Resisting a classic Buddhist Argument for Mereological Nihilism

Question

I’ve been getting into mereology and this a classic Buddhist puzzle that he recommended. How can these premises be resisted?

• A. If wholes exist, then either wholes are identical with their parts or distinct from them.
• B. Wholes and their parts have incompatible properties.
• C. Two entities cannot be identical if they have incompatible properties.
• D. So, wholes are not identical with their parts (B, C).
• E. The properties of wholes can be entirely explained in terms of facts about their constituent parts.
• F. Entities whose properties can be entirely explained in terms of facts about their constituent parts are not distinct from their parts.
• G. So, wholes are not distinct from their parts (E, F).
• H. Therefore, wholes don’t exist (A, D, G)

Answer 1

The problem as stated is equivocating on the meaning of "their parts". This phrase is used to mean two different things: "their mere collection of parts" or "their parts in the relationships that constitute the whole".

B, C, and D rely on the first meaning because a whole is not identical with the mere collection of its parts. Consider a car in your garage. Someone comes in and takes it apart, stacking all the body panels in one place, the wheels in another, the tires in another, etc. The pile is not a car, and so it is not identical to a car.

E relies on the second meaning, because the properties of the whole can be explained in terms of its parts, but only when you take into account the relationships between the parts. That is, you can explain the function of the car by referring to the function of its parts, but only when the parts are in their proper places. The engine isn't going to run if the pistons aren't in the cylinders.

In addition, F strikes me as in need of an argument itself. It's not obvious enough to be a premise.

Answer 2

The language in (B) could mean either of two different things, one of which is true but irrelevant and one of which would be relevant but is not supported, and as a result I would reject (D).

First let's clarify the language in (D). (D) is not really ambiguous but it helps to spell things out.

D. So, wholes are not identical with their parts.

The only reasonable interpretation I can find here is that "wholes are not identical with the union of all of their parts."

B. Wholes and their parts have incompatible properties.

Now, what does this mean? There are two readings I can see.

Reading 1. "For each part, the whole has different properties from that part." I would certainly agree with this statement, but it fails to support the conclusion (D).

Reading 2. "The whole has different properties from the union of all of its parts." This statement, if true, would support the conclusion (D). However, no evidence is given for this reading of (B). Therefore, (D) is not supported either.

Answer 3

This is an interesting problem, I’ll try my hand at it, here we go:

A. If wholes exist, then either wholes are identical with their parts or distinct from them.

This premise seems straight forward enough, no further comment.

B. Wholes and their parts have incompatible properties.

I am not sure about the usage of the term “incompatible” here, one could easily venture to say that the whole has properties that the part doesn’t have, but to assert incompatibility is a strong assertion. Either clarification regarding the usage is required or evidence for the claim or both.

C. Two entities cannot be identical if they have incompatible properties.

See the comment in (B). Though this seems to be an accurate statement, even if we understand “incompatible” in the sense of “different”.

D. So, wholes are not identical with their parts (B, C).

This follows, no further comments on this premise.

E. The properties of wholes can be entirely explained in terms of facts about their constituent parts.

This is a contentious claim, and hinges on what one would count as a valid explanation. Often times a “third” property (so to speak) arises out of the interaction or congealment of multiple parts, a simple example would be H2O. Hydrogen by itself has specific qualities, and oxygen by itself has specific qualities, though when combined they produce water, a compound with its own unique properties. Can these unique properties be explained? Perhaps. Can they be explained by the totality of facts regarding the interactions between the parts along with the general properties of each individual part? If the answer to the previous question is yes, so then is the answer to this.

(Note: I am not arguing against the premise here, just pointing out that it is contentious along with the highlighting of what I think to be a pertinent fact)

F. Entities whose properties can be entirely explained in terms of facts about their constituent parts are not distinct from their parts.

This is a problematic assertion, if we are to assert that entities with distinct properties are not identical, then that means they are distinct. If that is the case, what constitutes distinction is not how the entity is explained, but rather the perceived properties of the entity.

Either these properties that are explained by the interaction of the individual parts are assigned to the individual parts or they are assigned to some other entity, in the premise (B), it seems as if these properties are not assigned to the individual parts, so it is assigned to some other entity, the entity that owns that property, generally what we refer to as the whole.

Furthermore, why should it be the case that if something can be explained in terms of something, that it is identical to that thing? Just some food for thought.

G. So, wholes are not distinct from their parts (E, F).

No comment here.

H. Therefore, wholes don’t exist (A, D, G)

I see how this is derived from assuming the previous premises, but this causes an interesting question to arise from the assertion of premise (B). It was mentioned that wholes and parts have “incompatible” properties, but now we have concluded that wholes do not exist, a question regarding the properties you alluded to earlier is now lingering, that being, what happened to these properties? If we conclude that wholes do not in fact exist, then these properties that were mentioned should belong to the parts, but it was mentioned earlier that these parts are “incompatible” with such properties, a seeming dilemma in the position (unless you toss out the properties with the whole, but that really wouldn’t explain where the properties came from or provide any justification as to why you would discard them).

That’s my two cents, feel free to comment.

Addendum:

After getting some sleep, it has dawned on me that the argument makes an interesting claim, (C) states that “Two entities cannot be identical if they have incompatible properties” and (F) states that “Entities whose properties can be entirely explained in terms of facts about their constituent parts are not distinct from their parts”. These two premises for the criteria for “valid” distinction in the argument and can be formalized as follows:

IP - “Incompatible properties” (for practical purposes I will be understanding this as unique properties, see the comments above on B)

D - “Distinct”

EP - “Explained by parts”

1. A: IP -> D (Premise C)
2. B: EP -> ~D (Premise F)

The first premise reads “If the entity has unique properties (properties the parts do not have), then it is distinct (from its parts).

The second premise reads “If the entity is explained by its parts, then it is distinct (from its parts)”.

Given these two, further statements can be derived:

1. C: D -> ~EP (Contrapositive of 2B)
2. D: IP -> D -> ~EP (1A & 1C)
3. E: IP -> ~EP (2D & Transitivity)

Assuming I didn’t err in my logic, it can be said that the premises you have presented, specifically (C) and (F), state, albeit implicitly, that if an entity has incompatible properties with its parts, then its parts do not fully explain it. From this, one of three things must be the case if we wish to preserve the statement: Either premise (B) is false, that being wholes do not have unique or “incompatible” properties from their parts, or premise (E) if false, or one (or both) of the two premises (C and F) is false.

Now if the assertion is that “if wholes exists, then wholes have distinct or ‘incompatible’ properties from their parts and they are explained by their parts”, then it follows that wholes do not exist (assuming the contested premises and their derived statements are sound), but if this is the case, the issue regarding these unique properties (see the comments on conclusion H) still stands, resulting in premise (B) being very problematic if assumed to be true.

Answer 4

Interesting thought problem. I'll take a stab and see what happens.

If you divide the number 12 into the product 3x4, and then divide the number 12 into 2x6, you do not have 24. In fact, there are an infinite number of factorizations of 12 among the reals, thus it is arguable that 12 which is a finite number has an infinite number of parts. How do we make sense of this?

Because 12, a whole, is both identical with 3x4 and NOT identical with 3x4 at the same time. How? 12 is an expression with no operation, but 3x4 is an expression with the operation of multiplication, and yet both expressions evaluate to 12. So, for starters, A can be read as a false statement in a context demonstrating the Law of the Excluded Middle does not apply.

A. If wholes exist, then either wholes are identical with their parts or distinct from them.

12 is a number, and 3 and 4, which are parts are numbers, and numbers all belong to the class numbers which means necessarily they have compatible properties. Thus, B in a context can be shown to be false since if they didn't have compatible properties, there would be no closure of numbers under various operations.

B. Wholes and their parts have incompatible properties.

If you write 12 on a paper with ink, and then write 12 in the sand at the beach with your finger, it is not possible to write 12 with ink on the sand, nor is it possible to use your finger to write 12 on paper. Thus, two 12's which are identical have incompatible properties. Thus, in a context, it can be shown that C is false.

C. Two entities cannot be identical if they have incompatible properties.

Thus, we have the case that wholes can be identical with their parts, and not identical with their parts, and that entities can be identical even if they have incompatible properties, so the conclusion wholes can or cannot be identical with their parts depends on context. That means D is false under this derivative context.

So, wholes are not identical with their parts (B, C)

12 can be divided by an infinite number of numbers, and therefore no matter how many facts are listed about 12 in terms of factors, of any arity are enough to explain the whole, and there is no number without an infinite number pairs, so there are no entities whose properties can be explained in terms of factor pairs, therefore F is false.

F. Entities whose properties can be entirely explained in terms of facts about their constituent parts are not distinct from their parts.

12 has no set of factors that is not distinct from 12 so all factor pairs of 12 must be distinct from 12 itself, including 12x1. Therefore G is false under a context.

G. So, wholes are not distinct from their parts

One cannot presume 12 exists, and then reason about the relationship between it and its factors and conclude it does not exist because one has presumed it existed in the first place unless one produces a contradiction among the premises, but all premises A-G have been shown to be false, so no contradiction can be demonstrated. Under this context, the conclusion is necessarily false.

Therefore, wholes don’t exist (A, D, G)

Answer 5

This argument is riddled with issues in every premiss. The puzzle, in a way, is why anyone would have constructed it.

The puzzle reminds me of the paradox-mongering that Plato satirizes in the Euthydemus. In that dialogue, resolving the paradoxes is not the point; the point is to understand, in modern language, the difference between sophistry and philosophy.

It seems likely that an argument of this kind in a Buddhist text is not intended to be resolved but to help us to see through the conceptual chains that bind us to the wheel.

But there is nothing to prevent analytic (or existential-phenomenological) philosophers treating the problem in their own ways. But it is still worth understanding the basic issues that allow the problem to be constructed.

The root of the problem is the language, or the use of language. All the crucial terms are used (or rather misused) by ignoring their proper use.

The problem starts at the beginning. "Whole", on its own, is meaningless. We need to know what whole is in question. (Compare "entity" or "object".) We might think of Theseus' ship or a diamond or a song or a symphony or an argument or a number. The problem of Theseus ship arises, in different ways, for all of them.

In general, we can conclude that a whole is both identical and distinct from its parts. But this is not a paradox. It just means that "identical" does not have a single, determinate meaning; what it means depends on the context of its use.

The meaning of "part" does not depend simply on what whole it is meant to be a part of. From one point of view, the parts of Theseus' ship is, to put it paradoxically, are the different wholes into which it can be disassembled. But the colour, shape, size, weight, volume of the ship are not parts of the ship in the same sense. The diamond arguably has no parts of the first kind (unless you choose to count the molecules or atoms of which consists as parts; but I would argue that is a different sense of "disassemble"). Yet bits can be chipped off it and yet it be the same diamond.

"Explain" is just as empty as the other terms in the argument outside the context of its use. What counts as explaining depends on the context. Explaining a joke is one thing; explaining a map is another; and so on.

So these terms are all perfectly comprehensible in their proper contexts. But the argument does not provide the context needed to make them unambiguous and not open to misuse.

If philosophical analysis can free us from the illusions of misused language, then Buddha might not be entirely displeased with the use we put it to.

Answer 6

Re. F. Entities whose properties can be entirely explained in terms of facts about their constituent parts are not distinct from their parts.

This is a theme frequently mentioned by Tang Huyen on Heidegger Forum 2022

if B comes from A, A must not have what B has

quoting further:

Heidegger's Scheme - Part XXII (12/05/2023)

“Being cannot be explained through the beings” (Sein nicht durch Seiendes erklärt werden kann), (Sein nicht durch Seiendes erklärbar ist). B & T, 251, GA 2 275.

Heidegger's Scheme - Part XVIII (07/05/2023)

... The two sides share nothing in common, no essence, substance, kind, sort, nature, genus, stuff, etc., in any direction. This strict separation comes from Kantian logic, namely, that if B comes from A, A must not have what B has (A must not have the attributes and characteristics of B in toto). The beings (somehow, mysteriously) come from being, therefore being must not have the attributes and characteristics of the beings in toto.

Heidegger may have scavenged this absence of limitation in the whole from many sources, and Kant is one. <<Thus all the possibility of things (as regards the synthesis of the manifold of their content) is regarded as derivative, and only that which includes all reality in it is regarded as original. For all negations (which are the sole predicates through which everything else is to be distinguished from the most real being) are mere limitations of a greater and finally of the highest reality; hence they presuppose it, and as regards their content they are merely derived from it. ...>>

Tang's Kant quote also appears here: Epoché Magazine: God as Transcendental in Kant and Hegel - Feb 2023

Answer 7

A simple thought experiment should clarify your thinking. Imagine you have a set of Lego bricks (no doubt I should be acknowledging a trademark there). You can use the bricks to build variety of different objects. If the objects were identical with their constituent bricks, they would have to be identical with each other, which they are not, hence the objects cannot be identical with their constituent parts.

To suggest that the properties of an object are the same as the properties of its parts it simply incorrect. The properties of an object depend upon how its constituent parts are arranged, and that is not a property of the parts per se.

The supposed paradox you cite comes about because it confuses two aspects of the relationship between the whole and the parts. The first is, as I've illustrated above, the fact that the properties of the whole are not the properties of the parts per se. The second is that the properties of the whole can be explained in terms of the specific arrangements of their parts, which is quite another point altogether. In relation to that second point, the whole is indeed the specific arrangement of the parts.

Answer 8

"Wholeness" is a social construct.

Simply put, sure, in an objective sense, "wholeness" doesn't exist. It's a social construct. A car is an object, but it gains and loses atoms and there is no clear boundary between the atoms of the car and the atoms of the ground or air; there are just atoms that are more tightly bound to other atoms. There is no clear boundary between the Earth and Space, just a gradual reduction in air pressure. There is no clear boundary between humans, since we can exchange biological material by standing too close to each other or using the same cutlery without properly cleaning them, let alone more intimate activities we might engage in. And so on, and so forth, for all physical objects.

What we call a "car" or "the Earth" or "a human" is just a social construct that we agree on as a society to allow us to conceptualize the workings of the universe.

We draw a distinction between the atoms of the car and the road and the air because the molecular bonds between the atoms of the car allow it to (mostly) travel and act as a single unit; where the atoms of the road attract the atoms of the tires, we call that "wear". Where the atoms of the air are bonded to the atoms of the car, we call that "corrosion".

We draw a distinction between "the Earth" and "space" because one is a survivable environment and the other isn't, and we draw an arbitrary line to divide the two apart for regulatory purposes, since the laws that govern aircraft are different to the laws that govern spacecraft.

We draw distinctions between different people because of the senses of self we each possess, regardless of shared traces of biological matter we might possess.

All of these distinctions are useful, so that is why we draw them, even if the real world is a blurry mess where few things fit cleanly into one smooth category.

Answer 9

Point of interest: Buddhism uses koans to subvert the mind's habit of trying to analyze everything intellectually. Trying to analyze a koan intellectually should eventually lead one to the poignant conclusion: "This activity is really dumb." Granted that most people on a philosophy site aren't there yet, or even see that there's a there there, but still...

To the question, though... Principle F:

Entities whose properties can be entirely explained in terms of facts about their constituent parts are not distinct from their parts.

...is highly suspect. The fact the people can be explained (perhaps) in terms of facts about feet and hands and noses does not imply that we are identical with our feet, hands, and noses. That would (in fact) imply that feet, hands, and noses are all identical with each other — because they are identical to us — and that contradicts the premise that parts are different from each other. I mean, sure, feet and noses can both smell, but not in the same way.

Answer 10

The first line A is too vague and should be hammered out explicitly. What does "identical with their parts" mean? Is the whole consisting of two beans identical with the parts? Well it is not identical to bean #1 because it is two beans and not one bean. Is it likewise not identical to bean #2. Is it identical with both beans taken together. Of course it is. Because it is two beans. This contradicts "B. Wholes and their parts have incompatible properties." What would be the incompatible properties here? Do you mean the twoness? Well the twoness is not a property of either part. But it is a property of the parts since there are two parts.

Answer 11

I suspect this is rather more straight-forward than many of the answers and comments here make it seem. This is not a koan or an injunction to cast away rational thought, but a clear-cut logical argument, although it might have unexpected implications.

Buddhist philosophy is structured around the notion of two distinct truths: seeming truth and actual truth. (Often, more heavy-handedly, called relative and ultimate truth.) Whether wholes exist by convention or as social constructs is not what is at stake here. Buddhist philosophers wouldn't dispute that wholes exist conventionally, or seemingly. Rather, what is investigated is whether wholes have an actual ontological status as something apart from their parts.

The argument at hand is intended as a reductio. If wholes exist, they must be either identical to their parts or distinct from them. (In many texts, the further alternatives "both identical and distinct" and "neither identical nor distinct" are investigated -- not because Buddhist philosophers acknowledge these as valid ideas about how something may exist, but to counter other schools of philosophy who might see those alternatives as a way out of the reductio.)

If wholes are neither identical to or distinct from their parts -- then they have no independent ontological status. They are mere conventions.

So, are they identical to their parts? No, because they have "incompatible properties". There are different versions of this argument. A car can move, but its parts can't, either taken individually or when assembled into something that is not a car. If that seems unconvincing, we can move to the scale of fundamental parts (namely atoms, in the literal sense) and consider that wholes have extension, whereas parts do not. If the part had an extension, then by definition it itself would be a whole, because we could separate its left side from the right one, etc. (This applies to physical wholes, but a similar argument can be made about temporal wholes, ie continua.)

Are wholes then distinct from their parts? No, because a whole is never anything above or beyond its constituent parts.

So, since wholes are neither identical to or distinct from their parts, they have no actual existence. They have (merely) conventional existence. They seem to exist, but they don't truly.

Note that this conclusion more or less follows from the very idea of a whole made up of parts. So it can be regarded as an investigation into our preconceived notions about reality.

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How can this argument be resisted? I think, in modern terms, this is what a lot of arguments over "emergent phenomena" amounts to. People want to have their cake and eat it too by saying, that some "thing" supervenes on more fundamental parts but is also its own separate thing as an emergent phenomenon. Which is all fine if all you mean by that is that it seems to exist but doesn't at the fundamental level of physical reality. The only true challenge comes from "strong emergence", but I don't think that would resist the argument above.

Note that this particular argument and its conclusion, taken in isolation, are not particularly exotic from a modern, physicalist point of view. Pretty much everyone accepts that reality is a vast assemblage of some kind of fundamental parts, and that is all there is to it. We don't believe in the true or ultimate existence of wholes. Although, as I said, some people go to great lengths to explain how some macroscopic phenomena should still be granted an honorary status of ultimate existence.