In order to answer this question, there are three things that must first be addressed: what a ‘whole’ is, what a ‘part’ is, and how to evaluate the ‘sum’. Although axiological nihilism still holds, in order to answer this question, I have chosen to derive value from an object’s telos; this is a sort of ‘value monism’. A ‘whole’ can be any object, both physical and immaterial. A distinction between can be drawn between two sets of objects: mechanical or animate objects, such as an aeroplane or a monkey, and ‘plain’ or ‘natural’ objects, such as a rock. These mechanical (manmade or a tool) or living objects have various complex parts, all of which interact with each other. Within the aeroplane example, this would be how the engines interact with the chassis and the wheels etc. Plain objects will have fewer or no parts, which interact with each other in less complex or apparent ways, or have come about through former interaction, for example the layers of earth and soil, as parts of soil as a whole.
Often the constituent parts of an object are obvious, however certain rules must be established to standardise my method, in order to ascertain any understanding of value. The scale and level of detail of the parts must be suitable and consistent with the scale of the object, for example the parts of a macroscopic object must themselves be macroscopic. Just as for a plane, the parts would be the engines and the wheels etc., not the atoms or quarks that make up the elements that make up the plane. Otherwise the interactions and parts of each object are the same: just the smallest particles which can make them up, for example quarks and how they bond, so the scale must be preserved.
The value of parts compared to the whole must be determined to make a judgement as to whether it will be greater, lesser or equal. However, that purpose must be objective, or as Aristotle put it, a telos. In short, the value should not be derived from the value to humans or the value to the earth, but some inherent value to the object. Indeed, an object can be valued by assessing its ability to do something, some purpose. Mechanical objects are always either manmade or living. This means they have some. For living creatures, that purpose could be anything from the act of living, growing and reproducing or even intellectual curiosity in the case of humans, and in mechanical objects, they will always have purpose from their designer. This is objective value, as the purpose is a property of the object itself, not a subjective opinion of the value of the object such as monetary value.
Now we can begin to weigh the sum of the parts against the whole in mechanical objects. If we compare the sum of the parts with the whole, we get the same physical objects, yet we lack the interactions between these objects. However, it is often the interaction that provides the value in these types of objects. For example, a car: a whole car is much more able to drive than the independent parts of a car. This is because it is only the interaction between the engine and eventually the wheels that provides the extra value that is not present with just the parts, and which ultimately allows it to drive, and achieve its purpose. The question may arise: is an interaction not a part in and of itself, and so should it not be included in the sum of the parts? However, an interaction is not a part itself, but a property of two parts being put together in a specific configuration. For example, a simple water molecule: the interaction between the 2 Hydrogen and 1 Oxygen atoms would be the bond. However, this bond is not a part of that water molecule, but a property of the nature of the charges of the individual atoms. The bond only comes about when the atoms are together. The interaction is not a part, just an outcome of the parts together. Thus, when evaluating the sum of the parts, we cannot include the interactions between the parts. However, this interaction is ultimately what allows the object to achieve its purpose and provides some of the utility. Therefore, in mechanical objects with an inherent purpose that determines the objective value of the object, such as beings or machines, the whole is greater than the parts. This of course does not stand if the interactions are made to, on purpose, restrict wholly the ability of the object, but there exists a somewhat rare case.
However, this solution does not hold for plain or natural objects, which have no inherent telos, such as rocks. Although Aristotle never applied telos to this problem, he did consider it in his Metaphysics VIII: Eta. The title talks about value: being ‘greater’ or ‘less than’. However, for items with no inherent value, we cannot establish whether the sum of the parts is greater or lesser than that of the whole. Here we employ the view of both Aristotle and Kurt Koffka, one of the founders of Gestalt Psychology. This is echoed by Koffka who similarly states ‘the whole is something else than its parts’. In fact, Koffka disliked and discouraged the use of the mistranslation. While these accounts do not consider the possibility that mechanical objects can have inherent purpose and value relative to that purpose, they can help to explain the relationship of the parts to the whole in plain or natural objects. In natural objects, there is no apparent purpose and so no way of objectively valuing the object. This means the whole cannot be greater or lesser than. You cannot equate the whole to the parts, due to the lack of interactions within the sum of the parts (unless the object has only one part such as a monocrystalline crystal). Therefore, the whole must be something other than the parts in non-mechanical objects. For example, take a natural object with obvious and distinct parts: gold ore within a rock. While the sum of the parts in monetary value would be higher than the whole, since we cannot establish objective value due to a lack of purpose of the rock, the whole is just something else, distinct of the parts. In this example the interaction is minor, so the difference between the whole and the parts is less apparent. In natural objects where there are no interactions between the parts or the whole is a simple collection of parts this doesn’t work. Thus, we must exclude natural objects such as a pile of rocks, where there is a lack of interactions. In Metaphysics, Aristotle is similarly aware of this and so states that the whole is something other than the parts if and only if ‘the totality is not, as it were, a mere heap’. The parts being different from the whole can be demonstrated by an illustration from Gestalt psychology of a subjective contour:
Here, the triangle is a ‘gestalt’ (‘shape’ or ‘form’ in German) inferred through the interaction of the parts. The shape acts as a whole, and the obvious parts of it would be the three pac-man type figures at each vertex of the triangle. The white triangle we visualize, however is not actually a part; nothing there has been drawn in. The white triangle only comes about due to the specific configuration and interaction of the parts, the black pac-men. The white triangle therefore is not a property of the parts, only of the whole. When viewing the sum of the parts we see 3 pac-men, compared to the whole where we predominantly see the outcome of the interaction: the gestalt, the white triangle.
In conclusion, we can establish that, for the majority of mechanical, animate or man-made objects the whole is indeed greater than the sum of the parts, due to its greater ability to perform its designated and inherent purpose, thus I disagree with the title on this aspect. However, for natural objects, with no discernible purpose, we cannot establish objective value, and thus, the sum of the parts, for natural objects, rather than either being greater or less than, something other than the whole. Therefore, in this respect I agree with the title: the sum of the parts is no greater or lesser than the whole, when the whole is a natural object, as defined.
Aristotle. and Bostock, D. (1994). Aristotle metaphysics. Oxford [England]: Clarendon Press.
Plato.stanford.edu. (2019). Aristotle’s Metaphysics (Stanford Encyclopedia of Philosophy). [online] Available at: https://plato.stanford.edu/entries/aristotle-metaphysics/#UnitReco [Accessed 3 May 2019].
En.wikipedia.org. (2019). Gestalt psychology. [online] Available at: https://en.wikipedia.org/wiki/Gestalt_psychology#Theoretical_framework_and_methodology [Accessed 3 May 2019].
Russell A. Dewey, P. (2019). Gestalt Psychology | in Chapter 04: Senses. [online] Psycom. Available at: https://www.psywww.com/intropsych/ch04-senses/gestalt-psychology.html#thewhole [Accessed 3 May 2019].
Koffka 1935, Principles of Gestalt Psychology, p. 176
 The title follows a mistranslation, rather than ‘the sum of the parts is greater than the whole’, Aristotle, in Metaphysics VIII:Eta, states ‘the whole is something other than the parts’ (despite a different line of reasoning to the one set out in this essay).