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Synthetic a priori, mathematics, and not-self - Dhamma Wheel

Synthetic a priori, mathematics, and not-self

Exploring Theravāda's connections to other paths. What can we learn from other traditions, religions and philosophies?
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Pannapetar
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Synthetic a priori, mathematics, and not-self

Postby Pannapetar » Mon May 17, 2010 12:11 pm

The not-self (anatta) doctrine of Buddhism takes two forms: a special form and a generalised form. In the the special form, not-self means not belonging to me, not mine, not I, and it concerns false identifications of self with, for example, the five aggregates. In the generalised form, it states that all phenomena are not-self, meaning all phenomena are empty of inherent existence, that there is no elusive entity behind phenomena.

Now, there is a curious class of statements known to philosophers as a priori statements. Kant (who invented the term) has defined this as the class of statements that do not rely upon empirical verification. In other words, these are "logical" propositions that cannot be contradicted without violating logic. "All triangles have three sides" is an example of an a priori statement. More precisely, this is an example of an analytic a priori statement. Unfortunately, most analytic statements are quite boring. The other type is called synthetic a priori statement and these tend to be more interesting. For example, "11 + 9 = 20" is such a statement (though it could be seen as a border case because it follows directly from the definition of natural numbers). Anyway, take for example: C/2r= pi. The circumference of a circle divided by its diameter (radius *2) equals pi. There you have an example of a non-trivial synthetic a priori proposition.

You might begin to wonder why I am mentioning this. Well, the class of synthetic a priori statements appears to describe atta/atman, or perhaps better: the essence of things. For example, C/2r=pi describes the essence of the circle. For all we know, it is eternal, universal, and non-changing (within the confines of Euclidean geometry). Furthermore, pi plays an important role in various mathematical and natural laws ranging from physics to statistics. Conclusion: there are certain atman-like properties that we can know about certain phenomena. This brings up a number of interesting questions.

1. Are phenomena themselves manifestations of atta/atman as far as these laws are concerned?
2. Are there classes of mathematical laws that are subject to some kind of impermanence?
3. Are there physical laws that are subject to some kind of impermanence?
4. Does our mind/thoughts somehow experience atta/atman to the extent to which we can understand these laws?
5. What part of ourselves understands these laws?
6. An argument favoured by theologians (rejected by Buddhists): is it our atman/brahman nature that discovers and understands these laws?
...

Cheers, Thomas

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

Postby Prasadachitta » Mon May 17, 2010 1:41 pm

"Beautifully taught is the Lord's Dhamma, immediately apparent, timeless, of the nature of a personal invitation, progressive, to be attained by the wise, each for himself." Anguttara Nikaya V.332

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

Postby ground » Mon May 17, 2010 1:42 pm


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

Postby chownah » Mon May 17, 2010 2:03 pm

I am not aware of any "mathematical laws".....can you explain one to me?
chownah

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

Postby Pannapetar » Mon May 17, 2010 3:12 pm


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

Postby Prasadachitta » Mon May 17, 2010 4:39 pm

"Beautifully taught is the Lord's Dhamma, immediately apparent, timeless, of the nature of a personal invitation, progressive, to be attained by the wise, each for himself." Anguttara Nikaya V.332

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

Postby Sobeh » Mon May 17, 2010 4:59 pm

You wrote, "For example, C/2r=pi describes the essence of the circle. For all we know, it is eternal, universal, and non-changing."

(i) Math is merely a language of description, it doesn't exist "out there, essentially" and thus has no essence, nor can a shape described by such maths have such a thing. It is wholly convention, as all languages are, which means your questions are non sequitur.

(ii) For all we know... it is convention. It isn't eternal, nothing is: anicca. It isn't universal or non-changing for that reason as well. Math changes and maths die, general human history shows as much.

Your premise is unsound.

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

Postby Dan74 » Tue May 18, 2010 12:02 am

_/|\_

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

Postby Goofaholix » Tue May 18, 2010 12:16 am

So are you trying to say that because a circle has an essence there must be an atman?

Whether or not a circle has an essence is besides the point, the circle itself is subject to the laws of impermenence, unsatisfactoriness, and not self.

When you experience something that you can define as a self let us know.

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

Postby Dan74 » Tue May 18, 2010 12:34 am

Goofaholix,

I am not sure whom you are addressing but I for one would certainly not argue for a circle having any essence for reasons I've noted above.
_/|\_

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

Postby Goofaholix » Tue May 18, 2010 1:02 am


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

Postby Dan74 » Tue May 18, 2010 1:51 am

Impermanence refers to form and phenomena, I think, not ideas and concepts. So I don't see anything resembling atman in mathematics (but Plato would disagree I guess). A circle is an abstraction derived by our intelligence from a variety of forms that share some characteristics and then codified using the laws of logic + geometry, again created by us, for the purpose of codifying patterns. Thus a circle has no more essence than the word "red".

I think the Buddha was onto another thing entirely when he spoke about impermanence and anatta. Although to many mathematicians their abstract universe is more real than the chair they sit on.

PS Maths is certainly no path to the ending of suffering - I see plenty of it around (and within). It can be a bit of an escape though!
_/|\_

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

Postby Modus.Ponens » Tue May 18, 2010 2:19 am

He turns his mind away from those phenomena, and having done so, inclines his mind to the property of deathlessness: 'This is peace, this is exquisite — the resolution of all fabrications; the relinquishment of all acquisitions; the ending of craving; dispassion; cessation; Unbinding.'
(Jhana Sutta - Thanissaro Bhikkhu translation)

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

Postby alan » Tue May 18, 2010 2:28 am

Thomas,
You delight in complication!

Sure it is true that a circle can be defined with an unwavering mathematical formula. So what? How do you get from there to Essence?

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Dan74
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Re: Synthetic a priori, mathematics, and not-self

Postby Dan74 » Tue May 18, 2010 2:28 am

How do you reconcile Platonism with Buddhadhamma? A belief in an ultimately real and unchanging world of forms seems to go directly against it (cf Hinduism).
_/|\_

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

Postby alan » Tue May 18, 2010 2:51 am

Essence has different meanings depending on context. A switch in the understanding of essence as a description of the mathematical basis for a circle to the idea that there are Atman-like qualities that we can know about phenomena is the
essence
of the mistake at the heart of the argument.

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

Postby Pannapetar » Tue May 18, 2010 2:56 am


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

Postby alan » Tue May 18, 2010 3:06 am

Maybe you could ask this question to the nice folks over at Vedanta Wheel? :smile:

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

Postby Modus.Ponens » Tue May 18, 2010 3:10 am

He turns his mind away from those phenomena, and having done so, inclines his mind to the property of deathlessness: 'This is peace, this is exquisite — the resolution of all fabrications; the relinquishment of all acquisitions; the ending of craving; dispassion; cessation; Unbinding.'
(Jhana Sutta - Thanissaro Bhikkhu translation)

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

Postby Dan74 » Tue May 18, 2010 3:15 am

_/|\_


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