Synthetic a priori, mathematics, and not-self

Exploring Theravāda's connections to other paths - what can we learn from other traditions, religions and philosophies?
alan
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Re: Synthetic a priori, mathematics, and not-self

Post by alan »

The argument has been refuted so many times and in so many ways by so many people that I think it is fair at this juncture to say it is nonsense. That's not calling names. Calling for a boycott is just another way to say this thread has become useless, so please stop responding. I do that because it seems to me that anything we say will just give more fodder to needless proliferation. Nothing disrespectful about that.
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Pannapetar
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Re: Synthetic a priori, mathematics, and not-self

Post by Pannapetar »

Kenshou wrote:I'm aware of the utility of math and science in those aspects. But, is it necessary for dispelling ignorance and delusion as they pertain to the four noble truths?
Of course not, as you correctly stated. However, math and science dispel ignorance and delusion in other areas of life. There are many such areas about which Buddhism has nothing (or at least not very much) to say, for example medicine, science, ecology, and so on. Yet these are all things that affect the lifes of everyone directly. Some of us work in these fields and come into contact with them on a daily basis. Hence, it is more than justified to see how they fit in to the Buddhist world view.
gabrielbranbury wrote:For those of us who have accepted a path of practice and have faith in it, what use is there in ruminating about ideas which have no bearing on that practice?
Well, for one it helps to avoid "Buddhist tunnel view". You see, a regular problem for people becoming immersed into Buddhism is that they are keenly aware of clinging, yet often ignore clinging to views that their particular school endorses. They often do this even without realising it. Hence, an outside perspective is often useful to generate awareness for this particular problem.
alan wrote:OK, I'm going to propose a boycott.
Hilarious! :rofl: "To post or not to post... that is the question: Whether 'tis nobler in the mind to suffer..." Since discussion boards rely on voluntary participation, the proposal seems a little out of place. I suggest that you go ahead with your boycott, Alan.

Cheers, Thomas
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Re: Synthetic a priori, mathematics, and not-self

Post by tiltbillings »

Open for business.
>> Do you see a man wise [enlightened/ariya] in his own eyes? There is more hope for a fool than for him.<< -- Proverbs 26:12

This being is bound to samsara, kamma is his means for going beyond. -- SN I, 38.

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Re: Synthetic a priori, mathematics, and not-self

Post by chownah »

Pannapetar,
Sometimes a discussion goes awry because initial concepts are misunderstood. You have postulated that there exist a thing called a "mathematical law" and you talk as if it is widely understood that such a thing exists. I have a BA degree in mathematics from a major US university and while I do admit that it was a long time ago and that I have never worked in the field of mathematics (other than teaching and for engineering and personal use) I do not remember anyone ever talking about any "laws" of mathematics and I am reasonably sure that I have never been taught about any "mathematical laws"....axioms, postulates, groups, conjectures, proofs, and a host of other official sounding entities are discussed but never as far as I can remember is there a thing called a "law"....and this is for a good reason. Mathematics teaches that any system of mathematics (and there are thousands...or even one could say an unlimited number of them) and that the way these systems function is entirely dependent on initial assumptions...or in the Buddha's words they are dependent on conditions...

So....if the awe inspiring idea of "mathematical law" is dropped then you can perhaps develop a more approachable term such as "mathematical idea" which puts it squarely in the court as an object of the sense door called "mind"....and if you want to learn about that there are alot of reference in the Theravada Scriptures and Associated Commentaries which might benefit you in understanding its relationship to other stuff....I think....

Otherwise....can you please write down here a "mathematical law" and explain it to me...and why it is called a law....and the equation which indicates that pi is the ration between the circumfrence and diameter of a circle most assuredly does not count as a "law" because it is merely an equation which could be true or false...if you think it is true then please show me a proof...but even with a proof it should not be considered a "law".
chownah
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Re: Synthetic a priori, mathematics, and not-self

Post by nathan »

Pannapetar wrote:mountains are large three-dimensional objects with a complex fractal topology. While all of these are of course "mental constructs", they do form a special class of statements, namely a non-arbitray, objective class of statements that can be validated by purely logical (non-empirical) means.
I have no idea what this discussion is about or what purpose it serves but I have a question since I live on a mountainside. How would I go about 'objectively validating by purely logical or non-empirical means' that the terrain surrounding me has a complex fractal topology? Would I need to borrow Tilt's tinfoil hat for this exercise or are you perhaps not finished with it yet?
But whoever walking, standing, sitting, or lying down overcomes thought, delighting in the stilling of thought: he's capable, a monk like this, of touching superlative self-awakening. § 110. {Iti 4.11; Iti 115}
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Re: Synthetic a priori, mathematics, and not-self

Post by DNS »

chownah wrote: Otherwise....can you please write down here a "mathematical law" and explain it to me...and why it is called a law....and the equation which indicates that pi is the ration between the circumfrence and diameter of a circle most assuredly does not count as a "law" because it is merely an equation which could be true or false...if you think it is true then please show me a proof...but even with a proof it should not be considered a "law".
chownah
Exactly. As I understand it, mathematics deals with numbers and concepts, basically labels (nama). They are man-made concepts, with no intrinsic qualities.

They help us better understand the conventional world, but have no intrinsic nature.
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Re: Synthetic a priori, mathematics, and not-self

Post by nathan »

chownah wrote: Otherwise....can you please write down here a "mathematical law" and explain it to me...and why it is called a law....
I'm thinking maybe... the law of "rent is due on the last day of the month". Mathematical because you will need to remit the numerically specified amount of money on the specific numerically indicated day and a law because you will be legally evicted in due course if you do not.
But whoever walking, standing, sitting, or lying down overcomes thought, delighting in the stilling of thought: he's capable, a monk like this, of touching superlative self-awakening. § 110. {Iti 4.11; Iti 115}
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Re: Synthetic a priori, mathematics, and not-self

Post by Sobeh »

Pannapetar wrote:Sobeh, is it possible that you are taking this a bit too far? I had not intention of bringing in the five aggregates and the sixth senses, as this would further complicate the discussion of an already complicated matter.
We're talking about atta in this thread. That means, for a Buddhist practitioner, either the five aggregates or the six sense bases. Either way, if you're trying to talk about atta without recourse to the Dhamma on the subject, it's a non-starter.
Pannapetar wrote:Did I detect some aversion to metaphysics? For me, the point of getting acquainted with metaphysics is to learn the flaws of various metaphysical positions. Only then is it possible to avoid their trappings.
You didn't detect anything, I told you simply and clearly that they are ridiculous, mere idle speculation at best, intellectual masturbation at worst. Why? Because metaphysics has nothing to do with suffering or the cessation of suffering. Which brings us to:
Pannapetar wrote:Buddhism is, by the way, certainly not free of metaphysics. Although Buddhism wisely avoids extremes, I see it -especially in its Theravada form- leaning towards phenomenalism, which might explain why an objectivist understanding of science and math doesn't harmonise with it.
"In epistemology and the philosophy of perception, phenomenalism is the view that physical objects do not exist as things in themselves but only as perceptual phenomena or sensory stimuli (e.g. redness, hardness, softness, sweetness, etc.) situated in time and in space. In particular, phenomenalism reduces talk about physical objects in the external world to talk about bundles of sense-data."

Phenomenalism is epistemology, not metaphysics. The objectivism you refer to is otherwise known as philosophical realism, which is "the view that there is a reality or ontological realm of objects and facts that exists independent of the mind."

Phenomenalism, as shown here, is a metaphysical view, and as such it is bent to the task of posing questions and answers that have nothing to do with suffering or the cessation of suffering.

Once again, your proclivity to map the Dhamma onto a western philosophical tradition is flawed and results in a straw man.
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Pannapetar
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Re: Synthetic a priori, mathematics, and not-self

Post by Pannapetar »

Chownah, I had explained the motive for using the term "mathematical law" in post no. 5. Since I have also studied mathematics, I am aware that this is not a term that a mathematician would use. What you are saying is that an axiomatic system depends on its axioms. Well, yes. That is an important consideration which non-mathematicians often forget or overlook. In particular, much depends on fundamental axiomatic systems such as (Zermelo-Fränkel) set theory, the postulates of Euclidean geometry, or the inference rules of propositional calculus, just to name a few examples. So yes, these are idea systems. It doesn't really make a difference for my argument though. Here is why: A simple equation, such as C/2r=pi expression a relation of entities or -if you want- interdependence. Among other things, it implies that we know what the symbol "2" means; the symbol "2" implies natural numbers and for natural numbers we need the Zermelo-Fränkel set theory. Thus we find interdependence on a larger scale. Does this somehow constitute a deficiency? Does mathematics depend on conditions in any other way than the Buddhadhamma depends on conditions? That is to say, does the Buddhadhamma not depend on ideas, postulates, and theorems, some of which are simple, some of which complex, many of which are interdependent, all of which are expressed in symbolic language? Is the Buddhadhamma therefore deficient?

Nathan, there is a better way than doing this by hand: you can use computer software to generate mountains using fractal geometry. This is a run-off-the-mill feature in computer games, for example, for generating terrains. See here for example: http://scienceblogs.com/goodmath/2007/0 ... ntains.php" onclick="window.open(this.href);return false;

David, mathematics does indeed deal with nama, or perhaps better with "patterns" of nama. The interesting thing about these patterns is that they provide blueprints for constructing the universe. For example, you can (as mentioned) construct mountain- and plantlike shapes from the recursive application of fractal formulae. Or you can construct pine cones, snail shells, and other natural forms from the fibonacci sequence of numbers. You can use math to describe anything from force vectors and magnetic fields to the probability distribution in an electron cloud. Hence, wouldn't it be fair to say that math describes the "intrinsic nature" of these phenomena?

Sobeh, you are trying to press the term atta/atman into a very narrow mold which is, even from a Buddhist perspective, too limited. Apart from "soul", atta also means "inherent existence" which is the meaning I have used here. Furthermore, the terms "objectivism" and "philosophical realism" are often used synonymously in philosophy. I must also reject your objection that "phenomenalism is epistemology, not metaphysics". Such a broad claim would bring any philosophy professor to tears. Phenomenalism is firmly rooted in ontology. Actually, your very citation: "phenomenalism the view that physical objects do not exist as things in themselves" is a giveaway. It has ontology written all over it. Perhaps it would be wise to base your argumentation not entirely on Wikipedia verbatim snippets. Since your argument is based on questioning terminology, and since you haven't established a firm grasp of the same, I am afraid I have to reject your critique.

Cheers, Thomas
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retrofuturist
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Re: Synthetic a priori, mathematics, and not-self

Post by retrofuturist »

Greetings,

Those who mistake the unessential to be essential
and the essential to be unessential,
dwelling in wrong thoughts,
never arrive at the essential.

Those who know the essential to be essential
and the unessential to be unessential,
dwelling in right thoughts,
do arrive at the essential.


The Buddha (Dhp. 11-12)
http://www.accesstoinsight.org/tipitaka ... .budd.html" onclick="window.open(this.href);return false;

:buddha2:

Metta,
Retro. :)
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Re: Synthetic a priori, mathematics, and not-self

Post by nathan »

Pannapetar wrote:Nathan, there is a better way than doing this by hand: you can use computer software to generate mountains using fractal geometry. This is a run-off-the-mill feature in computer games, for example, for generating terrains. See here for example: http://scienceblogs.com/goodmath/2007/0 ... ntains.php" onclick="window.open(this.href);return false;
Cheers, Thomas
No dude, I don't need a computer at all, I live on a real mountain. You suggested that in shapes in nature, specifically
mountains are large three-dimensional objects with a complex fractal topology
As I see nothing about the surrounding terrain to suggest a fractal geometry on any scale I asked for you to explain how a real mountain could possibly be correctly described in any way by employing fractal geometry.

This is why I will now go on to suggest that computer models, while they may frequently appear to indicate various realistic patterns are actually frequently suggesting false and illusory projections. Which is why I think that twice now it has been clearly shown that fractal geometry has no real relationship of any kind to any actual mountain in the natural world. I think this demonstrates however, an accurate example of many of your presentations in that they have many of the appearances of communicating something of great importance when in fact they are completely empty of actual useful significance. With the notable exception of considerable potential entertainment value, of course.
But whoever walking, standing, sitting, or lying down overcomes thought, delighting in the stilling of thought: he's capable, a monk like this, of touching superlative self-awakening. § 110. {Iti 4.11; Iti 115}
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Re: Synthetic a priori, mathematics, and not-self

Post by Ben »

nathan wrote:This is why I will now go on to suggest that computer models, while they may frequently appear to indicate various realistic patterns are actually frequently suggesting false and illusory projections.
I couldn't agree more, Nathan. Years ago I was managing vast project data libraries of an environmental engineering company and using a GIS system to map contaminated groundwater - amongst other things. I could produce visually impressive graphical representations of contamination plumes but the accuracy of the krigging algorythm was largely dependent on the number and placement of data points. It was very easy to believe that what you were looking at was the truth rather than, what was at times, an elegant speculation.
kind regards

Ben
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Learn this from the waters:
in mountain clefts and chasms,
loud gush the streamlets,
but great rivers flow silently.
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Pannapetar
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Re: Synthetic a priori, mathematics, and not-self

Post by Pannapetar »

nathan wrote:As I see nothing about the surrounding terrain to suggest a fractal geometry on any scale I asked for you to explain how a real mountain could possibly be correctly described in any way by employing fractal geometry.
Well, maybe you can send me a picture of your mountain and then we can discucss whether it exhibits fractal geometry or not? Would that be acceptable? In the meantime, consider this example: http://wiki.tcl.tk/4560" onclick="window.open(this.href);return false; written in tcl/tk. It shows an algorithm for constructing mountains and a visual example of the result. As you can see, the algorithm is already fairly complex while the resulting mountain is slightly cartoonish (though clearly recognisable). For more realism, more complex algorithms are required.
nathan wrote:Which is why I think that twice now it has been clearly shown that fractal geometry has no real relationship of any kind to any actual mountain in the natural world.
Why would you say that? Because the processes that shape actual real-world mountains, such as tectonics, mechanics, and erosion aren't there in the computer model? Well, in a sense they are. They are expressed by the variables, constants, and control structure nuances of the algorithm. Abstractions... that's what math is all about.
Ben wrote: I could produce visually impressive graphical representations of contamination plumes but the accuracy of the krigging algorythm was largely dependent on the number and placement of data points.
Accuracy is always dependent on initial data points and often on computational complexity, especially for nonlinear dynamic systems. What can we conclude? That you can lie with data? Sure. You can lie even with a simple bar graph. Misrepresentation is always possible. I don't see that this has any bearing on the question whether mathematics can model actual phenomena.

Cheers, Thomas
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Re: Synthetic a priori, mathematics, and not-self

Post by Pannapetar »

retrofuturist wrote:Those who mistake the unessential to be essential...
Retro, your skill at quoting appropriate sutta is certainly unquestioned, but it comes across slightly condescending.

Cheers, Thomas
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Re: Synthetic a priori, mathematics, and not-self

Post by retrofuturist »

Greetings Pannapetar,
Pannapetar wrote:
retrofuturist wrote:Those who mistake the unessential to be essential...
Retro, your skill at quoting appropriate sutta is certainly unquestioned, but it comes across slightly condescending.
It's not intended to be condescending... it's intended to give you the opportunity of seeing how the Buddha might guide you on such matters if he were here today.

It is for the individual to discern according to their own reason whether my selection of Buddhavacana is relevant to their situation, and in turn, if they wish to adopt it in their practice. All I do is join the dots and let people decide for themselves. If others did the same for me, I would be delighted.

Metta,
Retro. :)
"Whatever is true, whatever is noble, whatever is right, whatever is pure, whatever is lovely, whatever is admirable—if anything is excellent or praiseworthy—think about such things."
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