Synthetic a priori, mathematics, and not-self

[alan]

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.

[Pannapetar]

Math is merely a language of description, it doesn't exist "out there...

In some way it does. We observe entities and forces "out there" that manifest according to mathematical rules.

For all we know... it is convention. It isn't eternal, nothing is: anicca.

Mathematics is definitely not just a convention, because it is not arbitrary. Only the symbols and notation are arbitrary. Neither is a formula such as C/2r=pi or F = G (m1 * m2) / r^2 (Newtonian gravity) subject to impermanence (anicca). They remain unchanged for eternity. These formulas are as valid in a billion years as they are now and they are as valid in the Andromeda galaxy as they are here on Earth. Any intelligent alien species that might exist somewhere in the universe will discover exactly the same laws, although they might codify them in a different way.

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.

How so?

Impermanence refers to form and phenomena, I think, not ideas and concepts.

Exactly my point. So could it then be said that concepts (in particular synthetic a priori aka eternal truth) are atman? What about the principle of consciousness that "sees" these eternal truths? I have no fixed opinion on this myself. It is puzzling and it is disregarded by the dhamma.

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?

Very easy: essence is suchness, and the predicate C/2r=pi describes "circle"-ness. It applies to any circle-like object in Euclidean space.

Cheers, Thomas

[alan]

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

[Modus.Ponens]

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).

To be honest I never dedicated myself that much to thinking in philosophy of mathematics and its relation to the dhamma. But anyway I can try a bit. Platonism comes in a variety of forms. I don't believe in a world of ideas hanging around waiting to be discovered. But I could never go to the other extreme and say that, for example, circles or prime numbers are mere constructions of our minds. Probably this is one of the questions to which the Buddha would remain silent if asked. I'll let the definitive answer come when I'm an arahat, whenever that may be. Until then I will identify myself loosely with platonism.

[Dan74]

Impermanence refers to form and phenomena, I think, not ideas and concepts.

Exactly my point. So could it then be said that concepts (in particular synthetic a priori aka eternal truth) are atman? What about the principle of consciousness that "sees" these eternal truths? I have no fixed opinion on this myself. It is puzzling and it is disregarded by the dhamma.

Here it would probably pay to have some definitions handy. But even without these, how could any concept be atman if it is dependent upon cognizing (which is itself dependent upon other conditions)?

[Modus.Ponens]

Impermanence refers to form and phenomena, I think, not ideas and concepts.

Ideas and concepts arise and fall in our minds, but their content may not be subject to impermanence. Hence my identification with platonism.

[Dan74]

Any intelligent alien species that might exist somewhere in the universe will discover exactly the same laws, although they might codify them in a different way.

This is a big claim! It is based on an assumption that the way we observe the universe is more or less, the only way.

But they may actually observe in a radically different way and perceive different patterns to us and develop different 'science/maths" to deal with those.

[Pannapetar]

This is a big claim! It is based on an assumption that the way we observe the universe is more or less, the only way. But they may actually observe in a radically different way and perceive different patterns to us and develop different 'science/maths" to deal with those.

Why should aliens observe different patterns? After all, the patterns themselves are universal. Fundamental manifestations are likewise universal. For example, gravitation is universal, electromagnetic force is universal, light is universal, etc. Aliens might indeed perceive patterns in a different way. For example, they might perceive different bands of electromagnetic radiation as light, or they might not perceive light at all. They might use a base 8 system instead of a base 10 system for counting. But they would not observe a different value for pi. They would not observe different prime numbers. They would not observe a different truth tables for Boolean logic. That is to say if aliens had developed a concept of circles, natural numbers, and Boolean logic, then these items would exhibit the same patterns/properties that we observe.

Cheers, Thomas

[Dan74]

Well, to me these are claims. Including "universal". All these are rooted in our perception which is conditioned, and in Buddhadhamma we learn that even the perception of arahats is fundamanentally different, because the conditions are changed.

There is self-reference and circular logic in these kinds of arguments and I am not convinced.

Again I think you start off by attributing a "universal" aspect to our perceptions and pattern-recognition and then other supposed universals follow. To me all these are conditioned and not universal.

[retrofuturist]

From MN 1: Mulapariyaya Sutta
http://www.accesstoinsight.org/tipitaka ... .than.html" onclick="window.open(this.href);return false;

The Blessed One said: "There is the case, monks, where an uninstructed run-of-the-mill person — who has no regard for noble ones, is not well-versed or disciplined in their Dhamma; who has no regard for men of integrity, is not well-versed or disciplined in their Dhamma — perceives earth as earth. Perceiving earth as earth, he conceives [things] about earth, he conceives [things] in earth, he conceives [things] coming out of earth, he conceives earth as 'mine,' he delights in earth. Why is that? Because he has not comprehended it, I tell you.

"He perceives water as water... fire as fire... wind as wind ... beings as beings... gods as gods...Pajapati as Pajapati...Brahma as Brahma... the luminous gods as luminous gods... the gods of refulgent glory as gods of refulgent glory... the gods of abundant fruit as the gods of abundant fruit... the Great Being as the Great Being ... the dimension of the infinitude of space as the dimension of the infinitude of space... the dimension of the infinitude of consciousness as the dimension of the infinitude of consciousness... the dimension of nothingness as the dimension of nothingness... the dimension of neither-perception-nor-non-perception as the dimension of neither-perception-nor-non-perception ... the seen as the seen... the heard as the heard... the sensed as the sensed... the cognized as the cognized ... singleness as singleness... multiplicity as multiplicity ... the All as the All ...

"He perceives Unbinding as Unbinding. Perceiving Unbinding as Unbinding, he conceives things about Unbinding, he conceives things in Unbinding, he conceives things coming out of Unbinding, he conceives Unbinding as 'mine,' he delights in Unbinding. Why is that? Because he has not comprehended it, I tell you.

Metta,
Retro.

[Goofaholix]

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.

How so?

Because all things are subject to the laws of impermenence, unsatisfactoriness, and not self.

Can you give me an example of a circle which is permanent, totally satisfying, and a self?

[Sobeh]

We observe entities and forces "out there" that manifest according to mathematical rules.

They may manifest according to mathematical principles, but that's putting the cart before the horse. There is a manifestation, and our maths can describe it. Those maths are not the cause of the manifestation, they simple describe the way in which the whole thing functions. An equivalent claim to the one you're making is that not only is paticcasamuppada a good description of how suffering arises, but that paticcasamuppada is also a thing out there. This is patently ridiculous.

Neither is a formula such as C/2r=pi or F = G (m1 * m2) / r^2 (Newtonian gravity) subject to impermanence (anicca). They remain unchanged for eternity. These formulas are as valid in a billion years as they are now and they are as valid in the Andromeda galaxy as they are here on Earth. Any intelligent alien species that might exist somewhere in the universe will discover exactly the same laws, although they might codify them in a different way.

General relativity showcases the approximation that Newton's equations are; terribly useful, but things did not operate according to those equations a mere picosecond after the Big Bang - just as the language of maths is anicca, so too is all that the language describes.

Your premise was:

Well, the class of synthetic a priori statements appears to describe atta/atman, or perhaps better: the essence of things. <example>

I contend (based on my understanding of the Dhamma) that, ultimately, all a priori statements are only possible within matrices of language structures that are necessarily anicca. In other words, all possible a priori statements are subject to anicca. You haven't gotten your premise off the ground yet.

[Pannapetar]

Well, to me these are claims.

To call them "claims" doesn't really say very much. What type of claims? Empirical? Epistemic? We have to distinguish propositions about empirical facts from logical propositions, for example. To say that the patterns we express with mathematics have no reality beyond our conditioned mind amounts to epistemological constructivism. Are you arguing in favour of "pure" constructivism?

Can you give me an example of a circle which is permanent, totally satisfying, and a self?

It appears that you confuse phenomena with concepts. You cannot argue about concepts in the same way you argue about phenomena. I had hoped this thread had at least established that much.

An equivalent claim to the one you're making is that not only is paticcasamuppada a good description of how suffering arises, but that paticcasamuppada is also a thing out there. This is patently ridiculous.

Why is that ridiculous? in a sense, dependent origination is out there, in Africa, in Australia, in America, and everywhere else where sentient beings are.

All a priori statements are only possible within matrices of language structures that are necessarily anicca.

This likewise amounts to epistemological constructivism, does it not? What you seem to say here is that symbolic systems, languages, are properties of mind and that their contents are therefore also just properties of mind. Well, I can't really argue with that, because you start off from a different epistemological premise, but neither can I agree with it. As previously stated, I don't have a fixed opinion, though I find epistemological constructivism not very attractive, because it seems that for epistemological constructivism to be consistent you must also argue in favour of idealism.

Here is another question: Do you think that Buddhism is more compatible with these views?

Cheers, Thomas

[alan]

The reason his statements have not got off the ground has nothing to do with anicca, or any other Buddhist ideas.
The problem is a fundamental misunderstanding of the idea of "essence".
Defining essence as "suchness" should set off alarm bells.

This is why going over to that Pali word of the day thread is so interesting. Many shades of meaning are contained in one word; context is always important.

[Pannapetar]

The problem is a fundamental misunderstanding of the idea of "essence".

Perhaps you could enlighten us about its proper meaning then?

Cheers, Thomas