Which Buddhists say that there are no conventionally existent wholes, and what's the best reason for the claim?
My "whole" I mean something more than the sum of its parts, an object that does not reduce to its parts.
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Any sect of Buddhism which emphasises the emptiness of all things probably says that there are no existent wholes but some sects would say that there are conventionally existent wholes. In other words, we can only talk about their existence from a conventional perspective.
Here's a nice description which talks about a car's existence and its emptiness
You're walking through town and you get to a street where you see a car. Is there a car? Sure thing! That's why we look left and right before crossing the street, and it would be dangerous to say that "there is no car" (without further explanation).
But if we take one car aside and take a closer look, there's no such thing as a car. The windshield isn't it, the wheels aren't it, the chassis isn't it, neither is the engine. What we call a car is just a bundle, a construct not only physically but conceptually.
It's a point which can be difficult to convey. Something is there which will hit you when you cross the street, we call this a car. On the other hand, if we take that car and dismantle it into its pieces we can not find any piece which is the essential car-like-nature.
This is the same as when we look at the self. We can investigate all five aggregates (body, feeling, perception, mental formations, consciousness) and there is no inerrant soul or "me" to be found. However, we can still talk about the "me" existing by convention.
There are conventionally existent objects. Whether you call them wholes or parts does not make a difference, since a part is also a whole and a whole a part. For instance, the petals of a flower are a part of the flower, but a petal is a whole [as a petal].
Whatever is an object found by a conventional valid cognizer (such as the eye-consciousness, the ear-consciousness, and so forth) exists conventionally. Since I can see you, you are conventionally existent.
However, no object can withstands ultimate analysis. Another way of saying is that a cognizer analyzing the ultimate will find only emptiness of true existence. For instance, you will not be found by a cognizer validly analyzing "are you your body? are you your anger? are you your feelings? etc." but you are found by an eye-consciousness (since I see you). In the same way that sound is not apprehended by an eye-consciousness, no conventional truth is found by a mind of ultimate analysis.
That is the Madhyamika-Prasangika view. This being said, there is no Buddhist school that posits there is no conventionally existent objects.
The standard Buddhist picture is that
so given that
it follows that wholes have no existence. You can find arguments for these two claims pretty easy.