Precision, Ideal and Real

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Reply Mon 28 Jun, 2010 08:05 pm
jeeprs wrote:

I have been investigating this question for a long time, because when I went to university, I couldn't help but notice how non-PC my naive hippie spirituality was. Nobody in philosophy could even mention the 'G' word, unless with a deprecating cough. All kinds of clever ideas had been melded into the hole where 'G' used to be. So that's why I ended up in Comparative Religion, rather than philosophy, although they have a common border.

Anyways, there is a rather good book I have read on this recently, called The Theological Origins of Modernity, by M A Gillespie. Highly illuminating historical analysis of the origins of the secular mindset. I recommend it. Also have a look at this much shorter but very important essay by Buddhist academic David Loy:

As I pointed out to you before (and you seem to have agreed) the origins of a position have nothing to do with the truth or falsity of that position. To believe it does is to commit the genetic fallacy.
Reply Mon 28 Jun, 2010 08:09 pm
GoshisDead wrote:

But doesn't belief in the metaphysical make us naive, delusional, and stupid?

In the elementary logic books that kind of question commits "the fallacy of many questions". It is of the same type as the lawyer's question, "have you stopped beating your wife?" Or, for example, doesn't someone who asks a question like, " doesn't belief in the metaphysical make us naive, delusional, and stupid?" show how prejudiced and ignorant he is?
Reply Mon 28 Jun, 2010 08:49 pm
In the mad post enlightenment scientific rush to classify, quantify, rheify, and measure anything and everything by hook or crook, society has assumed a mistrusting of quality and assumed the crutch of quantity.

I wonder if you are aware of The Reign of Quantity and the Signs of the Times, by Rene Guenon.
Reply Mon 28 Jun, 2010 08:52 pm

As I pointed out to you before (and you seem to have agreed) the origins of a position have nothing to do with the truth or falsity of that position. To believe it does is to commit the genetic fallacy.

Perhaps, although I don't recall the exchange. But the point I am making here is one about 'deconstructing secular modernism' by understanding its historical roots. It is more historical than philosophical.
Reply Mon 28 Jun, 2010 08:59 pm
I stumbled upon an interesting site, and am quite pleased to find those who share my concerns. Here's a snippet:
"8. The irrational reals in the continuum as forever absent

The problem with this mathematical conception of instantaneous velocity or the instantaneous rate of change of any other variable with respect to time is that mathematics did not have any way of conceiving the infinitesimals, which are non-zero magnitudes smaller than any real number. The infinitesimals are both within the real continuum and also outside it. This weakness in the foundations of mathematics was finally remedied only in the nineteenth century with the work by Cauchy and Weierstrass on mathematical limits and with Richard Dedekind's formulation of the real numbers as cuts in the rational numbers. Infinitesimals are infinite, countable sequences of numbers that approach the limit of zero without every reaching it. And an irrational, real number can be regarded as an infinite, countable sequence of rational numbers approaching a non-rational limit. Thus, an irrational, real number can only be approached by an infinite counting process that gets as close as you like to it without ever reaching this limit. This implies that an irrational real number can only be conceived as a counting movement toward that can never be made present as a logical, computable ratio of natural counting numbers.
An irrational real number is forever absent from the infinite series of rationals approaching it in a counting movement. The irrationality of an irrational real number could therefore be said to consist in its being never present, but forever arriving, forever heralded by the endless row of rational numbers announcing its arrival. The irrationals fulfil the illogical condition of the Aristotelean ontology of movement in general as a twofold of presence and absence. They are illogical because they can never be brought to a standing presence by the rationals. Otherwise they can only be symbolized by algebraic symbols symbolizing numbers that are forever absent and beyond the grasp of a calling to presence by the logos in a definite rational number amenable to arithmetic calculation.

Moreover, this movement of counting infinitely through a rational sequence toward an irrational limit takes place within the continuum of real numbers, so that each step from one rational number to the next must pass through an infinity of irrational real numbers. The movement of rational counting itself requires the medium of the real continuum, which is largely irrational. The continuum of real numbers can be imagined geometrically as an endless continuous line. It is geometrical figure that contours real, physical bodies, so the name 'real' for the real numbers is well-chosen. On the other hand, however, only rational numbers can actually be calculated to obtain a definite arithmetic number that is a kind of logos as the result of a calculating logismo/j.

9. The incalculable, indeterminate quivering of all physical beings

What can we infer from this for the being of digital beings? A digital being is, in the first place, a finite sequence of binary code, consisting perhaps of billions and billions of bits, that is interpreted and calculated by the appropriate hardware in sequences of nested algorithms to bring about a foreseen effect. As binary code, i.e. a string of zeroes and ones, a digital being is nothing other than a finite rational number, whereas even a single irrational real number is a countably infinite string of bits(13) and therefore never can be inscribed logically-digitally. And yet, this binary code, interpreted as commands to be processed by a digital processor, brings forth change and movement in the real world of real, physical beings. A digital being can only represent the real world in terms of binary bits, which are logical, rational, computable numbers that always must miss the irrational continuum of the real.
For example, a computer-controlled robot on a production line can bring the robot's arm into a precisely precalculated position, which is always a rational number or an n-tuple thereof. The robot's arm, however, will always be in a real, physical position, no matter how accurate the rational position calculated by the computer is. There is therefore always an indeterminacy in the computer-calculated position, a certain quivering between a rational position and an infinity of irrational, but real positions. An irrational, real position can never be calculated by a computer, but only approximated, only approached. This signals the ontological limit to the calculability of physical reality for mathematical science. It is not an experimental result, but is obtained from phenomenological, ontological considerations. We must conclude: physical reality is irrational.

What does this imply for the understanding of being as standing presence? The standing presence of being is a temporal determination that goes hand in hand with the understanding of time as composed of a continuum of now-instants. According to the ontology of standing presence, a physical body assumes a definite position at a definite instant of time. In mathematical physics since the beginning of the modern age, the position and motion of physical bodies become calculable, but only by developing a mathematics of the continuum of real numbers that allows also the calculation of velocity and acceleration as infinitesimal differentiations of position with respect to the real, continuous variable, t. An irrational, real instant of time or an irrational, real position, however, can never by precisely calculated, but only approached by rational approximation. Insofar, a phenomenological interpretation of the calculability of the real position of physical bodies by means of the infinitesimal calculus shows that there is no definite position of a physical body at time, t, but only ever an indeterminate quivering of it between a here-and-now and an incalculable infinity of irrational there-and-thens. "

They don't go on to emphasize the junction of discrete and continuous as a fundamental ontology, but they generally hover around it.
Reply Mon 28 Jun, 2010 09:27 pm

I forgot to leave the link. This is generally a good site, allowing that I can't vouch for all of it.
Reply Tue 29 Jun, 2010 07:09 am
Reconstructo wrote:

I forgot to leave the link. This is generally a good site, allowing that I can't vouch for all of it.
That's interesting. I guess if it's true that the eye works like a movie camera (the retina is flushed with vitamin-A, which degrades with light, producing an image, then the retina is reflushed for the next image) and it's been noted that vision involves an on-going sequence of glances... you don't look at things in an analog way, but are always collecting snap-shots.. you could say the mind is a digital-to-analog converter.... producing a sense of visual continutity which isn't the nature of the sense data.

Just as we imagine A-D conversion is lossy since it's done by sampling, somehow D-A conversion is the opposite.. like when you hear someone's voice on the telephone... the sound is produced from a digital stream, but the analog production is continuous (so we imagine), which means that somehow the space between the digits was filled. Filled how? Where? With what? Intuitively, there's some kind of inertia, like the digit is off-balance, getting ready to fall into irrationality.
Reply Tue 29 Jun, 2010 09:52 am
GoshisDead wrote:

But doesn't belief in the metaphysical make us naive, delusional, and stupid?
Depends of the belief and what you mean with "metaphysical".

Drinking does all of that, but people drink anyway =)
Reply Tue 29 Jun, 2010 11:31 am
Reconstructo wrote:

How sharp is the tip of an imagined cone? How small is a Euclidean point?

Can we imagine infinitely precise measurement? It seems we could never physically achieve this.

Can a chess game be perfectly notated? Can it exist as symbols, minus board and pieces? Yes. It has been and is. What about copies of digital files? They too are perfect. The essence of digital media seem to be their perfect precision. And is this not because they in some way "transcend" the spatial?

I think that we can conceive of «infinitely precise measurement» in the same way we can have a representation of an infinite set.
We seem to be able to grasp potential infinity, not the actual one.
This feature can be also expressed as countably infinite or uncountably infinite. Roughly, countable infinity proceeds by "steps", while with the uncountable one those steps can't be determined, those sets are "too" dense.

I guess that when you refer to the spatial, you refer to these dense sets. And, yes, I agree with you, this seems to be a limit of our experience.
It is tricky to specify what this limit is - maybe some bright mathematician would be able to give us some definition.
It would not be right to assert that man is not able to handle the continuum, because it seems that we do - in some way. I guess that we attain that only as long as we find a way to box that continuum in some brackets/"steps" - but I do not present this as an authoritative conclusion.
As for what goes on in our mind when processing those quantities, I dare not to say anything, and I believe we can only have conjectures.

That feelings relate to continuous while "reason" only with discrete (the right brain hemisphere against the the left one?) it's a recurrent theme of yours - I know. That would imply that, somehow, men perceive continuum. It's possible, but I never got the fulcrum of this argument.
Reply Tue 29 Jun, 2010 11:37 pm
I think that all thought/speech is essentially discrete. This is why I argue that we can perceive directly but not think/speak the continuum.

The uncountable sets just go to show, in my opinion, how crafty Zeno's paradox's are. Irrational numbers are no more real than Santa Clause, one might say. No one has ever done a calculation with an irrational number, but only with an approximation of one. I think we are dealing with potential infinity, with is something like an algorithm.

I agree that to say how the brain works is a difficult task. I am coming from a phenomenological angle. I think about thinking, send reports back from adventures in "self" "consciousness."

You basically say that we deal with the continuum by making it discrete, do you not? I agree. If we look at the limit concept in mathematics, we see the tension. We think in chunks, except that we imagine space as continuous.

I think a perfect example is human speech. One has simultaneously the sound element (hisses, clicks, pops, vowel-sounds) and the "meaning." We normally focus on the meaning, but the sound-element colors this meaning with an emotional message that it subtle, and I think continuous. Of course I can only think/speak digitally, and thus the digital concept must point away from itself.

I don't mean to harp on this too much. For me it's a beautiful sort of realization. Zeno's paradoxes and Parmenides as a linguistic philosopher. Also this, which is somewhat related:

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