Object-oriented correlationism

On Graham Harman’s object-oriented ontology, all objects withdraw from each other. Objects have an inner depth or essence that is not exhausted or disclosed by their relations to other objects. Universal withdrawal of objects is the core claim of Harman's object-oriented ontology. Now, Harman is a metaphysical realist. He thus construes his object-oriented ontology as a metaphysics of the absolute or reality in itself. He believes that the core claims of his object-oriented ontology are justified as claims about how the world is in itself. But what if correlationism is irrefutable and therefore inevitable? In that case, Harman may still defend his object-oriented ontology as a metaphysics posited within the correlationist circle and thus within the context of how the world is for us instead of how it is in itself. By doing so he would become an adherent of what we could refer to as object-oriented correlationism (OOC).

In fact, many of Graham's core object-oriented ontology theses - such as that there are multiple objects, that we have to make a distinction between objects and qualities, that there are real and sensual objects and real and sensual qualities, that objects maintain a degree of autonomy and can thus not be reduced to their relations, and that there corresponds exactly one real object to each sensual object of ordinary experience (e.g., a real hammer compared to a sensual hammer, a real table compared to a sensual table, and a real bike compared to a sensual bike) - are epistemically reasonable and defensible as claims within the correlationist circle, that is, as claims about how reality is for us as human beings, whereas these claims are not justifiable as claims about how reality is in itself. For on correlationism no claim at all can be epistemically justitied as claim about the absolute or the 'in itself'.

Harman maintains though that correlationists assume a strict division between humans on the one side and non-humans on the other side. He considers it utterly implausible that human beings deserve to fill up a full half of philosophy. But this critique of correlationism is misconceived. For correlationists do not introduce an implausible taxonomy between human thought and everything else within the realm of objects. They do not allow humans to fill up fifty per cent of ontology. Correlationists do not introduce a horizontal split between humans and all other objects. They introduce instead a vertical distinction between the transcendental level of the human conditions of knowledge of objects and the object level of the objects of human knowledge. For correlationists object-oriented metaphysics resides solely at the object level and thus not at the transcendental level. At the object level an object-oriented correlationist can initially posit any flat ontology that he or she wants to pick as his or her point of departure. There is on correlationism no need at all for a horizontal dogmatic split between humans and non-humans at the level of objects. The human conditions of knowledge only appear vertically at the transcendental level of knowledge of objects and not within the world of objects we perceive and think and speak about. So, as said, all core theses of Harman's object-oriented ontology, including his initial flat ontology, can be posited and reasonably defended - in fact, on correlationism only be posited and reasonably defended - within the correlationist circle. That is to say, they can only be posited and reasonably defended within the-world-as-it-is-for-us or within the world of objects of human knowledge.

An new a priori argument for atomism

In what follows I propose a new a priori argument for mereological atomism. Mereological atomism is the thesis that every composite object is ultimately composed of simple objects. Simple objects are objects without proper parts.

Take a formal additive measure of being. This measure measures the amount of being contained in each object. Let O be an object and denote the amount of being contained in O by being(O). Thus, being(O) is zero in case there is no object O. Let the objects {Oi}i compose object O. Hence {Oi}i is a composition of O. The additive nature of the involved measure implies that being({Oi}i) = Σi[being(Oi)].

Strictly speaking the aformentioned formula is not well-formed since being(.) has been defined as a function on objects and not as a function on sets of objects. Yet, this is not a problem. We can extend the domain of being(.) to the collection of all mereological sums. In that case the formula becomes being(sum{Oi}i) = Σi[being(Oi)].

According to the principle of composition-as-identity, object O simply is the objects {Oi}i taken together, that is, object O is nothing above or beyond the objects {Oi}i taken as a totality. From this it follows that being(O) = being(sum{Oi}i) = Σi[being(Oi)].

Next, let O be an object and let Ω and Ω* be two different compositions of O such that every object in Ω* is either equal to or a part of an object in Ω. In that case Ω* is called a refinement of Ω. It follows that being(Ω) = [being(Ω) – being(Ω*)] + being(Ω*). This formula indicates that the amount of being at a certain level of composition is the arithmetical sum of the amount of being at the previous level and the incremental amount between both levels.

Let {Ωn}n be a sequence of compositions of object O such that Ω0 = O and such that for all natural numbers n composition Ω(n + 1) is a refinement of composition Ωn. The sequence {Ωn}n is either finite or infinite. Suppose first that {Ωn}n is finite and let ΩN denote the final composition in the sequence. It follows that being(O) = Σ(n=1 to n=N) [being(Ω(n – 1)) – being(Ωn)] + being(ΩN).

How should this arithmetical formula be adapted to the case that {Ωn}n is infinite? This case is obtained if N proceeds to infinity and the final composition ΩN vanishes from the sequence. Hence, the only natural answer appears to be that in that case one obtains the formula being(O) = Σ(n=1 to n=∞) [being(Ω(n – 1)) – being(Ωn)].

Note that I’m not claiming here that the formula for the infinite case can be mathematically derived from the formula for the finite case. For, such a claim would be clearly ungrounded. The reasoning is qualitative and not quantitative. The structure of the formula for the finite case expresses the insight that the amount of being of some composite is obtained bottom-up in precisely two ways, namely (a) incremental influx of being between the levels of composition and, (b) inheriting the amount of being already available at the lowest level. But then the equivalent structure for the infinite case is just an infinite sum of incremental infusions of being. After all, in the infinite case there is no lowest level and therefore only (a) applies here. This conceptual reasoning should not be taken for a quantitative mathematical derivation of the infinite formula from the finite one.

Now suppose, for reductio, that atomism is false. In that case there is a composite object C that is not composed of simple objects. Due to the principle of supplementation C is composed of two or more other objects. So, there is a composition of C. Since C is not composed of simple objects there is an infinite sequence of compositions {Ωn}n of C such that for every natural number n composition Ω(n + 1) is a refinement of composition Ωn. It thus follows that being(C) = Σ(n=1 to n=∞)[being(Ω(n – 1)) – being(Ωn)].

Further, the principle of composition-as-identity implies that being(C) = being(Ω(n – 1)) and being(C) = being(Ωn). Hence, for all natural numbers n, it follows that being(Ω(n – 1)) – being(Ωn) = 0. This implies that being(C) = Σ(n=1 to n=∞)[being(Ω(n – 1)) – being(Ωn)] = Σ(n=1 to n=∞)[0] = 0. But then being(C) = 0 which implies that there is no object C. This contradicts with the fact that object C does in fact exist. Therefore, the initial assumption that atomism is false needs to be rejected. It thus follows that atomism is true.

This fragment is obtained from my dissertation (pp. 129-131)