Pannapetar wrote: 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?
Pannapetar wrote: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.
Pannapetar wrote:For example, C/2r=pi describes the essence of the circle.
gabrielbranbury wrote:I think numeric laws are simply a form of communication which correspond to phenomena. Without a circle there would be no pie.
TMingyur wrote:Why does "C/2r=pi" describe the essence of a circle? What does "describe" mean in this context? A definition?
chownah wrote:I am not aware of any "mathematical laws".....can you explain one to me?
Pannapetar wrote:One interesting philosophical question that has been discussed is whether mathematical properties do actually manifest in real world phenomena, or whether these properties are just ways of perceiving them, i.e. are purely mental constructs.
[/quote]I should probably have said "C/2r=pi describes the essential property of a circle" rather than it's "essence", because the essence (definition) of a circle is again a simple analytic statement: a line on which all points have the same distance from a given point p.
Sobeh wrote: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.
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.
Dan74 wrote: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!
Sobeh wrote:Math is merely a language of description, it doesn't exist "out there...
Sobeh wrote:For all we know... it is convention. It isn't eternal, nothing is: anicca.
Goofaholix wrote: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.
Dan74 wrote:Impermanence refers to form and phenomena, I think, not ideas and concepts.
alan wrote: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?
Dan74 wrote: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).
Pannapetar wrote:Dan74 wrote: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.