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Quantity is Fundamental

 
 
Reconstructo
 
  1  
Reply Tue 1 Jun, 2010 10:31 pm
@ughaibu,
ughaibu;171920 wrote:
Not in the case of random reals.


Ah, well this is a great issue. What is randomness? And is randomness anything like infinity, a sort of unthinkable paradox? Of course Chaitin found a way to define a random number in theory...sort of..

I used random numbers in programming, and they of course aren't truly random, as computers are extreme logical unless perhaps one spills a glass of water on them. I think random numbers are a bit paradoxical. Another sort of limit. The anti-algorithm. A great issue.

---------- Post added 06-01-2010 at 11:35 PM ----------

ughaibu;171920 wrote:
Not in the case of random reals.Generally, intuitionists reject this and allow only one infinity, because a consequence of Cantor's theory is that almost all real numbers are unconstructable, which means you cant get them by any iterative process based on unity.


Right! But we can spatially imagine infinite divisibility. Let's imagine as a thought experiment a purely continuous substance. Unlike our real physical world, there are no particles. None. The gray continuous goo. Can't we imagine dividing into halves for infinity? This touches Zeno's paradoxes. A number doesn't achieve full status, in my view, unless it is finite. So a number like e or pi is never finished taking its clothes off. One always has too work with a partial revelation. The limit concept is strange and impressive. The infinitesimal is strange and impressive. In my opinion, 1 should be viewed as the "center" of the positives. The smallest positive is 1/infinity and the largest is infinity/1. As far as infinity goes, this too is a sort of algorithm. Very strange. It's an arrow, even.
Deckard
 
  1  
Reply Tue 1 Jun, 2010 10:56 pm
@Reconstructo,
Reconstructo;170664 wrote:
All human conception includes quantity. That's my position. Quantity, often in the form of unity, is prior to all human thought, which is to say that all human thought involves quantity.

Concepts like nature, the self, and truth are singular. Pluralities are just iterated singularities.

I say quantity is fundamental to human thought, and that unity is fundamental to quantity. I'm saying that unity is a sort of Platonic Form or Absolute.

Any comments, disagreements?

Aristotle noticed that Quantity was important as well. He listed Quantity among his Categories. If the order that the categories are listed indicates degree of fundamentalness then Quantity is second only to Substance by Aristotle's reckoning.

Here's one of Ari's observations.

Quote:
The most distinctive mark of quantity is that equality and inequality are predicated of it. Each of the aforesaid quantities is said to be equal or unequal. For instance, one solid is said to be equal or unequal to another; number, too, and time can have these terms applied to them, indeed can all those kinds of quantity that have been mentioned.

That which is not a quantity can by no means, it would seem, be termed equal or unequal to anything else. One particular disposition or one particular quality, such as whiteness, is by no means compared with another in terms of equality and inequality but rather in terms of similarity. Thus it is the distinctive mark of quantity that it can be called equal and unequal.
Reconstructo
 
  1  
Reply Tue 1 Jun, 2010 11:22 pm
@Deckard,
Deckard;171960 wrote:
Aristotle noticed that Quantity was important as well. He listed Quantity among his Categories. If the order that the categories are listed indicates degree of fundamentalness then Quantity is second only to Substance by Aristotle's reckoning.

Here's one of Ari's observations.



Excellent quote. Thanks! I am basically making an argument in this thread that substance is unity is quantity. That number is just indeterminate being. It was actually thoughts about Kant and Heidegger that brought me to my view. The "transcendental unity of apperception" and the Being of beings. Singular! Always singular! And even polytheism is singular. The word unifies the plurality. But then I notice that all pluralities are unified. Just like big numbers are single quantities.

Being is the completely abstract substance? Or existence, that strange "property." It's not a property, they say. Because it doesn't compute right. Something is strange. Because, I argue, concept just is. It's prior to all other abstractions? It's at their core, each and every one?

Quote:

It is clear that only what is essential to the
most general propositional form may be included in its description--for
otherwise it would not be the most general form. The existence of a
general propositional form is proved by the fact that there cannot be a
proposition whose form could not have been foreseen (i.e. constructed).
The general form of a proposition is: This is how things stand.


4.53 The general propositional form is a variable.
5.472 The description of the most general propositional form is the
description of the one and only general primitive sign in logic.
More of this when I find it.

I think the form of forms just is. It's nothingness or pure being. Any name is already too much, because it's a variable. It's the corner stone. It exist in logical space, as the single transcendental category? Names like "being" and "one" and "nothingness" get close. Maybe I'm crazy, but this is also interesting:
Quote:

The tao that can be told
is not the eternal Tao
The name that can be named
is not the eternal Name.

The unnamable is the eternally real.
Naming is the origin
of all particular things.
0 Replies
 
ughaibu
 
  1  
Reply Wed 2 Jun, 2010 12:29 am
@Reconstructo,
Reconstructo;171956 wrote:
Can't we imagine dividing into halves for infinity?
Sure, but you'll only get a countable infinity.
Reconstructo
 
  1  
Reply Wed 2 Jun, 2010 12:34 am
@ughaibu,
ughaibu;171986 wrote:
Sure, but you'll only get a countable infinity.



On that we are agreed. I don't really believe in an uncountable infinity. I should stress that. I'm just saying that our intuition of space as continuous and more importantly perhaps our positional notation allow us to invent as many numbers as we please between any two numbers.

Cantor is fascinating, but I have a strong feeling for Kronecker. It's not that I don't see why someone would suggest "uncountable infinity" but that I think that potential infinity is all we can actually imagine/conceive. And even this is a stretch and we can't really write it or think it clearly, for obvious(?) reasons.Smile
ughaibu
 
  1  
Reply Wed 2 Jun, 2010 12:58 am
@Reconstructo,
Reconstructo;171988 wrote:
On that we are agreed. I don't really believe in an uncountable infinity.
Fair enough, but that puts you at odds with the statements of, for example, relativity.
Reconstructo;171988 wrote:
It's not that I don't see why someone would suggest "uncountable infinity" but that I think that potential infinity is all we can actually imagine/conceive.
The proof strategy for the uncountability of the power set of the natural numbers, is very useful. I dont think it's a good bargain to lose it in order to avoid uncountability.
Reconstructo
 
  1  
Reply Wed 2 Jun, 2010 01:20 am
@ughaibu,
ughaibu;172004 wrote:
Fair enough, but that puts you at odds with the statements of, for example, relativity.The proof strategy for the uncountability of the power set of the natural numbers, is very useful. I dont think it's a good bargain to lose it in order to avoid uncountability.


As far as practical matters go, I have no beef with anyone on mathematical issues. I'm coming very much from a Platonic Kantian angle. Didn't the physicist invent some function that is mathematically questionable but works?

My central issue is the way we perceive reality. I am especially arguing that all concept is finite and singular. Numbers are a special rarefied case. Of course the whole numbers seem more rarefied than e or pi or the transfinites.

I don't feel the need to lose anything. I love Cantor. I love the notion of power sets as I love the number 2. I think 2 is a crucial number. Any potential member of a set is either in or out. And then one has true or false, binary code, etc. One has 2 directions within any one dimension. And the number line is a matrix (nonmathematical meaning) where numbers are to either the left or the right of one another.

Yessir, I'm coming at math from a philosophical concern. I have no negative things to say about the way that mathematics is/are applied.

Do you see what i mean by linguistic concept being essentially finite and singular?
ughaibu
 
  1  
Reply Wed 2 Jun, 2010 01:29 am
@Reconstructo,
Reconstructo;172012 wrote:
I don't feel the need to lose anything.
You wrote "I don't really believe in an uncountable infinity", and there is a proof strategy which establishes the existence of an uncountable set, unless you either deny the validity of the proof strategy or adopt a formalist position, I dont see how you reconcile the two positions(?)
Reconstructo
 
  1  
Reply Wed 2 Jun, 2010 01:38 am
@ughaibu,
ughaibu;172017 wrote:
You wrote "I don't really believe in an uncountable infinity", and there is a proof strategy which establishes the existence of an uncountable set, unless you either deny the validity of the proof strategy or adopt a formalist position, I dont see how you reconcile the two positions(?)



Proof is persuasion, in my book. What justifies the truth or untruth of math? For me, the foundations are intuited. At higher levels, it seems like coherence or successful application. Do I think that one can find as many numbers as one likes between any two numbers? Yes.

Perhaps this is our misunderstanding. For me, all infinities are uncountable. Cantor's diagonal method shows in theory how to count one sort of infinity, but this is not really counting them. Still, he gives us a new perspective. And then the official uncountable infinity is presented as something more disturbing/fascinating. An ocean of transcendental numbers. Did i get that right? But as beautiful and strange as it all is, we can only conceive of it in finite terms.
ughaibu
 
  1  
Reply Wed 2 Jun, 2010 01:49 am
@Reconstructo,
Reconstructo;172022 wrote:
Cantor's diagonal method shows in theory how to count one sort of infinity, but this is not really counting them.
The proof of the uncountability of the power set of N doesn't use diagonalisation. Anyway, I get your point, and I'm not a realist about these things myself. Your mixture of positions strikes me as inconsistent, but if you can live with it, it's not my problem.
William
 
  1  
Reply Wed 2 Jun, 2010 10:00 am
@Reconstructo,
Recon, your thread is accurate if you mean and understand fundamentally ONE. When we think individually quantity, "more" is created. We can't create more. It's impossible. It's like trying to put ten gallons of water into a five gallon bucket, ha! There just "is" and no more than that. More and any thought of it creates waste and nature will take it's/her/god's course to maintain it's purity/balance.

You have to take it on faith that one is complete and has all the quantity it needs. To effort to "count" all that is that one and what that quantity is, we blow our mind and create illusions. Ever seen the movie "A BEAUTIFUL MIND". Yes, a mind gone to waste and he received a noble/nobel prize, I don't think it was so noble if it was a true story and schizophrenia is a good thing? I hope not. Just a horrible consequence....at best.

Now if one was not complete then we would surely spin out of balance. Now the earth is not but we surely are. Take a look at a map of the Earth and those red blotches that represent us and those aneurism's; those cancerous wads of people. A sebaceous cyst secreting waste, expending for far more energy than readily available to serve that so very small area.

Now what you are offering here, I think, rather than fundamental, a better word would be "equitable". Fundamental indicates a beginning and we have no idea of when or how much that is or was, micro or macro. We just need to strive for equitability, equilibrium and balance. If we don't, we will spin out of control. Not the Earth, Us. The Earth is always in balance and perfectly so. We just need to become balanced with her. Mathematically equally infinite on both sides of the equation. We can't figure all that, too many numbers to deal with and understand. A computer cannot even do it. The more we pile into memory the more confusing it gets. Quantity and more as we try to figure it SUCKS the life out of us and those blotches, hot spots, cysts, tumors, sores develop into cancers and eat us away.

Now let's observe quantity as an energy. Synergy energy means no energy wasted in and out are the same; balance and equilibrium. Earth, air, sun and water equal. E/energy M/motion pleasant, joy, kindness/complimentary/peacefully; synergy/one/energy. Quantity in balance. VS Inequity/imbalance/awful/misery/iniquity Quantity out of balance. Planned obsolescence occurring and ending in waste.

In other words value based on one quantity all objects/resources/us/fauna/flora/equitable/economical/growing/evolving/learning/efficiently/adequately with what we have. That is enough. Any concept of more ruins/contaminates/soils/cheapens any concept of value eventually leading to worthless.

Quality in a one quantitative analysis is a very good thing. Cooperating together objective/object quality we only need one of anything, never two. You can color it any way you please to satisfy one individuality to express uniqueness that 'is/are' us individually.

Now to better understand this metaphysically one must understand how so very balanced all things are. Observe a child; first he sits, then he crawls, then he stands, then he walks, then he runs not speedily only efficiently. If he runs to fast he uses excess energy creating waste. Waste in him waste in us. Too much carbon dioxide, not enough oxygen causing decay (nature taking it's course maintaining the one pure thing.

Now, as I said one must have faith all (quantity) is balanced. There is no more there is no less or nature will take it's balanced course evidenced by that we can observe as those acts of what is known as God the one. That is so very, very, verily I say unto you all of you..................Period. Those tell us of our conceive notions of more and God/nature erasing them. What we sow we will reap if more is a part of any equation/thought/process.

It is truly elementary. We have proven we can return any pure thing back to it elemental state and reuse it over and over again in our recycling processes. This is and will be if pure and quality is stress and use/utilized efficiently/adequately mentally, physically, materially, nutritiously all objectively onward...........................forever. Nothing plastic/fake/unreal will be in this pure mix.

I hope this help/aided/offered you a way to simplify what quantity truly means. A one pure thing united forever. One/won will win, to/two you too and three/all agree; A/aye, B/be/bee, C/see all a part of a one pure thing.

William
0 Replies
 
HexHammer
 
  1  
Reply Wed 2 Jun, 2010 10:26 am
@Reconstructo,
Reconstructo;170664 wrote:
All human conception includes quantity. That's my position. Quantity, often in the form of unity, is prior to all human thought, which is to say that all human thought involves quantity.

Concepts like nature, the self, and truth are singular. Pluralities are just iterated singularities.

I say quantity is fundamental to human thought, and that unity is fundamental to quantity. I'm saying that unity is a sort of Platonic Form or Absolute.
Can you give some examples of excatly where this quantity comes to play, I fail to see it in my everyday, also in all my friends everyday.
0 Replies
 
Ding an Sich
 
  1  
Reply Wed 2 Jun, 2010 10:38 am
@Reconstructo,
Reconstructo;170664 wrote:
All human conception includes quantity. That's my position. Quantity, often in the form of unity, is prior to all human thought, which is to say that all human thought involves quantity.

Concepts like nature, the self, and truth are singular. Pluralities are just iterated singularities.

I say quantity is fundamental to human thought, and that unity is fundamental to quantity. I'm saying that unity is a sort of Platonic Form or Absolute.

Any comments, disagreements?


I remember reading this from Locke, at least the part concerning quantity. That everything we are given (immediately mind you) is in a unity. It is only through the power of abstraction that we can break this unity down into a plurality.

---------- Post added 06-02-2010 at 12:41 PM ----------

HexHammer;172115 wrote:
Can you give some examples of excatly where this quantity comes to play, I fail to see it in my everyday, also in all my friends everyday.


have you ever counted? That involves quantity. Or are you referring to what Recon is talking about concerning unity and the Absolute?
HexHammer
 
  1  
Reply Wed 2 Jun, 2010 11:09 am
@Ding an Sich,
Ding_an_Sich;172121 wrote:
have you ever counted? That involves quantity. Or are you referring to what Recon is talking about concerning unity and the Absolute?
I have ADHD ..may Dylexi too, by that I can't really count rationally, as I lose count too easily, but my subconcious mass comprehension is good, though I fail to see how it's "fundemental"
Ding an Sich
 
  1  
Reply Wed 2 Jun, 2010 11:25 am
@HexHammer,
HexHammer;172141 wrote:
I have ADHD ..may Dylexi too, by that I can't really count rationally, as I lose count too easily, but my subconcious mass comprehension is good, though I fail to see how it's "fundemental"


Reconstructo means by "fundamental" that it is "a priori" or prior to experience. In essence, it is a capacity that we have to think in terms of quantity. There is no other way around it.

Even though you lose count easily you can still count to some extent in a "rational" manner (if by rational you mean in succession). Hope this helps.
HexHammer
 
  1  
Reply Wed 2 Jun, 2010 11:41 am
@Ding an Sich,
Ding_an_Sich;172146 wrote:
Reconstructo means by "fundamental" that it is "a priori" or prior to experience. In essence, it is a capacity that we have to think in terms of quantity. There is no other way around it.

Even though you lose count easily you can still count to some extent in a "rational" manner (if by rational you mean in succession). Hope this helps.
Sorry, I still have to disagree, I just don't see the fundemental aspects of it, sure in few situations it is indeed fundemental, but not for everything.
So Imo it's a misconception.
Ding an Sich
 
  1  
Reply Wed 2 Jun, 2010 11:44 am
@HexHammer,
HexHammer;172154 wrote:
Sorry, I still have to disagree, I just don't see the fundemental aspects of it, sure in few situations it is indeed fundemental, but not for everything.
So Imo it's a misconception.


Do you mean "everything" as in knowledge?
HexHammer
 
  1  
Reply Wed 2 Jun, 2010 11:59 am
@Ding an Sich,
Ding_an_Sich;172157 wrote:
Do you mean "everything" as in knowledge?
Not quite, from the very moment I wake up ..til I go to bed, year in year out.
0 Replies
 
attano
 
  1  
Reply Wed 2 Jun, 2010 04:41 pm
@Reconstructo,
Reconstructo;170664 wrote:
All human conception includes quantity. That's my position. Quantity, often in the form of unity, is prior to all human thought, which is to say that all human thought involves quantity.

Concepts like nature, the self, and truth are singular. Pluralities are just iterated singularities.

I say quantity is fundamental to human thought, and that unity is fundamental to quantity. I'm saying that unity is a sort of Platonic Form or Absolute.

Any comments, disagreements?


All this thread is brilliant work, alive research. It enters the forum in a new dimension, or maybe not, but it is still quite uncommon and it deserves an applause just for that, before considering anything else .

I know you have been after this idea for some time, and I feel your growing enthusiasm about this hypothesis.
Still, I hope you will forgive me, but I am here to try to create some problems to your view.
Simply put, I am not sure I understand it all.

I understand that you maintain that we always perceive a quantity, that everything we perceived is represented in our thought as quantity and that quantities are structures of single objects, units, that our mind then compounds/organises into a new unit.
This is purely formal, it has no implication on the structure of the real world.
Finally, when something is thought as continuous, actually this is a special case of unit that then the thought de-compounds to virtual units, else it cannot grasp it at all.

Hope I got it right so far.

Aspects:
If I taste a sip of wine that I like, is that a judgement about a quantity?
OK I have an object, a quantity of wine in my mouth that I can represent as a unit, but my judgement about taste is still quantity? Is my representation of the taste and flavour, which I would possibly be unable to describe, still linked to quantity? You mean a unit of taste? And this would be related to the quantity of liquid in my mouth, or it' d be something else? A new unit of tasteful wine, or a sub-unit of the wine in my mouth? Or both? Would that be a case of continuous?
If I focus on other aspects, like the grip or the length (usually tasters analyse these characters as independent from taste), these are still units, per se, and you mean that they become sub-units of the unit I have in my mouth?
This capacity to switch focus from one aspect to the other, isolating one character out of complex object, does this preserve the perception of some object as a unit? Or does it break that up into several units that I am not trying to compound, but to separate instead?

Ratio:
I am cooking my spaghetti and I want to check if they are al dente. This means that they have to be soft, but not too soft. Am I not considering here the ratio between to quantities (I guess that for this one you are going to say the two quantities of hard and soft in my pasta give way to a new unit/quantity of al dente). But what if they are not yet al dente, and I judge that they are still too hard and not enough soft? Am I not considering 2 distinct quantities that I'd like to compound in one unit but I can't?

Change:
If I am hot, and then cold, are quantities still in play? You mean quantities of heat and quantities of cold?
What about an intermediate state, a splash in a cold pool after a sauna? Isn't there a fraction of time when I would perceiving two quantities and not one? my feet in the cold water, my head still hot because of the hot steam in the sauna? Is there still a unit?
(This is, indeed, a tricky one. I guess that no one has ever survived to tell us what he perceived, and if he did he was too shocked to tell).

I confess that I feel a bit disoriented here.
Just hope that the above questions are not totally out of the scope of your hypothesis, because it'd mean I have understood nothing :listening:.
Reconstructo
 
  1  
Reply Wed 2 Jun, 2010 04:58 pm
@ughaibu,
ughaibu;172025 wrote:
The proof of the uncountability of the power set of N doesn't use diagonalisation. Anyway, I get your point, and I'm not a realist about these things myself. Your mixture of positions strikes me as inconsistent, but if you can live with it, it's not my problem.


I know he doesn't use diagonalization for everything. I'm talking about the rationals. Also, it's been a few weeks. I have been reading a little text on the philosophy of mathematics. The book divides between logicism, formalism, intuitionism. I don't think any of these are the full truth about math as I understand it. It seems that Hilbert suggested that arithmetic didn't need justification. Which makes him something of an intuitionist, doesn't it? I'm saying the core of mathematics is intuitive, but only the bedrock, the most basic concept of number. I don't deny your greater immersion in the subject. I dove into math a few months ago, got to a certain point, and swam back to philosophy. Plato and Kant and Wittgenstein.
I'm not a realist or a nominalist in the usual understanding of the word. Most concepts are generated in response to sensation and emotion. But the proto-concept just is, I suggest. And it's prior to our human talk of mind/matter realism/nominalism. It's what made this talk possible, I would argue.

I think we can only think the finite, but we can string finite concepts together in order to comprehend potential infinity. You didn't mention whether you thought that proof was just persuasion or not. That's crucial too.
Smile

---------- Post added 06-02-2010 at 06:02 PM ----------

attano;172245 wrote:
All this thread is brilliant work, alive research. It enters the forum in a new dimension, or maybe not, but it is still quite uncommon and it deserves an applause just for that, before considering anything else .

I know you have been after this idea for some time, and I feel your growing enthusiasm about this hypothesis.
Still, I hope you will forgive me, but I am here to try to create some problems to your view.
Simply put, I am not sure I understand it all.

I understand that you maintain that we always perceive a quantity, that everything we perceived is represented in our thought as quantity and that quantities are structures of single objects, units, that our mind then compounds/organises into a new unit.
This is purely formal, it has no implication on the structure of the real world.
Finally, when something is thought as continuous, actually this is a special case of unit that then the thought de-compounds to virtual units, else it cannot grasp it at all.

Hope I got it right so far.
.

First of all, thanks! Yes, I have been after this rabbit. You described it pretty well. You probably understand me on this better than anyone, with the possible exception of Fido.

As to the real world, it does have everything to do with it, but in a surprising sense. The real is rational. Our rational/conceptual understanding of the world is utterly dependent on the proto-concept. We experience the intelligible structure of the world as a system of finite (unified/quantified) concepts. But the tricky part is that we overlay our concepts on sensation. The objects we perceive in the real world are only objects because we have overlaid unifying concepts on sensation/qualia. Hegel was right on this, in my opinion. And Witt seems to have seen it this way. I think.

---------- Post added 06-02-2010 at 06:05 PM ----------

attano;172245 wrote:

If I taste a sip of wine that I like, is that a judgement about a quantity?
.

Now this is where we move into the other side of my "ontology." This is where we meet our good friend the Ineffable. Your sensations and emotions are continuous, I suggest. But we can only think about them in finite terms. We live the fusion of the discrete concept and continuous sensation/emotion. And this is the fundamental structure, in my opinion. And I think Plato was saying something like this.

---------- Post added 06-02-2010 at 06:11 PM ----------

attano;172245 wrote:

This capacity to switch focus from one aspect to the other, isolating one character out of complex object, does this preserve the perception of some object as a unit? Or does it break that up into several units that I am not trying to compound, but to separate instead?

I would answer that concept exists systematically, holonically. Ken Wilbur's A Brief History of Everything is brilliant but risky --he divides experience into holons, which are parts made of parts made of parts. I think he goes to far in some regards, but he's worth reading on Holons & Kant and Hegel.

If we think of a plurality, we are still thinking a unity. Our mind shifts from unity to unity, and few of these unities are actually atomic. But what all concepts have in common, referred to by the word concept and/or being, is atomic. It just that there is no right name for it. It's the Form of Forms. The presence of an absence. For humans, concept just is. It doesn't exist "out there" or "in here" because it is the source from which "out" and "in" are made. Absolute concept is what all intelligibility is made of. If I am wrong, at least I am wrong in an exciting way.Smile
 

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