:00 am
@ughaibu,
ughaibu;172884 wrote:
Does this interview have some purpose?

Not if you think it doesn't. Excuse me for bothering you.
 
Reconstructo
 
Reply Fri 4 Jun, 2010 05:47 pm
@Reconstructo,
I don't see how a formal system could work without at least the smallest core of intuition. The notion of a bit, for instance can be applied to or transmitted through any sort of material, for the material is only a vessel. (g kd aerf m kl oroe g) How many letters are in that parenthesis? Does writing this number change in various ways change its value? The mind looks at what are scribbles and finds pure perfect quantity. At its beginnings math was matching not counting. Matching is impossible without the intuition of unity, of individual stones and individual sheep.

However, I do like "a language, inference rules and axioms, allowing the construction of theorems." We need these things. Formalizing our basic intuition allows us to extend limitlessly into unthinkable but still writable quantities. Aren't inference rules ultimate based on intuition as well as on experiment? A rule makes sense. But it must also fit into the system as is. 0! is justified by the Zeta function, apparently. But isn't "0! = 1" counterintuitional? Or a twist on the usual method of factorilization?

I would be delight if someone saw why I find the discrete/continuous collision so fascinating. It was Zeno who pointed me toward math, with his paradoxes that brilliantly emphasize this collision. Heraclitus and Parmenides are also directly connected to this. After watching a brilliant video posted by Attano on my profile, I think the left brain / right brain issue is connected to this.
 
Twirlip
 
Reply Fri 4 Jun, 2010 05:56 pm
@Reconstructo,
Reconstructo;173133 wrote:
I don't see how a formal system could work without at least the smallest core of intuition.

I agree, emphatically.
Reconstructo;173133 wrote:
But isn't "0! = 1" counterintuitional? Or a twist on the usual method of factorilization?

It's a convenient and natural convention. There are many similar instances of "null cases" in mathematics and computer science. (I'm not entirely sure that that phrase would be understood as a technical term, but any mathematician or computer scientist or programmer would know instantly what it means.)
Reconstructo;173133 wrote:
I would be delight if someone saw why I find the discrete/continuous collision so fascinating.

I do. It has been a passionate, even sexual image for me for decades now. But by the same token, it is hard for me to put in words what it is or why it is important.
Reconstructo;173133 wrote:
After watching a brilliant video posted by Attano on my profile, I think the left brain / right brain issue is connected to this.

It could well be so. I'll try to get around to watching that video. Bit snowed under right now.
 
Reconstructo
 
Reply Fri 4 Jun, 2010 06:11 pm
@Twirlip,
Twirlip;173137 wrote:
I agree, emphatically.


I appreciate that, because the absolute concept is a diamond in my brain. It's always been there to, but I've revealed it or polished it w/ philosophy and math. It's numinous but not mystical.

---------- Post added 06-04-2010 at 07:14 PM ----------

Twirlip;173137 wrote:

It's a convenient and natural convention. There are many similar instances of "null cases" in mathematics and computer science. (I'm not entirely sure that that phrase would be understood as a technical term, but any mathematician or computer scientist or programmer would know instantly what it means.)


I think its a good convention. You know I love the number e, and it's necessary there. e is an orgy. Do you feel the beauty of e? Of proportional continuous growth/decay? I mean this number is discovered, not invented. Did you know that the maxima of x^(1/x) is e? Strange! And it must fit in with its other properties.

---------- Post added 06-04-2010 at 07:17 PM ----------

Twirlip;173137 wrote:

I do. It has been a passionate, even sexual image for me for decades now. But by the same token, it is hard for me to put in words what it is or why it is important.

I think of it as the male/female divide in human perception. Blake made Isaiah say "my sense discovered the infinite in everything." Sensation is continuous. Conception is discrete. That video is the description of a stoke experience by a neurologist. She experienced a cessation of the discrete. Experienced Nirvana. It blew her mind. She decided to survive/recover to share this w/ others. Very Blake/Buddha/awesome. And it ties in to math. The absolute concept is a skeleton key, a sword that strikes down all our deadening pseudo-explanations for this wonderful and terrible existence we are.

---------- Post added 06-04-2010 at 07:18 PM ----------

Twirlip;173137 wrote:

It could well be so. I'll try to get around to watching that video. Bit snowed under right now.

It will move you. I couldn't help but get tears in my eyes. Her boldness and passion are exceptional. What guts! What honesty!

I am truly grateful to be able to speak of these w/ someone who has their own kind of access to the beauty involved here. Write me a PM if you feel like sharing your thoughts more privately.
 
prothero
 
Reply Sat 5 Jun, 2010 12:58 am
@Reconstructo,
Is the ideal also "real"? Does perfection "exist" in the "real" world?
You seem to think all such concepts are merely human constructions
but
such concepts are almost universal and recurring.
For the Greek rationalists the ideal, the eternal, the changeless, the perfect was more real, more being, more existent than the world of change, flux, imperfection, sense experience and temporality.
 
Reconstructo
 
Reply Sat 5 Jun, 2010 11:02 am
@prothero,
prothero;173302 wrote:
Is the ideal also "real"? Does perfection "exist" in the "real" world?


Well, my view is that the world-sans-man and man-sans-world are both abstractions. I have wrestled with the problem of universals and the nature of number for awhile lately, and now think that Form/Concept is prior to abstractions like man, world, self, real, etc.

So perfection exists in the real world if only in our "heads." The clash in not between the human mind and the world, because these are distinctions imposed by concept. The clash is between conception which is digital and sensation and emotion which are continuous. As far as spatial form goes we do seem to have intuitions of perfect circles and perfect straightness, etc.

---------- Post added 06-05-2010 at 12:07 PM ----------

prothero;173302 wrote:

You seem to think all such concepts are merely human constructions
but
such concepts are almost universal and recurring.


Yes, the concepts are recurring. I think "human construction" is one more construction. All concepts but the empty proto-concept are vulnerable in my view. They exist systematically in relation to sensation and emotion. They ar created and destroyed. The most useful and pleasurable are always with us, though. For instance, the "self" seems like a practically necessary abstraction. But it is actually quite questionable.

Quote:

5.621 The world and life are one.


5.63 I am my world. (The microcosm.)


5.631 There is no such thing as the subject that thinks or entertains
ideas. If I wrote a book called The World as l found it, I should have
to include a report on my body, and should have to say which parts were
subordinate to my will, and which were not, etc., this being a method of
isolating the subject, or rather of showing that in an important sense
there is no subject; for it alone could not be mentioned in that book.--


5.632 The subject does not belong to the world: rather, it is a limit of
the world.


5.633 Where in the world is a metaphysical subject to be found? You will
say that this is exactly like the case of the eye and the visual field.
But really you do not see the eye. And nothing in the visual field
allows you to infer that it is seen by an eye.


5.6331 For the form of the visual field is surely not like this


5.634 This is connected with the fact that no part of our experience is
at the same time a priori. Whatever we see could be other than it is.
Whatever we can describe at all could be other than it is. There is no a
priori order of things.


5.64 Here it can be seen that solipsism, when its implications are
followed out strictly, coincides with pure realism. The self of
solipsism shrinks to a point without extension, and there remains the
reality co-ordinated with it.


5.641 Thus there really is a sense in which philosophy can talk
about the self in a non-psychological way. What brings the self into
philosophy is the fact that 'the world is my world'. The philosophical
self is not the human being, not the human body, or the human soul, with
which psychology deals, but rather the metaphysical subject, the limit
of the world--not a part of it.


---------- Post added 06-05-2010 at 12:12 PM ----------

prothero;173302 wrote:

For the Greek rationalists the ideal, the eternal, the changeless, the perfect was more real, more being, more existent than the world of change, flux, imperfection, sense experience and temporality.


I agree with this. And this is how I understand Hegel's "the real is rational." For after all, reality is a concept used to organize sub-concepts, at least to me. Raw sense-data and/or raw emotion means nothing in the absence of form/concept. Form is meaning imposed on this flux, and largely derived from this flux. I think most of our forms are temporal. But the proto-Form (or Form of Forms) exists automatically. In a way, Parmenides was right, but so was Heraclitus.

Spatial form is more complicated. Let's consider standards of visual beauty, both in painting and more importantly human beauty. THere are Forms which are not easily reduced to concept. For instance, Euclidean intuitions.
Intuitive geometry is a body of form that seems quite static. I put this in its own category, as I think it's truly different from the digital concept. Zeno's paradoxes illustrate this I think. Smile

I use the word "concept" to be understood, but I'm not an idealist. The Form of the self/world is the structure of the self-world. Our materialistic abstractions have most of us convinced that man and the world exist separately, even though humans have never experienced this. "No finite thing has genuine being.."
 
manored
 
Reply Sat 5 Jun, 2010 01:28 pm
@ughaibu,
ughaibu;172838 wrote:
It can be argued that only the area of a point has been proved equal to the area of any circumference. But in any case, mathematics (and logic) are separate from physical reality, that something is mathematically true doesn't imply that it's actually true, or even that it's actually meaningful.
Indeed, this is the reason of my disagreement.

Reconstructo;173142 wrote:
I appreciate that, because the absolute concept is a diamond in my brain.
That must hurt like hell.

Couldnt help it =)

"Diamonds im my brains" seems like a perfect name for something. I will actually note it down as an idea for a future computer game, if you dont mind =)

Reconstructo;173412 wrote:
For instance, the "self" seems like a practically necessary abstraction. But it is actually quite questionable.
Could you question it? I never understood how people question it =)
 
Reconstructo
 
Reply Sat 5 Jun, 2010 02:29 pm
@manored,
manored;173461 wrote:

That must hurt like hell.

Hurts like being in bed w/ a beautiful woman. :detective:

---------- Post added 06-05-2010 at 03:33 PM ----------

manored;173461 wrote:

Could you question it? I never understood how people question it =)


Of course sensation and emotion and embodiment just are. They are unquestionable. But to sew these together is to make an abstraction. Now this abstraction is justified in practice but not in theory. Really, one's self is all of one's experience, and not just that small part of it we usually call the self. The TLP is like the Tao, or something. It's a logical book with a spiritual purpose.
Quote:

5.621 The world and life are one.
5.63 I am my world. (The microcosm.)
5.631 There is no such thing as the subject that thinks or entertains
ideas. If I wrote a book called The World as l found it, I should have
to include a report on my body, and should have to say which parts were
subordinate to my will, and which were not, etc., this being a method of
isolating the subject, or rather of showing that in an important sense
there is no subject; for it alone could not be mentioned in that book.--
5.632 The subject does not belong to the world: rather, it is a limit of
the world.
5.633 Where in the world is a metaphysical subject to be found? You will
say that this is exactly like the case of the eye and the visual field.
But really you do not see the eye. And nothing in the visual field
allows you to infer that it is seen by an eye.
5.6331 For the form of the visual field is surely not like this
5.634 This is connected with the fact that no part of our experience is
at the same time a priori. Whatever we see could be other than it is.
Whatever we can describe at all could be other than it is. There is no a
priori order of things.
5.64 Here it can be seen that solipsism, when its implications are
followed out strictly, coincides with pure realism. The self of
solipsism shrinks to a point without extension, and there remains the
reality co-ordinated with it.
5.641 Thus there really is a sense in which philosophy can talk
about the self in a non-psychological way. What brings the self into
philosophy is the fact that 'the world is my world'. The philosophical
self is not the human being, not the human body, or the human soul, with
which psychology deals, but rather the metaphysical subject, the limit
of the world--not a part of it.

This is close to one of Hegel's best ideas. Reality is one. The world and the self are one. Smile
 
Greta phil
 
Reply Sun 6 Jun, 2010 12:18 am
@Reconstructo,
I meant that if anything has more than one meaning - even a single sentence, it is not precise. It could go off in several directions. This can how ever be fun!!

---------- Post added 06-06-2010 at 06:20 PM ----------

To be precise - it has one meaning, one direction. Rigid. No room for movement. (like many minds) Completely unarguable!!
 
Reconstructo
 
Reply Sun 6 Jun, 2010 12:22 am
@Greta phil,
Greta;173713 wrote:
I meant that if anything has more than one meaning - even a single sentence, it is not precise. It could go off in several directions. This can how ever be fun!!

---------- Post added 06-06-2010 at 06:20 PM ----------

To be precise - it has one meaning, one direction.


Yes, I agree with this. It seems that only some of mathematics can offer this, and formal logic, both of which are the same, really. Smile
 
Greta phil
 
Reply Sun 6 Jun, 2010 12:31 am
@Reconstructo,
are you one of these mathematicians?
 
wayne
 
Reply Sun 6 Jun, 2010 12:35 am
@Reconstructo,
I am beginning to see precision as a certain smallness, a perfection of point if you will. Aren't we discussing a 4th dimension of infinity?
 
 

 
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