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Panentheism and the Problem of World Inclusion: A Category-Theoretic Approach

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Abstract

Panentheism is a theism with great potential. Whereas pantheism takes God to be equivalent to the world, panentheism entertains as much while still asserting God’s transcendence of the mere world. There is much beauty in this idea that God is both “in the world” and “above” it. But there is also much subtlety and confusion. Panentheism is notoriously tricky to demarcate from the other theisms, and there is plenty of nuance left to be explored. The core problem of panentheism is this—what exactly does it mean for the world to “include God” and for God to “contain the world?” Numerous answers have been given, but it seems there is still something left to be desired. In this paper, we endeavor to give panentheism a firm and rigorous footing. Utilizing basic category theory, we provide a precise answer to the daunting problem of “world inclusion.” In the process, we also offer a new variety of metaphysical grounding, “morphic grounding.”

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Notes

  1. Crisp (2019).

  2. Mullins (2016).

  3. “Panentheism and its neighbors,” International Journal for Philosophy of Religion (2019) 85:23–41.

  4. Most notably, in Leidenhag (2020).

  5. “God’s omnipresence in the world: on possible meanings of ‘en’ in panentheism,” International Journal for Philosophy of Religion (2019) 85, 43–62.

  6. https://plato.stanford.edu/entries/panentheism/.

  7. Clayton (2017).

  8. See Peacocke & Clayton (2004).

  9. Walker Jr. & Wickramasinghe (2015).

  10. https://plato.stanford.edu./entries/panentheism/.

  11. Lataster & Bilimoria (2018).

  12. Stenmark (2019)

  13. Gasser (2019).

  14. Gasser (2019).

  15. Inman (2017).

  16. Pasnau (2011).

  17. Rozemond (2015).

  18. Lombard (1971–1981)

  19. Peacocke & Clayton (2004).

  20. Mullins (2016)

  21. Fine (2012).

  22. ibid.

  23. See Rydéhn (2018) for an in-depth investigation of the relationship between grounding and dependence.

  24. See Rabin & Rabern (2015) for a discussion of the technical and philosophical aspects of grounding.

  25. Sometimes there is confusion between grounding “within the world inside God” and grounding as a well-founded chain in its entirety. When the former vantage of grounding is considered, the core issues of panentheism—those of world-to-God and God-to-world relation—can become blurred.

  26. Note that in the formal sense of the word “ [ontological] dependence,” the relation is often antisymmetric, meaning that if W depends on G then it cannot be that G depends on W. We will investigate this property further shortly, but for now we intend the informal meaning of dependence.

  27. For more on the general problem of panentheistic creation, see Peacocke and Clayton’s In Whom We Live and Move and Have Our Being (2004).

  28. Stenmark (2019).

  29. We are carefully skirting around some areas of tension in modern philosophy of religion. Not all pantheisms or panentheisms are created equal, but one of the (if not the) distinguishing feature(s) of pantheism is that it is not only the case that the world depends on God for its origin; God, being in an identity relation with the world, also depends on the world for his origin.

  30. Here we assume that any given grounding chain is transitive. We do not mean to imply that W < G with no intermediate groundings such that, W, …, < G.

  31. Hudson (2009).

  32. Gasser (2019).

  33. See Arcadi (2017). See also Jedwab (2016, 148) and Gordon (2018, 537–539).

  34. We will provide a precise definition of this term, and “strong mutability,” shortly.

  35. There is a treasure trove of scholarship addressing various varieties of mutability and their implications. But unfortunately it is beyond the scope of this work to delve into it.

  36. Before we commence our discussion, we should mention the rich history of implementing category theory in metaphysics and philosophy in general. Categories for the Working Philosopher (2017) serves as a brilliant survey of the interface between category theory and philosophy. Another great anthology is Category Theory in Physics, Mathematics, and Philosophy (2019), in which the article “The Application of Category Theory to Epistemic and Poietic Processes” by Józef Lubacz highlights the metaphysical uses of categories. From a more “continental” point of view there is the book Diagrammatic Immanence: Category Theory and Philosophy (2016) by Rocco Gangle. Although we propose to acquaint category theory with philosophy of religion, we must maintain that to do so is nothing astoundingly original.

  37. Goldblatt (2006).

  38. The reader might have noticed that we have not yet given a defintion for a “category,” despite all the talk about “diagrams.” This is because, for our uses, the notion of a category needs only to be an overarching concept, as opposed to an axiomatic defintion. Diagrams are simply little “pieces” of the category they belong to. One intuitive way to informally define a category is as a “universe of mathematical discourse,” considering that such a universe is determined by “specifying a certain kind of object and a certain kind of ‘function’ between objects.” See Goldblatt’s Topoi: The Categorial Analysis of Logic (2006) for this explanation.

  39. This dynamic view of God is redolent of Peters’s notion of “eschatological panentheism.” As Peter puts things, this model “[sides] with theism in affirming that God is a se, independent, free, and omnipotent,” while also siding “with panentheism in emphasizing relationality and connectedness,” affirming both “creation out of nothing as well as continuing creation.”

  40. Arcadi (2017). See also Jedwab (2016, 148) and Gordon (2018, 537–539).

  41. Fine (2012).

  42. We take “grounding” to be any inclusion arrow from any object to any other object. Thus, even a self-mapping, X ↪ X is taken to constitute an instance of what we will call morphic grounding.

  43. See Rabin & Rabern (2015) for a technical discussion.

  44. Where we allow various different mappings between two of the same objects, we alter the technical details a bit. In this case, the partially ordered set of subobject inclusion (P(C), ⊆) is no longer a set but a “multiset,” a collection which permits repeating subsets. We will talk about this more shortly.

  45. No doubt, there has been much discussion of metaphysical grounding which violates any number of the three usual conditions. It is not clear, however, that unique forms of grounding have sufficiently worked their way into philosophy of religion.

  46. A “multiset” is simply a collection of objects in which repeating elements are permitted. Several pages ago, we gave an example where we considered two distinct arrows from the same object X to God. Permitting different arrows from like objects allows for a more detailed approach. For more on the concept of multisets, see Monro (1987). “The Concept of Multiset”. Mathematical Logic Quarterly.

  47. There is a subtle but hugely important difference between (1) God ↪ X translating to “X is actively contained within God” and (2) God ↪ X translating to “God is contained within X.” God himself, as a transcendent being, is not literally “contained within” any object. Rather, God “sends” a version of himself to interact with objects.

  48. Peacocke & Clayton (2004).

  49. We see a similar emphasis on the self-maintenance of God in Langan (2018). In fact, Langan goes even further into the technical details, contending that God is fundamentally “self-dual.” Self-duality as a mathematical notion is an elaboration on “duality.” A basic example of duality can be found in predicate logic. The existential quantifier ∃ is the dual of the universal quantifier ∀ by defintion. Although duality is construed differently across various contexts, the basic idea is that two dual objects stand in some sort of relation to one another, such that they can be transposed and still stand as well-behaving mathematical objects. In terms of ontology, a “self-dual” object has the power to dualize itself; the dualization of it is isomorphic to its original structure.

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  1. Philosophy & Religion, University of North Texas, Denton, TX, USA

    Jonathan J. Mize

  2. Zeppelin Universität, Friedrichshafen, Germany

    Vincent Geilenberg

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Mize, J.J., Geilenberg, V. Panentheism and the Problem of World Inclusion: A Category-Theoretic Approach. Philosophia 51, 857–882 (2023). https://doi.org/10.1007/s11406-022-00552-6

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